Journal of Electronic Materials, Vol. 17, No. 3, 1988

A Complete Quantitative Model of the Isothermal Vapor Phase Epitaxy of (Hg,Cd)Te

ZORAN DJURIC, ZORAN DJINOVIC and ZARKO LAZIC

Institute for Chemistry, Technology and Metallurgy, Njegoseva 12, 11000 Belgrade, Yugoslavia

JOZEF PIOTROWSKI

Institute of Plasma Physics and Laser microfusion, Kaliskiego St. Warsaw 49, Poland

A quantitative model of isothermal vapor phase epitaxy is proposed. It can be applied to both closed and open tube systems. This model enables the prediction of compositional profiles of the layers grown by isothermal vapor phase epitaxy with dependence on the growth parameters and thermodynamical data of the (Hg,Cd)Te system. The depen- dence of compositional profiles of the ISOVPE layers on temperature and time of de- position, source to substrate spacing, mercury and inert gas pressures are discussed for both solid and liquid sources. Modification of the compositional profiles by the post- growth annealing has also been studied. The proper choice of growth and annealing parameters makes the optimization of the profiles possible. The calculated profiles are compared with the experimental data and a satisfactory quantitative fit is found in most cases. The possible reasons for remaining discrepancies are discussed.

Key words : Model, ISOVPE, (Hg,Cd)Te

1. INTRODUCTION

Isothermal vapor phase epitaxy (ISOVPE) has be- come an important method of growing device qual- ity (Hg,Cd)Te layers. 1-7 Since this method in its conventional form produces graded gap structures, a careful selection of compositional profiles is re- quired to achieve optimized performance for any specific IR device. Until now, the compositional pro- files of the layers grown by the ISOVPE have mostly been determined experimentally in dependence on the growth parameters, s-ll The data delivered by various workers have exhibited significant discrep- ancies.

Theoretical calculations of compositional profiles of the layers have been difficult since the ISOVPE is a mutually coupled combination of two processes: the gas phase transport of tel lurium and mercury from the source to the substrate and the interdif- fusion of the components in the growing layer. A futher complication arises from a strong composi- tional dependence of the interdiffusion coeffi- cient. 12-13

Zanio and Massopust 12 presented an iterative nu- merical procedure for generation of compositional profiles of the (Hg,Cd)Te layers obtained by depo- sition of Hgl_xCD~Te onto CdTe substrates. They assumed that the composition at the surface of the growing layer and the composition of the deposited material are the same. This procedure enables one to calculate the compositional profiles, providing the composition of deposited material and the deposi- tion rate are constant and their values are a priori known.

(Received S e p t e m b e r 21, 1987; rev i sed D e c e m b e r 16, 1987)

0361-5235/1988/1401-22355.00�9 A1ME

In a typical ISOVPE, however, the surface com- position and the deposition rates vary significantly during the process. The mole fraction of CdTe at the surface of the growing layer remains significantly higher compared to that of the deposited material. Both values are to be determined as a function of the growth parameters.

Recently we presented a quantitative model of ISOVPE14 considering the process to be a combi- nation of tel lurium gas phase transport limited de- position of HgTe and interdiffusion of components into the growing layer. In this paper we report a further generalization of the model, obtaining full dependencies of the layer properties on the mercury pressure including the case of the liquid Hgi_yTey sources. We discuss here also the temperature and time of deposition, as well as source to substrate spacing (d) influence on the composition and the thickness of the ISOVPE layer.

2. ISOVPE THEORY AND MATHEMATICAL MODELING

The growth system is schematically shown in Fig. 1. It is composed of parallel source (Hgl_yT%) and substrate (CdTe or Hgl_xCdxTe), with the interspace filled with mercury vapor and, possibly, with inert gases. The deposition temperature, source to sub- strate spacing and partial pressures of mercury and inert gases are independent parameters, which are kept constant during the growth process.

The deposition process can be divided into follow- ing steps:

i) evaporation of the source, releasing Hg atoms and Te2 molecules.

