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On the way to thin film silicon solar cells : gas flow variation in an expanding thermalplasma and a first step towards a model to predict conditions for microcrystalline filmgrowth

van Egmond, S.

Award date:1998

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Eindhoven Univerisity ofTechnology Department of Physics Equilibrium and Transport in Plasmas

Ecole Polytechnique Fédérale de Lausanne Centre de Recherches en Physique des Plasmas

On the way to thin film silicon solar cells: gas flow variation in an expanding thermal plasma

and a first step towards a model to predict conditions for microcrystalline film growth

Under supervision of: Eindhoven: ir. W.M.M. Kessels dr. ir. M.C.M. van de Sanden prof.dr.ir. D.C. Schram

Suzanne van Egmond August 1998

VDF/NT 98-21

Lausanne: dr. A.A. Bowling dr. L. Sansonnens

dr. Ch. Hollenstein

ER WAS een regenworm in Sneek, die altijd naar de sterren keek. Hij riep: "Hoe schoon, hoe schoon!" Zijn moeder zei: "Doe toch gewoon, kijk naar beneden, naar de grond, dat is normaal, dat is gezond. Kijk naar beneden, zoals ik ... " En toen, toen kwam de leeuwerik!

Het wormpje dat naar boven staarde, zag hem op tijd, en kroop in de aarde. De moeder, die naar beneden keek, die werd opgegeten daar in Sneek.

Dus: doe nooit wat je moeder zegt, dan komt het allemaal wel terecht.

[Annie M.G. Schmidt]

Summary Solar energy is one ofthe most promising answers to the world wide increasing demand for alternative energy resources. In thin film silicon solar cells hydrogenated amorphous or microcrystalline silicon is used. This material can be deposited using a plasma. Work has been done on a expanding thermal plasma reactor in Eindhoven and on a large area rf reactor in Lausanne.

In the expanding thermal plasma setup an argonlhydrogen plasma is created in a cascaded are After that it expands in a vessel where silane is added just after the are exit. The consequences of argon flow reduction on the deposition of hydrogenated amorphous silicon are investigated. A lower total gas flow is desired because a large pump capacity is needed to cope with the high flows used at the present deposition conditions. Furthermore, it is thought that the main part of the argon added is not participating in the deposition process. It is shown that the plasma behaviour in the cascaded are as a function of argon/hydrogen flow ratio is important to the expanding plasma, silane dissociation and deposition processes.

The plasma in the are can be divided into two regions: an active and a passive plasma region, in which the heavy partiele temperature is high and much lower respectively. The number of ions and the atomie hydrogen flow emanating from the are is influenced by the argon/hydrogen flow ratio because the size of the active region in comparison with the size of the passive region has turned out to bedependenton the argon/hydrogen flow ratio. It is shown that the silane consumption (depletion) shows the same behaviour as a function of argon/hydrogen flow ratio as the atomie hydrogen flow leaving the are. This was expected from earlier work, which showed that the main silane dissociation reaction is the dissociation by atomie hydrogen. The depletion did not show a dependenee on vessel pressure and tumed out to decrease with argon/hydrogen flow ratio in a situation where the hydrogen flow is fixed, but increases with argon/hydrogen flow ratio if the total flow has a constant value. The growth rate did scale with the absolute depletion. In the current setup it seems not to be possible to maintain the high growth rate obtained at standard deposition conditions while decreasing the argon flow. The results conceming material quality are preliminary, but do not show a serious decrease in material quality with decreasing argon/hydrogen flow ratio.

Furthermore, a model has been developed to study the plasmaand the deposition of hydrogenated silicon in the large area Balzers KAl reactor. Main goal has been to predict the conditions for which hydrogenated microcrystalline silicon is grown. Tostart with, however, the model's calculations are checked with experimental data on depletion and growth rate for amorphous silicon. The model's calculations turned out to correspond to the experimental date within the experimental accuracy. The calculations on partiele densities could not be checked with experimental data, but did show that SiH3 is the main radical in the plasma, foliowed by H. The SiH2 radical density is at least two orders of magnitude lower than the SiH3 radical density. An indicator for microcrystalline growth conditions has been developed: aso-called 'rrs ratio' is defined as the ratio of number of SiH3 and H radicals coming to the growing surface. Further experiments are needed to judge the value ofthe rrs ratio, but preliminary calculations did show that high electron density, low silane/hydrogen flow ratio, low silane flow and low pressure are favourable for microcrystalline growth.

Table of Contents List of Symbols ....................................................................................................................................... 3

PART 1: INTRODUCTION One: lntroduction .................................................................................................................................. 7 Two: Silicon deposition using a plasma ............................................................................................... 9

2.1 Plasma ........................................................................................................................................... 9 2.2 Hydrogenated silicon deposition ................................................................................................ 11

2.2.1 Hydrogenated silicon ........................................................................................................... 11 2.2.2 Film quality ......................................................................................................................... 12 2.2.3 Microscopie growth model of hydrogenated amorphous silicon ........................................ 12 2.2.4 Probabilities: quantitative .................................................................................................... 14 2.2.5 Macroscopie modelsof microcrystalline silicon deposition ............................................... 16

PART 11: AN EXPANDING THERMAL PLASMA Three: An expanding thermal plasma setup to deposit amorphous hydrogenated silicon .......... 21

3.1 Experimental setup ..................................................................................................................... 21 3. 1.1 Cascaded are ........................................................................................................................ 21 3 .1.2 Vessel and substrate ............................................................................................................ 22

3.2 Diagnostic methods .................................................................................................................... 23 Four: Argon flow rednetion in the expanding thermal plasma deposition setup .......................... 25

4.1 Are plasma .................................................................................................................................. 25 4.2 Are stability ................................................................................................................................ 28 4.3 Effective are diameter and electron temperature ........................................................................ 30 4.4 lons ............................................................................................................................................. 33

4.4.1 Probe measurements ............................................................................................................ 33 4.4.2 Mass speetrometry measurements ....................................................................................... 35

4.5 Silane dissociation ...................................................................................................................... 37 4.5.1 Introduetion ......................................................................................................................... 37 4.5.2 Atomie hydragen flow ......................................................................................................... 37 4.5.3 Silane depletion ................................................................................................................... 38

4.6 Growth rate ................................................................................................................................. 41 4.7 Film quality ................................................................................................................................ 42 4.8 Conclusions ................................................................................................................................ 44

PART 111: A LARGE AREA RF REACTOR Five: Model of an rf silane discharge including growth processes ................................................. 49

5.1 Experimental Setup .................................................................................................................... 49 5.2 Description ofthe model ............................................................................................................ 50

5.2.1 Included processes and assumptions ................................................................................... 50 5.2.2 Model equations .................................................................................................................. 52 5.2.3 Surface equations ................................................................................................................. 54 5.2.4 Pumping losses .................................................................................................................... 55 5.2.5 Probabilities ......................................................................................................................... 56

Six: Modeling Results .......................................................................................................................... 59 6.1 Validity model ............................................................................................................................ 59

6.1.1 Electron density ................................................................................................................... 59 6.1.2 Silane dilution ...................................................................................................................... 61 6.1.3 Pressure ................................................................................................................................ 62 6.1.4 Silane flow ........................................................................................................................... 62

1

6.2 Partiele densities ......................................................................................................................... 64 6.2.1 Densities as a function of electron density .......................................................................... 64 6.2.2 Contribution to growth ........................................................................................................ 65

6.3 RRS ratio: conditions for microcrystalline silicon deposition ................................................... 66 6.4 Discussion ................................................................................................................................... 67

PART IV CONCLUSIONS Seven: General conclusions ................................................................................................................ 71

Literature ................•............................................................................................................................ 75

Technology Assessment ....................................................................................................................... 77

Appendix: structure of the MatLAB program ................................................................................. 79

2

List of symbols Symbols A diffusion term for silane radicals B diffusion term for hydragen c content c constant cl probability to cross-link d diameter E electric field e elementary charge F dissociation fraction outside plasma channel I electrical current I ion current (mass spectrometer) j current density k reaction rate k Boltzmann constant L distance I length M effective mass m mass N number of reactions N number of collisions N number of atoms n density p pressure r probability of reileetion r radius R* micro structure rrs rrs ratio s probe surface s pumping speed/inverse residence time s-1 s probability of sticking solS salution vector of model calculation T temperature t time V voltage V volume V velocity ( distribution)

Greek symbols 13 probability of physisorption 8 probability ofH-H recombination [-] E probability of etching r flux

<!> flow probability of reileetion argument of Coulomb logarithm mean free path

y A À

\jJ probability of passivating a dangling bond

3

s-1 s-1 [at%] [-] [-]

Vm-1 c [-] A

Am-2 m3s-1 JK-1 m m kg kg [-] [-] [-] m-3 Pa [-] m [-] [-] m2

[-]

K s V m3 ms-1

[ -]

s-1m-2 s-1 or sccs [-] [-] m [-]

p partiele density m-3 cr conductivity cr callision cross section m2

Subscripts + ion a neutral cont content d diffusion dissah dissociation of silane by atomie hydragen dissill dissociation of silane by electrans giving SiH3 dissil2 dissociation of silane by electrans giving SiH2 e electrical e electron e et eh eff effective g growth H hydragen

ion p plasma rad radicals sih2 reaction of SiH2 with SiH4 sih3 reaction of SiH3 with H Si-H Si-H bond Si-Si Si-Si bond th therm al tot total

4

Part I

INTRODUCTION

6 '-l.'·

Chapter One Introduetion The demand for alternative sourees of energy has only increased during the last few years. One of the most proruising new energy sourees is solar energy. To make it also economically favourable to apply solar cells as an energy source, a reduction of costs is one of the most important goals of research. This can be done by increasing the efficiency ofthe solar cell, such that less solar cells are needed to obtain the same amount of energy. Another possibility is to decrease the production costs of the solar cell. In this respect, hydrogenated amorphous silicon is one of the materials which can be produced at lower costs and is therefore a good candidate for solar cell materiaL

The hydrogenated amorphous silicon film is used as intrinsic layer in the solar cell, which is the layer where the incoming light causes the electrans to move from the valenee to the conduction band. The intrinsic layer is built in between an n-layer (bottom) and a p-layer (top), which cause a voltage gradient across the intrinsic layer [KIT96]. This potential difference causes the free electrans in the conduction band to move: an electrical current arises. The amount of light which is useful to the creation offree electrans depends on the material's bandgap. To increase the efficiency ofthe solar cells it is possible to produce a cell with a so-called tandem structure [TOR97]. In this cell two intrinsic layers with different bandgaps allow a better use of the solar spectrum. The two materials used as intrinsic layer could be hydrogenated amorphous silicon (band gap ± 1. 7 e V) and hydrogenated microcrystalline silicon (band gap ± 1.1 e V).

Hydrogenated amorphous and microcrystalline silicon can be deposited using a plasma. The silicon containing gas (for example silane, SiH4) falls apart due to the interaction with the plasma. The reaction products deposit on the substrate. An important parameter in plasma deposition is growth rate. A high growth rate is a one of the aspects contributing to a relatively low co st production of solar cells.

With an expanding thermal plasma deposition setup it is possible to obtain growth rates up to 10 nm/s. An expanding thermal plasma deposition reactor to deposit hydrogenated amorphous silicon is available at the group Equilibrium and Transport in Plasmas ofthe department of Applied Physics at Eindhoven University ofTechnology. To produce not only the intrinsic layer but also the other layers ofthe solar cells a device will be built at Delft University ofTechnology, within the framework ofthe DIMES project. In this device an expanding thermal plasma deposition setup will be used to produce the intrinsic layer ofthe solar cell. This setup will operateat lower total carrier gas flow, such that a lower pump capacity can be used. In standard deposition conditions an argon flow of 55 sccs1 is used. In this work the consequences of a reduction of argon flow for the deposited material are investigated by studying the are operation and the silane consumption by the plasma. Furthermore, depositions are performed to investigate growth rate and film quality.

Another plasma deposition reactor is the commercially available Balzers KAl reactor, which is investigated in the group 'Plasmas for the industry' at the 'Centre de Recherche en Physique des Plasmas', which is part ofthe 'Ecole Polytechnique Fédérale de Lausanne'. This reactor is a radiofrequency parallel plate deposition reactor and growth rates obtained are in the order of 0.1-1 nm/s. One of the research subjects is the deposition of microcrystalline silicon. Although some 'microcrystalline' deposition conditions are known empirically, the growth process of microcrystalline silicon is not really understood. Work has beendoneon the development of a simple

I The flow unit sccs is equal to 2.5·to19 particles per second.

7

plasma model to increase the understanding ofthe deposition process and predict the plasma conditions for which microcrystalline silicon is deposited.

To summarize, the two main subjects ofthis work are: • The influence of gas flow variation on the deposition of hydrogenated amorphous silicon by using

an expanding thermal plasma. Main goal is to determine whether it is possible to maintain material quality while decreasing the total carrier gas flow to be able to use lower pump capacity.

• The development of a model to describe partiele densities, silane consumption and growth rate in an rfplasma deposition reactor. The results ofthe model calculations should increase the understanding of the microcrystalline silicon deposition process and predict what conditions result in microcrystalline film growth.

This report can be divided in four parts. In part I, a short introduetion is given on plasmas to deposit hydrogenated silicon and growth processes during deposition of amorphous and microcrystalline silicon. Furthermore, we discuss some material quality features. In part 11 the expanding thermal plasma deposition setup is discussed. We will describe the experimental setup in chapter 3 and in chapter 4 the consequences of argon flow reduction are discussed. Then, in part lil, we will concentrate on the development of the model to increase the understanding of the deposition process in the Balzers KAl reactor. The results ofthe model calculations will be discussed in chapter 6. Finally, in part IV some conclusions and recommendations will be given.

8

Chapter Two Silicon deposition using a plasma In this chapter the subject of plasma deposition of amorphous and microcrystalline silicon will be introduced. The discussion will be short and divided in two parts, namely the plasma and the surface processes. In paragraph 2.1 we will discuss some properties ofthe plasma, such as reaction rates and diffusion. After that, the deposition ofhydrogenated silicon is discussed in paragraph 2.2. The growth mechanism of hydrogenated amorphous silicon will be discussed and a summary will be given of the different theories concerning the transition from amorphous to microcrystalline deposition. Furthermore, film quality parameters will be studied in relation to hydrogen content.

2.1 Plasma

In silicon deposition a plasma can be used to dissociate silane for the creation of reactive silane radicals. A plasma is created by supplying power to a gas. In this way, the gas temperature increases and ions and electroos are produced by ionization. Thus, the plasma state is a state in which not only neutral particles, but also ions and electroos exist. The plasma state requires a sufficiently high ion production to compensate for the partiele losses, which is expressed in the following mass balance for non-recombining plasmas:

_ Eion

k ioll - n k e kT. - ne ne . na . - ne . a . 0 • - -' ( 2.1.1) 1"11

where ne and na are electron and neutral density respectively. The last term depiets the electron loss, with •n the electron loss time, which is approximately equal to 1Q-5 s. The left hand term shows the ion production, with ionization rate kion. In a first approximation the rate ofthe inelastic ionization process can be written as the rate of a solid sphere collision multiplied by an exponential function containing the ratio of i ooization energy and electron temperature. In the solid sphere approximation the reaction rate ko is equal to:

k0 = O"·V. ( 2.1.2)

In this equation v is the electron velocity and cr is the collision cross section, which is correlated with the probability oftwo particles to interact In a simple interpretation this is connected to the size of the particles concerned. We could define the reaction cross section in the simple s?lid sphere interpretation as:

( 2.1.3)

In this equation ri is the radius of partiele i. The electron radius is much smaller than the radius of the neutral particle, and therefore it is neglected and only the radius of the neutral partiele is considered in electron-neutral interactions. Using the thermal velocity:

vth =~3:, ( 2.1.4)

we find for ko = I0-14- I0-15 m3s-1. Notice that the mass balance 2.1.1 is independent ofthe electron density. According to the mass balance it follows that ifthe neutral partiele density decreases, for example due to a decrease in pressure, the electron temperature increases.

9

To produce silane radicals, one couldjust use silane gas to create a plasma, as is often done in the Balzers KAl reactor, which will be discussed in chapter 5. In so-called remote souree approach a carrier gas is used to create the plasma. In that case, silane gas is added to the plasma afterwards. Often used carrier gases in silicon deposition are hydrogen and argon. In the expanding thermal plasma reactor, which will be discussed in chapter 3, a mixture of argon and hydrogen is used as carner gas.

There is an important difference between the Balzers reactor and the expanding thermal plasma reactor conceming the dissociation of silane. In the expanding thermal plasma setup the plasma is created in a cascaded are and it expands in a low pressure vessel, where silane is added. Due to the expansion the electron temperature decreases from approximately 1 to 0.3 eV. In paragraph 4.3 we will come back on the electron temperature in the are. As the electron temperature in the vessel is low, electroos are not efficient in dissociating silane. Thus, the dissociation of silane is mainly due to reactions with ions or atoms. However, in the Balzers KAl reactor, which will be discussed in chapter 5, the electron temperature is around 4 eV and therefore electroos are efficient in dissociating silane. The silane is therefore mainly dissociated by electrons, giving SiHx radicals and atomie and molecular hydrogen.

