CH

AP

TE

R6DIFFUSION, OXIDATION AND ION IMPLANTATION

This chapter will discuss some important processing techniques for device fabrication. These have beendiscussed earlier by Ghandy [1] and Sze [2]. The present chapter introduces some newer techniquessuch as laser annealing and presents some new research results on GaAs. While Diffusion and Oxida-tion are particularly important for Silicon-based devices, Ion Implantation is the preferred technique forall semiconductor devices including III-V and II-VI compounds, since all semiconductor devices re-quire a desired doping concentration and doping profile for optimum performance.

In the fifties doping was carried out during crystal growth and simple p-n junctions could thus bemade. In amorphous Si devices doping is still carried out during deposition as discussed in Ch 4.Nowadays however the bulk single crystal wafer forms a high quality substrate for further processing,which could include epitaxial growth followed by ion implantation. Till the seventies doping in Si wascarried out using high temperature diffusion. Since then ion implantation has become the workhorseespecially for shallow doping. Diffusion is still employed for deep junctions and a combination of the2 processes may be used. Since the implantation of high energy ions results in damage to the crystallinelattice, this must be followed by annealing in a furnace or by lamps as in a rapid thermal anneal (RTA)process.

6.1 DIFFUSION

Diffusion is a process that involves the motion of atoms through a solid and is driven by a concentrationgradient. In crystalline semiconductors the motion of impurity atoms occurs by

(a) substitutional(b) interstitial(c) substitutional-cum-interstitial mechanisms or(d) direct exchange and cooperative exchange.

These are shown schematically in Fig. 6.1. For substitutional diffusion there must exist a concen-tration of vacancies to which the impurity or host atom can jump. For interstitial diffusion the presenceof vacancies is not absolutely necessary while in the third case the impurity can move occupying bothsubstitutional and interstitial sites. Direct exchange and cooperative exchange have low probabilitiesand are not considered further.

358 SEMICONDUCTOR MATERIALS & DEVICES

Fig. 6.1 Diffusion mechanisms: (a) substitutional (b) interstitial (c) substitutional-cum-interstitial(d) direct exchange and cooperative exchange

6.2 FICKS FIRST LAW

Atoms in a lattice in thermal equilibrium can be considered to vibrate about their lattice positions. Withincrease in temperature these may acquire enough energy to overcome the potential barriers and thusjump to adjacent substitutional or interstitial sites. In the presence of a concentration gradient, moreimpurity atoms will jump in the direction of the gradient and than in the opposite direction and henceconstitute a flux of diffusing atoms. Thus diffusion is governed by Ficks First law which states that theflux F per unit area per unit time is proportional to the diffusion coefficient and the concentrationgradient:

dCF D

dx= ...(6.1)

where C = dopant concentration per unit volume. This is Ficks law in one dimension. The negative signindicates that the flux is from high to low doping concentration. The diffusion coefficient D depends onthe type of individual atom and is strongly dependent on temperature being given by

D = D0 exp (Ea/kT) ...(6.2)

(a) (b)

12

34

1

2 3

4 5

6

(c) (d)

DIFFUSION, OXIDATION AND ION IMPLANTATION 359

where D0 = diffusion coefficient extrapolated to infinite temperature in units of cm2/s and Ea = activa-

tion energy in eV.One of the standard methods for determining diffusion coefficients is by the radioactive tracer

technique. In this a radioactive species is coated on one end of a sample and diffused at a high tempera-ture for a given time. The sample is then taken out and sliced into sections. The radioactive counts forthe different sections are then measured and the diffusion profile thus determined and fitted with agaussian or error function profile as determined by the diffusion condition. The experiment has to berepeated over a range of temperatures to find D0 and Ea.

Interstitial Diffusion

Fig. 6.2 Diamond structure showing 5 interstitial voids [1]

Examining the diamond structure of Si (Fig. 6.2) it is evident that there are 5 interstitial voids in anunit cell. These are located at

(1/2, 1/2, 1/2), (1/4, 1/4, 1/4), (3/4, 3/4, 1/4), (1/4, 3/4, 3/4) and (3/4, 1/4, 3/4)

The tetrahedral radius of Si is 1.18 , computed as half the distance between nearest neighbours(assuming a hard sphere model). It can also be shown that the diameter of the interstitial void is 1.18 and the size of the constriction between the voids is 1.05 .

If Em is the potential barrier height between interstitial positions, the number of jumps/s

= 4 0 exp (Em/kT) ...(6.3)where 0 = vibrational frequency of lattice atoms = 10

13 1014/sec.

x

y

z

14

34

, ,

14

, 14

, 14

, , 14

14

,,

Atom sites

Interstitial sites

12

, 12

, 12

360 SEMICONDUCTOR MATERIALS & DEVICES

Considering diffusion in a concentration gradient (Fig. 6.3) in [100] direction it can be shown thatthe flux density j is

j = ( d2/6) N/x = /x [DN/x)]

= D (N/x)if D is constant independent of the doping concentration.

