PHYSICAL REVIEW 8 VOLUME 43, NUMBER 3 15 JANUARY 1991-II

Hydrogen chemical potential and structure of a-Si:H

R. A. StreetXerox Palo Alto Research Center, Palo Alto, California 94304

(Received 28 June 1990)It is proposed that the chemical equilibrium of hydrogen is an important factor in determining

the structure of thin films deposited from silane-hydrogen plasmas. Hydrogen interacts with thesilicon network to optimize the local bonding configurations. Raising the eA'ective hydrogenchemical potential reduces the disorder of hydrogenated amorphous silicon films and eventuallyinduces a transition to crystallinity.

The effects of hydrogen in a-Si:H are complex andvaried. For example, hydrogen termination of silicon dan-gling bonds improves the electronic properties; H dilutionof SiH4 in the plasma induces the growing film to be crys-talline rather than amorphous;' and defects in a-Si:Hreach thermal equilibrium at elevated temperaturesthrough the diffusion of bonded hydrogen. This paperaddresses the role of hydrogen in determining the struc-ture of a-Si:H films during growth, and proposes thatequilibrium chemical reactions involving hydrogen are amajor inAuence. The variations in structure are usuallyattributed to different mixtures of gas radicals. SiH3 isgenerally considered to be an important precursor togrowth of good quality material, while SiH2 or SiH arethought to result in poor material, largely due todifferences in their reactivity, sticking coefficient, and sur-face mobility.

Considerations of thermodynamic equilibrium andchemical bonding provide a different viewpoint. The equi-librium structure of a material is determined by aminimum of the free energy, independent of the growthprocess. The attention given to the growth process ofamorphous semiconductors is largely because the amor-phous structure is not the equilibrium solid phase. Never-theless, the structure of a-Si:H can adopt many alterna-tive bonding configurations, and it is reasonable to sup-pose that the structure in any small volume may representa minimum free energy, subject to the constraints imposedby the long-range disorder of the network. The equilibri-um of defects and dopants at temperatures near the nor-mal growth temperatures (200-300'C) is modeled withthis assumption. '

Equilibration of the structure requires sufticient atomicmotion to allow changes in the bonding configurations.Hydrogen in a-Si:H is mobile at the normal depositiontemperature and has the property of terminating silicondangling bonds and breaking weak SiSi bonds. Thushydrogen motion promotes structural change, and has fre-quently been proposed as the underlying mechanism of de-fect equilibration (e.g. , the hydrogen glass model). Thethermodynamic approach has been applied to the incor-poration of impurities during growth, and more recentlyto the growth of a-Si:H.

This paper extends the equilibrium model by consider-ing the role of hydrogen in the growth of films from silaneplasmas. It is proposed that the chemical potential, pH, of

atomic hydrogen in the plasma is a determining factor inthe structure of the deposited a-Si:H and microcrystallinefilms. %e suppose that the hydrogen reactions at thegrowth surface promote an equilibrium film structure,subject to other constraints on the network. The modelrelates pH to the disorder of the film and explains the con-ditions for optimum film growth, the transition to crystal-linity and the structure dependence of the equilibrationrates. The model is broadly based on the sequence ofgrowth proposed by Gallagher in which SiH, radicals at-tach to the growing surface. Since the hydrogen concen-tration of the radicals is much larger than of the resultingfilm, Gallagher envisions a subsurface region (with thick-ness, ds, of order 10 A at usual growth temperatures)from which the excess hydrogen is eliminated. The modelfocuses on hydrogen because it can diffuse into the filmand induce structural changes.

In plasma-assisted chemical vapor deposition, the plas-ma creates radicals which are not present in large quanti-ty in the unexcited gas. These metastable radicals reactwith the surface to cause growth, but the plasma is be-lieved to have a minimal direct role in the surface growth.Aside from silicon-containing radicals, the plasma createsatomic hydrogen whose concentration we describe by achemical potential,

pH =EH+kTln(NH/NHp),where EH is the energy of atomic H in vacuum (see Fig.2), NH is the concentration in the plasma, and NHp is theeffective density of states (2.5 x 10 cm at 550 K, theinverse of the quantum volume). The steady-state hydro-gen concentration is a balance between its creation by theplasma and its loss to various chemical reactions. Thechemical potential in this situation is analogous to thequasi-Fermi energy defined for electrons in a photocon-ductor under illumination.

