Growth of homogeneous bulk In1-xGaxP

Journal of Crystal Growth 41(1977) 93—99 © North-Holland Publishing Company

GROWTH OF HOMOGENEOUS BULK In1 ~Ga~P A.J. MARSHALL and K. GILLESSEN AEG-Telefunken Forschungsinstitu t, Frankfurt, Germany Received 15 February 1977; manuscript received in final form 2 June 1977

A major hindrance to the growth of homogeneous bulk In1 ~Ga~P crystals from solution is the very high segregation of gallium in indium. A method to overcome this problem is described. Gallium in the form of GaP is supplied automatically at a constant predetermined rate to an indium rich melt. The melt is therefore held at a constant composition, and with it, the growing crystal. The growth front conditions are maintained by lowering the system at a rate equal to the growth speed. With this method polycrystals of very homogeneous composition have been grown. The composition was determined by lattice constant measurements, and the band gaps of various compositions measured by determination of the absorption edge.

1. Introduction

been successfully applied to and optimised in the growth of GaP single crystals [14,15]. In section 2 the principle of the technique is presented followed in sections 3 and 4 by the theoretical considerations as to its function. The method was tested experimentally for various compositions (section 5). The results of these experiments are presented and the material is characterized by lattice parameter, electron microprobe and optical absorption measurements (section 6).

Solid solutions of indium gallium phosphide (Ini~Ga~P) have energy gaps which are a function of composition, having the property of direct transitions for 0 ~x ~ 0.7 [1]. Within this compositional range it should be possible to produce electroluminescent devices operating from the near infrared (9000 A) to the yellow (5800 A) with quantum efficiencies higher than similar systems e.g. GaAs~Pi_~ [1]. Ini~Ga~P has proven to be a material difficult to grow. The main problems arise from temperature changes during growth causing compositional inhomogeneities and structural defects, both of which greatly reduce the efficiency of the devices made thereof [2]. To overcome these difficulties various crystal growth techniques have been applied. Thin films of Ini~Ga~P have been deposited on GaAs and GaP substrates from the vapour phase [3,4] and on GaAs or GaAs1~P~ substrates by liquid phase epitaxy [5—9]. Attempts at the growth of bulk In1~ Ga~Pcrystals by a modified Bridgman and solution growth techniques have also been made [2,10—13]. However, no exact details were given of how the desired composition was chosen prior to growth. For the first time we report here on a method of solution growth where the required crystal composition is predetermined. The method is a variation of the synthesis, solute diffusion (SSD) technique which has

2. Growth system The principle of the method, schematically shown in fig. 1, is to constantly supply gallium to an indium melt to copensate for its high segregation from indium in the crystallization process. The polycrystalline GaP source material is so fixed in the graphite holder that its lower end is in contact with the surface of the indium melt. At the required temperature, this body dissolves and due to the temperature gradient and concentration difference, gallium and phosphorus are transported to the lower colder end of the crucible where supersaturation causes crystallization. The graphite cylinder helps to control the heat flow at the onset of crystallization thus preventing dendritic type growth which may tend to the formation of inclusions. The size of the GaP source is calculated 93

94

A.J. Marshall, K. Gillessen

/ Growth of homogeneous bulk In1 _xGaxP 3. Calculation of the size of the GaP source

Graphite holder

—

-

GaP source crystal-

)

Crucible

The size of the GaP source material is calculated using the notations shown in fig. 2. Let A1 be the cross-sectional of the cross-sectional crucible, i.e. growing tal and A2 thearea required area ofcrysthe GaP source. Assume the crystal grows by amount 4,

In melt ln1.~Go~p crystal

then its mass increases by

—

z~mk=pkA1z~y

Seed Graphite cylInder

/

—

with the crystal density I

I

Pk(l

~X)pInp+XpGap.

