KINETIC THEORY OF AUTODOPING IN REDUCED PRESSURE EPITAXY OF SILICON

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KINETIC THEORY OF AUTODOPING IN REDUCED PRESSURE EPITAXY OF SILICON

M. Onuki, A. Nishikawa

To cite this version:

M. Onuki, A. Nishikawa. KINETIC THEORY OF AUTODOPING IN REDUCED PRES- SURE EPITAXY OF SILICON. Journal de Physique Colloques, 1982, 43 (C5), pp.C5-93-C5-100.

�10.1051/jphyscol:1982512�. �jpa-00222231�

K I N E T I C THEORY OF AUTODOPING I N REDUCED PRESSURE E P I T A X Y OF S I L I C O N

M. Onuki and A. Nishikawa*

Department of Information Engineering, Kwnamoto University, Kurokanri, Kwnamoto 860, Japan

*Central Research Laboratories, ~ a t s u s h i t a E l e c t r i c Industria2 Co., LTD., Moriguchi, Osaka 570, Japan

RBsumg - Dans 18Bpitaxie du silicium sous une pression rgduite, nous proposons un modsle de piBgeage des impuretgs par des molg- cules de silane dans la couche limite du courant des gaz. A l'aide de ce modsle, nous pouvons expliquer les resultats obte- nus dans nos expgriences d'auto-dopage en fonction de la pression totale, de la fraction molaire du silane par rapport Z l'hydro- gsne et de la tempgrature de croissance. Nous calculons ensuite numsriquement le facteur dlauto-dopage dans de diffgrentes con- ditions en nous servant des paramstres physiques de la cingtique des gaz, ce facteur Btant dBfini comme le degr6 de lleffet de la capture. Nous comparons enfin nos rssultats expsrimentaux de llauto-dopage dans diffgrentes conditions avec la thgorie fondge sur le facteur d'auto-dopage dBfini ci-dessus.

Abstract - In the reduced pressure epitaxy of silicon, a model of impurity trapping by silane molecules in the boundary layer of the flowing gas is proposed to explain our experimen- tal results of autodoping as a function of the total pressure, the mole fraction of silane to hydrogen, and the growth tem- perature. The autodoping factor defined as the degree of the trapping is calculated numerically for different conditions by using physical parameters in the kinetic theory of gases.

Experimental results on autodoping are compared with the theory.

I. Introduction

Although reduced pressure epitaxy (RPE), in which autodoping is extremely suppressed, is applied for fabricating thin crystalline films of silicon necessary for very large scale integrated circuits, theoretical treatments of the small autodoping have been scarcely carried out in terms of physical parameters. While Pogge et a1 suggested that the probability of escape of impurity atoms evaporated from buried layers in a substrate and from a susceptor across the boundary layer of the gas should be increased with the decrease of the total pressure in a reactor, the theoretical dependences of autodoping on the total pressure, the mole fraction of silane to hydrogen, and the growth temperature have not been analysed definite- ly. [11 This paper describes the first trial in the theoretical analysis of autodoping in RPE by using physical parameters in the kinetic theory of gases. Autodoping during the film growth is explained by using a simple model of the discontinuous distillation step. The theory is compared with our experimental results on auto- doping for different conditions in RPE of the pyrolysis of silane.

Experimental results by many workers show that autodoping is remarkably suppressed by reducing the total pressure, PT, to about

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982512

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100 Torr which is not so low comparing with the atmospheric pressure.

[2,3,4] For 100 Torr and 1000°C, the mean free path of impurity atoms, arsenic (As) in this case, is as small as the order of 10'+cm.

On the other hand, the thickness of the boundary layer, 6 , in ordi- nary conditions is estimated to be 0.1-1 cm by the Eversteyn theory-

[5] and 1-10 cm by the usual theory [6], which are much larger than the above value of the mean free path, resulting the small escaping probability of As atoms beyond the boundary layer, about exp(-1000).

This paper is due to solve the ab'ove ploblem.

11. Experimental

Experiments of dependences of autodoping without a doping gas on the total pressure, P+, the mole fraction of silane to hydrogen, F, and the growth temperature, TI were carried out in a horizontal type reactor by using substrates the buried layers of which were formed at the centers of the front surfaces. Different substrates of p-type 10-20~crn (111) surface and n-type 4 - 6 w m (100) surface were used. The total pressure was ranged from 50 to 300 Torr and adjusted by varying the gas flow rate of the outlet under a constant flow rate of the inlet. The growth temperature was from 880 to 1130OC. The mole fraction of silane to hydrogen was from 1 X 10-sto 4x10') by varying the flow rate of silane or hydrogen, where the silane gas was diluted to 20 % by hydrogen. The growth rate was from 0.28 to 0.32 fim/min at different values of PI , when the flow rate of hydrogen in the inlet was 110 SLM (Standard Liter per Minute), the value of F 2.7 ~ 1 0 ' ~ , and T 1050°C. The thickness of films was controlled to