At the normal growth temperature, hydrogen diffuseswithin a-Si:H and redistributes between alternative bond-ing sites. Consequently, the hydrogen distribution is closeto equilibrium and can also be described by a chemical po-tential. The interchange of hydrogen across the growingsurface implies that the hydrogen chemical potentials inthe plasma and the film tend to equalize; the main as-sumption of the model is that this process causes the hy-drogen in the plasma to determine the atomic structure ofthe growing film.

2454 1991 The American Physical Society

HYDROGEN CHEMICAL POTENTIAL AND STRUCTURE OF. . . 2455

The relation between the hydrogen chemical potentialand the network structure of a-Si:H is developed next.One of the enduring concepts of amorphous semiconduc-tors is that each atom in the network tends to satisfy its lo-cal chemical-bonding requirements. Mott's 8 N ruleapplies broadly to amorphous semiconductors, and in amodified form is the basis of the equilibrium models ofdoping in a-Si:H. ' The 8 N rule follows from the for-mation of chemical bonds which minimize the electronicenergy. Singly occupied electronic states are not thelowest-energy structural configurations (they do not obeythe 8 Nrule), and are unstable with respect to astructural change which forms pairs of electrons in bond-ing states and leaves antibonding states empty. This reac-tivity tends to open a gap in the electronic density of statesat the Fermi energy, as illustrated in Fig. 1. It followsthat an ideal undoped amorphous semiconductor has fewparamagnetic dangling bonds, and doped a-Si:H has aminimum density of states between the charged dopantsand defects (both of which obey the 8 Nrule by virtueof their extra charge).

An analogous argument applies to hydrogen in a-Si:H.Atomic H forms a strong bond to silicon and the optimumstructure is one which minimizes the hydrogen which isnot strongly bonded to silicon. Thus, ideal bonding in a-Si:H consists of SiSi and Si H bonds, but not danglingsilicon bonds or interstitial hydrogen. The bond-angle andbond-length disorder cause a distribution of SiSi (andpossibly Si H) bond strengths. Figure 1 illustrates thehydrogen density-of-states distribution in a-Si:H. Theenergy is that of the hydrogen bonding to diff'erentstructural configurations. The SiH bonds lie below thehydrogen chemical potential, since they are occupied byhydrogen. The energy needed for hydrogen to insert intoa SiSi bond is larger, so that these states lie above pHand are mostly unoccupied by hydrogen. The weakestSiSi bonds are closest to p H, since these are most easilybroken by hydrogen through a reaction of the generaltype,

Nwa(E) =Npexp[ (Es E)/Epj; E & Es (3)where Es is indicated in Fig. 2 and is approximately theenergy of hydrogen in a normal SiSi bond, and Ep is theslope of the distribution. A density of weak-bond states,N;, at pH then gives

Ep = (Es p H )/P, where P = ln (Np/N;) . (4)Ep is a measure of the structural disorder of the material

dangling bond, and a weak bond which gains a hydrogenatom results in a similar defect. A high density of bothtypes of states at pH is therefore incompatible with the8 N rule for chemical bonding. The immediate con-clusion is that an ideal amorphous structure is formedwhen the hydrogen density-of-states distribution has aminimum at pH (see Fig. 1, right). The similar electronand hydrogen distributions illustrate a general principlethat any reactive species causes a gap in the distributionof bonding states to open at its chemical potential, be-cause the lowest-energy structures contain strong covalentbonds.

The minimization of the density of states at pH inducesan interaction between the hydrogen and the silicon net-work structure. Accordingly, the growth reactions deter-mine the structure by inducing a low weak-bond density atpH. If the growth conditions are such that pH is raised,the bonding structure is no longer in a stable state andthere is a tendency to change the distribution of SiSibonds by breaking weak bonds and reconstructing the net-work to give either SiH bonds or stronger SiSi bonds.The diff'erent network structures which follow from achange in pH are shown in Fig. 2.

The weak-bond model assumes an exponential distribu-tion of weak SiSi bonds, ' '

weak bond+ H ~ broken bond+ SiH . (2)

undoped a-Si:H

Ec

n-type a-Si:H

Ec

Hydrogen Bonding

EF

An SiH bond which loses its hydrogen becomes aUl

.s0)r

LLI

U)a'aC0

CQ IIU)U

Sl-HBonds

Ey Ey

Oensity of States

FIG. l. Illustration of the electronic density of states (leftand center), and the hydrogen density of states (right), showinga gap opening at the chemical potential (Fermi energy) as a re-sult of the interaction with the silicon network structure.