An important plasmaprocessis diffusion. For example, the flux ofradicals reaching the deposition substrate is dependent on the partiele's diffusion. In the plasma model, which will be discussed in chapter 5, we will needan expression for this diffusion process. We will derive a simple equation for the time a partiele needs to travel a distance L in a background of other partieles. The derivation is valid fora solid sphere approximation withno other interactions but collisions (i.e. Van der Waals or Coulomb interactions between the particles are not ineluded).

The average distance a partiele travels without meeting another partiele is called the mean free path 1:

A=-1- , ( 2.1.5) n. a

where nis the density ofthe partiele background and cris the collisioncross section, which is defined in eq. 2.1.3 for the solid sphere approximation. For arbitrary motion, the number of collisions needed to travel a net distance L is equal to:

L2 N= A-2. ( 2.1.6)

So, the actual distance traveled ifthe net distance traveledis Lis equal to N·À.. The time the partiele needs to travel a distance L in the background is equal to:

L2 t=--.

A·Vth ( 2.1.7)

In this equation Vth is the thermal velocity, given by eq. 2.1.4. Notice that t is proportional to the pressure due to the density dependency of À.. We will use this expression in the plasma model in chapter 5. The number of partieles coming to the wall per second per volume unit is equal to:

N =!!._= n·A·vth d t L2 '

( 2.1.8)

where n is the density of the partiele concemed.

1 We assume that the mean free path is much smaller than the vessel dimensions.

10

2.2 Hydrogenated silicon deposition

The radicals created in the plasma deposit either on the reactor walls or on the substrate. In this paragraph we discuss some aspects ofthe deposition process and material quality features. Furthermore, a summary ofthe different known microcrystalline deposition mechanisms is given. We will start with a short description of hydrogenated silicon.

2.2.1 Hydrogenated silicon

The atom silicon has atomie number 14 and has therefore 4 electroos in its outer electron shell. In a crystal it has a diamond-cubic structure, which is shown in Figure 2.2.1 a. In plasma deposition one can obtain hydrogenated amorphous silicon or hydrogenated microcrystalline silicon. An amorphous material has no long range order, bond angles are not the same for each bond. A sketch of an amorphous material is shown in Figure 2.2.1b. Because ofthe irregular ordering ofthe material, the material has a relatively high defect density. A defect is a unsaturated bond within the material, which is also called a dangling bond. The hydrogen in hydrogenated amorphous silicon reduces the

/ '

__ J)---__ J/-.. -

~ .... , .::=..::: ;--------J.._, I ,_/

(a) (b) (c)

Figure 2.2.1 Crystalline silicon (a), amorphous material (b) and SEM picture of microcrystalline silicon (c) [KOY96}

defect density of the material by passivating dangling honds. Microcrystalline silicon consists of parts crystalline material connected by amorphous materiaL A SEM photograph of microcrystalline material is shown in Figure 2.2.1 c. The crystalline parts are called grains. At the grain boundaries defects occur, which has been the reason that microcrystalline silicon at first was not used for solar cell applications. Now, however, is shown that microcrystalline silicon can be used successfully in solar cells [MEI94].

In solar cells microcrystalline silicon appears to be more stabie than amorphous silicon. As pure microcrystalline silicon is an n-type material, the material has to be doped with for example diborane, which is usually added in the gas phase in very small concentrations [MEI94]. An important problem ofthe microcrystalline silicon deposition is the relatively low growth rate, which is usually obtained. By using for example Very High Frequency (VHF) and high power techniques in an rf reactor as will be discussed in chapter 5, it is however possible to reach satisfactory high growth rates [TOR98].

2.2.2 Film quality

Fortheuse in solar cells, the hydrogenated amorphous silicon has to fulfill eertaio demands. These demands refer to the electrical properties ofthe material, such as conduction as wellas to the optica!

11

properties, such as refractive index, band gap and hydrogen content. The desired properties of solar grade hydrogenated amorphous silicon are listed in Table 2.2.1 [LUF93].

Table 2.2.1 Desired properties for sol ar grade hydrogenated amorphous silicon [LUF93].

1.6-1.8 eV 4.3

The hydrogen content seems to be a very important parameter [LUF93]. Hydrogen passivates the dangling bondsin the materialand reduces therefore the dangling bond density. Furthermore, adding hydrogen to amorphous silicon decreases the network stress. This decreases the dark conductivity of the materiaL Ifthe main part ofthe hydrogen in the amorphous silicon is bonded in Si-H bonds, this will increase the photosensitivity ofthe materiaL Poor quality a-Si:H has usually a high microstructure, which is defined as:

R* = [SiH2 ]

[SiH2 ] + [SiH]' ( 2.2.1)

where [SiH2] is the Si-H2 bond density in the material and [SiH] is the Si-H bond density. In material with high microstructure the hydrogen is mainly bonded as Si-H2 bonds and the photosensitivity is usually low.

The hydrogen content is shown to be strongly dependent on substrate temperature [SEV96], the hydrogen content decreases ifthe substrate temperature increases. Furthermore, the hydrogen on the growing surface plays an important role in the growth processof a-Si:H, as will be shown in the next paragraph. The hydrogen content shows no dependenee on deposition rate [VDS97] at low growth rates, but increases with the growth rate if the growth ra te is higher than 1 nm/s [KES97].

2.2.3 Microscopie growtlt model of ltydrogenated amorplwus silicon

In this paragraph we will discuss a growth model of hydrogenated amorphous silicon. A good review of the different growth processes is given in [VDS97]. The growth process will first be discussed qualitatively, foliowed by a more quantitative discussion with experimental data from literature.

The growth model discussed in this paragraph (which is the model ofMatsuda, Gallagher and Perrin, a good summary is given in [VDS97]), assumes that the main radical in a silicon depositing plasma is SiH3, and that it is the only radical responsible for growth. Furthermore, the growing surface is thought to be almost totally covered with hydrogen atoms. As a result, first dangling bonds have to be created before a radical can stick. A large hydrogen coverage is proven experimentally by, for example, Toyoshima [TOY91].

12

SiH3 reffection, t-p

1u desorption recombination as o-to Si2H6

ih H abstradion oJ giving SiH4

physisorption r ~ I/ ,,;~:~:-") ~~/~s

~ ~ f f f f ~f f f f f f I~ i7TI ~ f a-5i:H surface with Si-H bonds

Figure 2.2.2 Possible processes of SiH3 radicals on the growing surface [ROB98].

The different processes of SiH3 on the growing surface are sketched in Figure 2.2.2. A radical that comes to the growing surface first physisorbs with a probability P to the surface. A physisorbed radical is Van der Waals bonded to the hydrogenated surface and is able to hop from one H atom to another. Hopping is a thermally activated process, but because ofthe low activation energy the hopping probability is approximately unity on a fully hydrogenated surface. The process of a radical hopping from H atom to H atom on the surface is called surface diffusion. The surface diffusion wil! decrease dramatically if the surface is not fully covered with hydragen atoms [MA T83]. In that case, the radical sticks directly.

The hopping radical has a probability to find a dangling bond on the surface and will then stick to the silicon network by means of a chemica! bond (probability s). The chemically bonded radical canthen participate in a cross link process. In this process, with probability clone ofthe H atoms from the radical forms H2 with aH atom ofthe surface, with subsequent desorption ofthe H2 molecule. The two dangling honds left formanSi-Si bond. Another possibility is that the SiH3-radical abstracts an H atom from the surface leaving a dangling bond (probability y). The SiH3 atom leaves the surface as SiH4 in this process. Ifthe radical meets another hopping radical, it has a possibility to combine, creating a Si2H6 molecule with a probability Y2·

The processes of incoming hydragen radicals on the surface are sketched in Figure 2.2.3. Tostart with, the atom could simply reflect (without interaction with the surface), having a probability r. In [SEV97] the process ofH-abstraction by H is proposed, leaving a dangling bond and creating H2, having a probability ö.

. . cjetching pass1vatwn desorption O 0

reflection 0• 0..0 g \ i ~, r \1 ~ ÎIIÎÎIÎIÎÎ Î

H-abstraction

Figure 2.2.3 Possible processes of atomie hydragen on the growing surface.

13

If an hydrogen atom roeets a dangling bond on the surface it will passiva te this dangling bond (probability \1'). The last process of hydrogen atoms on the surface is the etch process of a chemisorbed SiH3 radical forming SiH4, with a probability E.

Ifthe substrate temperature is larger than 500 °e, the probability ofH2 molecule formation by association oftwo adjacent H-atoms at the surface becomes important. In this process, two dangling honds are created. The surface diffusion, being dependent on the hydrogen coverage of the surface [MAT83] will therefore decrease a lot while increasing the substrate temperature above 500 oe.

The probabilities of the processes with radicals have a re lation because the sum of all probabilities should he one. Besides ~, y and s, (1-~) should he taken into account. The relation is then equal to:

f3 = r + r 2 + s . ( 2.2.2) Adding the probabilities for the possible activities of an H atom at the surface should add up to one too:

( 2.2.3)

In literature, the determination of a lot ofthe probabilities is described. In the next paragraph, the probabilities will he discussed.

2.2.4 Probabilities: quantitative

The probabilities have to he known in the model that will he discussed in chapter 5. In this paragraph, we will give a survey ofthe values ofthe probabilities as found in literature. The probabilities are given macroscopie, which means that it is the probability of a partiele in the gas phase to participate in the process considered. An exception is the cross link probability, which is defined as the probability for a sticking radical to cross link.

physisorb (p), stick (s) andrecombine (y) The probability for a silane radical to physisorb on a growing surface is measured for example by Matsuda [MAT90]. The physisorption probability turns out to he different for microcrystalline and amorphous silicon. Furthermore, Matsuda assumes no SiH2 contribution to growth, and therefore finds ~ for SiH3. The value of~ for amorphous silicon is independent on the substrate temperature in the range from room temperature towards 500 oe. For microcrystalline silicon, however a temperature dependenee is seen. The values for SiH3 are at a substrate temperature of200 oe equal to 0.3 for amorphous and 0.5 for microcrystalline silicon.

In the same paper, Matsuda is able to calculate the value ofthe sticking probability sas a function of temperature. There is only a temperature dependenee at substrate temperatures higher than 350 oe and the value fors is the same for microcrystalline and amorphous material below 350 °e. The sticking probability s is approximately equal to 0.1.

The probability to recombine with another SiH3 radical to form Si2H6 (Y2) is estimated to he 0.08 [VDS97]. Knowing s, ~ and Y2, it is possible to calculate the probability of reileetion as SiH4 from the surface (y), using the relation given before. For SiH3 y turns out to be 0.12 for amorphous silicon and 0.32 for microcrystalline silicon (both at 200 °e).

If an SiH2 radical reaches the surface it actually does not physisorb, but sticks directly. Th is is possible because SiH2 has one dangling bond extra. It is assumed that in the sticking process the radical can insert in a Si-H bonding on the surface, resulting in a Si-SiH3 configuration. The reileetion probability y is thus assumed to he zero for SiH2, and therefore the sticking probability s is

14

equal to f3. Kae-Nune [KAE95] assumes a sticking probability of 0.8 and makes no difference between amorphous and microcrystalline materiaL

The probabilities conceming the silane radicals are summarized in the table below.

Table 2.2.2 Probabilities ofphysisorption, sticking and rejlection.

SiH3 SiH2

amorphous microcrystalline

f3 0.3 0.5 0.8 s 0.1 0.1 0.8 y 0.12 0.32 0

Y2 0.08 0.08 0

etching (s) The etch probability can be calculated using the measured etch ra te of microcrystalline silicon in a pure hydrogen plasma. This method is similar to the method used by Wei [WEI95]. The etch rateis measured to be 0.05 Als at a substrate temperature of250 oe, a pressure equal to 0.25 Torr, an input power of 150 Wand an hydrogen flow of 360 seem. Using the reaction rate [KUS88] for the dissociation of hydrogen and the i deal gas law to calculate the density of H2 in the reactor, the number of created H atoms is calculated. Multiplied by the half height of the reactor, an estimation of the number ofhydrogen atoms coming to the surface per square meter persecondis found. The number of etched silane radicals can be determined by using the mass density of microcrystalline silicon and the measured etch rate. Assuming that one H atom is needed to etch one silane radical from the surface, the probability to etch is the ratio ofthe number or etched silane radicals and the number of hydrogen atoms coming to the surface. In this way the etch probability is determined to be 2·1 o-3, which is a lower limit. The value is ofthe sameorder as the etch probability found by Wei.

lt is a lso measured that the etch ra te for amorphous silicon is 10 times higher than in the microcrystalline case. Therefore we estimate the etch probability for amorphous silicon at 2·10-2.

recombine H witlt H on surface ( 5) In [VDS97] the recombination of deuterium with atomie hydrogen forming HD and a dangling bond on the surface is discussed. The probability for this process is equal to 0.3-0.4. This is assumed to be equal to the probability of recombining H with H on the surface creating H2 and a dangling bond (ö). Thus, ö is approximately equal to 0.35.

passivating a dangling bond ( '1/) In literature no in formation is found on the probability of passivating a dangling bond. If atomie hydrogen arrives at a dangling bond, the probability of passivating is thought to be unity. So, the probability of passivating a dangling bond is strongly dependent on the dangling bond density of the surface. Aftersome test calculations, \V is taken to be 0.3 in the model.

rejlect H as H (r) The reileetion probability is easily calculated using the fact that the sum ofthe probabilities of processes conceming activities of H atoms at the surface is one. Th is gives that the probability of reileetion ofH is equal to approximately 0.33.

cross link (cl) The cross link probability is estimated to be 0.88, using the formula for the hydrogen content if it is assumed that only crosslinking causes a removal ofhydrogen out ofthe film given by [VDS97]:

15

C _ 2·~si-H

H-3 . ~ Si-H + ~Si-Si

( 2.2.4)

where Si-H is the growth flux and Si-Si is the crosslinking growth flux. Using a hydrogen content of 0.2 at 200 oe, as given in [SEV96], it is possible to calculate the ratio of Si-Si and Si-H. which is the probability fora sticking radical to cross link cl. It turns out that cl is equal to 0.88, which is an upper limit.

To summarize, the probabilities concerning the hydrogen atom are listed in the following table.

Table 2.2.3 Probabilities of surface processes concerning the H-atom for amorphous silicon.

E 0.02 ö 0.35 \jl 0.3 r 0.33 cl 0.88

2.2.5 Macroscopie models ofmicrocrystalline silicon deposition

The growth process of microcrystalline silicon is not really understood. Th ere exist three important models to descri he the growth process of microcrystalline silicon, which are the model of partial chemica! equilibrium [VEP72], the model ofpreferential etching [HEI93], [SOL93] and the model concerning surface diffusibility [MAT83]. A good summary ofthose modelsis given in [HAP95]. In this paragraph we will shortly address those the three models in relation to the growth model of amorphous silicon.

Partial Chemica[ Equilibrium (PCE) The model ofPartial Chemica! Equilibrium (PCE) is basedon a chemica! equilibrium between the etching and deposition of molecules at the growing surface. The process is described by the following reaction:

SiHx (gas) -H Si (solid) +x H (gas)

where the forward reaction is the deposition process and the backward reaction is the etching process. It is thought that during the etching process the energetically less favourable honds are broken by the hydrogen atoms, which are the 'amorphous' honds. This is advantageous for the formation of J-I.CSi:H, which continues to grow on the crystalline surface. Ifthe etching process is relatively slow, amorphous silicon is deposited.

An important feature ofthe PCE growth model is that the deposition is thought to bedependenton the ion flux (H+) towards the growing surface. A linear dependency is observed between the ion flux and the deposition rate. It is thought that the ions make it possible for the surface to dehydrogenate, like:

H+ SiH2 (absorbed) ~Si (surface) + H2 (gas).

Preferenfiat Etching The preferential etching model is an extension of the PCE model. It supposes a preferred etching of amorphous material rather than crystalline materiaL One of the evidences of preferential etching is thought to be the porous structure of J-lc-Si:H. The voids in the bulk material can represent up to 10%

16

of the film [SOL93]. In experiments in which a substrate with a film of f.!C-Si:H and a substrate with a film of a-Si:H are at the sametime exposed to an hydrogen plasma, it is seen that the etch rate of the a-Si:H is approximately six times higher than the etch rate of f.!C-Si:H [HEI93]. In other experiments it is shown that the upper atomie layers of an amorphous substrate are changed into microcrystalline silicon [ASA90]. The concept ofpreferential etching is the basis ofthe layer-bylayer deposition technique.

Using the layer-by-layer (LbL) technique [ASA90], [HAP97] two alternating steps are performed. First an amorphous layer is deposited using a silane plasma. Second, the just grown layer is exposed toa hydrogen plasma which etches away the amorphous material in the grown film. lt is seen that best results are reached with a relatively long hydrogen plasma exposure time (330 s with a deposited a-Si:H film of 100 Á) [HAP97]. As the etch rateis in the range of0.2 Als, and constant in time, most ofthe material is etched away in that case. If a fixed number of atomie layers which transform from an amorphous toa crystalline state is assumed, which is reasonable ifthe plasma properties do not change, it is not surprising that there is an increased relative fraction of crystalline material with increasing hydrogen exposure time. lt is shown that the crystalline fraction is also dependent on the rf frequency using the LbL technique, which is ascribed to a better phase transformation from amorphous to crystalline at higher plasma excitation frequency.

