Strain in thick epitaxial layers

Thin Solid Films 254 (1995)

ELSEVTER

?9%46

Strain in thick epitaxial layers K. Bickmann,

J. Hawk

Received 8 February 1994; accepted 7 July 1994

Abstract exhibit a strain ~~IO ’ < co < IO ’ r, is reached. The layers adhere to the substrates below T, and adopt different strains E” and E- parallel and perpendicular respectively to the substrate. The T, and E” v,llues often vary on annealing above 160-400 ‘C. The ratio -(E - t”)/(c” - E”) remains independent of temperature and annealing. Stable epitaxial layers with constant lo and T, values can be obtained in some cases by deposition on buffer layers or stepped substrates. Epit
Kq~~rr/.v:

Elastic properties;

Epitaxy;

Stress; X-ray diffraction

I. Introduction

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1

I

I

I

100

1000

I

1

\\ \

GaAsiSi(001)

I

I

0.1

1

10

0.04 _----_*

Epitaxial layers are usually strained because of different lattice parameters and different thermal expansion coefficients of the layer and substrate materials. Three main parameters have to be considered from a structural point of view: the thickness of the epitaxial layer, the misfit of lattice parameters between the layer and substrate and the thermal behaviour. Most important is the dependence of strain on the thickness of the layer, as outlined for GaAs/Si layers in Fig. 1 [ 11. The lattice parameters II, of the substrate and a, of the unstrained single-crystal layer material have a misfitf = (LI, - u,)/q, which is _ 0.04 for GaAs/Si. Very thin films of GaAs can grow coherently on Si with an elastic strain E” = ((I - ug)/qJ, parallel to the substrate interface given by the misfit ,f’= E”, while very thick films behave similarly to single crystals with very little strain, E“ 2 0 (Fig. I ). The strain E’ = (c - uo) /a,, perpendicular to the substrate interface is obtained from the lattice parameter c perpendicular to the substrate. The ratio cl/~” should be a constant value, which can be calculated from the elastic constants [l-4]. The critical thickness 11~ for coherent growth of thin films depends mainly on the misfit as given by different formulae [l-3] (Fig. 2). Misfit dislocations are formed at the interface between the film and the substrate above the critical thickness.

I

I

I

E 0.02

0

-0.02

-0.04

hlnm Fig. I Strain l” of GaAs layers parallel and strain t of GaAs layers perpendicular to the Si substrate for different thicknesses /I. Layers with /l < /r< grow coherently on Si [I].

Epitaxial films are usually obtained at temperatures of 400-l 000 ‘C. The mobility of the atoms of the growing layer must be high enough to reach the proper site on the surface. Very thin films growing coherently at the temperature T, of deposition are strained according to the misfit of lattice parameters [5, 61; very thick films grow unstrained with misfit dislocations between the film and the substrate. Fig. 3 outlines schematically

--__ k@ ___ _ __k

K. Bickmann, J. Hawk 1 Thin Solid Films, 254 (1995) 39-46

40

1

c

a0

a=a, _e--

_/-

_e--

Tt

L_l2tc

1

C

_e--

0.001

0.01

f

0.1

Fig. 2. Critical thickness h, of thin films for coherent growth on substrates with lattice misfit f according to the formulae of Fiory et al. [2] (curve a), Frank and van der Met-we, (curve b) and Matthews [3], (curve c).

