^{1,a)}

### Abstract

A thermodynamic model is used to analyze available experimental data relevant to point defects in the binary zinc-blende III–V compounds (Ga,In)-(P,As,Sb). The important point defects and their complexes in each of the materials are identified and included in the model. Essentially all of the available experimental data on dopantsolubility, crystal density, and lattice parameter of melt and solution grown crystals and epilayers are reproduced by the model. It extends an earlier study [Hurle, J. Appl. Phys.85, 6957 (1999)] devoted solely to GaAs. Values for the enthalpy and entropy of formation of both native and dopant related point defects are obtained by fitting to experimental data. In undoped material, vacancies, and interstitials on the Group V sublattice dominate in the vicinity of the melting point (MP) in both the phosphides and arsenides, whereas, in the antimonides, vacancies on both sublattices dominate. The calculated concentrations of the native point defects are used to construct the solidus curves of all the compounds. The charged native point defect concentrations at the MP in four of the six materials are significantly higher than their intrinsic carrier concentrations. Thus the usually assumed high temperature “intrinsic” electroneutrality condition for undoped material is not valid for these materials. In GaSb, the antisite defect appears to be grown-in from the melt. This contrasts with the defect in GaAs for which the concentration grown-in at the MP is negligibly small. Compensation of donor-doped material by donor-Group III vacancy complexes is shown to exist in all the compounds except InP where Group VI doped crystals are uncompensated and in InSb where there is a lack of experimental data. The annealing effects in GaAs, including lattice superdilation, which were shown in the earlier paper to be due to Group III vacancy undersaturation during cooling, are found to be present also in GaSb and InAs. Results for native point defects are compared with reported “first principles” calculations for GaAs. It is seen that, while there is some accord with experimental findings for low temperature molecular beam epitaxial (MBE) growth, they fail totally to predict the behavior under high temperature growth conditions. The analysis of data on liquid phase epitaxy (LPE) growth of GaAs from Bi solution in the earlier paper has been re-calculated in the light of experimental data that showed that the model used in that paper to represent the Ga–As–Bi phase equilibria was inadequate. An improved model reveals that Ga vacancies exert a greater effect in controlling the extent of the linear range of donor dopantsolubility than previously predicted. It has also led to a re-evaluation of the equilibrium EL2 and Ga vacancy concentrations in GaAs during MBE growth under As-rich conditions at low temperatures . The amended model predicts that the very high concentrations of EL2 and of Ga vacancies observed experimentally are near equilibrium values. The predicted increase in the equilibrium concentrations of these defects at low temperatures results from coulombic attraction between the two defects. At temperatures somewhat lower than 500 K the rate of increase becomes catastrophic.

The author gratefully acknowledges the valuable advice given to him by David Herbert on how to treat the strongly degenerate case. He is also especially grateful to Tom Foxon for his interest in the work and for his experimental work seeking to identify the predicted new phase of GaAs in low temperature As-rich MBE layers. He also thanks Irene Tretheway and Steven Madsen for their valuable assistance in preparing the manuscript. Finally, I thank my wife Pamela for her forbearance during the long gestation of this paper.