Density at StatesFIG. 2. The hydrogen density-of-states distribution, showing

the SiH bonds below p H and Si Si bond above pH which aremostly unoccupied by hydrogen, and the minimum at the hydro-gen chemical potential. The dashed line shows the modifieddensity of states for a higher pH, with a narrower distribution ofweak bonds. E& is the energy of H in a strong SiSi bond, andEH at rest in vacuum.

2456 R. A. STREET

Cg

c I0) X$QQ

l56$

~~ QE aLee

~M

'.,c-Si:H

surfacections

GrowthSurface

Hydrogen Concentration

FIG. 3. Illustration of the range of allowed structural orderand hydrogen concentration of a-Si:H and crystalline silicon (c-Si:H). The position marked by the circle corresponds to the sur-face structure during growth, and the dashed line illustrates thechange in .structure induced during the subsurface reactions.The H chemical potential is an equivalent measure of order, asdescribed in the text.

and in the weak-bond model is related to the slope, Ev, ofthe exponential valence-band tail, which has a density ofstates proportional to exp[ E/Ez j. '' Equation (3) isdoubtless approximate, but illustrates the nature of the re-lation between structural order and pH i.e., an increasein the hydrogen chemical potential reduces the disorder,as measured by the weak-bond distribution (see Fig. 2).From Eq. (1), it is expected that Eo increases with tem-perature, and is reduced with increased hydrogen concen-tration in the plasma.

The position of the H chemical potential is not the onlyconstraint on the structural disorder. An unhydrogenatedamorphous silicon network has a high bonding disorder,because a fourfold coordinated network is overcon-strained. The inclusion of hydrogen relaxes the networkand reduces the disorder. Many measurements show thatthe band-tail slope, Ey, can be reduced to 45-50 meV, butno a-Si:H films exist with substantially smaller values. ''We infer that there is a minimum disorder in a-Si:H. Fig-ure 3 illustrates the region of allowed a-Si:H structuresbased on this reasoning. The boundary line limits the pos-sible structures, which are constrained to have a higherdisorder at very low hydrogen concentrations (and possi-bly also at high hydrogen levels). Hydrogenated crystal-line silicon lies in a separate region of the space, charac-terized by a high structural order and generally a low hy-drogen content. Following the arguments used to obtainEqs. (3) and (4), we associate the structural order withthe energy of p H, such that a high order corresponds to ahigh chemical potential of H, as shown in Fig. 3.

The growing film surface is assumed to have a high hy-drogen concentration and a high disorder, both originat-ing from the attachment of SiH radicals; this startingpoint is illustrated by the circle in Figs. 3 and 4. Duringthe subsurface reactions, the structure follows a trajectoryof H concentration and structural order, towards a stablestructure determined by the position of pH. The modeldoes not consider the specific reactions, but there is evi-dence that bonded hydrogen in the film is removed by re-action with hydrogen from the plasma. ' The hydrogenreactions create Si dangling bonds which may bond to

VH

,

annealingreactions

bsurfacereaction

ng Temper

(c)

Hydrogen Concentration

FIG. 4. Illustrations of the various hydrogen-inducedstructural reactions, showing three types of growth, as describedin the text.

each other or may acquire another hydrogen. Similarly,weak SiSi bonds are broken by the hydrogen and maybe reformed as different stronger bonds. These processeschange the hydrogen content and modify the localstructural order of the silicon network.

The ideal structure only occurs when there is sufficienthydrogen mobility to complete the reactions. The subsur-face zone of interaction, d~, is defined by the balance be-tween hydrogen diffusion DH and growth rate g,

ds =DH/g. (5)At depths below ds, the bonded hydrogen is not in com-munication with the plasma hydrogen, although somebulk structural changes may still occur. The thermallyactivated H diffusion gives a strong temperature depen-dence to dq.