Tc a5

a

1

L __--

the different thermal behaviours of thin films (Figs. 3(A), (B), (E), and 3(F) compared with thick films Figs. 3(C), (D), (G), and 3(H)). The lattice parameter a, of the unstrained thin film material, e.g. its value in a single crystal, can be larger than the lattice parameter a, of the substrate, as in Figs. 3(A) -3(D), or smaller, as in Figs. 3(E) -3(H). The lattice parameters change after deposition as the temperature is decreased to room temperature because of the thermal expansion coefficient r0 of the thin film material, is different from the thermal expansion coefficient CY,of the substrate. The thermal expansion coefficient q, can be larger than a,, as in Figs. 3(A), 3(C), 3(F) and 3(H), or smaller than a,, as in Figs. 3(B), 3(D), 3(E) and 3(G). The schematic drawings show that thick films become strained below T, as has been observed experimentally [7-121. The films can glide on the substrate, forming dislocations above T, and sticking to the substrate below T,. Therefore the lattice constant a, parallel to the substrate, contracts with the same thermal expansion coefficient as the substrate for T < T,. The increased lattice constants a, compared with ctO, have the same effect as a uniaxial compression on the thin film (which causes a decrease in c, an increase in a and a concave bending) of the thicker films (Figs. 3(C) and 3(H)). The decreased lattice constants a and increased lattice constants c are similar to a uniaxial tension in the c direction, which causes a convex bending of the thicker films (Figs. 3(D) and 3(G)). The strain corresponding to Figs. 3(A) -3(H) is shown in Fig. 4. The strain E” parallel to the substrate in thin films amounts to the temperature-dependent misfit f as shown in Figs. 4(A), 4(B), 4(E) and 4(F). The misfit dislocations 6 = (a, - ~“)/a, of thick films in Figs. 4(C), 4(D), 4(G) and 4(H) amount to the misfit f

a

a0

a= a, __-__-a0

/_____?_____!l)

a_,:cc 1

@as

il-’ C ___-_-_ __-- _-a

a0

Fig. 3. Lattice constants a of thin films parallel to the substrate, lattice constants c perpendicular to the substrate, unstrained lattice constants a, and lattice constants a,, of the substrate at different temperatures T, film thicknesses and thermal coefficients c( (see text). T, is the temperature of deposition, and T, the critical temperature of lattice distortion.

above T, and stay constant at lower temperatures. The misfit dislocations 6 can be calculated from the strain E” parallel to the substrate and the misfit f by f = 6 + 6”. A comparison of Figs. 4(A)-4(H) shows the corresponding cases Figs. 4(A) and 4(E), Figs. 4(B) and 4(F), Figs. 4(C) and 4(G), and Figs 4(D) and 4(H), which are symmetrical about the E = 0 line. Therefore only the cases in Figs. 4(A) and 4(B) for thin films and Figs. 4(C) and 4(D) for thick films are discussed below. The strain E” parallel to the substrate is positive in Fig. 4(C) and negative in Figs. 4(A), (B) and (D). A comparison of Figs. 4(A) and 4(C), which can belong to

K. Bickmcmn.

J. Huuck / Thin Solid Films. 254 (1995) 39- 46

2. Characterization

% ----__ &

techniques

----_

t 0

41

6

l-z f=&”

T

T!.

Fig. 4 Elastic strain E” parallel ( -) and elastic strain E’ perpendlculat- ( ~~ ) to the substrate at different temperatures T. film thicknesses and thermal coefficients x (see text). T, is the temperature of deposition. T, the critical temperature of lattice distortion, f the misfit of lattice constants and 6 the misfit dislocations.

thin dnd thick films of the same material with a, > a, and xc’> z,, shows that the strains in thin and thick films exhibits different signs [ 131. The strain t” is reduced on annealing of the film above 160-400 “C, which causes different misfit dislocations [7, 81 and eventually other effects such as: (a) the formation of cracks or blisters [7, 9, lo], (b) the formation of hillocks [14], (c) a planar rotation of the film on the substrate [ 151, (d) a rotation perpendicular to th,: plane [ 1 l] and (e) a decreased bending [7, 81. The formation of cracks or blisters [7, lo] and a rotation perpendicular to the plane [I I] at reduction of strain are outlined in the present investigation. Some physical properties, e.g. the electrical efficiency of solar cells, are affected by the strain and dislocation density and might change with temperature and time [9, 16, 171. Thick films with a frequent variation in the misfit dislocations 6 at varied temperatures will peel off from the substrate [7].