I. INTRODUCTION

II. THE TASK

III. A SUMMARY OF THE POINT DEFECTS IN GALLIUM ARSENIDE

IV. THERMODYNAMIC MODEL

A. Thermochemistry of the nutrient phase

B. Neutral native point defects

C. Ionized native point defects

D. Dopant atom incorporation

E. The cooling crystal

V. METHODOLOGY

A. Principal procedures

B. Determining the enthalpy and entropy of formation of the native point defects

C. Defects included in the model

1. Undoped material

2. Doped material

D. Iteration procedure

VI. NATIVE POINT DEFECT CONCENTRATIONS IN THE VICINITY OF THE MP

A. Introduction

B. GaAs

C. GaP

D. GaSb

E. InAs

F. InP

G. InSb

H. Summary

VII. GROUP VI DONOR DOPING BY MELT-GROWTH, SOLUTION GROWTH AND LPE

A. Introduction

B. GaAs: Te and Se doping

C. GaP: Te, Se, and S doping

D. GaSb: Te doping

E. InAs: S, Se, and Te doping

F. InP: Te doping

G. InSb

H. Summary

VIII. GROUP III ACCEPTOR DOPING BY MELT-GROWTH, SOLUTION GROWTH, AND LPE

A. Introduction

B. GaAs:Zndoping

C. GaP:Zndoping

D. GaSb:Zndoping

E. InAs:Zndoping

F. InP:Zndoping

G. InP: Cd doping

H. InSb:Zn and Cd doping

I. Summary

IX. GROUP IV DOPING BY MELT GROWTH, SOLUTION GROWTH, AND LPE

A. Introduction

B. GaAs: Sn doping

C. GaAs:Gedoping

D. GaAs: Si doping

E. GaP: Sn, Ge, and Si doping

F. GaSb: Si, Ge, and Sn doping

G. InAs: Sn doping

H. InP:Gedoping

I. InP: Sn doping

J. InP: Si doping

K. InSb: Si, Sn, and Gedoping

L. Summary

X. ANTISITE DEFECTS AND LOW TEMPERATURE EPITAXIAL GROWTH UNDER GROUP V-RICH CONDITIONS

A. Introduction

B. GaAs

C. InP

D. GaSb

E. GaP

F. Summary

XI. DISCUSSION

A. Introduction

B. Comparison with results of first principles calculations

C. Comparison with previous data

D. Charge states of the As vacancy in GaAs

E. The Ga vacancy and the donor-Ga vacancy complex in GaAs

F. Limitations of the analysis

XII. SUMMARY OF THE PRINCIPAL CONCLUSIONS

### Key Topics

- Doping
- 245.0
- Vacancies
- 145.0
- Crystal defects
- 118.0
- III-V semiconductors
- 95.0
- Germanium
- 85.0

## Figures

Density of GaAs vs atom fraction of As in the melt. (Bublik *et al.* (Ref. 32).] The line is the dependence predicted by the model.

Density of GaAs vs atom fraction of As in the melt. (Bublik *et al.* (Ref. 32).] The line is the dependence predicted by the model.

The calculated solidus of gallium arsenide showing the catastrophic deviation from stoichiometry at low temperature under arsenic-rich conditions. Arrow marks the congruent point.

The calculated solidus of gallium arsenide showing the catastrophic deviation from stoichiometry at low temperature under arsenic-rich conditions. Arrow marks the congruent point.

Calculated GaP solidus. Arrow marks the congruent point. Experimental data: Jordan *et al.* (○); Morozov *et al.* (◻).

Calculated GaP solidus. Arrow marks the congruent point. Experimental data: Jordan *et al.* (○); Morozov *et al.* (◻).

Density of GaSb vs atom fraction of Sb in the melt [Wilke *et al.* (Ref. 47)].

Density of GaSb vs atom fraction of Sb in the melt [Wilke *et al.* (Ref. 47)].

Calculated GaSb solidus. Arrow marks the congruent point.

Calculated GaSb solidus. Arrow marks the congruent point.

Density of InAs vs atom fraction of As in the melt. [Bublik *et al.* (Ref. 33).]

Density of InAs vs atom fraction of As in the melt. [Bublik *et al.* (Ref. 33).]

Calcuated InAs solidus. Arrow marks the congruent point. Data points: Bublik *et al.* (○).

Calcuated InAs solidus. Arrow marks the congruent point. Data points: Bublik *et al.* (○).

Calculated InP solidus. Arrow marks the congruent point. Data points: Morozov *et al.* (Ref. 34) (○).

Calculated InP solidus. Arrow marks the congruent point. Data points: Morozov *et al.* (Ref. 34) (○).

Calculated InSb solidus. Arrow marks the congruent point.

Calculated InSb solidus. Arrow marks the congruent point.