Surface diJfusion model The surface diffusion model is based on the assumption that hydrogen covers the growing surface [MAT83], which is in accordance with the assumptions in the amorphous silicon deposition process. The hydrogen on the surface enhances the surface diffusibility ofthe SiHx radicals, which diffuse on the surface until they find an energetically favourable place to bind. lt is shown, that the grain size is larger with higher hydrogen coverage ofthe surface. The importance ofthe hydrogen coverage for the f.!C-Si:H growth process is also shown in the case that the substrate temperature rises above 400 oe. At this temperature, the hydrogen starts to desorb from the surface. lt is seen that the deposition ra te of f.!C-Si:H decreases dramatically for substrate temperatures above 400 oe. If the LbL technique is used and an additional step is added, namely doing nothing for a eertaio time period, it turns out that if the time period is long, an amorphous film is grown. If this time period is short, a microcrystalline film is grown. This can be explained by the hydrogen, which can thermally desorb from the surface during the long time period, but had not the chance to do the same in the short time period.

17

Part 11

THE EXPANDING THERMAL PLASMA

Chapter Three An expanding thermal plasma setup to deposit amorphous hydrogenated silicon A fast metbod to deposit amorphous hydrogenated silicon is expanding thermal plasma deposition. In this method, the plasma is created in a cascaded are at high pressure. The plasma expands into a low pre ss ure vessel where silane is added. The growth rates are in the range of 10 nm/s, which is approximately ten to hundred times higher than in conventional plasma deposition setups. In this chapter, the expanding thermal plasma deposition setup is discussed.

3.1 Experimental setup

The expanding therm al plasma deposition setup is shown in Figure 3 .1.1. The setup can be divided in three main parts: the cascaded are, the expansion vessel and the substrate. The plasma and the deposition process are studied using several diagnostic methods. The three parts as weii as some diagnostics wiii be treated in the following sections.

Optional RF bias Tgu~lJ

Leadloek

Rotating compensator ellipsometer

Langmuir probe

To turbomolecular ~pump

Detector

1_Argon + Hydroge

Figure 3.1.1 Expanding Thermal Plasma setup to deposit amorphous hydrogenated silicon.

3.1.1 Cascaded are

The cascaded are is a de voltage plasma source, in which a discharge is maintained at subatmospheric pressure. The are is shown in Figure 3.1.2. There are three cathodes, from which one is shown in the picture. The catbodes are placed such that the mutual angles are 120°. The anode is the end plate of the are. The voltage difference between catbodes and anode is between 50 and 200 V, depending on the gas mixture. The current from anode to catbode can be varied between 25 and 75 A, but in this work it has been 45 A. The plasma is confined in a plasma channel, which consists of a stack of water caoled capper plates with a central bare of 4 mm. The capper plates are electrically insulated from each other by a PVC spacer. To prevent contact between the plasmaand the PVC spaeer the middle part of the spaeer is replaced by a baron nitride ring. In principle, the length of the plasma channel can be changed by varying the number ofplates. In the current work, however, the number ofplates is 10, giving an are channellength of approximately 5 cm.

21

Figure 3.1.2 The cascaded are souree [GRA94].

vacuum PVC spaeer seal

shielding ring

The pressure in the are is approximately 3-4·104 Pa. A mixture of argon and hydragen is used. The gases are mixed in a separate vessel before entering the are. The gas flows are controlled by flow controllers. The plasma leaves the cascaded are through a parabollically shaped nozzle, which is screwed into the anode plate.

The electrical circuit ofthe are is shown in Figure 3.1.3. The are supply is current controlled. The are current is adjusted, and the voltage between catbodes and anode is chosen such that this current is maintained. Each catbode is connected in series with a resistor. The resistance of each resistor is equal to 3 or 6 n. These resistors induce a self-stabilizing effect of the are. If one of the catbodes fails, no current flows through the resistor. Therefore, the voltage difference between the failing catbode and the anode is larger than the voltage between the working catbodes and the anode. Therefore, the failing catbode has larger probability of starting again. The plasma in the are does not always have ohmic behaviour: the voltage-current (vi) characteristic ofthe plasma could have a negative slope, depending on the gas mixture. The are supply, however, does have ohmic behaviour. The extra resistors are to correct for the negative slope of the vi-characteristic of the plasma, such that the total circuit resistance remains positive.

resistors

3 cathocles

anode

Figure 3 .1.3 Electrical circuit cascaded are.

Therefore, the extra resistors have an important role in are operation. If the gas mixture is changed such that the slope ofthe vi-characteristic becomes more negative, one should increase either the resistance of the resistors or the are voltage to maintain the adjusted are current. The are voltage is limited, because a too high are voltage will cause the catbode tips to become very hot and eventually evaporate.

3.1.2 Vessel and substrate

After leaving the are, the plasma expands supersonically into the vessel. A shock occurs approximately 4 cm after the are exit [VDS91]. After the shock the plasma particles' velocity is about 1000 m/s.

22

The vessel is a cylinder of0.6 min diameter and a length of0.8 m. The vessel volume is approximately 180 l. There is a roots pump system with a maximum pump capacity of 1500 m3fhr. The pump capacity can be adjusted by partially closing the valve between the pump system and the vessel. In this way it is possible to influence the vessel pressure. During plasma operation, the vessel pressure is around 20 Pa. Ifthe reactor is not in use the vessel is pumped by a turbo pump, maintaining a base pressure of approximately 1 o-4 Pa.

Six centimeter after the are exit silane is added to the expanding plasma through a silane injection ring. The silane is partly dissociated by the reactive particles teaving the are. The created radicals are deposited on either the vessel walls or the substrate. The distance between the are exit and the substrate is 0.35 m. To insert the substrate, the vessel is equipped with a loadlock. The substrates are put on a substrate holder which can contain three substrates of 25 mm x 25 mm. The substrate material is either crystalline silicon [100] or Coming 7059 glass (500 J.lm). The substrate holder is put onto the yoke using a magnetic manipulating arm. The substrates can be protected by a shutter during plasma ignition.

The substrate temperature is controlled at a constant temperature between 50 and 500 oe. In the work presented in this report the substrate temperature has been 400 oe. A helium backflow enhances the heat exchange between substrate holderand substrates, teadingtoa good temperature control even when the plasma is on.

3.2 Diagnostic methods

In this paragraph the diagnostic methods used tbraughout this work to investigate the plasma and the deposition process are mentioned. In the next chapter a more detailed description will be given.

ARC • Projection method: with the help of a lens it is possible to look at the plasma in the are. Th is gives

information about are stability and effective are diameter. • Voltage-current characteristics: measuring voltage-current characteristics can give information

about effective are diameter or electronic temperature.

IONS • Langmuir probe measurements: give ion density and effective ion mass at the measuring position. • Mass spectrometer: a mass spectrometer placed on the position of the substrate holder is used to

study the ions reaching the substrate qualitatively. Information on absolute ion densities is nat easily abstracted from mass spectrometer data.

PLASMA PARTICLES • Residual gas analyzer (RGA): gives information about what particles are present in the plasma

background. The RGA is used todetermine the silane consumption by the plasma (depletion) and to check the vacuum befare starting depositions.

FILM QUALITY • Ellipsometry: is used to investigate the film during deposition. It gives information about growth

rate, refractive index and extinction coefficient. • Fourier transformed infrared (FTIR) spectroscopy: after deposition refractive index, thickness,

hydragen contentand microstructure ofthe material can be obtained using FTIR spectroscopy. • Conductivity: the film is supplied with electrical contacts. The conductivity is determined by

measuring the current through the material as a function of applied voltage. This is done in a absolutely dark box and under well-defined illumination giving the photo and dark conductivity respectively. The ratio between photo and dark conductivity is defined as the photo sensitivity of the materiaL

23

Chapter Foor Argon flow reduction in the expanding thermal plasma deposition setup In the near future, an experimental setup will be built to produce a complete solar cell in one deposition tooi. The expanding thermal plasma (ETP) setup will be used in this device to make the solar cell's intrinsic layer. A large pump capacity is needed in the current ETP setup to cope with the high argon flow (55 sccsl) used at standard deposition conditions. This large pump capacity is not available for the new solar cell deposition setup. Besides, it is thought that the main part of the argon put in does not contribute to the deposition process. Therefore, it might be favourable to reduce the argon flow. In this chapter a study ofthe consequences of decreasing the argon flow is presented.

While decreasing the argon flow, there are two possibilities: I. reducing the argon flow, but maintaining the total flow constant, which means an increase ofthe

hydrogen flow at the same time. This is not a solution to the pump capacity problem, but it is interesting from a scientific point of view.

11. reducing the argon flow and keeping the hydrogen flow fixed, meaning that the total flow will decrease. In this situation, there is not only a change of flow composition, but also a change in total flow, which introduces a difference in vessel pressure ifthe pump capacity is not adjusted. Therefore, two different situations can be distinguished:

Ila. Reducing the argon flow while keeping the hydrogen flow fixed and keeping the pressure constant by adjusting the pump capacity,

lib. Reducing the argon flow while keeping the hydrogen flow fixed and allowing the pressure to change.

lt will turn out that the behaviour ofthe plasma in the cascadedareis a key factor in the effects of argon flow reduction in the deposition setup. Therefore, we will start with a short discussion on the plasma in the are channel. The concept of effective are diameter will be explained here. After that, are stability and are efficiency are studied. Effective are diameter and voltage-current characteristics are used todetermine the electron temperature in the are (paragraph 4.3). The ions emanating from the are are investigated quantitatively (Langmuir probe) and qualitatively (mass spectrometer), which will be discussed in paragraph 4.4. The atomie hydrogen flow will turn out to be an important factor in the silane consumption (depletion), which will be explained in paragraph 4.5. Finally, the silane depletion, growth ra te as well as film quality (refractive index and photo response) will be discussed in paragraph 4.7.

4.1 Are plasma

To understand the experimental results that will be discussed in this chapter, some knowledge about the are plasma is needed. In this paragraph the plasma in the are will be discussed briefly. We first discuss the electrical and heat conductivities in an argon/hydrogen mixture, which is necessary to understand the are behaviour if hydrogen is added to the argon in the are. Furthermore, the channel narrowing effect will be explained and some remarks are made about the dissociation of hydrogen. Finally, the electrical conductivity in the are is discussed, teadingtoa relation between effective are diameter and electron temperature.

1 The flow unit sccs is equal to 2.5·1019 particles per second.

25

In the are, a discharge is maintained between cathocles and anode. The plasma in the cascaded are is wall-stabilized. As explained in paragraph 3.1, the are channel consists of water cooled copper plates with a central bore. Ifthe plasma moves accidentally towards the channel walls, the heat conduction increases which causes the plasma temperature and therefore the electrical conductivity to decrease, which will he discussed below. As the current through the plasma should remain constant, the plasma is forced to move back towards equilibrium position. In this way, the plasma is stabilized within the are walls.

ARGOH-HYDROGEN lotiXTURES, P'= 100 kPa ~ x Ar + ( 1-x) H2 x=O. 1 to 0.9 by step of 0.1

;:: ... u

~ ~ 8 ,.,~10

~ ~ ... u .... r;j

0

TEMPERA TURE,

(a)

10 TEt.IPERATURE,

(b)

Figure 4.1.1 Electrical (a) and thermal (b) conductivity of an argon/hydragen mixture at 1 bar. [BOU94].

25

The electrical and thermal conductivity of a plasma for different Ar/H2 mixtures are shown in Figure 4.1.1. The electrical conductivity increases with increasing temperature and is almost independent on the argon/hydrogen ratio. The thermal conductivity does show a dependency on the argon/hydrogen ratio. If more hydrogen is added, the therm al conductivity increases, especially near the dissociation and ionization temperatures of hydrogen, which cause the two peaks in the figure.

In a pure argon are, there is a flat temperature profile with strong gradients near the are walls [QIN95], as is shown in Figure 4.1.2. The ionization degree in the are is between 1-15 %. As the electron density is high, there is a good coupling between the electron temperature and the heavy partiele temperature, thus the plasma is near LTE. Because ofthe high electron density, Coulomb collisions (electron-ion collisions) dominate over electron-neutral collisions.

If hydrogen is added to the are, the heat conductivity of the plasma increases as is seen in Figure 4.1.1 b. The hydrogen diffuses faster to the are walls than argon due to the lower mass and at the are walls hydrogen atoms are able to recombine creating H2. In this wall association a fraction ofthe recombination energy is supplied to the are wal!. Botheffects leadtoa decrease oftemperature near the are walls, which causes the plasma channel to narrow. Two regions arise in the are channel: a region where the ionization degree is high and the heavy partiele temperature equals the electron temperature, which is called the active plasma region or plasma channel, and a region outside the plasma channel, where the ionization degree is much lower and the heavy partiele temperature is lower than the electron temperature (see Figure 4.1.3).

26

effeetive are diameter

are diameter

are diameter

D effeetive are diameter

water eooled are wall

plasma ehannel

Figure 4.1.2 Temperafure profile in an argon are. Lower picture shows the active plasma region in the channel cross section. The active plasma region accupies a/most the whole are channel.

effeetive are diameter

Te

Th

are diameter

plasma ehannel

. . . . effeetive are diameter

Figure 4.1.3 Temperafure profile in the are for an argon/hydragen mixture. Lower picture shows the active plasma region in the channel cross section, where the active plasma region diameter is much smaller than the are diameter.

Inside the plasma channel the plasma is in LTE and Coulomb collisions dominate over electron neutral collisions because of the high ionization degree, similar to the argon are. Outside the plasma channel the electron temperature is thought to remain at high temperature, but the electron density is lower so that the coupling between heavy partiele and electron temperature no longer sufficient to remain in L TE. As a result, the heavy partiele temperature is lower than the electron temperature in this region. Due to the lower electron density Coulomb collisions no longer dominate and electronneutral collisions become more important.

Because of the high heavy partiele temperature within the plasma channel, all hydrogen molecules are thought to be dissociated. The dissociation degree depends strongly on temperature [BOU94], which is not well known outside the plasma channel. Therefore it is difficult to estimate the dissociatioh degree in the outer ring, on which we will comeback in paragraph 4.5.3.

Besides the relative amount of hydrogen added, the effective diameter is influenced by the pressure in the are. Ifthe total flow through the are is lower, the pressure will be lower. Furthermore, the lower viscosity of hydrogen causes the are pressure to decrease with increasing argonlhydrogen flow ratio. A lower pressure causes the particles in the are channel to diffuse faster towards the are walls. At the are walls energy is lost more easily due to recombination processes and heat conduction. As a result the heavy partiele temperature decreases near the are walls and as a result the effective are diameter decreases.

Now, we will consicter the electrical conductivity ofthe plasma. Because ofthe high ionization degree inside the plasma channel the conductivity in this region is high. Outside the plasma channel, the electron density is much lower and therefore the conductivity is negligible to the conduction in the

27

active plasma region. Hence, the are channel conductivity can be evaluated consiclering only the active part ofthe channel [DAH94]. The electrical conductivity is in general given by Ohm's law:

_j_ O"e- E. (4.1.1)

If the electric field is homogenous over the plasma cross section, the current density j can be written as:

j= I d 2' 4 · 7r · eff

I ( 4.1.2)

where I is the are current and de.ffis the effective are diameter, which is the width ofthe plasma channel. Assuming a linear electric field profile through the plasma channel, the electric conductivity can be written as:

I ·I ( 4.1.3)

Here is I the di stance and V the potential difference between cathocles and anode. The conductivity as a function of electron temperature for plasma's dominated by Coulomb collisions with an electron temperature higher than 1 eV is given by Spitzer [SPI64]:

2·104• rx

0" = e e lnA

where lnA is the Coulomb logarithm given by:

lnA = ln(1.49 ·1013 • ne -.X· f/~).

( 4.1.4)

( 4.1.5)

Using 4.1.4 and 4.1.3 we find a re lation between are resistance (V 11), effective are diameter and the electron temperature:

V

I

/-lnA L tr . d 2 • 2 . 1 04 . T X . 4 eff e

( 4.1.6)

In paragraph 4.3 this relation will be used todetermine the electron temperature using experimentally obtained values for the effective are diameter.

4.2 Are stability To determine which argon/hydrogen flow ratios are possible while maintaining an are plasma the are stability is studied. The are stability is evaluated by looking at the plasma inside the are. This is simplified using a projection ofthe plasma in the are on a screen. The projection setup is described in Frame A.

28

Frame A

ARC PLASMA PROJECTION A lens is used to create an image of the cathode environment on a screen. The lens has a focal point equal to 120 mm and is placed such that the cathode tips are approximately in the focal point ofthe lens. The setup is shown in the tigure below.

±3m ±5cm

~·. . [ .::: screen lens

Projection setup to investigate the plasma in the are.

On the screen the cathode tips and the plasma are clearly visible. If the plasma is unstable, it either fluctuates or interrupts. Moreover, the temperature of the cathodes can be evaluated by looking at the colour ofthe cathode tips. Todetermine the stabie conditions objectively, the are stability is judged only by the flow ratio for which the plasma in the are interrupts.

The projection setup is also used to look at the are channel by focusing at the are channel instead of the cathode tips. In this way it is possible to determine the effective are diameter, which will be used in paragraph 4.3.