Distance from Buried Layer (mmf

Fig.1 The impurity concentration vs. the distance from the buried layer

equal distances from the center of the buried layer and decreased with the increase of the distance away from the center in all radial

directions as shown in Fig.1. With the decrease of T below 980.C and the increase of F above 3.3X10-4, the impurity concentration at a position in the downstream of the flow was larger than that of the corresponding position in the upstream. The above results indicate that autodoping in our case is not due to evaporation of As from the back surface of the substrate and the surface of the susceptor, but due to that from the buried layer in the front surface, where careful preback was carried out before each growth experiment. The surface impurity concentration, q , vs. the total pressure, P+, for F = 2.7

X loa3 and T = 1050°C are plotted in Fig. 2 for different positions of different films, 2 p m thick, fabricated at different total

pressures, where the values of a- in arbitrary unit are normalized to those at 300 Torr. The growth rate, G, was increased slowly with increases of PT and TI and was proportional to F in our experimental

ranges.

General features of autodoping in RPE were as follows ; Autodoping is, (i) decreased with the decrease of PT, when F and T are constant, (ii) decreased with the increase of T, when

I

2 ~ m thick creased slightly with the decrease of

F, when T and PT are constant.

r\ *

111. Theoretical

In order to explain experimental data, we propose the following model : 1) The volume concentration of As atoms in the near-surface

k

5 6 t a

im-

0

layer of the substrate, Ns, is equilibrium with the As density in the gas of the interface, nl. We assume the thickness of the solid layer of equlibrium to be l/a as shown later. 2) From the substrate surface, As atoms diffuse out into the boundary layer, colliding with hydrogen molecules ( H a ) without reaction. 3) Silane molecules (SiH4) diffuse to the silicon surface and combine with As atoms during the travel in the boundary layer, resulting the growth of autodoped crys- tal. 4) Arsenic atoms escaping beyond the boundary layer/or the stagnant layer are less effective to autodoping, and only As atoms trapped in the boundary layer play a role to doping of the grown crystal because of the gas flow in the external region of the boundary layer. The above model is sketched in Fig.3. The diffusion of As atoms in the gas is similar to that of minority carriers in semi-

60 100 200 400

t,

^,

positions. The curve is the theoreti- cal one. obtained by using Eq. (12) for

a = 25 pm'' and 6 = 0.35 cm. where the gas temperature, TQ, is 1000°C and the value of F 2.7 x 10'~ .

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Fig.3 A schematic diagram of the behavior of As atoms near the boundary layer the thick- ness of which is shown as 6 . the boundary layer is defined as

conductors. The collision of As atoms to Ha molecules and the trapping time by SiH+ molecules in the former correspond to the scattering of minority carriers by lattice vibration and the life time due to recombination in the latter, respectively.

From the above model, the behavior of As atoms in the gas is given by,

where nl is the density of As atoms in the gas, D12 the mutual dif- fusion coefficient of As atoms in Ha gas, and T t d the trapping time of As atoms by SiH+ molecules. Here subscripts 1, 2, and 3 denote As, Ha, and SiH+ , respectively. The autodoping factor, A, which corre- sponds to the degree of trapping of As atoms by SiH4 molecules in follows ,

where x is the distance in the direction from the interface to the gas and nrgo the density of As atoms in the gas at the interface.

Because of exsistence of the density gradient of SiH4 gas [51, z w in the boundary layer may be approximately given by,

where Ti3 is the constant value for the external-region out of the boundary layer. When Tq3is approximated as 2 T 4 3 , the value at x = 6/2, the diffusion length of AS atoms in the gas, L, is given by,

Under the boundary conditions that f (0) = 1, f(oo) = 0, and f (x) is uniformly continuous at x = 6 , f(x) is given by,

f(x) = a.exp(-x/L) + (1-a).exp(x/~), f o r x S 6 , ⁽⁶⁾

= 2a/(1+ VT).exp(- 6 / ~ ) exp[-(x-b)/(L/\/Z)I, for x>b,(7) with

For (L/ 6 ) < ^{1; f} (x) is approximated as exp (-x/L) in the boundary layer, x 5 6 . The error in calculated values of A in Eq.(2) is

approximated as follows,

where (vz/vq l2 = mt /me and nl<njap, vt and vn are the mean thermal velocities of As atoms and Ho molecules, respectively, rl ,.re and r3 the radii of As atoms and Ho and SiH+ molecules, respectively, and mi , ^m2 , and mg their masses, res ectively. We use the following values of radii ; rr = 1.4 1, ra= 1.2 1, ^{and r3= 3 1.} [8,9] In order to obtajn curves of A vs. PT, different curves of A vs. b are shown in Fig. 4, which are calculated by using Eqs. (2) , ^{(5), and (6), for}

F = 2.7X10-3, and for different values of diffusion length, L. We assume that the gas temperature, Tq, is uniform near the boundary layer and 50°C lower than the growth temperature, T. In Fig.4, are designated on the curves different values of L which is inverse- ly proportional to PT@, shown in Eq.(9), and is shown the dashed curve of a strict solution by using Eq.(4) for reference.** Fig.5 shownscurves of A vs. Pr obtained from Fig.4 for different values of 6 in the vicinity of A = 1.