Calculated concentrations of the significant native point defects in the vicinity of their MPs vs atom fraction of Group V element in the melt. The symbol (◼) indicates the intrinsic carrier concentration at the congruent MP. The upward facing arrow at the base of each figure shows the melt composition in equilibrium with a stoichiometric crystal. Note that the concentration scale for the antimonides (c) is an order of magnitude lower than for the phosphides and arsenides (a) and (b).

Calculated concentrations of the significant native point defects in the vicinity of their MPs vs atom fraction of Group V element in the melt. The symbol (◼) indicates the intrinsic carrier concentration at the congruent MP. The upward facing arrow at the base of each figure shows the melt composition in equilibrium with a stoichiometric crystal. Note that the concentration scale for the antimonides (c) is an order of magnitude lower than for the phosphides and arsenides (a) and (b).

Carrier concentration vs Bi/Ga ratio for GaAs(Te) grown by LPE from Ga–Bi solutions. Te concentration in the solution, . Growth temperatures are 1100 K (○) and 920 K (x) [Yakusheva and Pogadaev (Refs. 55 and 58)].

Carrier concentration vs Bi/Ga ratio for GaAs(Te) grown by LPE from Ga–Bi solutions. Te concentration in the solution, . Growth temperatures are 1100 K (○) and 920 K (x) [Yakusheva and Pogadaev (Refs. 55 and 58)].

Lattice parameter of melt-grown GaAs(Te) vs carrier concentration. Data points: Mullin *et al.* (Ref. 63); Kuznetsov *et al.* (Ref. 57) and Dobson *et al.* (Ref. 64). The curve is the model fit for a dilation per defect of 0.7 (see text).

Lattice parameter of melt-grown GaAs(Te) vs carrier concentration. Data points: Mullin *et al.* (Ref. 63); Kuznetsov *et al.* (Ref. 57) and Dobson *et al.* (Ref. 64). The curve is the model fit for a dilation per defect of 0.7 (see text).

Carrier concentration and concentration of Se in the crystal vs concentration in the melt for Bridgman-grown GaAs(Se). [Vieland and Kudman (Ref. 61).] Carrier concentration (x) and dashed line; total Se concentration (○) and full line.

Carrier concentration and concentration of Se in the crystal vs concentration in the melt for Bridgman-grown GaAs(Se). [Vieland and Kudman (Ref. 61).] Carrier concentration (x) and dashed line; total Se concentration (○) and full line.

Carrier concentration and concentration of Te in the crystal vs concentration in the solution for LPE-grown GaP(Te). Growth temperature 1313 K. [Trumbore *et al.* (Ref. 62).] Carrier concentration (○) and dashed line; total Te concentration (x) and full line.

Carrier concentration and concentration of Te in the crystal vs concentration in the solution for LPE-grown GaP(Te). Growth temperature 1313 K. [Trumbore *et al.* (Ref. 62).] Carrier concentration (○) and dashed line; total Te concentration (x) and full line.

Carrier concentration and concentration of Se in the crystal vs concentration in the melt for LPE-grown GaP(Se). Growth temperature 1313 K. [Trumbore *et al.* (Ref. 62).] Symbols as in Fig. 14.

Carrier concentration and concentration of Se in the crystal vs concentration in the melt for LPE-grown GaP(Se). Growth temperature 1313 K. [Trumbore *et al.* (Ref. 62).] Symbols as in Fig. 14.

Carrier concentration and concentration of S in the crystal vs concentration in the melt for LPE-grown GaP(s). Growth temperature 1313 K. [Trumbore *et al.* (Ref. 62).] Symbols as in Fig. 14.

Carrier concentration and concentration of S in the crystal vs concentration in the melt for LPE-grown GaP(s). Growth temperature 1313 K. [Trumbore *et al.* (Ref. 62).] Symbols as in Fig. 14.

Carrier concentration vs total Te concentration in the crystal for melt-grown GaSb(Te). Data points: Sunder *et al.* (Ref. 69) (○); Wilke *et al.* (Ref. 70) (◼).

Carrier concentration vs total Te concentration in the crystal for melt-grown GaSb(Te). Data points: Sunder *et al.* (Ref. 69) (○); Wilke *et al.* (Ref. 70) (◼).