For L\mk to be of composition Ini~Ga~P, ~GaP

Phosphorus

=

X(MGapIM~3~.mk,

where MGap and Mk are the molecular weights of GaP and of the crystal respectively. At the same time the solution level climbs z~z.For constant composition it is required that the same amount of GaP (i~mGaP) 15

—

$

500

‘

‘

iOO°c

dissolved. ~mGappGapA2Liz.

Fig. 1. Ini~Ga~Pgrowth ampoule with temperature profile.

In forming &flk, the amount of indium required is: z~.m1~(1 —X)-~-~-~.1flk

so that as gallium is removed from solution by crystallization it is replenished at the rate necessary to keep the solution composition and with it, the growing crystal composition constant. This is possible since the indium level climbs during crystallization as little indium is used, and the volume of the crystal is larger than the volume of the liquid from which it is made. The ampoule contains phosphorus at its lower end at a temperature of 420°C.This produces a vapour of 1 atm allowing operation at normal pressure, and prevents evaporation of phosphorus from the indium melt produced by the GaP source. At the same time

where M10 = mol. wt of indium. Since the solution is composed almost entirely of indium L~m1

=

p10A1(4

A2

GOP

J-————

the phosphorus reacts with the exposed indium surface, goes into solution and adds to the flux of phos-

phorus being transported from the GaP source. This additional phosphorus is used to form the InP content of the crystal. To maintain constant growth front conditions the ampoule is lowered at the rate equal to the growth speed.

-

h Melt -

ln. Go~P

-

A

Fig. 2. Geometrical consideration for crystal growth.

A.J. Marshall, K. Gillessen

/ Growth of homogeneous bulk In1 _~Ga~P

By rearrangement it follows: /12 fl M~ PGaP ~=xl~ ~--(1 ~ LMGaP Pk

M10 -x)~

~

MGap Pin

1

—1

(1)

For example one obtains3, A2/A~ = 0.788 for PK -x pJ~~ = 4.79 g/cm3, MGap = 100.69,

MK

=

114.22 and M10 = 114.82.

4. Thermodynamical considerations of process feasibility The temperature at the In surface has to be chosen so that the calculated amount of GaP completely dissolves to form the required crystal composition. The thermodynamical relationship governing the equilibrium of the In—Ga—-P ternary liquid with the mixed

Ini~Ga~P solid are, after Panish [16]: GaP[solid]

KGap ~====~

Ga [liquid]

+

P[liquid] (2)

K1~~

InP[solidj-----—---~In[liquid] + P[liquid] (3)

with the additional relationships I

,

X1~p=

XGap +

1,

(4), (5)

the equilibrium between solid and liquid, We set all activity coefficients except ‘yp, the activity coefficient of phosphorus to unity. 7p is approximated to be, after [16],

fi

0

SXGa, 2XGa,

‘(XGa ( 0.1 1

0.1 ~XGa~

.

(6)

~0.52 O. The equation ln KGap = 7.246 1.57 X 104/T (7) (where Tis in K), is a good approximation to the data of Thurmond [17] on the Ga—P binary system. Similarly —

In K

4/T 1~~ = 6.489

—

1.0467 X 1 0

—

C~‘~ Xp and CGa

‘~

XGa

then

with X1 the atom fraction of species i in the liquid, X~1the mole fraction of species ij in the solid and KGap, K1~~ the proportionality constants governing

=

any particular temperature K~~p= 6.9 X l03K? 0~. (9) One has to solve eqs. (2)—(6) and (9) for the growing crystal surface and the dissolving GaP/melt surface which are refered to as (A) and (B) respectively. This yields twelve independent equations. An additional relationship is required to physically connect the two surfaces. If the crystal has the cornposition lni_~Ga~P, its Ga, In and P content is xGa,(1 x)In,P. Therefore, the flux of gallium Faa, to the growing interface and the flux of phosphorus F~, needed to produce this composition has to be related by xFp = FGa. It is easily seen from Fick’s Law of diffusion, assuming the diffusion coefficients of Ga and P in the In to be equal that x [Cp(B) Cp(A)] = CGa(B) CGa(A), (10) where C~(B),Cp(A), CGa(B), CGa(A) are the phosphorus and gallium concentrations at positions (A) and (B) respectively. As