223

224 Djuric, Djinovic, Lazic and Piotrowski

0

Cdle SUBSTRAI'E

F x(o)

Hgl_?y SOURCE

Fig. 1 - - The geometry of the ISOVPE system.

d

A ii) transport of Hg atoms and Te2 molecules in the

gas phase from the source to the substrate, iii) the formation of the Hgl_xCdxTe at the sur-

face of the growing layer, and iiii) interdiffusion of the components into the layer. i) If the pressure of the mercury over the source

is kept within the existence region of the solid HgTe at a given temperature (line AB in Fig. 2), the source HgTe remains solid and it evaporates dissociatively according to the reaction:

HgTe ---> Hg + 1/2 Te2 (i)

If the Hg pressure is higher or lower compared to the relevant borders (points A and B in Fig. 2) of the existence region of the solid HgTe, the source becomes a mercury or tellurium rich Hgl_yT% liq- uid. The use of the mercury-rich sources is imprac- tical because of the excessive mercury pressures, so only Te-rich liquid sources are considered.

ii) Since the tellurium partial pressures over a solid Hgl_xCdxTe are at least three orders of magnitude lower compared to the pressures of mercuryJ T M the transport of tellurium from the source to the sub- strate in the gas phase is the factor which deter- mines the deposition rate of HgTe. The driving force of this transport is the difference in equilibrium partial pressures of tellurium over the source and the growing layer. The process can proceed only if the pressure of tellurium over the source is higher compared to the one over the substrate. For exam- ple, when solid (Hg,Cd)Te source is used, the layer surface composition x can never exceed the source composition, since the pressure of tellurium over solid Hgl_xCdxTe (for fixed temperature and mercury

100

1.0

01 0.9 1.0 1.1 12 13 IO00/T, K -1

Fig. 2 - - The schematic representation of Hg ature diagram of Hgl-xCdxTe.

~Hgl- x Cd x Te

pressure-temper-

pressure) decreases with x. However, in the case of the solid HgTe source, any layers with 0 < x < 1 can be grown.

Under isothermal conditions, the tellurium is transported by the diffusion of Te2 molecules in the ambient of much more concentrated mercury va- pors and, possibly, inert gases. In such conditions, the pressures of the main components remain con- stant in the growth chamber, while the partial pres- sure of tellurium decreases in the direction towards the substrate. The tellurium diffusion limited de- t)osition rate of HgTe can be calculated 14 as:

V ---- 2Dwe[pSe - - pLe]/kTNd (2)

where , Die is the diffusion coefficient of tellurium in the gas phase, pS and p~ are pressures of tel- lurium over the source and the layer surfaces, N is the concentration of Te atoms in solid HgTe (ap- proximately equal to the concentration in the Hgl-xCdxTe). In further calculations it is assumed that the deposition proceeds in near equilibrium conditions, therefore p~e and pL e are equal to the equilibrium pressures of the tellurium over the source and the surface of the growing layer. The diffusion coefficient of tellurium in a gas mixture of Te, Hg and//2 is: 17

Dwe = (1 - f)/(Zfi/D~e) (3)

where f and f / a r e the mole fractions of tellurium and i-th component of the mixture, D~ is the dif- fusion coefficient of tellurium in a binary mixture of tellurium and i-th component of the mixture. D~e can be calculated according to the standard rigid elastic spheres model: 17

D~ = [4/(3V2)]*(kT/~) 3/2

*(1 /mwe + 1/mi)l/2/[p(rwe + r/)] 2 (4)

Quantitative Model of the Isothermal Vapor Phase Epitaxy 225

where mwe, mi, rTe and ri are respectively atom (or molecule) weights and effective radii of tel lurium and i-th component, p is the sum of all partial pres- sure components. These values can be taken from the handbooks, or they can be calculated from the molar volumes at critical, melting or boiling points. 17 Substituting the proper values to Eq. (3) and (4), the expression for the diffusion coefficient of tellur- ium in a mixture of tellurium, mercury and hydro- gen, with partial pressures Pie, PHg and PH2, respec- tively, is:

Dwe = [2.17"10-4T3/2]/(1.66 Prig + 0.131 PH2)

(Dwe in m2/sec, T in K, p in Pa) (5)

For mercury vapor, partial pressures within the existence region of HgTe (line AB in Fig. 2), ac- cording to the mass action law, are:

s PTe ---- P T e ( 0 ) ---- K2(0 g

p L e ---- PWe(X) : K2(x)//p2g ( 6 )

(7)