(a) Density and (b) lattice parameter vs total Te concentration in the crystal for melt-grown crystals of GaSb(Te). Dashed curve in (b) is Vegard’s law change assuming all Te is on the Sb site. Solid lines are the calculated values assuming the presence of compensating acceptors that produce the labeled dilation per defect. [Wilke *et al.* (Ref. 70).]

(a) Density and (b) lattice parameter vs total Te concentration in the crystal for melt-grown crystals of GaSb(Te). Dashed curve in (b) is Vegard’s law change assuming all Te is on the Sb site. Solid lines are the calculated values assuming the presence of compensating acceptors that produce the labeled dilation per defect. [Wilke *et al.* (Ref. 70).]

(a) Carrier concentration and (b) density vs S concentration in the crystal for InAs(s) grown from the melt by the LEC technique [Bublik *et al.* (Ref. 73)]. The dashed curve in (b) is the expected density change assuming Vegard’s law.

(a) Carrier concentration and (b) density vs S concentration in the crystal for InAs(s) grown from the melt by the LEC technique [Bublik *et al.* (Ref. 73)]. The dashed curve in (b) is the expected density change assuming Vegard’s law.

Lattice parameter vs dopant concentration in the crystal for Te (●) and S(o) in LEC-grown InAs. [Bublik *et al.* (Ref. 73).] Dashed curves are the expected changes assuming Vegard’s law.

Lattice parameter vs dopant concentration in the crystal for Te (●) and S(o) in LEC-grown InAs. [Bublik *et al.* (Ref. 73).] Dashed curves are the expected changes assuming Vegard’s law.

(a) Carrier concentration and (b) density vs Se concentration in the crystal for InAs(Se) grown from the melt by the LEC technique [Bublik *et al.* (Ref. 73)]. The dashed curve in (b) is the expected density change assuming Vegard’s law.

(a) Carrier concentration and (b) density vs Se concentration in the crystal for InAs(Se) grown from the melt by the LEC technique [Bublik *et al.* (Ref. 73)]. The dashed curve in (b) is the expected density change assuming Vegard’s law.

Lattice parameter vs dopant concentration in the crystal for melt-grown InAs(Se) [Bublik *et al.* (Ref. 73).] The dashed curve is the expected Vegard’s law dependence.

Lattice parameter vs dopant concentration in the crystal for melt-grown InAs(Se) [Bublik *et al.* (Ref. 73).] The dashed curve is the expected Vegard’s law dependence.

(a) Carrier concentration and (b) density vs Te concentration in the crystal for InAs(Te) grown from the melt by the LEC technique. [Bublik *et al.* (Ref. 73).] The dashed curve in (b) is the expected density change assuming Vegard’s law.

(a) Carrier concentration and (b) density vs Te concentration in the crystal for InAs(Te) grown from the melt by the LEC technique. [Bublik *et al.* (Ref. 73).] The dashed curve in (b) is the expected density change assuming Vegard’s law.

Carrier concentration vs Te concentration in the melt for InAs(Te) grown by LPE from In solution at 809 K. [Harrison and Houston (Ref. 51).]

Carrier concentration vs Te concentration in the melt for InAs(Te) grown by LPE from In solution at 809 K. [Harrison and Houston (Ref. 51).]

Carrier concentration vs Te concentration in the melt for InP(Te) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74).]

Carrier concentration vs Te concentration in the melt for InP(Te) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74).]

Zn concentration in the crystals vs atom fraction Zn in the solution for GaP(Zn) crystals grown from Ga solution at 1313 K. Data points: Trumbore *et al.* (Ref. 62) (◻); Panish and Casey (Ref. 85) (○,△). Dashed curve is the calculated variation assuming that the Zn-related compensating donors were grown-in. The full curve is the calculated variation assuming that they formed by complexing of some of the acceptors during cooling.