K1~~ = X10Xpyp/X~~p ;

Xp =

functions can be combined to give at

—

KGaP = XGaXpypIXGap;

X1~+ XGa +

describes the InP equilibrium constant according to the work of Panish and Arthur [18] on the In—P binary system. These two

= 0.7 with PGaP =~ 4.13 g/cmg/cm3, = 4.328 g/cm3, = 7.31

95

(8)

x[Xp(B)

—

X~(A)]=

XGa(B)

XGa(A)

.

(11)

With this “transport equation” we have thirteen equations and sixteen variables. Therefore, by choosing three variables the system can be completely solved. We present here the solution for a crystal with the composition x = 0.7. According to section 3, the area of the GaP source has to be 0.788 of the area of the crucible. This is equivalent to a mixed source with the same areaIfaswethat of the but with XGaP(B) = 0.788. choose thecrucible, growth temperature to be 900°C,we obtain the set of parameters shown in table 1. From the calculated equilibrium constants at position (B) one obtains the temperature at the source to be 1036°C. At this the sourcesource will completely dissolve. A temperature plot of the calculated dissolution temperature as a function of the desired crystal composition for various growth temperatures

96

A.J. Marshall, K. Gillessen

Table 1 Parameters for x

A B

/ Growth of homogeneous bulk In1

0.7 at a growth temperature of 900°C

Xlnp

XGa

XIn

Xp

‘yp

K~~p

KGaP

0.3 0.212

0.0522 0.111

0.909 0.765

0.0392 0.124

0.739 0.498

0.0877 0.222

0.00216 0.00869

is shown in fig. 3. These values must be considered as estimates to start experiments as several approximations have been made: The melt was considered to consist only of indium, all activity coefficients except ‘yp were equated to unity and the diffusion coefficients of gallium and phosphorus in indium were assumed to be equal.

5. Experimental The temperature profile shown in fig. 1 is produced by a two-zone vertical furnace system. According to fig. 3 it should not theoretically be possible to produce crystals with values of x ~ 0.8 because tern-

1250

C 1200

1150

iroo°c 1100

~ i~o E

ioso°c

1000

1000°C

950

950°C 900 C

~

~Ga~P

~°°

01

0.2

0.3

0.4

0.5

0.6

0.7

0.B

0.9

crystal composition x Fig. 3. Source dissolution temperature versus crystal cornposition for different growth front temperatures,

peratures above 1140°C, the maximum allowable temperature using quartz ampoules, cannot be realized in this system. We found experimentally, however, that the GaP source dissolved at approximately 1120°Ceven for x = 0.8. We attribute this discrepency to the assumption made in section 3 that the melt was composed almost entirely of indium. This statement is apparently valid for values up to x = 0.7 since there is good agreement between theory and experiment. The polycrystalline GaP source material used in this method is produced similarly to that described in ref. [14] for the growth of GaP single crystals. The polycrystals are reduced to the required diameter by a diamond tipped core drill using an oil lubricant. Non-porous carbon crucibles and 6N indium are used in this work. The amount of indium necessary is dependent on the source dissolution temperature. High values of x and low growth temperatures require 1 lt 1 F 1 ~f = 0 7 d th growth temperature is 900°C,it is known that the source will completely dissolve at 1060°C.To achieve this range in the temperature profile of our system, the melt needs to be 3.9 cm deep and for a 2.1 cm diameter crucible 99 g of indium are needed. On the other hand, if x = 0.3 at a growth temperature of 900 °C, the source dissolves at 970 C. The melt depth then required is 1.4 cm or 36 g of indium. The diffusion path length of Ga and P in In is the melt depth. With increasing x, that is, melt volume, attention must then be paid to the time interval required for the diffusion profile in the melt to become stationary [19] before the lowering mechanism can be started. When setting up the crucible assembly allowance has to be made for the expansion of the melt so that when the system is “at temperature”, the lower side of the source is in contact with the melt surface. If the GaP source crystal is held in a position that is too low, the crystal will be gallium rich at the start, and In rich if it is too high. The crucible assembly is

