On the mechanism of semi-insulating property formation in In-doped GaAs

Journal of Crystal Growth 97 (1989) 483-488 North-Holland, Amsterdam

483

ON THE MECHANISM OF SEMI-INSULATING PROPERTY FORMATION IN In-DOPED GaAs A.N. MOROZOV

~‘,

V.T. BUBLIK and N.A. ANASTAS’EVA

X-Ray Diffraction A nalysis Laboratory, Department of Semiconductor Materials and Devices, Moscow Steel and Alloys Institute, Leninskii Prospekt 4, Moscow 117936, USSR

Received 16 February 1989; manuscript received in final form 24 April 1989

6—2.1 x102° In atoms The precision lattice parameter and density of Czochralski GaAs: In crystals doped to the level of 2X10’ cm3 were measured by Bond X-ray diffraction and comparative hydrostatic weighting methods, respectively. It appears that semi-insulating GaAs: In crystals always contain a remarkable amount of overstoichiometric arsenic interstitials ((5—10) >< 1018 atoms cm 3), On the other hand, low-resistivity GaAs: In samples turn out to be enriched by overstoichiometric arsenic vacancies in the concentration range of 0 to 6 x 1018 cm ~. A thermodynamic model is developed according to which indium doping of GaAs up to concentrations of (2.2—10)>< 1019 atoms cm3 provides the same native point defect concentration changes (including antisite Asc;adefect and EL2-related complex) as in the case of undoped melt composition changes of 48—54 at% As.

I. Introduction Iso-electronic doping of A1”B” compounds is widely used for industrial production of high-quality, low-dislocation density and completely dislocation-free crystals (see, for example, refs. [1—3]). Besides this, in the case of indium doping of GaAs this method provides the basis for reproducible growth of semi-insulating ingots making unnecessary any additional modifications of the standard LEC equipment. In this case it is not necessary to use PBN crucibles, high-pressure and in-situ direct synthesis processes [1—3].The maximum resistivity equal to 108~109S2 cm appears on the concentration dependence of specific resistivity of GaAs: In crystals near an indium concentration of (2—10) X 1019 atoms cm3. This maximum was obtained for the first time by Solov’eva et al. [41in the case of 20 mm diameter GaAs: In ingots grown by the standard low-pressure Czochralski method (fig. 1~ It is known also that semi-insulating properties of GaAs: In crystals are determined by EL2 deepdonor family centres which are the same as in the case of undoped GaAs [5~ *

Present address: MASPEC—CNR, Via Chiavari 18/A, i43100 Parma, Italy.

Up to the present, a few models have been proposed to explain the anomalous behaviour of GaAs: In resistivity [6—8]. All these models, at least to some extent, are based on the analysis of native point equilibria insidethat thethe crystal. However, nowdefect it is well established characteristic properties of In-doped GaAs as well as of undoped GaAs [9] are determined mainly by deviation from stoichiometric composition which, in its turn, depends on liquid—solid equilibria during crystallization. The aim of the present work was to provide an experimental test of an, at first sight according to which GaAs:abnormal, In crystals proposal grown from stoichiometric or near-stoichiometric are enriched overstoichiometric As inmelts comparison with by undoped GaAs Czochralski ingots. Hypotheses of this type, in combination with native point defect equilibria calculations [10], make it possible to give a reasonable explanation of the reproducible growth of semi-insulating material. As a matter of fact, overstoichiometric compositional changes can cause a remarkable increase in EL2 concentration from 5 X iO~to 2 X 1016 cm3 which, in its turn, provides the basis for complete residual acceptor compensation.

0022-0248/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

484

A. N. Morozoc et al.

/ Mechanism

of SI property formation in In-doped GaAs

2. Experimental A 0

~

o I

I

A

-

I

1

A 19

r

~

17

.

\ Interstitial

I

18

a

\

~

19

calculated according to [11]:

~Vacancies

18

z’z

Specimens of GaAs: In with sizes of 0.5 x 0.5 lattice parameter and denx 1.5measurements cm3 for precision sity carried out with the help of the Bond method and hydrostatic comparative weighing were cut from 25—30 mm diameter ingots grown in a [100] direction from a melt of stoichiometric composition by the standard Czochralski method. The specific resistivity of the GaAs was measured by the four-probe method. The net point defect concentration, i.e., the difference of vacancies and interstitial atom concentrations, was

.

pa

—

~

b

20

3j~ A

A \ m “As)

41.4 —

—

I .4 ~.“‘in

A —

\ ~.r 3 ia)1’~lna

Nd—

cm~.