Zn concentration in the crystals vs atom fraction Zn in the solution for GaP(Zn) crystals grown from Ga solution at 1313 K. Data points: Trumbore *et al.* (Ref. 62) (◻); Panish and Casey (Ref. 85) (○,△). Dashed curve is the calculated variation assuming that the Zn-related compensating donors were grown-in. The full curve is the calculated variation assuming that they formed by complexing of some of the acceptors during cooling.

Segregation coefficient of Zn in GaSb(Zn) as a function of melt composition. Zn concentration . [Merten and Hatcher (Ref. 48).]

Segregation coefficient of Zn in GaSb(Zn) as a function of melt composition. Zn concentration . [Merten and Hatcher (Ref. 48).]

Segregation coefficient vs Zn concentration for GaSb(Zn) crystals grown from a congruent melt . [Merten and Hatcher (Ref. 48).]

Segregation coefficient vs Zn concentration for GaSb(Zn) crystals grown from a congruent melt . [Merten and Hatcher (Ref. 48).]

Hole concentration vs mole fraction Zn in solution for InP(Zn) LPE layers grown from In solution at 898 K. Data points; C-V measurement (●); van der Pauw (○). [Kuphal (Ref. 90).]

Hole concentration vs mole fraction Zn in solution for InP(Zn) LPE layers grown from In solution at 898 K. Data points; C-V measurement (●); van der Pauw (○). [Kuphal (Ref. 90).]

Hole and Zn concentrations in LEC-grown InP(Zn). [Roeksnoer *et al.* (Ref. 92).] Data points: hole concentration (x); Zn concentration (○). Full curve is the calculated Zn concentration. Dashed curve is to guide the eye to the experimental hole concentration data only.

Hole and Zn concentrations in LEC-grown InP(Zn). [Roeksnoer *et al.* (Ref. 92).] Data points: hole concentration (x); Zn concentration (○). Full curve is the calculated Zn concentration. Dashed curve is to guide the eye to the experimental hole concentration data only.

Variation in lattice parameter with doping concentration for InP(Zn) (△) and InP(Ge) (◻). [Morozov *et al.* (Ref. 98).] Dashed line is Vegard’s law dependence. Full line is the calculated dependence. Note that Zn obeys Vegard’s law, whereas, Ge shows a small dilation while Vegard’s law predicts a large contraction of the lattice.

Variation in lattice parameter with doping concentration for InP(Zn) (△) and InP(Ge) (◻). [Morozov *et al.* (Ref. 98).] Dashed line is Vegard’s law dependence. Full line is the calculated dependence. Note that Zn obeys Vegard’s law, whereas, Ge shows a small dilation while Vegard’s law predicts a large contraction of the lattice.

Hole concentration vs atom fraction Cd in solution for InP(Cd) LPE layers grown from In solution at 843 K(x) and 943 K(○). [Umebu and Robson (Ref. 91).]

Hole concentration vs atom fraction Cd in solution for InP(Cd) LPE layers grown from In solution at 843 K(x) and 943 K(○). [Umebu and Robson (Ref. 91).]

Hole concentration vs mole fraction Cd in solution for InP(Cd) LPE layers grown from In solution at 898 K. [Kuphal (Ref. 90)].

Hole concentration vs mole fraction Cd in solution for InP(Cd) LPE layers grown from In solution at 898 K. [Kuphal (Ref. 90)].

Segregation coefficient of Zn in InSb(Zn) grown by pulling from the melt vs Zn concentration in the crystal. [Belaya and Zemskov (Ref. 100).]

Segregation coefficient of Zn in InSb(Zn) grown by pulling from the melt vs Zn concentration in the crystal. [Belaya and Zemskov (Ref. 100).]

Carrier concentration vs Bi/Ga ratio for GaAs(Sn) grown by LPE from Ga–Bi solutions. Sn concentration in the solution, (○) and (x) Growth temperature 1100 K. [Yakusheva and Pogadaev (Ref. 55).]

Carrier concentration vs Bi/Ga ratio for GaAs(Sn) grown by LPE from Ga–Bi solutions. Sn concentration in the solution, (○) and (x) Growth temperature 1100 K. [Yakusheva and Pogadaev (Ref. 55).]