For a complete structural characterization of a single-layer heterostructure, the misfit between the layer and substrate material, the lattice constants in the plane and perpendicular to the substrate, the bending and a rotation or inclination must be measured independently at different temperatures. The lattice distortion and orientation of the thin films on the substrate (rotation or tilting) and the bending of the substrate has been investigated by X-ray diffraction (Biierger precession and the Bond method) at 255400 C for different samples of EuS/Si in the (111) orientation [ 71, GaAs/ Si( 001) [ 8, 91, InP/GaAs( 001) [ IO], (Al, Ga) As/GaAs (001) [5], (Ga, In)As/GaAs (001) [6]. CdTe(iii)/ GaAs(OO1) [ 111 and the double layers SrS/EuS/Si ( 111) and InP/GaAs/Si(OOl) [ 121. The epitaxial layers were 0.4-6.3 urn thick in order to obtain appropriate X-ray intensities of the film and substrate reflections within about 3 h at constant temperature. The half-width of the high quality thin films had to be less than _ 0.2” for accurate measurements. The measurements at 255 400 C in inert gas were extrapolated to higher temperatures, because of three major difficulties which arose at higher temperatures: ( 1) a reaction between the layer and the substrate or an evaporation of the layer material, (2) the increased half-width of the reflections and (3) overlap of the thin film and substrate reflections. The strain of the different samples was calculated in the present investigation and will be compared with the schematic drawings in Fig. 4.

3. Results The variations in strain with temperature of different epitaxial layers (Figs. 5, 6 and 7) are expected to be similar to those in Figs. 4(B), 4(C) and 4(D) respectively. The layers are deposited on the substrates at r, = 430-900 “C. The strain of the (Al, Ga)As and (Ga, In)As layers (Fig. 5) and of 500 nm EuS (Fig. 6) can be compared with Figs. 4(B) and 4(C) respectively. The Al, ,,,Ga,,,,As layer and 500 nm EuS layer are cubic at T,with the same lattice constants as observed in single crystals. The strains E Uand E ’ (broken curves) are identical at point A with E”= E” = E z 0. The other layers exhibit positive or negative co values for the virgin samples (point A) and different to values after the first or second annealing process (points B and C respectively). The positive (or negative) E” = E” = c ’ values at points A, B or C indicate an increased (or decreased) cubic lattice parameter of the thin film material compared with the values of unconstrained small single crystals. The 2.8 urn Al, ,,Gao,,,As layer [ 51. I .6 urn Ga,, jI In,, ji) As layer [6] and the 1. I urn CdTe layer ((I

1 Thin Solid Films, 254 (1995) 39-46

K. Bickmctnn, J. Hack

I

1000 2.6pmAl,,Ga,,,,AsIGaAs(OOl) E.106

2

I

1

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’

_-l.lpmCdTe (lll)/GaAs(OOl)

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Fig. 5. Four examples direction.

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(

500

for the variation

in strain

T/k

with temperature

1000

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500

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axis in Fig. 5) [ 1 l] growing as strained layers at T,. The small misfit .)‘= E” = -0.000 02 of the Al,,,Ga,,,,As layer on the GaAs substrate permits coherent growth at T, = 830 “C (Fig. 2). The strain increases on cooling to f = E” = -0.001 I, which is close to the limit for coherent growth (Fig. 2). The room-temperature strain E” =,f= -0.0016 of the 1.6 urn Ga,,,,In,,,As layer is even larger. These examples demonstrate the advantage of a high deposition temperature T, for coherent growth of the layers in Fig. 4(B). -__ The I .l pm CdTe layer with (111) orientation was deposited on GaAs(OO1) with a vicinal angle i of _ 2” [ 1 I]. The [ 1121 axis of the CdTe (a axis) is oriented in the [ 1 lo] direction of GaAs, and the [ ilO] axis of CdTe (h axis) in the [ 1011 direction of GaAs (Fig. 8). The misfit f’ = 0.007 of the lattice parameter u to the GaAs substrate permits coherent growth in the a direction (Fig. 2). The lattice parameters (2 and c approach the CdTe single-crystal value at 122 “C (point A in Fig. 5). In the h direction, however, with the large misfit fb = -0.128, the layer grows unstrained at T, and forms misfit dislocations below T, [ 1 l] similar to that outlined in Fig. 4(D). The strain E’ at point B in Fig. 5 is negative. Negative deviations co = E” = E’ at points A, B or C from the single-crystal value E” = 0 were also observed for GaAs (Fig. 6) and InP (Fig. 7) in single layers and