The present model identifies three broad regions ofgrowth, illustrated in Fig. 4, as follows:

a. Kinetically limited growth IFig 4(a)J. Low-.temperature growth results in defective material becausehydrogen is not properly equilibrated due to its lowdiffusion coefficient. The interaction depth defined by Eq.(5) has essentially zero width. The H content and the dis-order are higher than for an ideal a-Si:H film because theequilibration reactions cannot occur. Subsequent anneal-ing of the film improves the structural order and reducesthe defect density, without changing the hydrogen concen-tration [see Fig. 4(a)i. The annealing effect is a well-known phenomenon in films deposited below about200'C.

b. Amorphous structures determined by p H IFig.4(b)j. At higher temperatures, the H diffusion is fastenough to allow the film structure and H content to bedetermined by the chemical potential. We expect that the

HYDROGEN CHEMICAL POTENTIAL AND STRUCTURE OF. . . 2457

surface reactions first establish a structural order deter-mined by pH, and then continue to remove hydrogen untilconstrained by the inability of very-low-hydrogen-con-centration films to maintain the same structural order;these two processes are illustrated in Fig. 4(b). Optimumfilms require a sufficiently high pH so that the structurereaches the limits imposed by the network disorder. Ahigher temperature reduces pH, and therefore induces amore disordered film and a lower hydrogen concentration.Optimum films are therefore grown at the lowest tempera-ture at which the kinetic limitation can be avoided. Ourmodel further predicts that high-temperature growth(& 300'C) benefits from a high hydrogen concentrationin the plasma gas and increased rf power. In contrast, atdeposition temperatures of 250'C or below, the increasedgrowth rate of a high rf power reduces dg and causes ki-netically limited growth.

c. 1nstabiliries at high pH IFig. 4(c)j. A sufficientlyhigh hydrogen chemical potential leads to an unstable sit-uation, because the degree of structural order determinedby pH greatly exceeds that available in the amorphousnetwork. As shown in Fig. 4(c), pH does not intersect therange of structures available to a-Si:H material. We pro-pose that this is the condition necessary for a transition togrowth of crystalline silicon. The model suggests that thetransition to crystalline growth is enhanced by high Hconcentration in the plasma, high rf power, and low tem-perature, since all three raise the chemical potential.These are indeed the observed conditions, although thefilms revert to being amorphous at low temperature be-cause the H diffusion rate is too low to allow equilibration.The predicted suppression of microcrystallinity at highdeposition temperature is observed. '

The model accounts for many of the observed trends inthe growth of a-Si:H, and also gives some insights into thegrowth-dependent bulk properties of a-Si:H. For exam-ple, the most ordered a-Si:H films have the highest pH,and these structures have the lowest defect density due tothe equilibration between defects and weak bonds. Sincethe H diff'usion also depends on the position of pH, themodel predicts that the material with the best electronic

properties has the fastest equilibration rate; this effect isobserved. '

Only a very approximate quantitative evaluation of themodel can be made. The proposed equalization of pH inthe plasma and the film applies best at high depositiontemperatures, above 700 K, ' where the structural orderis not limited by the network. Equation (1) places pH inthe plasma at roughly EH 1.7 eV for this temperature,with an estimated H concentration of 10' cm . Equat-ing the minimum density of weak bonds, N;, with theequilibrium defect density of about 10' cm, and as-suming Eo= 2Ev = 90 meV, as suggested by the weak-bond model, then pH in the film is at Eq 1.1 eV. Theenergy Eg is estimated to be about 1 eV below EH, ' thusplacing pH at EH 2. 1 eV. The difference of 0.4 eV be-tween the two values of pH is within the accuracy of thevarious estimates. Much more information is neededabout the hydrogen bonding and the interaction of theplasma with the growing surface to obtain acurate ener-gies.

Combining Eqs. (1) and (4) givesEs ln (N Hp/N H )2Ev =Eo= +kT 6ln(Np/N;) ln(Np/N;)

The parameters used above predict that the valence-bandslope increases roughly as kT in the high-deposition-temperature regime, which is in reasonable agreementwith experiment. ' The effect of plasma hydrogen con-centration on the slope of the absorption tail should be aninteresting test of the model.

In summary, hydrogen promotes structural changethrough chemical reactions with the silicon. The lowest-energy structure has a minimum bonding energy, subjectto the long-range topological constraints of the structure.The hydrogen chemical potential is proposed to be the im-portant parameter determining the network disorder of a-Si:H and the transition to microcrystalline growth.

The author is grateful to C. Herring, W. Jackson, andK. Winer for many helpful discussions. The research wassupported by the Solar Energy Research Institute.

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