(a) Density and (b) lattice parameter vs Sn concentration in LEC-grown crystals. The dashed line in (b) is the Vegard’s law variation. [Anastas’eva *et al.* (Ref. 104).]

(a) Density and (b) lattice parameter vs Sn concentration in LEC-grown crystals. The dashed line in (b) is the Vegard’s law variation. [Anastas’eva *et al.* (Ref. 104).]

Carrier concentration vs Bi/Ga ratio for GaAs(Ge) grown by LPE from Ga-Bi solutions. Ge concentration in the solution, (x) and (●). Note the p to n transition at high Bi/Ga ratio. (The ringed data points indicate n type conduction). Growth temperature 1100 K. [Yakusheva and Pogadaev (Ref. 36).]

Carrier concentration vs Bi/Ga ratio for GaAs(Ge) grown by LPE from Ga-Bi solutions. Ge concentration in the solution, (x) and (●). Note the p to n transition at high Bi/Ga ratio. (The ringed data points indicate n type conduction). Growth temperature 1100 K. [Yakusheva and Pogadaev (Ref. 36).]

Compensation ratios for the LPE layers in Fig. 37 for . Ringed points indicate n type conduction.

Compensation ratios for the LPE layers in Fig. 37 for . Ringed points indicate n type conduction.

Calculated concentrations of the individual point defects vs Bi/Ga ratio for the layers shown in Fig. 37. For .

Calculated concentrations of the individual point defects vs Bi/Ga ratio for the layers shown in Fig. 37. For .

Carrier concentration and total Si concentration in GaP(Si) solution-grown crystals vs atomic percent Si in the solution. Mean growth temperature 1324 K. [Trumbore *et al.* (Ref. 108).] Carrier concentration: n type (○), p type (●). Spectroscopically determined total Si concentration (x). Full and dashed curves are the calculated total Si and carrier concentration, respectively.

Carrier concentration and total Si concentration in GaP(Si) solution-grown crystals vs atomic percent Si in the solution. Mean growth temperature 1324 K. [Trumbore *et al.* (Ref. 108).] Carrier concentration: n type (○), p type (●). Spectroscopically determined total Si concentration (x). Full and dashed curves are the calculated total Si and carrier concentration, respectively.

Carrier concentration and total Sn concentration in GaP(Sn) solution-grown crystals. Mean growth temperature 1343 K. [Trumbore *et al.* (Ref. 108).] Carrier concentration: n type (○), p type (●). Photometrically determined total Sn concentration (x). Full and dashed curves are the calculated total Sn and carrier concentration, respectively.

Carrier concentration and total Sn concentration in GaP(Sn) solution-grown crystals. Mean growth temperature 1343 K. [Trumbore *et al.* (Ref. 108).] Carrier concentration: n type (○), p type (●). Photometrically determined total Sn concentration (x). Full and dashed curves are the calculated total Sn and carrier concentration, respectively.

Carrier concentration and total Ge concentration in GaP(Ge) solution-grown crystals. Mean growth temperature 1320 K. [Trumbore *et al.* (Ref. 108).] Symbols and curves are as for Fig. 41.

Carrier concentration and total Ge concentration in GaP(Ge) solution-grown crystals. Mean growth temperature 1320 K. [Trumbore *et al.* (Ref. 108).] Symbols and curves are as for Fig. 41.

(a) Lattice parameter and (b) density vs Si concentration in the crystal for melt-grown crystals of GaSb(Si). Full lines are the calculated variation assuming the presence of only acceptors. [Wilke *et al.* (Ref. 114).]

(a) Lattice parameter and (b) density vs Si concentration in the crystal for melt-grown crystals of GaSb(Si). Full lines are the calculated variation assuming the presence of only acceptors. [Wilke *et al.* (Ref. 114).]

(a) Lattice parameter and (b) density vs Ge concentration in the crystal for melt-grown crystals of GaSb(Ge). Dashed lines are the calculated Vegard’s law variation assuming the presence of only acceptors. [Wilke *et al.* (Ref. 114).]