A.J. Marshall, K. Gillessen / Growth of homogeneous bulk In

1 ~Ga~?

placed in an etched, outgassed quartz ampoule contaming about 10 g of 6N red phosphorus at its lower end. If the required crystal is to be extrinsically doped n-type, a small amount (0.3 mg) of sulphur is added to the ampoule. The ampoule is sealed under a pressure of 10—6 Torr after purifying the crucible region by a short bake-out procedure at about 600 C.

6. Results and discussion Typically, ingots grown by this method were 21 mm in diameter and 30mm in length. Preliminary experiments showed that the growth rate was about 1.6 mm/day for an eighteen day growth period. This is about twice that of values published elsewhere [12, 13]. In order to maintain growth front conditions, the ampoule was lowered with this speed. In all cases the ingots were polycrystalline. The grain size was typically 1—2 mm and was found to vary neither with composition nor over the length of the ingot. Selected, 550 j.im thick slices cut perpendicular to the growth direction were divided into two, one half then powdered for Debye—Scherrer X-ray lattice parameter measurements to determine the composi-

1.0

...

I

\

\

0

~ °\

\..~

\

08

~

- — — \~°°°°°°-°—~°-

0.7

~

0.6

20

0

length

Fig. 4. Composition profiles

in the growth direction by X-ray lattice parameter measurements: (I) grown in pointed quartz crucible; (II) grown in glassy carbon crucible with graphite insert; (III) same as (II) plus seed.

97

tion assuming Vegard’s law and the other half prepared for electron-microprobe, and optical absorption measurements. In fig. 4 the composition profiles, determined from the lattice parameter measurements, of three typical crystals are shown. Here the aim was to obtain ingots with a 70% gallium content, that is in the region of the direct-indirect (Er = E~) transition crossover point. The growth temperature in each case was 900°C.Ingot I has a gallium content of 78 ±0.5% practically over its entire length. The slight decrease in gallium content at the end is probably due to the fact that at this stage the GaP source crystal had cornpletely dissolved. Ingot II was a repeat of this attempt, but instead of using a pointed quartz crucible a constant diameter glassy carbon crucible with a graphite insert was incorporated, fig. 1. Although at the start of growth sufficient allowance for melt expansion had not been made, the composition eventually became constant at 68% gallium ±0.5%. The difference in the obtained compositions for these two attempts could only be attributed to the pointed crucible, the geometrical calculation in section 2 having been made for the constant diameter case. Ingot III was an attempt at seeding using a GaP single crystal seed disc. The GaP source was deliberately placed about 2 mm lower as in I to obtain a graded composition starting with 100% Ga content. The seed completely dissolved, its gallium content, however, added to that of the source crystal and raised the overall value in the system resulting in a composition of 80% gallium ±0.5%over the middle 8 mm. To test the homogeneity of the slices over their crosssection, electron-microprobe scans were made of various compositions. Typical indium and gallium radiation traces of two samples are shown in fig. 5. It can be seen that for both samples the composition varies slightly towards the edge. This was to be expected as it was observed at the end of growth that the interface of the ingots was generally slightly concave. Both samples presented were grown with the graphite insert to help to control the heat flow at the onset of crystallization and only a few inclusions are present as can be seen in fig. 5. However, samples grown in pointed quartz crucibles containedvery many indium inclusions. .

a further method of characterization, the absorption edge of various samples was determined As

A.J. Marshall, K. Gillessen

98

/

Growth of homogeneous bulk In

1 xGa~P

2.7 0,9

2.5 08

0.7

0.6

—-~..---~.