During the are stability measurements the argon flow is gradually reduced until the are plasma interrupts.2 Two situations are distinguished: situation I, in which the total flow is kept at a constant value, and 11, in which the hydragen flow is fixed. In situation I the total flow is 65 sccs, starting with 55 sccs Ar and 10 sccs H2. In situation 11 the hydragen flow is fixed at 10 or 5 sccs and the argon flow is reduced starting from 55 sccs. The argon/hydragen flow ratio for which the plasma in the are interrupts as a nmction of are current is shown in Figure 4.2.1.

At a specific current, the plasma in the are is considered stabie ifthe argon/hydragen flow ratio is higher than the interruption argon/hydragen flow ratio. This does not necessarily mean that the plasma is totally steady in that situation. As can be seen in the figure, the plasma in the are is stabie for argon/hydragen flow ratios larger than 0.5 ifthe are current is higher than 45 A. Considering lower are currents, the are tums out to be more stabie in situation 11 than in situation I. If the circuit resistance is doubled (6 n instead of3 Q) the are stability increases. To conclude, to maintain a stabie are plasma, the are current should be higher in situations where relatively more hydragen is supplied to the are. A higher circuit resistance is favourable for the are plasma stability. In further experiments described in this report, the circuit resistance has been 6 n.

2 It is not possible to ignite the plasma at very low flows and/or at a relative high hydrogen flow. Therefore, the experiment is perforrned going from high to low flows instead ofthe other way around.

29

4

\ \

-•-11. hydragen flow= 10 sccs

- e- 11, hydragen flow= 5 sccs

. ·A ·. I, total flow= 65 sccs

- ·T-· 11, hydragen flow= 10 sccs •· · · ·• · · · .. •

doubled circuit resistance

I

\ I \ \ \ \ \

•

\ \ \

\

'

·,

' '

T ·, ·,

are current [A]

Figure 4.2.1 Interruption argon/hydragen flow ratio as a .function of are current for different situations. The lines are a guide to the eye.

4.3 Effective are diameter and electron temperafure

The projection setup used to determine are stability can also be used to measure the effective are diameter. As discussed in paragraph 4.1, in an argon/hydrogen mixture the plasma in the are channel can be divided into two regions: the plasma channel, which is in LTE and at high temperature and the region outside the plasma channel, where the heavy partiele temperature is lower than the electron temperature. The amount of atomie hydrogen leaving the are is important to the dissociation of silane and is probably linked to the effective are diameter. Inside this effective are diameter the hydrogen is totally dissociated due to the high temperature. The dissociation degree outside this diameter, however, depends on the heavy partiele temperature in this region, which is not well known. We will study the effective are diameter in this paragraph. We will start with a short explication why the are projection setup could be used to determine the effective are diameter. After that, the results of effective are diameter measurements are shown. Finally, the relation between effective are diameter and electron temperature (eq. 4.1.6) is used todetermine the electron temperature in the plasma channel.

The effective are diameter is measured using the are channel projection metbod as described in Frame A. The radiation from the plasma in the are channel is dependent on the electron density. Inside the plasma channel the emission is dominated by continuurn radiation, which is proportional to the square of the electron density [SCH96]. The electron density in the are channel depends strongly on the radial position and decreases towards the are walls. Therefore, it is assumed that the size ofthe region visible at the projection screen is a good approximation for the effective are diameter.

In Figure 4.3 .2 the effective are diameter measured is shown as a function of argon/hydrogen flow ratio for situation I (total flow constant) and situation 11 (hydrogen flow fixed). In both situations, the effective are diameter decreases with decreasing argonlhydrogen flow ratio. This is ascribed to the increase ofthe relative amount ofhydrogen in the mixture, which is explained in paragraph 4.1.

30

70 'L:' Q) ....... Q)

60 • E ro "0 0

• u 50 s.... ro

0 .... • 0

~ 40 0 ........ 0 s.... • Q) .......

30 • Q)

E 0

ro "0

20 Q) • 1: total flow fixed > 0

:.oJ 0 11: hydrogen flow fixed u & 10 Q) 2 3 4 5 6

argon flow I hydragen flow[-]

Figure 4.3.2 Effective are diameter as ajunetion of argon/hydragenflow ratio for situations I and ll Measured using the are channel projection technique. Are current equal to 45 A. Error on data is estimated at 15 %.

400 • • 350 •

0 'L:' ro ..c 300 .s

• • 0

Q) s.... 250 ::::J (/) 0 (/) Q) s....

200 c.. u s.... ro 0

150 • 1: total flow fixed

0 o 11: hydrogen flow fixed

100 0 1 2 3 4 5 6


Figure 4.3.3 Upstream are pressure as ajunetion of argon/hydragenflow ratio in two situations. Error approximately JO%.

31

In situation 11 the effective are diameter decreases more with decreasing argon/hydragen flow ratio than in situation I. As explained in paragraph 4.1, this can be explained by a lower pressure in the are. The pressure is measured as a function of argon/hydragen flow ratio. The pressure is determined near the catbodes (upstream). The pressure at the end ofthe plasma channel will be even lower than the pressure measured. The are pressure measured is shown in Figure 4.3.3. In situation 11 the total flow decreases and therefore the pressure decreases more than in situation I.

It is expected that the amount of ions leaving the are decreases with decreasing argon/hydragen flow ratio due to the decreasing effective are diameter. In paragraph 4.4 the ion density in the plasma will be studied. lt might be possible to increase the are efficiency (i.e. the ionization degree) by decreasing the are diameter. At the same flow, this causes a higher pressure and therefore a relatively larger effective are diameter. The atomie hydragen flow emanating from the are, which is important to silane dissociation, is also connected to the effective are diameter. This will be discussed in paragraph 4.5.2. Now, the effective are diameter will be used todetermine the electron temperature in the plasma channel.

The relation between are resistance, effective are diameter and electron temperature is given by equation 4.1.6 and can be used to calculate the electron temperature in the are. The are resistance as a function of argon/hydragen flow ratio is measured and used in the calculation. The electrooie density in the are is determined by Beulens et al. [BEU93], and approximately equal to 1·1 o22 m-3. The distance between the catbodes and anode is 6 cm.

The obtained electron temperature is shown in Figure 4.3 .4 as a function of argon!hydrogen flow ratio. The electron temperature decreases with increasing argon/hydragen flow ratio. This can be explained by consiclering the electron density balance. When the pressure and thus the neutral density decreases the electron production decreases. Furthermore, the electron losses increase as the electrans can reach the walls more easily. As aresult the electron temperature is forced to increase to rnaintaio about the same electron density. A rough calculation gives approximately the electron temperature increase as shown in the figure. Notice that the electron temperature should increase more in situation 11 (hydrogen flow fixed), where a larger pressure drop is observed. In a pure argon are the electron temperature is measured to be 1 eV [BEU93]. As can beseen in the figure, at higher argon/hydragen flow ratio the electron temperature is calculated to be lower than 1 eV. This could be due toa higher electron density than assumed.

32

2.0

• 1: total flow fixed 1.8 0 11: hydragen flow fixed

5' 1.6 Q) .........

Q) .... :::s 1.4

I ...... ro .... Q) a.

1.2

I E Q) ...... c: 1.0

I 0 .... ...... u Q)

0.8 I Q)

0.6 0 1 2 3 4 5 6

argon flow I hydragen flow [-]

Figure 4.3 .4 Electron temperafure as a function of argon/hydrogen flow ratio. Calculated using measurements of are resistance and e.ffective are diameter.

4.4 Ions

Ion measurements have been performed in the expanding argon/hydragen plasma to investigate the amount and type of i ons leaving the are. The ion density is obtained using a Langmuir probe. Mass spectrometer measurements give information on which ions are present in the plasma.

4.4.1 Probe measurements

The principles ofLangmuir probe measurements are explained shortly in Frame B. The probe measurements are performed at two different axial positions in the vessel, namely 5 cm behind the are exit and 2 cm in front of the substrate.

Frame B

LANGMUIR PRO BE MEASUREMENTS

1 insulation :-····························~

plasma

Langmuir probe measurements in a plasma.

33

In principle, a Langmuir probe is just a piece of metal which is put in the plasma. A sketch ofthe probeis drawn in the figure. Ifzero voltage is applied and the probeis not grounded, the net probe current must be zero. Because oftheir higher mobility, the electron flux towards the probe is larger than the ion flux. The probe is negatively charged and a positive sheath is created around the probe. If a sufficiently large negative voltage is applied to the probe it repels all the electroos in the plasma. Only ions will reach the probe and the ion saturation current is measured. If ho wever a sufficiently large positive voltage is applied, the electron saturation current is measured. The measured currents are a function of electron-orion density (n) and thermal velocity (v), which is dependent on partiele's mass (m):

1 _ 1 ( 8kT )t l=4·n·e·S·v=4·n·e·S· -- ,

tr·m (Fl)

where S is the probe surface, e the elementary charge, k is the Boltzmann constant and T the partiele temperature. Re lation (F I) is valid under assumption that the distri bution function is Maxwellian and that Te=Ti. An equation for the effective ion mass (M+), which could be interpreted as the mean mass of i ons reaching the probe, is derived by dividing the ion and electron saturation current:

(F2)

where the iudexes e and i denote electron and ion respectively. Using the effective ion mass and estimating the partiele temperature one can determine the ion and electron densities. A more extensive discussion about probe measurements is given in [BEE97].

The ion densities obtained are shown in Figure 4.4.1. In the three situations, total flow fixed and hydrogen flow fixed with and without vessel pressure fixed, the ion concentration decreases with decreasing argon/hydrogen flow ratio, as expected consirlering the decreasing effective are diameter. As can beseen the ion density decreases much more than the square ofthe effective are diameter (Figure 4.3.2). Mass speetrometry measurements, which will be discussed in the next paragraph, will show that the main ion is H+. There must be an extra process which decreases the amount of hydrogen ions in the plasma. A candidate could be the following reaction mechanism proposed by [MEU96]:

H+ + H r,v ~ H + + H 2 2 ' (4.4.1)

H2 + + e- ~ H + H * The ro-vibrationally excited H2 might emanate from the are channel outer ring, where the hydrogen is presumably not fully dissociated. It could alsoenter the plasma beam due to recirculation processes [MEU96].

34

1x1Q1B

-----·~· -----· -----·-· ~0-----.......

("") I

E ......

~' .---· (!)_...........--

·-·----- +~ 0

+~-are outlet, 1: total flow= 65 scc/s

0 -0- are outlet, llb: hydragen flow = 10 scc/s

/

-•- substrate, 1: total flow= 65 scc/s

+ substrate, lla: hydragen flow = 1 0 scc/s,

+ constant vessel pressure (0.14 mbar

0 -0- substrate, llb: hydragen flow = 10 scc/s

c 0 1x1 Q17 :.;:; ro L.. -c (I) (.) c 0 (.)

c 0 1x1 Q16

0 2 3 4 5 6

argon flow I hydrogen flow [-]

Figure 4.4.1 Ion concentration as ajunetion of argon/hydragenflow ratio.

Although the difference is within the experimental error, the ion concentration in situation Ila (vessel pressure fixed) is somewhat higher than that in situation lib. Increasing the vessel pressure causes the plasma beam to narrow. The plasma volume decreases and therefore the ion density increases when going to a higher vessel pressure at the same argon/hydrogen flow ratio.

The results obtained ju st bebind the are exit and in front of the substrate match if both are normalized to one. The ion concentrations measured at the substrate are approximately one order lower than those measured justafter the are exit. The ion concentration is thought to decrease due to the beam expansion and due tothefact that the measurement position is near to the wa11 (the substrate) where ions and electrans recombine.

4.4.2 Mass speetrometry measurements

A mass spectrometer is able to separate ionized species relative totheir rnass-over-charge ratio. The ionic species can either be ionized in the mass spectrometer itself or for example be directly attracted from a plasma. In these measurements, the ionizer of the mass spectrometer is switched off, and only i ons emanating from the plasma are measured. The result of a mass spectrometer experiment is a number of counts for each different mass, so there is no direct information about the density of the i ons.

The number of counts as a function of argon/hydrogen flow ratio in situations I and Ila are shown in Figure 4.4.2 and Figure 4.4.3. The dominant ion in the plasma is H+, which corresponds to the effective mass found using the Langmuir probe measurements. The Ar+ ion has not been detected.

The signals are almost constant as a function of argon/hydrogen flow ratio, except for the ArH+ signal, which decreases with decreasing argon/hydrogen flow ratio. Furthermore, in situation Ila the number ofH+ ions detected decreases ifthe argon flow is decreased. This means that H3+ becomes important besides H+ at low argon flow.

35

107 -•-H+

-+-H + --· • 2 • 106 ·-· -e-H+ 3

-&-ArH+ 7ii'

--------· - 105 ·--------() ........ ·-· ....... ..c: • C> ·__.r • "(i) •

..c: 104 • ~ m Q) ,._____. c..

103

102 ~--~--~--~--~----~--~--~--~--~--~--~ 1 2 3 4 5 6


Figure 4.4.2 Situation 1: Number of counts persecondas ajunetion of argon/hydragenflow ratio. Mass spectrometer measures exactly at the position ofthe substrate.

108

-•-H+

107 -+-H + 2

-e-H+ ·-· 7ii' 3 .--- 106 -&-ArH+ .-----(/) .......

-~· . • c • ::J 1 os 0 • u ........

....... ..c: 104 C>

"(i) ~ ..c: ~

103 . ·~· m • --· Q)

.~ c.. 102

1 Q1 0 1 2 3 4 5 6

argon flow I hydragen flow [-]

Figure 4.4.3 Situation !la: Number of counts persecondas ajunetion of argon/hydragen flow ratio. Hydragen flow fixed at I 0 sccs. V esse/ pressure constant at 0.15 mbar.

36

4.5 Silane dissociation

About six cm behind the are exit, silane is added to the plasma. The silane is dissociated by the reactive particles emanating from the are and the reaction products deposit either on the substrate or on the vessel walls. The silane consumption ( depletion) of the plasma is important to the growth rate, which will be discussed in paragraph 4.6. In this paragraph the depletion of silane is discussed. The main dissociation mechanism is dissociation by atomie hydrogen, which makes the atomie hydragen flow emanating from the are an important factor. After a short introduction, we will study the atomie hydragen flow teaving the are. The silane depletion is determined using an residual gas analyzer (RGA). As the silane depletion is correlated with the H-flow an attempt is made to estimate the dissociation degree in the outer ring of the are channel.

4.5.1 Introduetion

The silane is dissociated by either ions or hydragen atoms. The electrans are nat efficient in dissociating silane, because the electron temperature is toa low. If no or little hydragen is added, the silane is mainly dissociated by argon ions:

Ar+ +SiH4 ~ SiHx + +qH + pH2 +Ar

SiHx + +e- ~ SiHY +rH +sH2

(4.5.1)

Wh ere x:S;3 and the number of hydragen atoms is conserved. The secoud reaction is very fast due to the high electron density and a high reaction rate. The dissociation mechanism of silane by hydragen ions is similar:

H+ +SiH4 ~ SiHx+ +qH + pH2

SiHx + +e- ~ SiHY +rH +sH2

( 4.5.2)

It is shown that the dissociation of silane by atomie hydragen is the most important dissociation process ifthe argon/hydragen flow ratio is smaller than 5.5 [BAS96].

( 4.5.3)

This means that silane dissociation by ions is minor to the dissociation by atomie hydragen in the experiments described in the report.

4.5.2 Atomie hydragenflow

The atomie hydragen flow emanating from the are is estimated using the effective are diameter which is stuclied in paragraph 4.3.

As already discussed in paragraph 4.1, the heavy partiele temperature is high in the plasma channel. Therefore the dissociation degree in this region equal to 100%. Outside the plasma channel, however, the heavy partiele temperature is nat well known. The dissociation degree outside the plasma channel is therefore nat known exactly. If 100 % H2 dissociation in the plasma channel and F% H2 dissociation outside the plasma channel is assumed, we can estimate the atomie hydragen flow teaving the are by using:

de./+ F ·(d2

-dei/) rpH =2·rpH

2• d2 ( 4.5.4)

where <j> is the flow, deJJthe effective radius and d the are radius.

37

50 dissociation in

•, outer ring:

fi 40 -•-0%

•, -y--25% 0 ~ .. 50%

3: 30 .. ·- -•--75% 0

0::: c: .. Q) '•--0> ... e 20

" ·- .. >- ...., ___ .. .r::; -· .2 _", ____ ..

E 10 ----. ·--· .9 -~·-----. .,

0 0 2 3 4 5 6

argon flow I hydragen flow[-)

Figure 4.5.4 Atomie hydragenflow as ajunetion of argon/hydrogen flow ratio for s ituation l Different plots for different assumed dissociation outside plasma ehannel. Within plasma ehannel I 00% dissociation is assumed Are eurrent equal to 45 A.

16 o-~--o--------0--------o---- ---0--------0

14

"[ 12 "' "' ~ ·"' ~ 10 "' "' "'

q::: -V c: 8 _v-Q) ___ .-v-0> e 6 -- v- dissociation in

" v-V

>- outerring .r::;

.2 4 ~0 -o-0% E -v--25%

~ 2 0-------------- "' 50%

0/ --o--75% 0

0 2 3 4 5 6

argon flow I hydragen flow[-)

Figure 4.5.5 Atomie hydragenflow as ajunetion of argon/hydrogen flow ratio for situation Il Different plots for different assumed dissoeiation outside plasma ehannel. Within plasma ehannel I 00% dissoeiation is assumed Are eurrent equal to 45 A.