(a) Lattice parameter and (b) density vs Ge concentration in the crystal for melt-grown crystals of GaSb(Ge). Dashed lines are the calculated Vegard’s law variation assuming the presence of only acceptors. [Wilke *et al.* (Ref. 114).]

Donor and acceptor concentrations vs total Sn concentration in the crystal for LEC-grown InAs(Sn). The full lines are the calculated values assuming that the donor is and the acceptor is . [Anastas’eva *et al.* (Ref. 117).]

Donor and acceptor concentrations vs total Sn concentration in the crystal for LEC-grown InAs(Sn). The full lines are the calculated values assuming that the donor is and the acceptor is . [Anastas’eva *et al.* (Ref. 117).]

(a) Lattice parameter and (b) density vs Sn concentration in the crystal for melt-grown crystals of InAs(Sn). Full lines are the calculated variation assuming the presence of donors and acceptors. [Anastas’eva *et al.* (Ref. 117)]. Dashed curves are the variations predicted by Vegard’s law. The dotted-dashed curve in (b) corresponds to doubling the Sn concentration for each data point (see text). The fit to the lattice parameter is obtained with a dilation per defect of 0.4.

(a) Lattice parameter and (b) density vs Sn concentration in the crystal for melt-grown crystals of InAs(Sn). Full lines are the calculated variation assuming the presence of donors and acceptors. [Anastas’eva *et al.* (Ref. 117)]. Dashed curves are the variations predicted by Vegard’s law. The dotted-dashed curve in (b) corresponds to doubling the Sn concentration for each data point (see text). The fit to the lattice parameter is obtained with a dilation per defect of 0.4.

Carrier concentration vs atomic percent Sn in solution for LPE-grown InAs(Sn) layers. Growth temperature 809 K. [Harrison and Houston (Ref. 51).]

Carrier concentration vs atomic percent Sn in solution for LPE-grown InAs(Sn) layers. Growth temperature 809 K. [Harrison and Houston (Ref. 51).]

Carrier concentration vs total Ge concentration in LEC-grown InP(Ge) crystals. The dashed curve assumes that, in addition to donors, is present as an ionized acceptor complex. The full curve assumes that the complex is neutral. The infilled data points (●) are for crystals having second phase inclusions. [Zakharenkov *et al.* (Ref. 120).]

Carrier concentration vs total Ge concentration in LEC-grown InP(Ge) crystals. The dashed curve assumes that, in addition to donors, is present as an ionized acceptor complex. The full curve assumes that the complex is neutral. The infilled data points (●) are for crystals having second phase inclusions. [Zakharenkov *et al.* (Ref. 120).]

Carrier concentration vs Ge concentration in the solution for InP(Ge) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74).]

Carrier concentration vs Ge concentration in the solution for InP(Ge) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74).]

Carrier concentration vs Sn concentration in LEC-grown InP(Sn) crystals. Infilled symbols (●) refer to crystals having second phase inclusions. [Zakharenkov *et al.* (Ref. 120).]

Carrier concentration vs Sn concentration in LEC-grown InP(Sn) crystals. Infilled symbols (●) refer to crystals having second phase inclusions. [Zakharenkov *et al.* (Ref. 120).]

Carrier concentration vs Sn concentration in the solution for InP(Sn) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74).]

Carrier concentration vs Sn concentration in the solution for InP(Sn) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74).]

Carrier concentration vs Si concentration in the solution for InP(Si) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74)].

Carrier concentration vs Si concentration in the solution for InP(Si) layers grown by LPE from In solution at 923 K. [Astles *et al.* (Ref. 74)].

EL2 concentration in annealed melt-grown GaAs vs atom fraction As in the melt from which the crystal was grown. Data of Otoki *et al.* (Ref. 14) (x), Kiessling *et al.* (Ref. 49) (○) and Holmes *et al.* (Ref. 50) (◼). (see Sec. X A). The curve is the model result.