The expression for deposition rate of HgTe can be obtained substituting (6) and (7) to (2):

V ---- 2 D w e [ g 2 ( 0 ) - K2(x)]/dkTNp~g ( 8 )

K2(x) can be calculated from thermodynamical data of Hgl_~CdxTe. 15-1~

K2(O)[Pa 3] = 1.51 "1033 exp ( -40904 /T) (9)

Ke(O) - K2(x)[Pa 3]

= 1.51 "1033 exp ( -40904 /T)

*[1 - (1 - x) 2 exp ((4325/T

- 3.598)x2)] (10)

Since K2(0) - K2(x) is an exponential function of temperature, the deposition rate of HgTe, when mercury pressure is fixed (line DE in Fig. 2), will strongly increase with temperature.

For a given temperature (line AB), the deposition rate depends strongly on mercury pressure, v

- 3 -1 Prig, a s Die -- Prig (for H2 and Hg + H2 mixtures), except for the case when Prig < PH2 ~ 10prig (see Eq. 5).

The maximum deposition rate is achieved when the mercury pressure is close to the pressure at the boundary of the existence region of solid, Te-rich HgTe (point B in Fig. 2). At this point the source is two-phase (solid + liquid) mixture, while the layer of solid Hgx_xCdxTe can grow at a maximum rate, since pT~(0) - PWe(X) reaches its maximum value. The temperature dependence of the growth rate for a two- phase source (line BD) is weak compared to the solid HgTe source, as the increase of K2(0) - K2(x) with temperature is largely compensated by the increase in the mercury pressure, thus making the differ- ence in tel lurium pressures weakly dependent on temperature.

When the mercury pressure drops below the point B (line BC in Fig. 2), the source becomes the liquid Hgl_yTEy with y > 0.5. The pressure of tel lurium over liquid Hgl_yTey source in dependence on mer- cury pressure Prig was calculated using the proce- dure similar to that used by Vydyanath.

PWSe = [1 - 0 20 PHO/( ~/PHg) ] PTe (11)

where y is the mercury activity coefficient, pO e and pOg are the pressures of free tel lur ium and mercury. According to: 15-16

logp~ = -5960 .2 /T + 4.7191 (12)

log p~ = - 3 0 9 9 / T + 4.920 (13)

The value of 7 was calculated taking into account that the pressure of tel lurium at the border of the existence of the solid HgTe and tel lurium rich liq- uid Hgl_yT%, calculated using Eqs. (6) and (11), should be the same. As Eq. (11) shows, the equilib- rium pressure of tellurium over liquid Te-rich source weakly increases with decreasing mercury pres- sure, reaching eventually the value of the pressure over free tellurium. The equilibrium pressure of tel- lurium over the growing layer continues to increase with decreasing mercury pressure, resulting in a decrease in the difference of pSe(0) - pL(x) . Con- sequently, at low mercury pressure, the deposition rate decreases with decreasing mercury pressure. The minimum CdTe mole concentration of the layer which can grow at low mercury pressure is set by the condition that the equilibrium pressure is set by the condition that the equilibrium pressures of tel- lurium over the layer and source are the same. Ac- cording to (7) and (11):

( o 2 o K2(x)/p~g = [1 - Pc, g~ YP~g)] Pre (14)

If the pressure of mercury drops below the bound- ary of the existence region of the Hgl_xCd~Te (be- low the point C in Fig. 2), the Hgl_~CdxTe substrate or previously deposited layer of this composition melts.

The discussion explains the peculiarities of ISOVPE observed experimentally at low mercury pressure. T M

iii) At the surface of growing layer, the incident Hg atoms, Te2 molecules and solid CdTe present there react according to the reaction:

(1 - x)(Hg + 1/2 Te2)

+ x CdTe --~ Hgl_xCdxTe (15)

iiii) The CdTe which is required to fulfill Eq. (15) is transported to the surface of the growing layer by interdiffusion of Cd and Hg, mainta ining a high x-value at the surface.