1000

TI'C

500

T/'C

to Fig. 4(B). The CdTe layer grows

1000

incoherently

in the h

in the InP/GaAs/Si double layer (Fig. 9). Positive E” values at points A, B or C were obtained for GaAs which was grown on Si with a vicinal angle i = 4’ [9], for EuS in single layers (Fig. 6) and in the SrS/EuS/Si double layer (Fig. 9). SrS of this double layer has a negative E”. The e0 values at point A increase after annealing at 160-400 C to point B or C in the EuS and GaAs layers A-C (Fig. 6). The increased co values are related to an increased relative volume AI’/ V z 3~“. The volumes of the GaAs and EuS samples increase further below points A, B, or C to as much as _ 1% in EuS at room temperature [7]. The increased number of misfit dislocations on annealing disrupt part of the bonding between the EuS and the Si layers. The layers peel off and form blisters or corrugations because of the increased volume [7]. The volume of InP layers is decreased by 0.2-0.5% at room temperature and can give rise to cracks [ lo]. Points B and C are at lower temperatures than point A because of the reduction in strain on annealing with the exception of the two GaAs samples A and C (Fig. 6). The GaAs samples A-C were grown on 30 nm ‘amorphous’ GaAs buffer layers which were deposited at the temperatures of point B [8]. These layers are stabilized with co 5 0 at point B and a defined strain at lower temperatures, which does not vary on further

/ Thin Solid Films. 254 (1995) 39~-46

K. Bickmnnn, J. Huud 1 (.108

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annealing processes. The strain of GaAs in the InP/ GaAs,‘Si double layer (Fig. 9) is still negative at point B but would be reduced to zero at - 460 “C, the growth temperature of the GaAs buffer layer. The InP top layer of this sample adheres to the GaAs layer below 500 C (point C), while the GaAs layer is still mobile on Si. Therefore the slope of E” (InP) changes at 300 C as the GaAs layer adheres to Si (points A and D in Fig. 9). The SrS top layer of the SrS/EuS/Si double layer stays mobile below 380 “C (point A in Fig. 9) where the 400 nm EuS layer becomes distorted. This temperature is between 309 C and 490 C for the 425 nm and 500 nm EuS single layers respectively. The 2.3 um GaAs layer on Si with a vicinal angle i = 4 was grown at 450-600 ‘C [9]. The initial 0.03 urn of the sample was deposited at temperatures close to point A in Fig. 6. The remaining layer grew coherently at increased temperatures. The steps in the vicinal plane

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temperature

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4. Conclusions X-ray diffraction measurements with a precision of Ad/d 2 10 m4(the Bond method) between room temperature and 400 C exhibit some details in the variation in strain in epitaxial layers - 1 urn thick. These layers should grow coherently at a lattice mismatch ,f’s 0.001 between layer and substrate and incoherently at 1arger.f’ values (Fig. 2). Figs. 4(A) and 4( B) outline the variation in strain for coherent growth, and Figs. 4(C) and 4(D) that for incoherent growth. The slope At”/ AT z x, - q, of the strain E” parallel to the substrate is negative (Figs. 4(A) and 4(C)) or positive (Figs. 4(B) and 4(D)) because of the different thermal expansion

K. Bickmann, J. Hauck / Thin Solid Films, 254 (1995) 39-46

44 1000

c-IO6

a-cos i = as f cos (i+6)

I I.,

3pm InP / GaAs (001)

..

I

I

I

1000

1

E.106 -

I

I

500

0 I

1

,

,

as

TI’C I

Fig. 8. Schematic presentation for the coherent growth of the a axis of CdTe ( 1 II) on GaAs(OO1) with vicinal angle i. The c axis of CdTe [ili] is tilted by 6 = 1.33’ at 400 “C and 1.44’ at 25 ‘C relative to GaAs [OOI] and by /I z 90.017-90.030” to the a axis. m = 5 steps of the CdTe layer with step height d + Ad correspond to four steps of C&As with step height d [Ill.