(1)

where p (g cm3) and a (cm) are the GaAs: In precision density and lattice parameter values, AG.4 69.723, AA, 74.9216 and A 10 114.818 (atomic mass units) are the atomic masses of Ga, As and In, respectively [111, NA 6.022045 x 1023 3) is concentration. of mol~ is the the indium Avogadro number andThe ~ value (atoms cm the arsenic atomic mass in the dominator of eq. (1) is related to the fact that the predominant

18 14

=

=

=

I ~

10

‘

=

6

T~ 2

.~

C io18

1019

io20 N

io21 3

, at.crn Fig. 1. Dependences of experimentally1 obtained values of specific resistivity ((s) present work: (a) results of ref. [4]) (a); deviation from the stoichiometric composition (b) and calculated antisite Asca-defect concentration (c) in Czochralski grown GaAs crystals on In-doping level,

native point defects which particularly determine the GaAs deviation from stoichiometric composition are arsenic interstitials and vacancies [11]. In this case, the value of Nd, determined by the method described in detail in ref. [11], is equal to the deviation from stoichwmetnc composition (S, see definition (4d) below) in GaAs with a high level of accuracy. The error of the net point defect concentration measurements according to ref. [11] is approximately equal to 8 x 1017 cm3. .

.

.

.

3. Experimental results In the present work, the authors have made an attempt of simultaneous determination of In-concentration dependence of specific resistivity, as well as deviation from stoichiometric composition using the same GaAs: In specimens.

Results of the determination of the dependences of GaAs specific resistivity and deviation from stoichiometric composition on indium concentration are shown in fig. 1 and table 1. According to the method developed in ref. [111, in order

A.N. Morozov et al.

/

485

Mechanism ofSI property formation in In-doped GaAs

Table I Precision values of the lattice parameter a, density p and net point defect concentration N

9 in as-grown and heat-treated In-doped

Czochralski-grown crystals of GaAs ~ Indium concentration (atoms cm _3)

As-grown a (A)

p (g cm _3)

a (A)

p (cm 3)

N51 (cm _3)

Iindoped 4 X iU’~ 9 21.4 x1019 x iO’

5.65367 5.65375 5.65397

2.2 >< 1019

5.65407 5.65452 5.65537

5.31669 5.31657 5.31636 5.31705 5.31707

5.65374 5.65387 5.65434 5.65440 5.65438

5.31616 5.31 546 5.31653 5.31705 5.31753

5.31753 5.31897

5.65473 5.65556

5.31712 5.31840

5.32155

5.65742

5.32104

—1.3 >< 10°~ —6.3 X >< 10~ 308 —4.6 8.7x101’ 1.1 x 10~~ 4.9 x i0’~ 9.8 x lO~ —5.OxlO°1

4

x 10~

8

>< 1019

2.1 x102°

5.65402

5.65776

Heat-treated at 1150 ° C. 20 mm +rapid quenching

The lattice parameter and net point defect concentration values are related to the latest values of Cu Ko X-ray wavelength (1.5405934 A) and Avogadro number (6.022045 X 1023 mol _1),

to determine the deviation from stoichiometry, it is necessary to measure the net point defect concentration in a homogeneous crystal (i.e., a crystal with extremely low concentrations of microdefects of different types). Such a crystal, in the case of GaAs, can be obtained [10,11] by high-temperature (T 11500 C), short-time (20 mm) heat-treatment and successive rapid quenching into ethyleneglycol. The results of net point defect concentration determination after such a heat-treatment are shown in fig. lb. The indium concentration in GaAs crystals investigated was varied in the range of 2 x 1016 (0 2.1 x 1020 atoms cm3. As it can be seen from fig. la, in the concentration range of (2.2—10))< 1019 atoms cm3, the material turns out to be semi-insulating. After an increase of In concentration up 3, the to the level higher thansemi-insulating 1020 atoms cm crystals are no longer and the specific resistivity falls to the value of 1 Q cm. It is also seen from fig. lb that semi-insulating GaAs: In crystals contain a remarkable amount of overstoichiometric arsenic interstitials ((5—10) X 1018 atoms cm3). At the same time, low-resistivity crystals contain overstoichiometric arsenic vacancies in the concentration range of (0—6) X i0~cm3. Hence, in GaAs crystals doped with indium to the level of (2.2—8.0) 3< 1019 atoms cm 3, enriched by excess arsenic, the EL2 concentration, according to ref. [9], is high enough to produce a complete compensation of residual acceptors. =