Fig. 6.3 Diffusion in a concentration gradient [1]

Thus D = d2/6 where d = tetrahedral spacing in the diamond lattice.Therefore j = (4 0 d

2/6) exp (Em/kT) = D0 exp (Em/kT) ...(6.4)

Substitutional Diffusion

For substitutional diffusion it is necessary to have a vacancy as a nearest neighbour. If the energynecessary to create a vacancy is Es, the number of available vacancies is proportional to exp (Es/kT).In a diamond lattice each lattice site has 4 nearest neighbours and if the height of the potential barrieris En the probability of jumps to nearest neighbours is proportional to exp ( En/kT). Thus the numberof jumps per unit time

j = (4 0 d2/6) exp [(En + Es)/kT] = D0 exp [(En + Es)/kT] ...(6.5)

Table 6.1 Substitutional Dopants in Silicon

Impurity P As Sb B Al Ga In

Type n n n p p p p

D0 (cm2/s) 10.5 0.32 5.6 10.5 8.0 3.6 16.5

Ea (eV) 3.69 3.56 3.95 3.69 3.47 3.51 3.9

Temp range (C) 950-1235 1095-1380 1095-1380 950-1275 1080-1375 1105-360 1105-350

Tetra. radius () 1.10 1.18 1.36 0.88 1.26 1.26 1.44

Misfit factor 0.068 0 0.153 0.254 0.068 0.068 0.22

Sol. solub.(/cm3) 1021 2.1021 8.1019 6.1020 2.1019 4.1019 3.2.1019

The activation energies for substitutional diffusion are (3 4) eV for impurities, 0.6 2.4 eV forinterstitials and 5.5 eV for self-diffusion in Si. Thus substitutional diffusion is much slower than interstitial

N

x

[100]

d/ 3

21

d/ 3

DIFFUSION, OXIDATION AND ION IMPLANTATION 361

diffusion and requires higher temperatures and longer times. The variation of D vs 1000/T for impuritiesin Si is shown in Fig. 6.4(a).

The substitutional impurities belonging to Groups III & V are the ones used for doping since thesegive rise to shallow acceptors and donors respectively. These single-charged donors are positivelycharged while acceptors are negatively charged when ionized.

Impurity Vacancy Interactions

The process of diffusion of substitutional impurities involves interaction with vacancies which can havevarious charge states such as V+, V, V, V2 etc. These impurity atoms will interact with vacanciesdepending on their charge state and each I-V combination will have its own activation energy. Thuscorresponding to each I V+, I V , I V , I V2 pair there will be intrinsic diffusion coefficientsD D D Di i i i

+ , , ,0 2 etc. Thus the overall intrinsic diffusivity will be given by

D D D D Di i i i i= + + ++ 0 2

For the case of extrinsic diffusion the variation of the Fermi level with doping has to be taken intoaccount as discussed by Ghandy [1]. This also affects the population of different charged vacancies. Sivacancies exhibit the charge states V+, V and V2 with locations in the energy band gap at EV + (0.06 0.16) eV, EC 0.44 eV and EC 0.11 eV respectively. Thus diffusing acceptors have only I V

+ typeinteractions while donors interact with negatively charged species I V and I V2.

Choice of n-type impurities in Silicon

Impurity Diffusion coefficient Energy level CommentsED (eV)

P High-same as B 0.044 Short diffusion time, shallow donorMost widely used

As Low 0.049 Slow diffuser - first diffusion;Shallow donor. Small misfit factor Highest solubility. Toxic

Sb Low-high EA 0.039 Slow diffuser - Shallow donor.Preferred to As as less toxic.

Choice of p-type impurities in Silicon

Impurity Diffusion coefficient Energy level CommentsEA (eV)

B High-same as P 0.045 Short diffusion time, shallow donorHighest solubility; Most widely used

Al Moderate 0.065 Highly reactive with O not commonly used

Ga Moderate 0.065 Highly diffusion coefficient in SiO2;Used only for high power diodes

In Slow diffuser; low 0.16 Deep acceptor partly ionized at 300K;solubility used as 78 m IR detector

362 SEMICONDUCTOR MATERIALS & DEVICES

Table 6.2 Interstitial dopants in Silicon

Impurity Li S Fe Cu Ag Au O Ni Zn

D0 (cm2/s) 2.5 102 0.92 6.2 103 4 102 2 103 1.1 103 0.21 1.3 102 0.1

Ea (eV) 0.655 2.2 0.87 1.0 1.6 1.12 2.44 1.4 1.4

ED/EA (eV) 0.24, 0.37, 0.79 D 0.76 D 0.16 D 0.21, 0.76 0.31,0.52 A 0.89 A 0.57 A A 0.56 A

The values of D0 and Ea for interstitial diffusion are given in Ta