We shall discuss autodoping in relation to the film growth according to an approximation of a series of discontinuous step. 1101 We assume that main source of autodoping is due to impurities in the buried layer. In the first step, a thin film of some thickness is deposited on the substrate and the dopant concentration of the first

Fig.4 The autodoping factor, A, vs. the thickness of the bound- ary layer,b, for different values of diffusion length of As

atoms in the gas, L. The calculation is carried out for T = 1000°C and F = 2.7X10-3. The dashed curve is due to the strict solution by using Eq. (4).

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0

- PT (Torr) -

film, NI , is given by,

where Nso is the concentration of As in the, solid thin layer at the near-surface and k a constant concerning with the growth rate, the solid-state diffusion coefficient of As during epitaxial growth, and the evaporation rate of As from the growing surface. In the geometrical progression to the i-th film, the dopant concentration, Ni, is given by,

In each step, the density of As atomsin the gas is assumed to be in equlibrium to the concentration of As in the one step layer of the near-surface, since in the solid layer an amount of evaporated As atoms is very small compared with the total amount of As atoms during the one step growth.

Eq. (11) is transformed to the following expression,

Fig.5 The autodoping N(Y) = ( ~ A I ~ N , ⁽¹²⁾

factor, A, vs. the

total pressure, PT, where y is the vertical distance from the for different values surface before the growth to the grown film, of 6. and Q a constant. since values of k and A

are smaller than unity, Eq. (12) shows the suppression effect of autodoping with the decrease of A according to a factor of AQY, where k may be independent of PT and F, and dependent of T.

From the equilibrium condition of As atoms between the gas of the interface and the thin layer of the solid, the thickness of the one step growth, 1 / a , in Eq.(12) may be equal to the solid-state diffusion length of As atoms in the time of the one step growth, Ls, in this discontinuous model. Therefore,

Where Ds is the anomalous solid-state diffusion coefficient in epitaxial growth and G the growth rate.

In our case, the following relation prevails according to our conditions of experiment and theory ; (The diffusion velocity of As atoms in the gas)a(The flow speed of the gas in the reactor) (The growth rate of epitaxial film)z(The solid-state diffusion velocity of As atoms)

* Under the condition of f (0) = 1 and ( a£/ ax)X,& = ^{0, the}

solution of f (x) behaves as cosh (x/L) for x 2 8 , and f (x) = 00

at x = 0 0 , that is unreasonable. Even in this solution,

£(XI" exp(-x/L) for x 1 8 , when (L/b )el.

** We calculated Eq.(2) by using the numerically strict solution of Eq.(l) with Eq.(4) under the condition of uniform continuity at x = 8 , where f (x) behaves as the exponential decay for x 2 6 . The error is very small in using Eq. (5), when we compare the corresponding solid curve with the dashed one calculated from the strict solution of Eq.(4), as shown in Fig.4.

vs. the total pressure shown in ~ i g . 2 with the theory. In the approximation of the discontinuous step growth, OC in Eq.(13) is estimated to be 25 pm-1, when we use Ds = 2 X10~~crn~/sec, which is about a hundred times larger than the normal one [11,121, and

G = 0.3 pm/min. The value of 8 is obtained as 0.35 + 0.04 cm, when we fit the experimental data of Fig.2 to the theoretical curves

such as those shown in Fig.5 with the use of Eq.(12). In Fig.2, a theoretical curve corresponding to that d = 25 pm-1 and b = 0.35 cm is shown for reference.

In the usual theory of the boundary layer [6], the thickness of the layer is given by,

where )A is the viscosity, z the position in the direction of the flow,pthe density of the gas, U the velocity of the flowing gas.

In the experiment of w vs. P r , bis probably unchanged in varying Pt, since p U in Eq.(14) is constant under our experimental conditions.

Although the dependences of autodoping on F and T are rather complicated to analize because of the changes of 6 and a with the change of F and T under our experimental conditions, general

characteristics are explained in terms of L , 8 , and a as a function of F and T. In the first approximation, the general features of autodoping are qualitatively described by the change of L which is increased with the decrease of F and the increase of T, when we assume that the values of 6 and a are not so much changed.

When the model is confined in the approximation of the discon- tinuous step growth, the solid-state diffusion is considered only as supplying As atoms from the inner part of the layer of the one step to the surface emitting As atoms, so that the concentration of As should be uniform everywhere in the one step layer. A more detailed and dynamic theory containing the solid-state diffusion from the one step layer to the next one during evaporation of As will be presented in future to explain the experimental results more perfectly.

V. Acknowledgments

The authors are indebted to Messers K. Kikuchi, T. Komeda, Miss Y. Yoshioka, and Dr. H. Sato in Matsushita Electric Industrial Co., LTD. for experiment, calculation, and discussion. Thanks are also due to Prof. T. Ogawa in Gakushuin University, and Dr. J. Chikawa in NHK Technical Research Laboratories for discussion.

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