4. The mechanism of formation of GaAs: In semiinsulating properties The main thermodynamic factors determining the concentration of native point defects in the solid state during GaAs crystallization are equilibrium pressure of arsenic (or, by analogy. As activity in the liquid phase) and crystallization temperature [10,12,13]. It can be easily shown that the temperature of crystallization (T), as well as the arsenic pressure above the melt (P), decrease as the In concentration in the melt increases, both according to a linear law: r= i~, ax~ if 0
=

[VA.

—

i

~

~‘

exp(

H,, H,

[As~] ~

r~”exp(

(3)

—

where n is the number of arsenic atoms in the As, molecule in the gaseous phase, kB is the Boltz-

486

A.N. Morozoc et al.

/

Mechanism of SI property formation in In-doped GaA

mann constant, and H, and H~are the effective values of the enthalpy of arsenic vacancy and interstitial formation equal to the algebraic sum of enthalpy of any possible heterophase quasi-chernical reaction and reactions of formation of Schottky (0 VAS + VG 5) and Frenkel (A5A., As + MA,) defects, respectively [10,12]. One can see that predominant point defect concentration dependences on pressure and temperature obey power and exponential laws. Hence, taking into account eq. (1), it can be seen that the main factor determining the possible changes of point defect concentrations in GaAs due to indium doping is the decrease of crystallization temperature. In this case native point defect equilibria must shift to the defect with minimum formation enthalpy, i.e., according to refs. [10,11], to the arsenic interstitial. Hence, as the indium doping level increases, a slight excess of Ga in the solid phase [10—12] decreases. When the doping reaches the value 3, itlevel becomes possible to of N~0GaAs: 2.2 x In 1019crystal cm with near-stoichiometric obtain

concentration of EL2-related defects in as-grown crystals (< 3 3< 10~cm 3) turns out to be far less than the concentration (1019 cm3) of the predominant point defects (As and VA,) which particularly determine the deviation of GaAs corn-

=

=

=

position from the stoichiometric one [18,19]. Let us assume that the concentration of EL2-related complexes in GaAs is determined by the concentration of the minor antisite defect As(1. Then it is possible to calculate As~1.1 using the thermodynamic model developed in ref. [10] if the deviation of the GaAs composition from the stoichiornetric one is known: 0=V5 +V~., K (S=9.1 k ‘ ‘

.

H =3.6eV).

ii

“

(4a) AsAS VA, + As. Kf(Sf 9.1 kB, Hf 3.1 eV). A5A, + VG 5 As(1.1 + VA,, K (S 8 0 k H 0 5 eV) =

=

4b

=

=

composition. If the doping level continues to increase, then one may obtain semi-insulating GaAs In crystals containing a considerable amount of overstoichiometric arsenic interstitials (figs. Ia and ib). If the indium concentration becomes as high as x 0.01, eq. (2) is no longer valid and, as a result, GaAs: In crystals grown from such meltsa 3 and contain more of than 1020 In atoms metallic cm slightly excess overstoichiometric cornponent (i.e., excess of arsenic vacancies, see fig. Ib). This model is in good agreement with the results of thermodynamic calculations of the homogeneity region of GaAs and other similar A’°B’ compounds in ternary systems: Ga—As—Sn [14], Ga—As--Si, In—As—Sn [15] and In—Ga—As [16]. The latter work was carried out under the assumplion that the predominant native point defects in =

GaAs are VA, and ~ [17]; nevertheless, Blom et a]. [16] have obtained a similar result according to which the GaAs homogeneity region shifts towards an arsenic excess as the level of In-doping increases, Literature data analysis [10] shows that the nature of the EL2 deep-level family is due to a point defect complex (or complexes) including the antisite defect As~1.It is known also that the

=

~iS

~

—

.1).