I

3.9pm InP I GaAs (001)

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--..

_looo:_ 1 -2000

t 0

Fig. 7. Two examples for the variation according to Fig. 4(D).

loo0 I

2pm InP / O.$m

GaAs/

Si (001)

i 500

Tl’C

in strain with temperature

[IO]

coefficients X, and a, of the substrate and thin film materials. The use of strain instead of lattice constants shows a close relation between the corresponding pairs in Figs. 4(A) and 4(E), Figs. 4(B) and 4(F), Figs. 4(C) and 4(G), and Figs. 4(D) and 4(H). The experimental results shown in Fig. 5, 6 and 7 are expected to be similar to those in Figs. 4(B), 4(C) and 4(D), respectively but deviate in particular for the incoherent growth in Figs. 4(C) and 4(D). (1) The lattice parameters of the cubic layers, which are deposited at high temperatures T,, deviate from the lattice parameters of the single crystals at this temperature. Therefore a strain -lo-”
400nm SrS / 400nm EuS / Si (111)

_5000[ , , , , , , , , , _1 0

Fig.

9. Two

TI’C samples

[ 121 for SrS/EuS/Si InP) > a(EuS or GaAs) > c((Si).

1000

for the variation in strain with temperature and InP/GaAs/Si double layers with rr(SrS or GaAs) z a(Si) and a(SrS or InP) < r(EuS or

K. Bickmann,

J. Hawk

/ Thin Solid Films, -754 (1995) 39-46

(2) The 6’ values of all planar GaAs and EuS samples at point A can be increased by one or two annealing processes at 160-400 “C to point B or C (Figs. 6 and 9). (3) The slope Ae”/AT of the strain E” parallel to the substrate between room temperature and points A, B, or C can deviate substantially from the difference of thermal expansion coefficients x, - x0, e.g. for the b axis of CdTe (Fig. 5) which is not parallel to the strain of the (I axis. The CdTe layer is supposed to form bonds to the GaAs substrate only in the u direction. (4) The ratio --E ‘~/e” of the uncorrected strain E” and E’ parallel or perpendicular to the substrate is not constant. Approximately constant ratios --(cl - co)/ (E” - co) are obtained, if the co values at points A, B or C arc considered as reference values instead of the E = 0 values of the single crystals (Table 1). These ratios can deviate for different layers of the same material, e.g. between 1.07 in sample A and 0.75 in sample B of GaAs or between 0.48 in 425 nm EuS and 1.27 in 500 nm EuS layers. These values are also different from the \.alues of 0.75 (EuS), 0.90 (GaAs) and 1.13 (InP), which are obtained from the elastic constants [4]. The temperature of the points A, B or C (Figs. 5-7 and 9) should depend on the kind of bonding between layer and substrate. A high temperature close to T, as in InP/GaAs (Fig. 7) is expected for strong bonding between layer and substrate. A low temperature of points A, B, and C as in EuS/Si (Figs. 6 and 9) might indicate weak bonding. An increasing number of bonds

Table 1 The r ttios of E ’ to e” values, which are corrected by the E” = 6” = E value> at points A. B or C for different layers with thickness h as showri in Figs. 5 7 and 9

Figur :

Layer

11

-(E

’ ~ l)/(E” - EO)

(Pm) Point A 5 5 5

5

Al,, &a. 70As CdTe (i = 2’)

1.6 2.8 2.6 1.1

6 6 6 6 6 6

GaAs GaAs GaAs GaAs EuS EuS

1.X 1.8 6.3 2.3 0.425 0.500

0.76 0.82 1.01 0.48 I .27

7 7

InP InP

3 3.9

I .26 1.15

9 9 9 9

SrS EuS InP GaAs

0.4 0.4 2 0.5

Ga,, 51In,, 49As Al,, ,,Ga,, ,,As

(A) ( R) (C) (I = 4‘)