The atomie hydragen flow as a function of argon/hydragen flow ratio is shown in Figure 4.5 .4 for situation I and in Figure 4.5.5 for situation 11 with different dissociation fractions taken into account in the outer region. In situation I the hydragen flow increases with decreasing argon/hydragen flow ratio, so there is a competition between the decrease of the effective are diameter and the flow increase. At certain dissociation rates the atomie hydragen flow thus increases with decreasing argon/hydragen flow ratio. In situation 11, where the hydragen flow is fixed, the atomie hydragen flow increases with argon/hydragen flow ratio due to an increase of effective diameter of the plasma channel.

It is a simplification to assume that the dissociation degree outside the plasma channel is constant for each different argon/hydragen flow ratio. In situation 11, the pressure in the are decreases significantly with decreasing argon/hydragen flow ratio (Figure 4.3.3). Ifthe pressure drops below approximately 250 mbar the plasma is no longer in L TE [BOU94]. Therefore, in situation 11 a constant Fis most probable nota valid assumption. In situation I the pressure decreases only a little with decreasing argon/hydragen flow ratio. Therefore, the approximation of a constant dissociation in the outer ring is easier satisfied in this situation.

4.5.3 Silane depletion

In this paragraph the depletion is stuclied in relation to the atomie hydragen flow teaving the are and the partial pressure of silane in the vessel.

The silane depletion, which is the consumption of silane by the plasma, is measured using an residual gas analyzer. This method is described in Frame C.

38

Frame C

DEPLETION Generally, the depletion is defined as:

D l t. Pp,off- Pp,on lOO% epezon = · o

Pp,off (Fl)

where Pp, offand Pp, on denote the partial pressure of the gas considered when the plasma is off and on respectively. If a mass spectrometer is used todetermine depletion, one has to convert ion currents (the signa! ofthe RGA) into partial pressures. The measured current is related to the partial pressure and the conductance of the extraction system. Assuming a constant conductance for plasma on and off, the depletion can he calculated as:

Joff- Jon Depletion = ·100%,

1o.ff

(F2)

where 10.ffand Ion are the measured ion currents when the plasma is off and on respectively. lt is notstraightforward that the conductivity remains at a constant value while putting the plasma on and off. It is shown, however, that in our case it is a good approximation [AAR98], [KES97].

As depletion is defined relatively, it is not dependent on the partial pressure. This is easily shown using the definition of silane depletion:

( 4.5.5) d l . PsiH4 ,o[f- PsiH4 on

ep etzon = · " " P SiH4 ,con.sumed

PsiH4 ,olf PsiH4 ,olf

where PSiH4 is the partial pressure of silane, the subscripts on and off denote the situations where the plasma is on and off respectively. Th is equation is only valid for small depletion. In the third step it is assumed that dissociation by atomie hydrogen is the only dissociation reaction and H denotes the atomie hydrogen flow. Because the depletion is not dependent on the partial pressure of silane, it is expected to have the same trend as the atomie hydrogen flow as a function of argon/hydrogen flow ratio, which is discussed in the previous paragraph.

39

16 • 14

• 12

~ 0 10 ....... c 0 8

:.;::::; Q)

0.. 6 Q)

"'0 4

2

0 + 0 I

1

•

+ 0 0

2 3

• I. total flow = 65 scc/s

+ lla. hydrogen flow = 1 0 scc/s

vessel pressure fixed

o lib. hydrogen flow = 1 0 sccls

+ • 0

0

+ +

4 5

argon flow I hydrogen flow[-]

6

Figure 4.5.6. Depletion as ajunetion of argon/hydrogenjlow ratio in the three situations. Silanejlow is equal to 5 sccs.

The results ofthe depletion measurements are shown in Figure 4.5.6. In situation I, where the total flow is fixed, the silane depletion increases with decreasing argon/hydragen flow ratio. lfwe now go back to the atomie hydragen flow, which is discussed in paragraph 4.5.2 and increases only with decreasing argon/hydragen flow ratio ifthe assumed dissociation fraction outside the plasma channel is larger than 0 %. The depletion increases approximately two times ifthe argon/hydragen flow ratio decreases from 5.5 to 1. Ifthe dissociation fraction (F) in the outer ring ofthe are channel is constant as a function of argon/hydragen flow ratio, and the dissociation of silane is mainly due to reactions with atomie hydragen, this could give information about the dissociation fraction of hydragen in the outer ring of the are channel. A decrease of two times in atomie hydragen flow occurs for a dissociation fraction in the region outside the plasma channel between 25 and 50 %.

In situation 11 the depletion decreases with decreasing argon/hydragen flow ratio as is expected when looking at the atomie hydragen flow. The vessel pressure has no influence on the depletion results, which is due to the fact that the partial pressure of silane has no influence on the silane depletion. The depletion decreases appraximately a factor 9 ifthe argon/hydragen flow ratio decreases from 5.5 to 1. To teil sarnething about the dissociation fraction in the outer ring ofthe plasma channel, one has to assume a constant dissociation fraction as a function of argon/hydragen flow ratio, which is nat likely due to deviations from L TE. The only possible conclusion is that it must be larger than 0 % at higher argon/hydragen flow ratios, otherwise a decrease of a factor of 9 is nat achieved.

40

4.6 Growth rate

The growth rateis determined using in-situ ellipsometry, which is shortly described in Frame D. The growth rate as a function of argon/hydragen flow ratio is shown in Figure 4.6.1. The growth rate scales with depletion in situations I and lib. In situation Ila, where the vessel pressure is fixed, the growth rate is nat equal to the growth rate in situation Ilb, unlike the depletion measurements.

16

• 1: total flow fixed

14 + lla: hydragen flow fixed,

I I vessel pressure fixed

12 0 llb: hydragen flow fixed

'ëii' I - 10 I E

I c ......... Q) 8 -ro

I I...

.c 6 -3: I ~ 0 4 I...

C)

Q 2

I :0:

0 0 2 3 4 5 6


Figure 4.6.1 Growth rate, measured using in-situ ellipsome try, as a function of argon/hydragen flow ratio.

We can explain the difference between growth rate and depletion measurements if it is realized that the growth rate should in fact scale with the absolute depletion if the radicals are mainly lost due to deposition on the substrate and the vessel walls, which is the case in an expanding thermal plasma3. The absolute depletion is usually calculated as the depletion times the incoming silane flow:

absolute depletion = depletion · siH4

• ( 4.6.1)

If the pump speed is changed during the measurements, however, this equation is oot correct. The absolute depletion should in that case be correlated with initia! partial pressure instead of incoming flow:

absolute depletion* = depletion · PsiH4,off. ( 4.6.2)

The absolute depletion is therefore dependent on silane partial pressure. In situation Ila, where the vessel pressure is fixed, a difference with situation Ilb is expected due the silane partial pressure, which increases with decreasing argon/hydragen flow ratio, because the pump speed decreases with decreasing argon/hydragen flow ratio4.

3 The silane depletion does not scale with depletion ifthe pump speed is relatively high or polymerization occurs.

4 Th is is due to the fact that the vessel pressure in this case is equal to the vessel pressure at standard deposition conditions (55 sccs Ar and 10 sccs H2), at which maximum pump capacity is used.

41

FrameD

ELLIPSOMETRY Ellipsometry is used to investigate the film during deposition. lt gives the refractive index, extinction coefficient and growth rate of the deposited materiaL The basic principles of ellipsometry are described qualitatively in this paragraph [RIE88]. A more quantitative description is given by, for example, [HOV97] and [PAS96].

Consider a reflection from a surface. The plane of incidence is defined by a vector perpendicular to the surface and a vector in the propagation direction ofthe incident beam. Now, the wave is composed out of a wave which lies in the plane of incidence and a wave perpendicular to it. In general, the parallel and perpendicular components hebave different while transmitted or reflected according to Fresnel's equations which can he deduced from the continuity of the electric and magnetic field along the surface [PED93]. Therefore, the polarization ofthe wave is changed. Since this change is a function ofthe optical parameters ofthe system, it can he used todetermine them.

In an ellipsometer setup the change in polarization of a reflecting wave is measured by measuring the state of polarization of the reflected wave, while the polarization of the incident wave is known. The ellipsometer used in silicon deposition setup is called a rotating compensator ellipsometer (RCE). A compensator induces a phase difference between components of the linearly polarized wave going through, dependent on its angle with the polarizer. Ifthe compensator rotates, the wave coming out has a polarization state oscillating between linear and circular. The beam with asciilating polarization reflects on the surface investigated, where it changes its polarization state. The component ofthe reflected wave that is parallel to the polarization axis ofthe analyzer is detected by the detector. By investigating the measured intensity as a function of time, it is possible todetermine the polarization state ofthe reflected wave and thus the change of polarization of the wave while reflecting on the surface.

4.7 Film quality

The quality ofthe deposited film in the three situations is evaluated using in-situ ellipsometry, infrared transmission spectroscopy (FTIR) and electrical conductivity measurements.

In-situ ellipsometry gives information about refractive index (632.8 nm) and growth rate. The principle of ellipsometry is described in Frame D. The refractive index at 632.8 nm as a function of argon/hydragen flow ratio is given in Figure 4. 7 .1. No clear trend is observed and the refractive index at 632.8 nm is in the range of 4.4-4.6.

42

5.0 632.8 nm

• I: total flow fixed

+ lla: hydragen flow fixed,

4.8 vessel pressure fixed

0 llb: hydragen flow fixed "_..,

I 0 .......... x 4.6 • <D +

"C + + c: •o <D • > 4.4 + 0 u m • s.... -<D s.... 4.2

1 2 3 4 5 6


Figure 4.7.1 Re.fractive index at 632.8 nm as ajunetion of argon/hydragenflow ratio. Typical error ±O.I.

The FTIR experiments, giving the refractive index in the infrared, thickness, hydrogen contentand microstructure5 ofthe material, yielded transmission spectra with a lot ofnoise and therefore the results are less valuable. The FTIR results will not be presented in detail. The hydrogen content is measured to be in the range of 4-10 at.%. The growth rate results were comparable to the growth rate obtained with ellipsometry. At low argon/hydrogen flow ratio in situation 11 the microstructure turned out to be zero, in other situations it was in the range of 0.2-0.6.

The setup for photo and dark conductivity measurements is described in Frame E. The ratio of photo and dark conductivity is called photo response. The photo response should be higher than 1 o4 for solar grade materiaL The results, which are preliminary, are shown Figure 4.7.2 as a function of argon/hydrogen flow ratio. The photo response decreases with decreasing argon/hydrogen flow ratio, which means that the material quality is worse compared to the material deposited at standard conditions. This is unsatisfactory, but before drawing final conclusions the results should be reproduced.

5 Microstructure is defined as [SiH2]/([SiH2]+[SiH]). See paragraph 2.2.2.

43

Frame E

ELECTRICAL CONDUCTIVITY The photo- and dark conductivity of the deposited films is measured by measuring the voltage-current characteristic ofthe film. On the sample, two electrical contacts are applied with defined size and distance to each other. From the current through the material between the two contacts at a certain voltage the conductivity ofthe material can be derived. Por dark conductivity measurements, the sample is placed in a dark box. To perform photo-conductivity measurements, the sample is illuminated with a lamp with defined illumination ofthe sample. A more accurate description is given in [VER95].

106

• 1: total flow fixed

0 llb: hydrogen flow fixed •

,......, 105 I -.. 0

<1> (/) 0 c 0 0 c.. (/) Q) .... • 0 104 0

+-' 0 • ..c c.. •

1 2 3 4 5 6

argon flow I hydrogen flow[-]

Figure 4. 7.2 Photo response as a function of argon/hydragen flow ratio. The fine is a guide to the eye.

4.8 Conclusions

The behaviour ofthe plasma in the cascaded are channel has tumed out to he an important factor in varying the flow conditions. It is shown that the active plasma in the are channel does not occupy the whole are channel. This divides the plasma in two regions, which are called the active and passive region. The width ofthe active region is called the effective are diameter.

The effective are diameter decreases with decreasing argon/hydrogen flow ratio, and therefore the number of i ons emanating from the are decreases also with decreasing argon/hydrogen flow ratio. A second effect in the decrease of the number of i ons is the partic i pation of hydrogen molecules in a reaction mechanism that decreases the ion density. These hydrogen molecules might emanate from the outer region of the are channel, where the heavy partiele temperature is not high enough to dissociate all hydrogen molecules.

44

The silane dissociation in the expanding plasma is shown to be mainly due to reactions with atomie hydrogen. The silane depletion has shown the same behaviour as the atomie hydrogen flow teaving the are as a function of argonlhydrogen flow ratio. The dissociation degree within the effective are diameter is assumed to be 100 %. For constant total flow the dissociation degree outside this region could be estimated by correlating the silane depletion and the atomie hydrogen flow, assuming a constant dissociation degree as a function of argon/hydrogen flow ratio. The dissociation degree in the outer region ofthe plasma channel determined in this situation turned out to be between 25 and 50%.

Depositions revealed that the growth rate scales with absolute depletion. The absolute depletion is defined as the depletion times the partial pressure of silane. The growth rate, therefore, is dependent on vessel pressure and increases with increasing vessel pressure. If the total flow is decreased with argonlhydrogen flow ratio, the growth rate decreases. lt does not seem to be possible to maintain the high growth rates obtained at standard conditions when reducing the total flow.

The material quality of the deposited films did not show a serious deterioration with decreasing argon/hydrogen flow ratio, but the results are preliminary and should be reproduced before drawing final conclusions.

45

Part 111

A LARGE AREA RF REACTOR

Chapter Five Model of an rf silane discharge including growth processes Another way to deposit hydrogenated silicon films is by using a rf discharge. An example of a setup based upon such a discharge is the commercially available Balzers KAl reactor. This reactor is subject of research at the Centrede Recherche en Physique des Plasmas (CRPP, part ofthe 'Ecole Polytechnique Fédérale de Lausanne'). Work has been done to improve the understanding of hydrogenated amorphous and microcrystalline silicon growth. Therefore, a model is developed to describe plasma chemistry and surface processes like growth and etching. It is attempted to determine the conditions where the transition from microcrystalline to amorphous silicon deposition occurs. To start with, however, the model is checked with measurements of depletion and growth rate in amorphous conditions, which is the ma in part of the work presented in this report.

5.1 Experimental Setup

An important feature ofthe Balzers KAl reactor is the large deposition area. The deposition reactor is shown schematically in Figure 5.1.1. The reactor is basedon the plasma box concept, where the plasma is confined in aso-called plasma box, which is placed in a larger vacuum chamber. The reactor floor and the reactor walls are grounded. An rfrectangular electrode (569 mm * 469 mm) is placed such that the di stance between the two electrades is equal to 2.5 cm. The rf power is coupled into the rf electrode via a matching network. The substrate can be put on the reactor floor.

rf electrode wilh vacuum gas showerhead / chambcr ..---4----"":"":=~--....;...-----:-ï ma lching