~

fl,,.

~

~.~-=‘

‘‘-~--.

X~p(12/29) -“—— ~ ‘°°“°y-.

Ex

2 3

o

21

X~p (11/30)

a °‘

0,5

W Er

O

1 7 -

X~5c~F(11/30) 04

~

-

-300K 0 3 ~12/29/

1 5-

0.2

13

01

0

-

llnPl crystal

Fig. 5. Electron

crystal

5a,a,

0.2 -

04

‘

06 -

0.6

X

1.0

IGaP)

Fig. 7. Band gap versus composition obtained by absorption edge and lattice parameter measurements. The solid curves

5

position in crystal microprobe scans perpendicular to the

growth direction,

on a simple spectrometer arrangement with a silicon photodetector. The results of such measurements made at room temperature are shown in fig. 6. For all samples the absorption edge was readily directed. In

give the direct Stringfellow et a).(Er) 110].and indirect (E~) gap according to

fig. 7, the values of energy gap and composition of the ingots obtained by this method are compared to 2 and is ais described summary those of the literature. The curve shown by .35 + O.73x et + 0.70x madeEGby= 1Stringfellow al. [10] of their work and that of various authors. It can be seen that to within the experimental error of the spectrometer arrange-

330K

~

energy (eV)

Fig. 6. Absorption coefficient

‘

versus photon

energy for various compositions at 300 K.

A.J. Marshall, K. Gillessen / Growth of homogeneous bulk Ini ~Ga~P

ment (±0.03eV) the points are in excellent agreement to the curve. It has been shown that with the method described large polycrystalline Ini_~Ga~P ingots with very uniform composition in the whole volume can be grown. The growth of single crystals of this material by this method remains a problem, although graded compositions from a GaP seed have been obtained. The fact that the grain size did not vary appreciably over the ingot length is a directive that the growth conditions have to be controlled even more accurately.

Acknowledgements We would like to thank Dr. J. Hesse and Dr. W.C. Clark (University of Bath, England) for their support and encouragement and Dr. H. Preier for critical reading of the manuscript. We would also like to thank I. Meier for careful sample preparation, I. Linnemann for X-ray powder photography and G. Grabe for electron microprobe measurements.

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99

[3] C.J. Neuse, D. Richmann and RB. Clough, Met. Trans. 2(1971)789. [4] AG. C.J. Neuse, RE. and T. Zamerowski,Sigai, J. E)ectrochem. Soc. 120Enstrom (1973) 947. [5] B.W. Hakki, J. Electrochem. Soc. 118 (1971) 1469. [6] W.R. Hitchens, N. Holonyak Jr., M.H. Lee and J.C. Campbell, Soviet Phys.-Semiconductors 8 (1975) 1575. [7] S. Izozumi, Y. Komatsu, T. Kotani and 0. Ryuzan, Japan. J. App). Phys. 12 (1973) 306. [8] H.M. Macksey, M.H. Lee, N. Holonyak Jr., W.R. Hitchens, RD. Dupuis and J.C. Campbell, J. App). Phys. 44 (1973) 5035. [9] G.B. Stringfel)ow, P.F. Lindquist and R.A. Burmeister, J. Electron. Mater. 1(1972) 4. [10] H. Itoh, K. Hara, A. Tanaka and T. Sukegawa, App). Phys. Letters 19 (1971) 348. [11] RD. Burnham, N. Holoyak Jr., D.L. Keune, D.R. Scifres and PD. Dapkus, Appl. Phys. Letters 17 (1970) 430. [12] A. Laugier and J. Chevallier, Phys. Status Solidi (a) 7 (1971) 427. [13] G. Voigt, H. Raidt, H. Peibst, H. Menniger, and L. Hi)disch, Phys. Status Solidi (a) 36 (1976) 173. [14] K. Gillessen and A.J. Marsha)), J. Crystal Growth 32

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