The interdiffusion of Hg and Cd in the growing layer is described by Fick's second law for the com- position dependent diffusion coefficient, with boundary and initial conditions:

226 Djuric, Djinovic, Lazic and Piotrowski

ox ox - - - v - (16) Oz Oz at

D(x)(ax/az) = v x(O,t) z = 0 (17)

x(%t) = 1 (18)

x ( z , O ) = l z > 0 (19)

where x(z,t) is the position and t ime dependent com- position, z the position calculated from the surface of the growing layer, D(x) the composition depen- dent interdiffusion coefficient. The term - a x / O z in Eq. (16) reflects the selection of a moving coordi- nate system with z = 0 at the layer surface (see Fig. 1).

From (2) and (17):

D(x)(ax/Oz) = (2Dwe/dkTN) [pTSe -- p L e ] X ( O , t ) (20)

Equations (16), (18), (19) and (20) enable the cal- culation of the compositional profiles x(z) as a func- tion of temperature, t ime and mercury pressure, provided that the D(x) is a known function of com- position and temperature.

Zanio and Massopust ~2 obtained an expression for the diffusion coefficient:

D(x ,T) [ftm2/sec] = 3.15"101~ -315x

exp [(-2.24"104)/T] (21)

Recently Tang and Stevenson ~3 reported experi- mental studies of interdiffusion coefficient. They found no mercury pressure dependence of D(x ,T) at temperatures of interest for the ISOVPE (>400 ~ C). Their values a r e close to the ones of Zanio and Mas- sopust for low x, but they are almost an order of magnitude lower for high x.

Equation (16) with initial (19) and boundary (18), (20) conditions are solved numerically, using the method of finite differences. D(x,T) was taken from. ~3

3. N U M E R I C A L CALCULATIONS, A N A L Y S I S O F O B T A I N E D R E S U L T S

A N D C O M P A R I S O N T O T H E E X P E R I M E N T A L D A T A

The calculations were performed mostly for a temperature of 500 ~ C, which was often used in our laboratory to grow (Hg,Cd)Te layers for an un- cooled detector of 10.6 ftm radiation. Figure 3 shows calculated compositional profiles of the layers for various deposition times and for mercury vapor pressure equal to the equilibrium pressure at the border of existence of tellurium-rich solid HgTe. The calculated compositional profiles have the typical shape observed by numerous workers. As Figs. 3 and 4 show, the layer thickness increases with time, but the deposition rate decreases as a result of decreas- ing x-value at the surface. The surface x-value for long deposition is close to, but always higher than 0. An increase of source to substrate spacing (Fig. 5) results in decreased layer thickness and in- creased surface composition due to decreasing tel- lurium transport rate.

Figure 6a and 6b shows the influence of mercury pressure on layer properties for different tempera- tures of deposition. For pressures higher than the equilibrium pressure at the point of coexistence of solid HgTe and liquid, Te rich Hgl_yTey, the thick- ness decreases and surface composition increases with increase of mercury pressure. The opposite is true for low mercury pressure. Therefore the max- imum deposited rate is achieved at these specific mercury pressures. The min imum surface compo- sition increases with deposition temperature. These results agree well with experimental findings of Becla; 3-4 however, a quanti tat ive comparison is not possible, since the source to substrate spacing was not specified in these papers.

Figure 7 illustrates the influence of the postde- position annealing on layer profiles when the de-

The Eq. (16) was wri t ten as: 10 I1

X; +1 = [D(x}) + (Av)/2](At/A2)x]_l [

+ [1 - -2D(x])(At /k2)]x} + [D(x]) 0.8 J

- (kv)~2](at(;2)X,+l • " 0.6

+ At[x)+t - x j _ 1] *[D(x ]+I ) 8

- D(x]§ 2 (16') - - x

0.4 O

and the boundary condition (17) as:

n+l n+l n+l n+l V / / / ~ ~ . 7 1 ~ s D(x. )[ ] (17') = , xx l - X o / A = V X o 02

Here j describes the division of the z-axis (A = zj -- Zj_ 1 is the step), and n the division in t ime (At is 0 5 1'0 1'5 2'0 2'5 30 time interval, therefore in the n-th moment t = nat). TH,CKNESS , (urn Equations (16'-17') were solved for different tem- Fig. 3 - - The calculated compositional profiles of layers grown peratures, pressures and source to substrate spac- by ISOVPE at 500 ~ C for different deposition times. Prig = 0.18 ings. atm, spacing 5 mm.