47 ·m nelwork

~~~~~

rf genera tor I

subslrate grounde 45 cm x 35 cm x 1 mm walls

Figure 5 .1.1 Schematic view of the plasma box reactor for large area silicon deposition [SAN95]

The process gases are introduced through a showerhead, which is built into the rf electrode. The whole reactor is heated uniformly. The pressure is controlled by a butterfly valve between the roots pump and the plasma box. In genera!, the pressure is in the order of 0.2 Torr (27 Pa). Gas flows used are in the range of 150 seem= 2.5 sccs. The input power can be varied between 0 and 500 Wand the frequency between 13.56 and 70 MHz. The electrooie density is dependent on frequency and input power and typically ofthe order 1015 m-3.

49

To investigate the processes in the plasmaand on the substrate, several diagnostic techniques are used, which will not he discussed extensively. In-situ FTIR in the gas phase is used todetermine the depletion of silane [SAN98a]. A microwave resonant cavity technique is used to measure the electrooie density. The growth rateis determined using an in-situ laser interferometer.

5.2 Description of the model

The development of the model is clone in two steps. First, the equations which form the backbone of the model have to he deduced and solved for situations for which measurements are clone too. The calculations ofthe model are compared with the measurement's results to see whether the calculations and equations of the model are acceptable. Second, the model can he used to calculate things which are not yet measured, such as the switch between microcrystalline and amorphous deposition. The results ofthe calculations ofthe model are shown in chapter 6.

5.2.1 Included processes and assumptions

The in the model the assumed picture is depicted in Figure 5.2.1. The gases come into the reactor at a certain flow rate. A fraction ofthe molecules is dissociated into radicals. Particles are pumped away with the same pumping speed for each particlel. The radicals reach the walls ofthe reactor by diffusion (no gas flow towards walls), where surface processes can take place.

gas flows pumpmg

surface processes

Figure 5.2.1 Sketch ojthe in the model assumedpicture

The model consists of five gas phase equations, which are continuity equations for five particles in the plasma (SiH4, SiH3, SiH2, H2 and H). Apart from reactor temperature, pressure and incoming flows, electron density is used as an input. For the electron density experimental results are used where possible. Below we will address the model assumptions and the specific processes included in the model.

Assumptions and starting points • The model is defined for a steady state situation. • Only six different particles are considered, which are SiH4, SiH3, SiH2, H2, Hand electrons.

The electron density is an input. The densities of other particles are calculated using the five gas phase equations, which include also loss and gain processes at the surface.

• The surface features, such as growth rate are calculated afterwards, using the calculated densities. The probabilities of the surface processes are treated as constants, which might introduce an error in the results. This is discussed in paragraph 5.2.4.

• The pump speed is the same for each particle. Because the velocity of the particles is not the same for the whole reactor, particles nearer to the (roots) pumps have higher speed. It is an important question whether the continuity equations are valid at each point in the reactor. lt is shown that this is the case [SAN98b] if the equations are considered to he equations for a small

1 This is only correct ifthe flow is a viscous flow.

50

volume fraction dV. The pump loss term in this view has to he handled carefully, consiclering hoth incoming and outgoing flows, which will he discussed in paragraph 5.2.4.

• Ion formation is not taken into account, which might he dangerous in view of the macroscopie growth models which ascribe an important role to the hydrogen ions. The modeled plasma has a low electron density compared to the densities of other particles. Furthermore, taking into account ions would severely complicate the model's equations.

• In formulating the surface processes a hydrogen covered growing surface is assumed. This is proven to he the case, as is discussed in chapter 2.

• The film is thought to he already started growing, which implicates that no initial growth processes are considered.

• The Si2H6 particles created do not appear in any continuity equation, which means that the Si2H6 disappears hy pumping and do not participate in processes in the gas phase.

Below a summary is given ofthe included processes. Procèsses that are not mentioned, are not included in the model. The reaction rates ofthe reactions are given hy Kushner [KUS88]. In the model a correction factor is introduced to correct for differences in electron temperature. All reaction rates of reactions with electrons are multiplied hy this factor ( see chapter 6). The prohahilities of the surface processes are discussed in chapter 2 more extensively.

Gas phase reactions rate [mJs-1] symhol [KUS88] ofrate

Dissociation of silane SiH4 + e ~ SiH3 + H + e 1.59·10-1 () kdissill SiH4 + e ~ SiH2 + H + H + e 1.87·10-1 I kdissi/2 SiH4 + H ~ SiH3 + H2 2.68·10-ll:S kdissah Dissociation of hydragen H2+e~H+H+e 4.49·10-ll:S kdissh Reaelions between radicals SiH4 + SiH2 ~ Si2H6*L 1·10-ll:S ksih2 SiH3 + H ~ SiH2 + H2 1·10-HJ ksih3

Surface Processes The probahilities given is the prohahility for the first mentioned partiele to participate in the process. All probahilities are valid for amorphous silicon deposition. For more information is referred to chapter 2.

I prohahility I symhol P hys isorpfion SiH3 (gas)~ SiH3 (phys) 1 o.3 I 131 SiH2 (gas)~ SiH2 (phys)J 1 o.8 1132 Sticking SiH3 (gas)~ SiH3 (surf) 1 o.1 I SJ SiH2 (gas)~ SiH2 (surf) 1 o.8 I S2 Recombination SiH3 (phys) + H (surf)~ SiH4 (gas) 1 o.12 Ir SiH3 (phys) + SiH3 (phys) ~ Si2H6 (gas) 1 o.o8 IY2

2 The mark * means that the Si2H6 molecule is excited. The molecule will be de-excited by heavy partiele collisions leading to Si2H6. In the model the Si2H6 does not reappear.

3 SiH2 actually does not physisorb, but sticks directly. Therefore P=s for this radical.

51

H (gas)+ H (surf)---+ H2 (gas) 1 o.35 lö Etching H (gas)+ SiH3 (surf)---+ Sif4 (gas) 1 o.o2 IE Passivation of a dangling bond H(gas) +Si- (surf)---+ Si-H (surf) 1 o.3 l'l' Cross linking4 SiH3 (sticking) + H (surf)---+ H2 (gas)+ SiH2 (surf) 1 o.88 Ie! H reflection H(gas) ---+ surface ---+ H(gas) 1 o.33 Ir

5.2.2 Model equations

In this paragraph, we will discuss the model's equations. All terms ofthe equations are given in units ofm-3s-1. There are five balance equations, which include surface processes where species are gainedor lost. The growth features ofthe surface are given by a set of surface equations, which are derived using the densities following from the five gas phase equations. The surface equations will be discussed in paragraph 5.2.3. Below, the equations will be deduced. Each equation can have six parts, which are: 1. a flow souree term, 2. a pump loss term, 3. plasma souree term(s), 4. plasma loss term(s), 5. surface souree term( s ), 6. surface loss term(s). Below, the model's equations will be given. The right hand side of each equation is zero, because the model describes a steady state situation.

Silane equation (1) The silane equation is written as follows (the numbers between brackets indicate the part number of the term, which are discussed above ):

(1) (2) (4)

tP SiH• V- n!>'iH • . s- kdissill . nsiH • . ne- kdi.lsi/2. nSiH4 . ne- kdissah. nsiH • . nH + ( 5.2.1)

-k,., ·ns··H ·ns .. H +ns·H ·r·A+nH·&·B=O ,J/12 • I -t I 2 I 3

(5)

Where the first term is the incoming flow ~SiH4, which should be expressed in particles/second, divided by the reactor volume V. The second term shows the loss of silane due to pumping, where S is the pumping speed per volume unit [s-1] which can be regarcled astheinverse residence time of a partiele ifthe pumping was uniform throughout the reactor. This pumping factor will be discussed in paragraph 5.2.4. The third, fourth and fifth terms depiet the lossof silane due to dissociation by electrans into SiH3, by electrans into SiH2 and by atomie hydrogen respectively. For partiele densities the symbol nis used, kdissilJ, kdissi/2 and kdissah are the reaction rates for the three dissociation reactions. The sixth term shows the loss of silane due to the reaction with SiH2, where ksih2 is the reaction rate for this reaction. The two surface processes which produce silane molecules are the last two terms in the equation. The seventh term is due to the SiH3 recombination at the

4 The probability given is the probability for a sticking radical to cross link.

52

surface, where A is an abbreviation ofthe diffusion term for silane species in the gas phase (see paragraph 2.1 ):

Às··H . Vh s·H A - I .J I, I 4

- 2 L

( 5.2.2)

and y is the probability of recombination of SiH3 with H. The last term is due to the etching of SiH3 from the surface by a hydrogen atom. In this term a diffusion term of atomie hydrogen is needed, which is given by B:

( 5.2.3)

and E is the etching probability.

SiH3 equation (2) The SiH3 equation is given by:

kd. · ··11 • ns·H · n + kd. · · h · ns.H · nH - ks··H · ns·H · nH - ns .. H · S - ns .. H · fJ1 · A = 0 · I.'J.\1 I .t e /.\.\U I 4 I J I J I J I J ( 5.2.4)

(3) (4) (2) (6)

The third term shows the loss of SiH3 radicals due to reactions with H giving H2 and SiH2. The rate for this reaction is given by ksiH3· The last term takes the Ioss of SiH3 radicals due to physisorption at the surface into account, where 131 is the probability of physisorption for SiH3 radicals. Once the radicals are physisorbed on the surface they are lost, because they either stick or reflect as either SiH4 or Si2H6.

SiH2 equation (3) The SiH2 equation is similar to the SiH3 equation. There is an extra loss due to reactions with SiH4 and the last term in the SiH3 equation appears as a souree term for SiH2. lt is given by:

(3) (4) (2)

Hydrogen equation (4) The hydrogen equation can be written as follows:

(1) (2) (3) (4)

fjJ ; 1 - nH

1 • S + kdi.nah. nSiH

4 • nH + kSiH

3 • nH. nSiH

3 - kdissh. ne. nH

1 +

+n ·5·B+n ·s·cl·A =0 H SiH3

(5)

( 5.2.5)

(6)

( 5.2.6)

where H2 is the incoming hydrogen flow. The second term depiets the loss ofhydrogen due to dissociation by electrons, kH2 is the reaction rate for this reaction. The third term is the loss due to

53

pumping, where the pumping speed is taken equal to the pump speed for silane species. If silane is dissociated by atomie hydrogen, molecular hydragen is created. The fourth term accounts for this process. The last three terms give the surface processes gaining H2. The fifth term is the term for H recombining at the surface with Hand giving H2. The last term, finally, shows the crosslinking process, where cl is the probability fora sticking radical to cross link and thus producing H2.

Atomie hydrogen equation (5) Atomie hydrogen is gained and lost in a lot of gas phase and surface processes. Tostart with, there are the gain processes in the gas phase due to dissociation of silane and hydrogen. Losses in the gas phase are due to pumping, due to dissociation of silane by atomie hydragen and to the reaction ofH with SiH3. At the surface atomie hydragen is lost by recombining with H giving H2 and passivation of a dangling bond by H. Including those processes, the atomie hydragen equation is:

(3) (4)

kdis.,i/1 ·nsiH, ·ne +2·kdissil2 ·nsiH, ·ne +2·kdissh ·ne ·nH, -kdis . .ah ·nsiH, ·nH +

- k . · n · n . - n ·S-n · & · B- n · 8 · B- n "'" · B = 0 8tH3 H StH3 H H H H 't'

(2) (6)

5.2.3 Surface equations

( 5.2.7)

The number of radicals sticking on the growing surface per secoud is given by the number of radicals reaching the surface by diffusion multiplied by the product of the probability of sticking and the reactor volume:

N =n ·s·A·V. rad rad ( 5.2.8)

Wh ere s is the probability of sticking and nrad the density of the radicals considered. To calculate the growth rate, the number of SiH3 radicals sticking as well as the number of SiH2 radicals sticking is needed, with sticking probabilities s 1 and s 2 respectively. The mass density of amorphous silicon, which is equal to 2.2·103 kg/m3 and camparabie to the mass density of microcrystalline silicon, is used to determine the total volume of the particles sticking to the surfaceS. It is known that the hydragen density in amorphous and microcrystalline silicon is low, and therefore, the mass of silicon atoms is used. The radicals are supposed to deposit uniformly on the reaetar's surface. The formula for the growth rate then becomes (unit Als):

( 5.2.9)

Wh ere Netched is the number of radicals etched, given by:

N etched = n H • & . B . V . ( 5.2.10)

The etch ra te is derived in a similar way. U sing the number of radicals etched, the etch rate is equal to:

5 lt is also possible to use the total number of particles in amorphous silicon (5· 1 o28 m-3) in the growth rate calculation.

54

N ·M V = rtchcd Si ·1 QIO

e 2.2·10 3 ·A sub

(5.2.11)

The hydrogen content can be calculated by actding all hydrogen atoms sticking to the surface, which are the hydrogen atoms in SiH3 and SiH2 radicals and the hydrogen atoms which passivate dangling honds on the surface. This number has to be corrected for the hydrogen that leave the surface in the processes cross linking, etching, modifying, and recombination with H giving H2. The hydrogen content can be calculated by dividing this total number of hydrogen atoms by the total number of particles in the film which is equal to the sum of the number of hydrogen atoms plus the number of silicon atoms:

N H = _____ ....._ ___ _ COlli N + (N + N - N )

H SiH3 SiH2 etched

( 5.2.12)

The number of hydrogen atoms NH is given by the total number of hydrogen atoms coming in minus the number of hydrogen atoms teaving from the surface:

N = {3 · n . · s · A + 2 · n . · s · A + n · "' · B - 3 · n · & · B + H StH3 2 StH2 2 H 't' H

-n · 8 · B- 2 ·cl· n . · s · A - 2 ·cl· n . · s · A} ·V H StH3 I StH2 2

( 5.2.13)

To be able to teil sarnething about the transition from amorphous towards microcrystalline hydrogenated silicon, it is thought that the ratio between the incoming radicals and the incoming hydrogen atoms is important. Therefore in the model the so called 'rrs ratio' (radicals reaching surface ratio) is calculated. It is a quite arbitrary choice to take this specific ratio, because it is not known which mechanism really induces microcrystalline growth (see chapter 2). The rrs ratio is chosen because SiH3 is the main contributor to growth (see paragraph 6.2.2) and H is thought to be the main initiator in processes that enhance microcrystalline deposition, such as etching and chemica! annealing (see paragraph 2.2.5). In the rrs ratio no assumption is put in about the importance ofthe different processes, which makes it a better choice than for example the ratio between growth and etch rate. The rrs ratio is defined as:

n:,ïH, ·A rrs =

5.2.4 Pumping losses

The pump loss terms in the equations look like:

loss pump = n · S.

( 5.2.14)

(5.2.15)

The unit of each term in the equations should be m-3s-1, and therefore the 'pump speed' S should be expressed in units s-1. A problem appears, because the residence time is not the same for each particle, but dependent on where the partiele is located in the reactor. A residence time for all

55

particles in the reactor seems not to be easily defined. If a volume fraction dV is considered, there is not only a flow of particles towards the pump, but also an incoming flow of particles out ofthe neighbouring volume fraction. The residence time in such a volume fraction is corrected for the fact that some ofthe outgoing particles are replaced by incoming particles. This appears to be the residence time as ifthe volume fraction was uniformly pumped.lt is proven that the equations valid for a volume fraction dV are valid for the whole reactor [SAN98b ], and therefore Sin the equations is equal to the net residence time of a partiele in this volume fraction, which is equal to the derivative of the speed of the partiele to space coordinate x:

S= dv = <!>tot

dx ntot ·V

5.2.5 Probabilities

( 5.2.16)

Whereas the probabilities in the model are considered to be free to choose, this is not exactly the case. lt is possible to formulate three continuity equations for the surface. These are equations for the amount of dangling honds, silicon atoms sticking and hydrogen atoms in the film. Besides the equations above, these three equations have to be fulfilled also. The equations are not yet ioclucled in the model. In this paragraph an onset is given to include them in the future.

The continuity equations use either given or calculated fluxes of hydrogen and silane radicals to the surface and the probabilities of the different processes on the surface. The fluxes can be calculated using:

n~ïHx ·A· V r SiH = ----'----

x Atol

and

( 5.2.17)

(5.2.18)

where V is the reactor volume, A and B are the diffusion coefficients defined in paragraph 5 .2.2 and A tot is the total reactor surface. The dangling bond equations is the sum of processes which create dangling honds minus the processes which passivate dangling honds:

(5.2.19)

where the first term depiets the abstraction ofH by H giving H2 and a dangling bond, the second term is the etching of SiHJ, the third term is the recombination of SiH3 with an H from the surface. The last two terrus are processes in which dangling honds are passivated: passivation by H and sticking of SiH3. Sticking of SiH2 is thought to be take place without passivating a dangling bond [KAE95]. The right hand term is zero, the dangling bond density doesnotchange in time and is considered to be near zero. The next equation is the balance equation for the Si atoms coming to the surface, resulting in a growth rate Vg.

56

r SiH3

• pI + r SiH2 • p 2 - r SiH3 • Y - 2 . r SiH3 • Y 2 - r H • 8 = V g • p ( 5.2.20)

where f31 and f32 are the physisorption probabilities of SiH3 and SiH2 respectively. The last three left hand terms show recombination of SiH3 giving SiH4 and Si2H6 at the surface and etching of SiH3 by H. The right hand term is the flux of sticking silicon atoms, p is the partiele density of the grown material, for amorphous silicon equal to 5.2·1028 m-3. Ifthe right hand term is multiplied by a constant c, which is defined as the number of hydrogen atoms per silicon atom in the material and connected with the hydrogen content c J[.

( 5.2.21)

one gets the number of hydrogen atoms in the grown film, which can be used as right hand term in the hydrogen surface equation:

r . 111 + (3- 2. cl). s . r . + (2- 2. cl). s . r . - r . ö- 3. r . 8 + H 't' I StH3 2 StH2 H H

-r .. ·y=c·v ·p 5tH3 g

( 5.2.22)

Here is the first left hand term the passivation of a dangling bond by H, the second and third terms are the H atoms coming to the surface due to sticking of silane radicals, and the last left hand terms are the terms due to recombination ofH with H, etching and recombination of SiH3 with an H from the surface.

Together with the three probability equations: r + t5 + B + Ij/= 1 , P 1 = y + y 2 + s and P2 = s2 there are six equations and nine unknowns, provided that the hydrogen content and growth rate and the fluxes are known. To be able to solve the system one should choose three probabilities to be fixed. This should be done carefully, so that the equations do not lead to a contradiction in themselves.