Point

B

Point

1.00 0.82

I .oo 0.74

0.35

I .09

1.04 0.75 0.80 0.48 1.27

0.48

0.47 0.49

I .2X 0.80

0.80

C

45

between EuS and Si are disrupted on annealing before the layer peels off. The negative co values at point A for GaAs and InP, the positive co values for EuS and the different mechanism for the variation of co at point B or C cannot be explained at present. Point B is reached either by variation in E” as in GaAs sample A and C. by variation of E’ as in EuS or by variation of E” and E’ as in GaAs, sample B (Fig. 6). The temperature of point B of the GaAs samples is identical with the deposition temperature of the ‘amorphous’ GaAs buffer layer [8]. These layers are unstrained at point B (co z 0). The different mechanisms for the variation of E” in GaAs depend on whether point B is at higher or lower temperature than point A. The volume of the strained epitaxial layers would be identical with the volume of the single crystal at --t ‘/ E” = 2. The decreased ratios (Table I) give rise to an increased volume at E” > E ~’(Fig. 4(C) and Fig. 6) or a decreased volume at E”
46

K. Bickmann,

J. Hnuck / Thin Solid Films. 254 (1995) 39-46

is reduced because of the different interactions with the top layer and substrate. The compression in the c direction of the EuS/Si or GaAs/Si system (Fig. 3(C) and Fig. 6) is partly compensated by the tension of the SrS/EuS or TnP/GaAs system (Fig. 3(D) and Fig. 7).

References [I] J. Narayan, S. Sharan and J. C. C. Fan. 1. Met., 41 (1989) 10. [2] A. T. Fiory, J. C. Bean, L. C. Feldman and I. K. Robinson, J. Appl. Phys.. 56 (1984) 1221. [3] J. W. Matthews in J. W. Matthews, (ed.) Epitaxial Growth, Part B, Academic Press, New York, 1975, p. 559. [4] J. Hornstra and W. J. Bartels. J. Crysr. Growth, 44 (1978) 513. [5] M. Leszczynski, CrJ)s/. Res. Tech&., 25 ( 1990) 721. [6] M. Leszczynski, A. Kulik and P. Ciepielewski, Php. Stuius Solid A., 119 (1990) 495. [7] J. Hauck and K. Bickmann, Thin Solid Films, 151 (1987) 191.

[81 K.

Bickmann, J. Hauck, A. Brauers and J. Leiber, Thin Solid Films, 190 ( 1990) 279. [91 S. F. Fang, K. Adomi, S. lyer. H. Morkoc, H. Zabel. C. Choi and N. Otsuka, J. Appl. Ph_v.~.. 68 (1990) R3 1. t101 K. Bickmann and J. Hauck. Muter. Leti., /I (1991) 236. [Ill K. Bickmann, J. Hauck, P. Mock and H. Berger. J. Crysr. Growth. 131 ( 1993) 133. [I21 K. Bickmann and J. Hauck. Acfcr Cr>~stailogr. A Suppl.. 46 (1990) c-377. T. Iijima and T. Ishida, Jpn. J. Appt. Phys., 27 1131 T. Matsumoto, (1988) L892. C. J. Kircher and M. Mu1141 H.-C. W. Huang, P. Chandhari, rakami. Philos. Mrrg. A, 54 (1986) 583. iI51 H. Ebe and H. Takigawa, Mu&r. Sci. Eng., B/6 (1993) 57. [I61 M. Murakami, CRC Crif. Reu. Solid Sfate Mafer. Sci., II ( 1984) 317. A. V. Drigo and A. Carnera. J. [I71 M. Mazzer, F. Romanato, Crysf. Growth, 126 (1993) 125. [I81 Y. Okadd, Y. Tokumaru and Y. Kadota, Appl. Phys. Left., 48 ( 1986) 975. [I91 E. Ligeon. C. Chami, R. Danielou. G. Feuillet, J. Fontenille, K. Saminadayar, A. Ponchet, J. Cibert, Y. Gobil and S. Tatarenko, J. Appl. Phys.. 67 (1990) 2428.