30

20

0.08 T = 773 K ~j= 0.18 otm

x 0.06 T = 20

o {"-- (D

0.04 -v- ~E o 10

0.02

TIME , h

Fig. 4 - - The calculated surface composition and thickness of the layers grown at 500 ~ C as a function of deposition time. prig = 0.18 atm, spacing 5 mm. Our experimental data for 21 h depo- sition time is also denoted.

position of HgTe is suppressed. It can be achieved, for example, by increasing mercury pressure (see Eq. 8). The calculations have been performed using Eqs. (16'-17') and assuming indicated different mercury pressures for the deposition and for the anneal step of the process. The interdiffusion of the components during annealing changes the shape of the compo- sitional profiles, making them more flat at the sur- face and within most of the layer, while the thick- ness is almost not affected. This feature is a result of the strong compositional dependence of the in- terdiffusion coefficient; the interdiffusion at the low x-value surface region of the layers is much faster compared to the high x region close to the interface with the CdTe substrate. This makes it possible to grow thin layers with a low compositional gradient, which are required for most applications. The rate of the changes of the compositional profiles is quite fast at the beginning of annealing, and decreases as the annealing proceeds. The decrease of the rate of change is caused by the decrease of the interdiffu- sion coefficient with increased x-value. We often ob- served such changes due to unintentional annealing during the postdeposition cooldown procedure which,

\ T : 773 K ~ ~ ~5 L o.lo \ ~r o18 o,m . / "

x T= I h Io ~ g _o

0.05

0 10 20 30

SPACING , m m

Fig. 5 - - The calculated surface composition and thickness as a function of source to substrate spacing. Temperature of deposi- tion 500 ~ C, prig = 0.18 atm, and deposition time 1 h.

m s ~

300 350 400 ,~50 0'61 \ \ 773 K ' 823 ' 873K

0,l i ' / / / I t V ~ I

t /',, / / /~ ~ / \ / / \ / /

~176 0.2

O.l/ t / v r : l h

L I~k// d = 5 mm

1.90 1.80 1.70 1.60 1.50 l.Z,,O 1.30 IO00/T , K "I

15

E= 1 h 873 K

d= 5mm A

823 K / ~

E

" 10

z

:2z

5

Quantitative Model of the Isothermal Vapor Phase Epitaxy 227

I~0 IBO 1.70 1.60 150 t~O 130 IO00/T, K -1

Fig. 6 - - Calculated surface composition and thickness as a func- tion of mercury pressure (free Hg source temperature) for dif- ferent temperatures. Deposition time 1 h, distance 5 mm. The dashed curves denote the surface composition for an infinite de- position time.

if not fast enough, can seriously alter the initial compositional profile.

In Figs. 4 and 7 some of our experimental surface compositions and thicknesses of layers grown in a two zone open system 7 are denoted. The calculated and experimental thicknesses agree well, while the surface compositions agree only for layers subjected to the postgrowth anneal. The higher experimental surface compositions of layers, which have not been intentionally annealed, are probably caused by con- trolled annealing during the cooldown procedure.

The comparison of theoretical calculations with

228

tO

T=773 K f ~

II I I • 0.8 d= 5 mm / / / /

- 0.6

J -~0.4 8

0.2 ~

THICKNESS , (urn

Fig. 7 - - The calculated compositional profiles of layers grown at 500 ~ C for different postdeposition annealing times. Deposi- tion time 1 h, mercury pressure 0.18 atm, spacing 5 mm. The mercury pressure during the postdeposition anneal was 1 arm.

reported data is possible only for experiments with properly controlled growth parameters. Most of the experimental profiles published to date, however, were obtained for one thermal zone, closed ampoule approach. As it was shown by Bailly e t a l . , ~9 with such a system, the actual mercury pressure depends both on the stoichiometry of the HgTe source and the source to free space volume ratio. It also varies in time. This is probably the reason why the results reported by various groups exhibit significant dif- ferences. Reproducibility problems can be solved us- ing one of the following stabilized mercury pressure systems: two zone system with free mercury in the colder zone, 4 two phase (solid + liquid) system, 7 or constant composition liquid source systems. 3

In Fig. 8 calculated and experimental composi- tional profiles of a layer grown at 550 ~ C for 24 h are displayed. The last experimental profile was re-

1.0

08

• 06

i 0 . 4

8 0.2

T= 823 K ~.~ 0.6 otto Z"= 24 h

d= 30 rnm ( 10 20 30 40 50 60 70 80

THICKNESS, (urn

Fig. 8 - - The calculated (1) and experimental (2) compositional profiles of the layer grown at 550 ~ C. Time of deposition 24 h, spacing 30 mm, mercury pressure 0.6 atm. Experimental profile was taken from 11.