Calculating the fluxes using the five gas phase continuity equations and putting them together with the probabilities used to calculate the fluxes into the three equations should give true relations. This is not yet the case, and therefore it is recommended to expand the model with the three surface equations, leaving the probabilities as variables with a value between 0 and I.

57

Chapter Six Modeling Results The model calculations are done with MatLAB (The MathWorks Inc, version 4.0). The structure of the MatLAB program written is discussed in the appendix. As input variables the model uses electron density, taken from experimental results as far as possible, pressure, reactor temperature and a correction factor for the reaction rates given by Kushner [KUS88], which accounts fora different electron temperature ofthe plasma (taken equal for all calculations).

Totest the model some calculations are performed for situations for which experimental data are available. This is the main part of the work presented in this report. In paragraph 6.1 these results will he shown. After that the densities of the different particles in the reactor as a function of electron density will he discussed. Furthermore, the contribution of SiH2 and SiH3 radicals to growth is shown. In paragraph 6.3 the transition from microcrystalline to amorphous silicon deposition is studied. We willend with some conclusions.

6.1 Validity model

The experimental data from the Balzers reactor are obtained using the microwave cavity technique (electron density), Fourier transformed infrared spectroscopy (depletion) and in situ interferometry (growth rate). These measurement techniques are discussed elsewhere [SAN98b]. In the next paragraphs the modeling results of depletion and growth rate as a function of electron density, silane dilution, pre ss ure and silane flow during the deposition of hydrogenated amorphous silicon are shown. The electron temperature in the Balzers reactor is not known, but estimated to he around 4 eV. The calculated results are compared with measured data, and will show a good correspondence.

6.1.1 Electron density

An increase in power as wellas an increase in frequency results in an increase in electron density. It is assumed that the other parameters remain approximately constant changing power or frequency. The results of the calculations of depletion and growth rate are shown in Figure 6.1.1 and Figure 6.1.2. The depletion calculation shows a good coincidence with the measured data if the rate constants given by Kushoer are corrected with a factor 8.51. In the following calculations the rate is corrected with this factor too. The magnitude and trend ofthe calculated growth rate is quite good, although the slope ofthe calculated line is less steep. Notice that in contrast with the expanding thermal plasma setup, which is discussed in chapter 4, the depletion does not scale with growth rate in this reactor. This is thought to he due to polymerization processes.

An interesting result is that the data for frequency variation as well as for power variation fit the calculated curve. This illustrates that power and frequency variation are correlated strongly with changes in the electron density.

l This is acceptable because of the higher electron temperature and the strong dependenee of the rate constant on electron temperature.

59

1.0

--model

0.8 • measurement: frequency

• measurement: power • ........ I ...._.

0.6 c • 0 • :.;::::; Q) • 0.. 0.4 •• Q) "U • Q) c

0.2 • rn Cf) •

0.0 ~

1013 1014 1015 1016

electron density [m-3]

Figure 6.1.1 Silane depletion as a function of electron density as calculated by the model. The points are experimental results from frequency and power variation respectively. The error 10% and 20% on the power and frequency data respectively. (T=200 oe, p=0.2 Torr, ~SiH4 = 100 seem, ~H2=0)

8

--model 7 measurement: frequency • • 6 •

7ii' • ~

5

Q) 4 • +-' rn '-..c • +-' 3 ~ • 0 '- 2 • Cl

•

0 1013 1014 1 Q15 1016


Figure 6.1.2 Growth rate as a function of electron density as calculated by the model in comparison with the experimental results. Experimental data are jrom jrequency variation.

Typical error equal to 20%. (T=200 °C, p=0.2 Torr, tPSiH4 = 100 seem, tPH2=0)

60

The difference in slope between the calculated and measured plot of the growth rate can only he due toa process which acts on the derivative ofthe model equations to the electron density. This leaves only the dissociation by electrans reaction terms. A change in the rate of these reactions by changing the correction factor for the reaction rate given by Kushner will also change the calculated depletion curve, which is already in good correspondence with the measured data. The only possibility left is that the calculated hydragen or silane density is somewhat too low, leading to a smaller slope of the calculated curve. In the density plots, which will be shown in paragraph 6.2.1, this is not an important error, because difference of orders of magnitude between different densities.

6.1.2 Silane dilution

The silane dilution, which is defined as the silane/hydrogen flow ratio, is varied by keeping the total flow fixed at 500 seem. The result of the calculation of silane depletion is given in Figure 6.1.3. The growth rate results are not shown, because no experimental data were available. The calculated growth rate increases with silane flow from 1 Als at 50 seem to 6 Als at 500 seem.

The calculated depletion is not as good in accordance with the measured data as in the electron density calculation. This could be due to an electron temperature which is not constant, which leads to a change in the dissociation reaction rates. The dissociation rate is highly dependent on electron temperature, soa small change in electron temperature can change the reaction rate significantly (see chapter 2). To conclude, the results ofthe model have to be treated carefully in cases where the electron temperature is expected to change.

1.0

0.9 ~

0.8

,........, 0.7 I ........ c 0.6 0

:;=; Q) 0.5 a. Q)

0.4 'U Q) c ro 0.3

Cl) 0.2

0.1

0.0 0

•

0 ---o---o" • • • "e -o

100 200

• • --0 -----0

300

-o-model

• measurement

• • •

------0--0---0

400 500

silane flow [seem]

-

Figure 6.1.3 Silane depletion as a function of silane flowfora constant tata! flow in a mixture of silane and hydrogen. (T=200 oe, p=0.4 Torr, electron density measured and used as an input.) Error on data is approximately 10%.

6.1.3 Press ure

In the model the pressure can be changed independently. The electron density is measured and used as an input. The results ofthe calculation ofthe silane depletion is given in Figure 6.1.4. Again, the growth rate results are not shown because no experimental data were available. The calculated

61

growth rate increases with pressure and ranges from 0 to 5 Als with a pressure going from 0 to 1 Torr.

The experimental results are somewhat higher than the calculated data, which could be due to a difference in electron temperature and therefore a difference in dissociation reaction rate.

0.8

0.7

0.6 ,........, ...!... c 0.5 0 ~ Q) 0.4 a. Q) • ""C 0.3 Q) c • ro 0.2 en

0.1

0.0 0.0

• •

• •

0.2 0.4 0.6

pressure [Torr]

--model

• measurement

0.8 1.0

Figure 6.1.4 Silane depletion as ajunetion ojpressure as calculated by the modeland compared with

experimental results. Error on data is equal to 10%. (T=200 °C, c=8.5, r/JSiH4 = 100 seem, r/JH2=0, '

electron density is measured and used as an input.)

6.1.4 Silane flow

The calculations are done with varying silane flow with a hydrogen flow equal to zero. The results of model calculation and measurements are given in Figure 6.1.5 and Figure 6.1.6. The depletion results show a good correspondence with the measured results. The growth rate results are very good in comparison with the measured results for low silane flows. At higher silane flows the correspondence is not that good, possibly due to non-uniformity problems during the growth rate measurements. It is not expected that the growth rate decreases at higher flows. Pumping will not be important at such low flows if it is compared to the diffusion of particles to the walls and subsequent loss, which is much faster.

62

1.0 ..--. • .---r----r--~-.----r-----.--.------r---.--,-----,

...... 0.7 !-

......... c 0 ~

0.6

Q) 0.5 0.. Q)

"C Q) c ctl

U)

0.4 1-

0.3

0.2

0.1

-o-model

• measurement

0.0 .___..___.....__.....__ _ _._L __ .____..___.....__.....___....._ _ __._ _ __,

0 100 200 300 400 500

silane flow [seem]

Figure 6.1.5 Silane depletion as a function of silane flow with zero hydragen flow and a

power input of 150W. (T=200 °e, p=0.2 Torr, tPH2=0,, electron density measured and used as an input.)

8 • • 7 •

------~ o-----_

6 ----0 0

Ui' /0

~ 5 10 Q) lilt) .... 4 .; ctl ..... 0

.s::: I .... 3 3: •o • 0 I ..... 0> 2 0

-o-model

• measurements

0 0 100 200 300 400 500

silane flow [seem]

Figure 6.1.6 Growth rate as a function of silane flow with zero hydragen flow and a power

input of 150 W. (T=200 oe, p=0.2 Torr, tPH2=0,, electron density measured and used as an input.)

63

6.2 Partiele densities

The absolute densities of SiH4, SiH3, SiH2, H2 and H as calculated by the model cannot he checked with experimental results. In literature, however, data ofthe radical densities are available for camparabie setups [KAE95]. The densities calculated and converted to growth rate and silane depletion are shown to he in correspondence with experimental results, at least in order of magnitude. Whereas the absolute value ofthe densities calculated may he inaccurate, the relative values and the order of magnitude are assumed to he reliable. In this paragraph the partiele densities calculated as a function of electron density will he presented. Furthermore, the contri bution of different radicals to growth is studied.

6.2.1 Densities as ajunetion of electron density

The density plots as a function of electron density are typical. That is to say, the mutual position of the different plots is the same for each calculation done. Therefore, only one calculation is discussed. The graph ofthe different densities as a function of electron density is shown in Figure 6.2.1. The rad i cal densities are almast three orders in magnitude lower than the densities of silane and hydrogen. Silane and hydragen have a camparabie density, although the calculation is done fora pure silane plasma. The lowest density is the SiH2-density due tothefast reaction of SiH2 with SiH4. The atomie hydragen density is smaller than the SiH3-density, duetoasmaller loss time ofH and a larger probability to react.

M"' I .s >-....... ·u; c Q) "0

1022

1021

1020 ---· ---· -·-· -·-· -·-1019

1018

1017

1016 Ir _ .. -

1015 ........ .

-·---·-·-·

---------------------------~

---

_ ......

------- -------

--~·SiH 4

---- SiH 3

....... SiH 2

-·--- H 2

- ·-·- H 1014 L---~--._~~~~----~--~~~~~----~~~~~~

1013 1014 1015 1016


Figure 6.2.1 Density ofthe different particles as ajunetion of electron density. (T=200 oe, p=0.2

Torr, c=8.5, tPSiH4 = 100 seem, tPH2=0).

The radical densities as well as the hydragen density increase with electron density mainly due to an increase of the dissociation of silane, as can he seen looking at the silane density which decreases with electron density.

The ion density is in a quasi neutral plasma equal to the electron density, and it is seen in the graph that this ion density is always at least an order of magnitude lower than the densities of the other particles in the plasma.

64

Kae-Nune [KAE95] bas measured the SiH3 and SiH2 density in an RF plasma as a function of input power per cm2 electrode surface, which is approximately 0.04 W/cm2 in the Balzers reactor ifthe input power is 100 W. The pressure in Kae-Nune's experiment is equal to 0.06 Torrand a silane flow is used of 5 seem. The frequency in this experiments bas been equal to 13.56 MHz. In our case, the electron density is approximately 3·1014 at 100 Wand 13.56 MHz. Using Figure 6.2.1, the SiH3 density at that electron density is calculated to be 2·1 018 m-3 while the SiH2 density is approximately 3·1016 m-3. In bis experiment, Kae-Nune finds 0.2·1018 and 0.7·1016 m-3 respectively. The differences could be due to the difference in pressure, a lower pressure gives a lower electron density, and thus a lower radical density.

The total density, being the sum ofthe densities plotted plus the density ofSi2H6, should be the same as the density which can be calculated by using the reactor pressure and the ideal gas law. This is not put in the model as a restriction, because it leaves the system overdetermined giving some numerical problems (see Appendix). Therefore, it is not always the case. The pressure inthereactor is kept constant by adjusting the pump speed. In the model the pump speed is not adjusted ifthe number of particles increases due to dissociation reactions. This causes a higher total density in the model reactor than in reality. The difference, however, is two times at maximum and thought not to be important for the modeling results.

6.2.2 Contribution to growth

As discussed in paragraph 2.2.3 most growth models assume a major contri bution of SiH3 radicals to the growth of amorphous silicon. The SiH2 radical is thus thought to be unimportant for the growth process. The modeling results are used to see which radicals mainly contribute to growth. The result is shown in Figure 6.2.2.

.......... en

~ Q) ...... ro ......

.s::::. ...... 3: 0 ...... 0>

8

--growth rate 7 ----. contribution of SiH

3

6 ....... contri bution of SiH 2

-·- -·- etch rate 5

4

3

2 /

/

/ /

/ /

/

/ /

.-·-· o~=-~~~~~~~~~~~~~~--~~~~~~

1013 1014 1015 1016


Figure 6.2.2 Growth rate as ajunetion of electron density: contributions ofthe different radicals and

etching.(T=200 °C, p=0.2 Torr, c=8.5, r/JSiH4 = 100 seem, r/JH2=0.)

65

The growth rateis the sum ofthree processes, being the contribution of SiH3 plus the contribution of SiH2 minus the etch rate. In the graphit is seen that for lower electron densities the SiH3 radical is the most important contributor to growth. For higher electron densities, the SiH2 radical as well as etching start to be more important. For the Balzers reactor the electron density will be larger than 1015 m-3 ifthe power is larger than 100 Wand the frequency equal to or larger than 30 MHz, thus the contribution to growth of SiH2 is not negligible in this case.

6.3 RRS ratio: conditions for microcrystalline silicon deposition

The conditions for which microcrystalline instead of amorphous silicon is grown are not yet known for the Balzers reactor exactly. One ofthe main goals ofthe model was to predict the microcrystalline conditions. This subject is not yet extensively studied, but in this paragraph an onset is given to approach the problem.

The model uses a Radicals Reaching Surface (rrs) ratio. This is simply the ratio ofthe number of SiH3 radicals and the number ofH atoms reaching the growth surface. The rrs ratio is discussed in paragraph 5.2.3.

In the Balzers reactor one transition from microcrystalline to amorphous deposition is measured. Going up in silane/hydrogen flow ratio, the transition occurs at a silane/hydrogen ratio of O.I. This means that the silane is highly diluted with hydrogen in that condition. In Figure 6.3 .1 the rrs ratio is plotted against silane dilution. Using the known transition, it is concluded that microcrystalline material is deposited at a rrs ratio smaller than 2.

0 :.;:::: ro ..... en ..... .....

6~----~----~------r-----~----~------r-----,

4 f-

0.0 0.2 0.4 0.6

silane flow I hydragen flow [-]

Figure 6.3 .1 RRS ratio as ajunetion of silane/hydrogen flow ratio. The transition from microcrystalline to amorphous deposition occurs at a.flow ratio ofO.l, which means at a rrs ratio of 2.

The rrs ratio of smaller than 2 is now used to predict microcrystalline growth conditions in situations for which a transition from amorphous to microcrystalline is not experimentally known. The rrs ratio calculated as a function of electron density and silane flow with zero hydrogen flow is shown in Figure 6.3.2. As is seen in the picture, the electron density has to be highfora rrs value below 2,

66

whereas these rrs ratio values are only obtained for very low silane flow. This means that microcrystalline conditions are for high power and/or high frequency or low silane flow. Unfortunately, the latter condition gives a low growth rate (see Figure 6.1.6) and is therefore nota desirabie condition. At high electron density, however, a high growth rate is obtained, which is preferred.

Th ere exist some other conditions for which it is possible to reach a rrs ratio below 2. If the pre ss ure is decreased, the rrs ratio decreases. A pressure below approximately 0.1 Torr gives an rrs ratio below 2, and is therefore expected to be a microcrystalline deposition condition. However, it is not always possible to obtain both low pressure and sufficiently high flows to obtain an acceptable growth rate. This is limited by the pump capacity.

The calculations of the rrs ratio as a function of silane/hydrogen flow ratio, silane flow and pressure are done for an electron density of approximately 1015 m-3, that is to say, for relatively low power and low frequency. The calculation as a function of electron density is done at a silane flow of 100 seem. Another set of parameters will without doubt lead to more microcrystalline deposition conditions.

..--.. I ...._.

0 :.o::; ca '-U) '-'-

electron density [m-3] 1013 5F=~~~~.-~~~~.-~~~~~

1014 1015 1016

4

3

2

/0 /0

/o I /

0 t

/0 -------0

a-Si:H

-----0 0

t

····0············································································ .... d

J..tC-Si:H

1 ~--~--~--~--~---L--~--~----~--~--~--~ 0 100 200 300 400 500

silane flow [seem]

Figure 6.3.2 RRS ratio as ajunetion silanejlow at zero hydragenflow and as ajunetion of electron density.

6.4 Discussion

The model calculations of depletion and growth rate are comparable to experimental results if the electron temperature does notchange too much. The SiH3 radical is the most important radical, H2 and SiH4 have a much higher density in the plasma. The SiH3 radical is also the main contributor to growth, but at higher electron densities also SiH2 becomes important.

lt seems that the ratio of SiH3 radicals and H atoms reaching the surface, the so-called rrs ratio must be smaller than 2 for microcrystalline deposition conditions. This value is reached at high electron

67

density (thus high power and/or high frequency), low silanelhydrogen flow ratio, low silane flow and low pressure. More experiments must be performed to judge the value ofthe predictions.

In the conditions where microcrystalline deposition is expected the amount of H-atoms reaching the surface must be relatively large with respect to the amount of SiH3-radicals reaching the surface. An interesting question is whether this conditions could be obtained in the expanding thermal plasma setup. If it turns out to be possible to deposit microcrystalline silicon using an expanding thermal plasma, the growth rate could be higher than in the rf reactor.