[V]

=

B’

‘ —

[As,]

—

.i..

[V~.1I [As j. —

(4d)

All the thermodynamics parameters of the quasichemicalbyreactions above were determined in refs. [10,12] a least-squares method as the best-fit parameters using the available experimental data on the net point defect and EL2 level concentration dependences on the respective melt composition for undoped GaAs. Similar semi-empirical calculations of the InAs homogeneity region, performed by Bublik et al. [20] on the basis of available net point defect concentration data for this compound [11], had led to the best-fit values H, 3.2 eV, H~ 2.8 eV and 5, 12.4 k 11, which are of the same order of magnitude as those for GaAs. eq. (4). So we can assume that an In concentration of about 0.5 at% would not change significantly the defect formation energies (4) calculated for undoped GaAs. Solving the system of equations formed by mass-action laws for the quasi-chemical reactions (4a)—(4c) and the equation of material balance (4d), where different point defect concentrations =

=

=

.4 .N. Morozoc et aL

/

Mechanism of SI property formation in In-doped GaAs

provides the same point defect concentration changes (including antisite AsGa-defect and EL2family related complexes) as in the case of undoped melt composition changes from 48 to 54

20 18 16 ‘~

487

at% As.

14

U

~

10 1~

—~ 50 0

5. Conclusions The mechanism of semi-insulating property for-

ciesA,~InterstitialsAsl

8

-

S

4

2 0

I

,

Excess of Ga 10

8

6

4

2

Excess of As 0

2

4

6

8

10

12

S. 10~ at.cm3

mation in In-doped Czochralski GaAs crystals may be due to the presence of an overstoichiometnc excess of arsenic interstitials in the crystals with indium concentration of (2.2—10) X 1019 atoms cm3. As a consequence, these GaAs: In crystals contain a high concentration of EL2 deep-level family related antisite defect ASGa.

Fig. 2. Calculated dependence of antisite Asna-defect concentration on deviation from stoichiometric composition in GaAs.

Acknowledgements are particular unknowns, we get an expression for the A5GS concentration: 1/21 —1

We would like to thank V. Osvenskii, 0. Stollarov and I. Stepantsova for the supply of samples, providing precision density data and valuable discussions.

[A5 05]=KSSK,[0.5S+(0.25S2+Kf) (5)

Here point defect concentrations and deviation from stoichiometric composition (S) are cxpressed in mole fraction units. In the case of overstoichiometric excess of Ga, S > 0; in the opposite case, S < 0. The results of A5G5 concentration calculations at the melting point are shown in fig. 2. On substituting into eq. (5) the obtained values for the net point defect concentration Nd S (fig. lb), one can calculate a dependence of A5t;a concentration on In-doping level (fig. ic). It can be easily seen that the A5t,a concentration rises from x 1015 tofrom 20 ><1.4 1015 3 as the In-doping levels increases X cm to 2.2 X 1019 atoms cm’3. The former ASGa 1019 concentration range agrees with the magnitude of the EL2 concentration changes in as-grown undoped Czochralski GaAs crystals as the arsenic atomic fraction in the melt increases from 48% to 54% [9]. Hence, indium doping of GaAs in the concentration range of (2.2—10) 3< 1019 atoms cm3 =

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Mechanism of SI property formation in In-doped GaA,s

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[16] [17] [18]

[19]

[20]

Karataev and MG. Milvidskii. Krisiallografiya 30 (1985) 548. G.M. Blom and J.M. Woodall. 1. Electron. Mater. 17 (1988) 391. J.A. Van Vechten, J. Electrochem. Soc. 122 (1975) 1556. VT. Bublik. V.V. Karataev. R.S. Kulagin. MG. Milvidskii, yB. Osvenskii, 0G. Stoliarov and 0G. Holodnii. Kristallografiya 18 (1973) 353. IS. Areiev. VT. Bublik. AN. Morozov. V.V. Karataev. l.A. KovaLhuk, MG. Milvidskii and 0.Yu. Morozova. Kristallografiya 32 (1987) 460. VT. Bublik, V.V. Karataev. MG. Milvidskii and AN. Morozov. Kristallografiya 26 (1981) 554.