Djuric, Djinovic, Lazic and Piotrowski

ported by Fleming and Stevenson. 11 They grew the layer in a closed ampoule system, using a HgTe source and with no excess mercury. Although the mercury pressure was not specified, it is expected to be stable and equal to the equilibrium pressure at the boundary of the existence region of solid HgTe, since the source in this experiment was partially molten. This is due to the large source to substrate spacing used, and a high ratio of free volume to the source volume. 7 A value of 0.6 atm was used in a theoretical calculation of the profile. This value was based on published results. 15-~6 A satisfactory agreement can be seen taking into account 15% composition errors reported. The experimental thickness is slightly lower, and surface composition is higher compared to the calculated values.

We frequently observed a significant decrease in layer thickness and decrease in surface composition when the source or substrate surface was oxidized. This readily happens in the closed ampoule ISOVPE, when no hydrogen containing gas mixture is used. The complete agreement between the calculated compositional profile and the data from Ref. 11 can also be achieved taking the mercury pressure to be 0.65 atm instead of 0.60 atm.

It should be pointed out that the theoretical pro- files were obtained without use of any fit t ing pa- rameters. The proposed model is capable of explain- ing quantitatively many features of the [SOVPE and can be used for the design of the growth procedures. The model can also be applied to the case of liquid Hg-Cd-Te sources, (Hg,Cd)Te and (Cd,Zn)Te sub- strates.

R E F E R E N C E S

1. S. H. Shin and J. G. Pasko, Appl. Phys. Lett. 44, 423 (1984). 2. E. R. Gertner, S. H. Shin, D. D. Edwall, L. O. Bubulac,

D. S. Lo. and W. E. Tennant, Appl. Phys. Lett. 46, 851 (1985). 3. P. Becla, L. Lagowski, H. G. Gatos and H. Ruda, J. Electro-

chem. Soc. 128, 1171 (1981). 4. P. Becla, L. Lagowski, H. Gatos and H. Ruda, J. Electro-

chem. Soc. 129, 2855 (1982). 5. P. Becla, J. Vac. Sci. Technol. A4, 2014 (1986). 6. T. L. Koch, J. H. de Loo, M. N. Kalisher and J. D. Philips,

IEEE Trans. ED-32, 1593 (1985). 7. J. Piotrowski, Z. Djuric, W. Galus, V. Jovic, M. Grundzien,

Z. Djinovic and Z. Nowak, J. Cryst. Growth 83, 122 (1987). 8. G. Cohen-Solal, Y. Marfaing, F. Bailly and M. Rodot, Compt.

Rend. 261,931 (1965). 9. O. N. Tufte and E. L. Stelzer, J. Appl. Phys. 40, 4559 (1969).

10. J. Piotrowski and S. Wojciechowski, J. Electron. Technol. (Warsaw) 12, 79 (1979).

11. J. G. Fleming and D. A. Stevenson, J. Cryst. Growth 82, 621 (1987).

12. K. Zanio and T. Massopust, J. Electron. Mater. 15, 103 (1986). 13. M. F. S. Tang and D. A. Stevenson, Appl. Phys. Lett. 50,

1272 (1987). 14. Z. Djuric and J. Piotrowski, Appl. Phys. Lett. 51, 1699 (1987). 15. T. Tung, C. H. Su and R. F. Brebrick, J. Vac. Sci. Technol.

21,117 (1982). 16. C. H. Su, P. K. Liao and R. F. Brebrick, J. Electrochem. Soc.

132, 942 (1985). 17. A. N. Matveev, Molecular Physics (in Russian). Ed. "High

School," Moscow (1981). 18. H. R. Vydyanath, J. Appl. Phys. 59, 958 (1986). 19. F. Bailly, L. Svob, G. CohenoSolal and R. Triboulet, J. Appl.

Phys. 46, 4244 (1975).