The rrs ratio is dependent on the amount of atomie hydragen created in the plasma on one side and the creation of SiH3 radicals on the other si de. The amount of hydragen added to the plasma could be varied in both reactors, but there is an important difference in the silane dissociation process. The major silane dissociation mechanism in the expanding thermal plasma setup is dissociation by H atoms giving SiH3 and H2, which an important difference with the major dissociation mechanism in the rf reactor. As shown, in this reactor the silane is mainly dissociated by electrons, giving SiH3 or SiH2 and H. Therefore, where in the rf reactor H is created, in the expanding thermal plasma reactor it is used in the dissociation process of silane. Therefore, in the expanding thermal plasma setup the amount of silane radicals and the amount of hydragen atoms are less easily independently varied. Thus, it is more difficult to obtain a rrs ratio less than two in the expanding thermal plasma setup. Besides, as the distance between plasma souree and the substrate is large and H-atoms diffuse fast in radial direction with respect to the SiH3 radicals, the rrs ratio is further increased. The relative amount of hydrogen atoms reaching the substrate in the expanding thermal plasma setup could be increased by using pure hydrogen as carrier gas and a low silane flow. Furthermore, one could try to increase the atomie hydragen density near the substrate by instaHing some additional cascaded arcs on the vessel walls near this region. In this way it might be possible to increase microcrystalline conditions in the expanding thermal plasma silicon deposition reactor.

68

Part IV

CONCLUSIONS

Chapter Seven General conclusions The consequences of argon flow reduction in the expanding thermal plasma deposition setup to deposit amorphous microcrystalline silicon have been investigated. From the experiments the following conclusions can be drawn:

• It is possible to maintain are stability for lower argon flow. The argonlhydrogen flow ratio should not be decreased below one with are used in the current expanding thermal plasma deposition setup.

• The effective are diameter decreases with argonlhydrogen flow ratio. The behaviour of the plasma in the are channel is strongly connected to the ions emanating from the are and the dissociation of silane.

• The electron temperature in the plasma channel increases with decreasing argon/hydrogen flow ratio.

• The number of i ons emanating from the are decreases with argon/hydrogen flow ratio, due to the effective are diameter decrease. On one si de this just decreases the amount of i ons produced, on the other side, some hydrogen outside the plasma channel is not dissociated and is thought to participate in a reaction mechanism that reduces the number of i ons.

• The amount of atomie hydrogen teaving the are is strongly influenced by the argon/hydrogen flow ratio. The silane depletion, which is mainly due to reactions with atomie hydrogen shows the same behaviour as the atomie hydrogen flow.

• The growth rate scales with absolute silane depletion. Ifthe total flow is decreased the growth rate decreases with argonlhydrogen flow ratio, so it is not possible yet to maintain the high growth rate at lower total flow. The lower total flow is a necessary condition in the new solar cell deposition tooi due to the lower pump capacity in that device.

• The experiments conceming material quality are preliminary, but do not show a serious decrease in material quality with decreasing argon/hydrogen flow ratio.

• In general it can be concluded that it is possible to deposit good quality hydrogenated amorphous silicon at lower total flow. The growth rate decreases due to the total flow decrease, but this might improve ifthe are channel width is decreased, which is explained below.

In view ofthe experiments and the obtained results the following could be recommended:

• To increase the efficiency ofthe cascaded are it might be favourable to decrease the physical are channel diameter. At the same total flow the pressure in the are will then be larger, which causes the ratio of plasma channel cross section and are channel cross section to increase. Decreasing the are channel width will have a positive effect on the atomie hydrogen flow teaving the are en will therefore increase growth rate at the same total flow.

• The behaviour ofthe plasma in the are channel has been shown to be very important to the deposited film. To increase the understanding ofthe phenomena in the are channel it is necessary to extend the investigations done on effective are diameter and are resistance, from which an onset is given in this work. The use of more diagnostics could give more information about the processes in the plasma.

• Because the growth ra te increases with decreasing argonlhydrogen flow ratio if the total flow is fixed, it is thought that if the absolute amount of hydrogen added to the are is favourable to the

71

growth rate. It might be favourable for the growth rate to choose a condition in which the total flow is lower, but where the hydrogen flow is larger than in standard deposition conditions. Such a condition could be Ar/H2= 20/20.

• To obtain maximum silane efficiency, one should optimize the silane flow used. It has been shown earlier that for example the depletion is strongly dependent on the silane flow [BAS96], [AAR98], [GAB97]. Up till now the silane flow has been constant at 5 sccs.

• The experiments conceming film quality as a function of argonlhydrogen flow ratio should be repeated to obtain more reliable results.

A model has been developed to describe the plasma in the Balzers KAl reactor. In fact it is just a diffusive plasma model which can also be used for other plasmas where diffusion processes are dominant. From the model we could draw the following conclusions:

• The model calculations of depletion and growth rate are comparable to experimental results if the electron temperature doesnotchange too much.

• The calculations of partiele densities could not be checked with measurements, but do correspond to values given in literature. The SiH3 radical is the most important radical in the gas phase, whereas the density ofH and SiH2 is much lower. The molecules H2 and SiH4 have much higher density in the plasma.

• The model does not take into account variations of electron temperature.

• The radical pump loss is negligible in comparison with the loss due to deposition, i.e. the diffusion towards the reactor walls is thus faster than pumping.

• The SiH3 radical is the main contributor to growth, but at higher electron densities (> 10 15) a lso SiH2 becomes important.

• Whether the 'radicals reaching surface (rrs)' ratio could be an indicator for microcrystalline growth conditions should be checked by experiments. A preliminary result on the rrs ratio used as an indicator for microcrystalline deposition conditions revealed that the rrs ratio must be smaller than 2 for microcrystalline deposition conditions. This value is reached at high electron density (thus high power and/or high frequency), low silane/hydrogen flow ratio, low silane flow and low pressure.

The model could be improved and expanded. The following could be recommended:

• Include the surface equations mentioned in paragraph 5.2.5, which will needan adjustment ofthe used calculation method. See appendix. This will give a more realistic picture ofthe probabilities concemed, and will possibly lead to a good approximation of the hydrogen content of the deposited materiaL

• Include the restrietion that the sum of the densities is equal to the density calculated using the pressure and the i deal gas law.

• Include a Si2H6 continuity equation, which makes it possible to consider reaction mechanisms with Si2H6.

• To take into account the variations of(electron) temperature, reaction rates should be included as a function of (electron) temperature.

• Doing more experiments could be useful to correct the model further towards reality, in particular on the indication of microcrystalline deposition conditions.

• Because the model is developed for a plasma where diffusion is the main transport mechanism, the model can be used for other plasmas too. In the expanding thermal plasma reactor it could be

72

a good approximation for the region just before the substrate, where the expanding flow stagnates.

Camparing the deposition conditions in the expanding thermal plasma deposition reactor and the rf reactor, we could conclude the following conceming microcrystalline silicon deposition:

• The low ratio between SiH3 radicals and H atoms, which is thought to be necessary for microcrystalline silicon deposition, is less easily obtained in the expanding thermal plasma setup. A higher hydrogen density near the substrate might be obtained by using pure hydrogen as carrier gas and low silane flow or using extra cascaded arcs near the substrate.

73

Literature [AAR98] Igor Aarts, Massaspectrometrie aan een expanderend argon-waterstof-silaan-plasma,

stageverslag, TUE, VDF/NT 98-13 (1998) [ASA90] A.Asano, Appl. Phys. Lett. 56 (1990) 533-535. [BEU93] J.J.Beulens, M.J.de Graaf and D.C.Schram, Plasma Sourees Sci. Technol. 2 (1993) 180-

189. [BEN93] Daniel Benoy, ModeHing of thermal argon plasmas, thesis, TUE (1993). [BOU94] Maher I. Boulos, Pierre Fauchais and Emil Pfender, Thermal Plasmas: Fundamentals and

Applications, Vol.l, Plenum Press, New York (1994). [BUR85] Richard R. Burden and J.Douglas Faires, Numerical Analysis, third edition, Prindle,

Weber and Schmidt, Boston (1985) eh. 9. [DAH94] R.P.Dahiya, M.J.de Graaf, R.J.Severens, H.Swelsen, M.C.M.van de Sanden and

D.C.Schram, Phys. Plasmas 1 (1994) 2086. [HAP95] P.Hapke, VHF-Plasmaabscheidung von Mikrokristallinem Silizium (mc-Si:H): Einfluss

der Plasmaanregungsfrequenz auf die strukturellen und elektrischen Eigenschaften, thesis, ETH Zürich (1995).

[HAP97] P.Hapke, R.Carius, F.Finger, A.Lambertz, O.Vetterl and H.Wagner, Mat. Res. Soc. Symp. Conf. Proc. 452 (1997) 737-742.

[HEI93] M.Heintze, W.Westlake and P.V.Santos, J. of Non Cryst. Sol.164-166 (1993) 985-989. [KAE95] Patriek Kae-Nune, Caractéristaion par spectrométrie de masse des radicaux des

mécanismes de dépöt dans des décharges de silane, méthane et hydrogène, thèse, l'Universite Paris 6 (1995).

[KES97] W.M.M.Kessels, R.J.Severens, M.C.M.van de Sanden and D.C. Schram, Conf. on Amorphous and Microcrystalline semiconductors, Budapest, 17 (1997).

[KES97b] W.M.M.Kessels, depletie, intemal report (1997) [KIT96] Charles Kittel, Introduetion to solid state physics, 7th edition, Wiley and Sons, New York

(1996). [KOY96] S.Koynov, S.Grebner, P.Radojkovic, E.Hartmann, R.Schwarz, L.Vasilev,

R.Krankenhagen, I.Sieber, W.Henrion and M.Schmidt, J. Non-Cryst.Sol. 198-200 (1996) 1012.

[KUS88] M.J. Kushner, J. Appl. Phys. 63 (1988) 2532. [LUF93] Wemer Luft and Y. Sirnon Tsuo, Hydrogenated amorphous silicon alloy deposition

[MAT83] [MAT90] [MEI94]

[QIN95] [RIE88] [ROB98] [SAN95]

processes, Marcel Dekker Inc, New York, 1993. A.Matsuda, J. Non-Cryst. Sol. 59-60 (1983) 767. A.Matsuda and T. Goto, Mat. Res. Soc. Symp. Proc. 164 (1990) 3. J.Meier, S.Dubail, R.Flückiger, D.Fischer, H.Keppner and A.Shah, WCPEC, Waikolaa, Hawaii, 1 (1994). Zhou Qing, The magnetized hydrogen plasma jet, thesis, TUE (1995). Karl Riedling, Ellipsometry for industrial applications, Springer-Verlag, Wien (1988). J.Robertson and M.J.Powell, Mat. Res. Soc. Symp. Proc., San Francisco (1998). L.Sansonnens, D.Franz, Ch. Hollenstein, A.A.Howling, J.Schmitt, E.Turlot, T.Emeraud, U.Kroll, J.Meier and A.Shah, proceedings of 13th EC Photovoltaic Solar Energy Conf. Nice (1995).

[SAN98a] L. Sansonnens, A.A. Howling and Ch. Hollenstein, Plasma Sc. Sci. Technol. 7 (1998) 114. [SAN98b] Laurent Sansonnens, Déposition assistée par plasma radiofréquence dans un réacteur de

grande surface: Effets de la contamination particulaire et de la fréquence d'excitation, thèse, EPFL, CRPP (1998).

[SCH96] D.C.Schram, J.C.M.de Haas, J.A.M.van der Mullen and M.C.M.van de Sanden, Plasma Chem. and Plasma Proc. 16 (1996) 198.

[SEV95] R.J.Severens, G.J.H.Brussaard, H.J.M.Verhoeven, M.C.M.van de Sanden and D.C.Schram, Mat. Res. Soc. Symp. Proc. 377 (1995) 33.

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[SEV96] R.J.Severens, M.C.M.van de Sanden, H.J.M.Verhoeven, J.Bastiaanssen and D.C.Schram, Mat. Res. Soc. Symp. Proc. 420 (1996) 341.

[SEV97] R.J.Severens, F.van de Pas, W.M.M.Kessels, M.C.M.van de Sanden and D.C.Schram, Barcelona (1997).

[SOL93] I.Solomon, B.Drévillon, H.Shirai, N.Layadi, J.ofNon. Cryst. Sol. 164-166 (1993) 989-992.

[SPI64] Lyman Spitzer, Physics of fully ionized gases, 2nd Edition, Interscience Publishers (John Wiley & Sons, New York (1964).

[TOR98] P. Torres, J. Meier, U. Kroll, N. Beek, H. Keppner and A. Shah, Proc. of IEEE, to be published.

[TOY91] Y.Toyoshima, K.Arai, A.Matsuda and K.Tanaka, J. Non-Cryst. Sol. 137-138 (1991) 765. [VDS97] Richard van de Sanden, The growth mechanism of amorphous hydrogenated silicon,

Eindhoven Summerschool on Low Temperature Plasma Physics and Applications , TUE, ETP (1997).

[VEP72] S.Veprek, J.Chem.Phys, 57 (1972) 952. [VER95] Eric Verhoeven, Electrical characterization of plasma beam deposited amorphous

hydrogenated silicon, afstudeerverslag VDF/NT 95-12 ( 1995). [WEI95] Yi Wei, Lian Li and S.T. Tsong, Appl. Phys. Lett. 66 (1995) 1818.

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Technology assessment The question for alternative sourees of energy has only increased during the last few years. One of the most promising new energy sourees is solar energy. To make it also economically favourable to apply solar cells as an energy source, a reduction of costs is one of the most important goals of research. This can be done by increasing the yield ofthe solar cell, for example by using a cell structure which uses both amorphous and microcrystalline silicon to allow a better use ofthe solar spectrum. Another possibility is to decrease the production costs of the solar cell. Hydrogenated amorphous silicon is one of the materials which can be produced at lower costs and is therefore a good candidate as solar cell materiaL

This graduation work has been done in the group 'Equilibrium and Transport in Plasmas (ETP)' at the Eindhoven University ofTechnology (TUE) and in the group 'Plasmas for the industry' ofthe 'Centre de recherche en physique des plasmas (CRPP)' which is part ofthe Ecole Polytechnique Fédérale de Lausanne (EPFL). In this groups workis doneon the deposition of amorphous and microcrystalline silicon. The group ETP concentrates on the high rate deposition of amorphous silicon using an expanding thermal plasma, whereas the group at CRPP investigates a large area deposition reactor to deposit amorphous or microcrystalline silicon. The development and application oftechnology is the major motive of both groups.

The work described in this report contributes to the development of the thin film silicon solar cells. To implement the expanding thermal plasma deposition reactor into a device for the production of a complete solar cell the effects oftotal flow reduction are investigated. Furthermore, a model has been developed to increase the understanding of microcrystalline growth conditions.

77

Appendix: structure ofthe MatLAB program The model calculations are done with MatLAB (The MathWorks Inc, version 4 or 5). We will discuss the structure of the program shortly in this appendix.

In MatLAB, the executable files are called m-files. An m-file is executed by typing the name ofthe m-file as a cammand in the cammand window. For more information one could consult the MatLAB manual. The program could be divided in two parts: the calculation m-files and the program m-files. In the program m-files calculate 'everything' as a function of a specific parameter, whereto is referred in the name ofthe program m-file. In the program m-file the calculation m-files are used to calculate for example densities and growth rate. In the table below the different m-files are addressed.

Table Survey of the m-.fi/es used to calcu/ate the model's resu/ts. program m-files calculation m-files e1ectronic den si ty. m calculates constants. m declaration ofthe constauts such densities, depletion and growth rate as a function as flows and pressure of electron density di11 necor. m calculates densities, depletion in i tia1. m calculation of some parameters and growth rate as a function of dilution, using such as pump speed and initial silane density experimental data for electron density using the constauts declared in constants. m di 11 u te . m calculates densities, depletion and newton. m calculation ofthe densities using the growth rate as a function of dilution using a five continuity equations by the newton iteration constant electron density of 1015 m-3 methad [BUR85]. di 11h yd. m calculates silane depletion as a growth2 .m calculation ofthe surface function of silane flow for different hydragen parameters such as growth rate and radical fluxes flows and hydragen content using the densities

calculated with newton. m pressure increase. m calculates densities,

-depletion and growth rate as a function of pressure, using experimental data for electron density si1ane increase .m calculates densities, depletion and growth rate as a function of pressure, using experimental data for electron density etch_p1asma. m calculates densities and growth ra te as a function of hydragen flow with zero silane flow, using a constant electron density of3·1015 temper at ure . m calculates densities, depletion and growth rate as a function of reactor temperature, using a constant electron density of 1015 m-3

To calculate sarnething one should first deelare the constauts with the constants m-file. Furthermore, the program needs an electron density and a correction factor for the reaction rates, which is called c. The densities as a function of a eertaio variabie should be calculated in a loop. In each step one should call on the m-files ini tia1, newton and growth2 respectively. The salution is given as a vector, solS, whose elements are the densities ofthe different particles:

79

nsiH,

nSiH3

solS= nsiH2 ( 1 )

nH2

nH

After calculating solS it is used in the growth2 m-file, where growth rate and, for example, hydragen content are calculated. In each step the calculated data are put in an array, which is after the calculation loop used to produce the plots.

80

Dankwoord Ziezo. Dat is dat. In het bijzonder wil ik bedanken de volgende mensen:

Erwin en Richard en Daan, als directe begeleiders. Christian, Maikel, Ben, Igor en Tanya voor een leuke studentenkamer ("hoe is het met de cursor crypto?" en "heb je de harmpje al uitgeknipt?". Cas, Amo, Iain en Bas voor "is deshutter al dicht?" en "mag ik je computer vandaag gebruiken?"). Bertus, Ries en Herman voor (computer)technische zaken. Alle andere mensen van ETP.

A Lausanne je veux dire "merci" à: Alan, Laurent, Clothilde, Christoph, Jean-Luc, Herbert, Christian et les autres. Dans la maison 'Rhodanie', Ie 3ème etage: j'ai eu une bonne temps.Merci pour tous, maïs spécialement pour Sirnon (ça va?).

Dan, mijn huisgenoten: Bert, Marc, Pascal, Jeroen, Jeroen, Jeroen, Henk, Gijs en Douwe. Mooi wonen blijft het op Toko 39, vind ik.

Vervolgens mijn ouders en zus, Annemieke en Wim en Marjolijn. Dank je wel!

En natuurlijk mijn vriend Richard. Je bent de liefste van mijn wereld.

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