EL2 concentration in annealed melt-grown GaAs vs atom fraction As in the melt from which the crystal was grown. Data of Otoki *et al.* (Ref. 14) (x), Kiessling *et al.* (Ref. 49) (○) and Holmes *et al.* (Ref. 50) (◼). (see Sec. X A). The curve is the model result.

Calculated equilibrium total concentrations of , , and vs reciprocal temperature for crystals grown from under conditions corresponding to the As-rich solidus. (●) and (○) from Luysberg *et al.* (Ref. 17). (x) from Otoki *et al.* (Ref. 14) for crystals that have had a long duration anneal under As-rich conditions. (see Sec. X B). Full lines are model results for and and the dashed curve are for ; all are summed over all their charge states.

Calculated equilibrium total concentrations of , , and vs reciprocal temperature for crystals grown from under conditions corresponding to the As-rich solidus. (●) and (○) from Luysberg *et al.* (Ref. 17). (x) from Otoki *et al.* (Ref. 14) for crystals that have had a long duration anneal under As-rich conditions. (see Sec. X B). Full lines are model results for and and the dashed curve are for ; all are summed over all their charge states.

Carrier concentration vs growth temperature for low temperature gas-source MBE layers of InP grown under P-rich conditions [Liang *et al.* (Ref. 30)].

Carrier concentration vs growth temperature for low temperature gas-source MBE layers of InP grown under P-rich conditions [Liang *et al.* (Ref. 30)].

Hole concentration vs reciprocal temperature for LPE growth of GaSb. [Anayama *et al.* (Ref. 31)] (●) GaSb grown from Sb-rich solution; (▲) GaSb grown from Ga-rich solution; (○) GaSb grown from stoichiometric melt; (Takeda *et al.*). (△) AlGaSb grown from Ga-rich solution.

Hole concentration vs reciprocal temperature for LPE growth of GaSb. [Anayama *et al.* (Ref. 31)] (●) GaSb grown from Sb-rich solution; (▲) GaSb grown from Ga-rich solution; (○) GaSb grown from stoichiometric melt; (Takeda *et al.*). (△) AlGaSb grown from Ga-rich solution.

Experimental data of Yakushaev and Chikichev (Ref. 167) on the solubility of GaAs in Ga/Bi solutions of varying Ga/Bi ratio at temperatures of, reading downwards, 850, 800, and . The dashed curve is the result of using a model due to Jordan (Ref. 24) [see Hurle (Ref. 1)] for a temperature of . The full curves are the result of using the formula in Appendix C.

Experimental data of Yakushaev and Chikichev (Ref. 167) on the solubility of GaAs in Ga/Bi solutions of varying Ga/Bi ratio at temperatures of, reading downwards, 850, 800, and . The dashed curve is the result of using a model due to Jordan (Ref. 24) [see Hurle (Ref. 1)] for a temperature of . The full curves are the result of using the formula in Appendix C.

## Tables

Defects incorporated into the thermodynamic model for each compound.

Defects incorporated into the thermodynamic model for each compound.

Entropies and enthalpies of formation of the native point defects. Data in italics indicates an estimate of the enthalpy was made by comparing with related values. The italicized subscripts, and denote the growth condition (temperature) for which the fit was made.

Entropies and enthalpies of formation of the native point defects. Data in italics indicates an estimate of the enthalpy was made by comparing with related values. The italicized subscripts, and denote the growth condition (temperature) for which the fit was made.

Mass action constants for dopant incorporation. The first number against each K is the entropy (in entropy unit). The second number is the enthalpy (in electron volt). Italicized entries are estimated in comparison with adjacent values when experimental data was available at a single temperature only. The italicized subscripts and indicate the growth process (temperature) for which the fit was obtained.

Mass action constants for dopant incorporation. The first number against each K is the entropy (in entropy unit). The second number is the enthalpy (in electron volt). Italicized entries are estimated in comparison with adjacent values when experimental data was available at a single temperature only. The italicized subscripts and indicate the growth process (temperature) for which the fit was obtained.

Binary regular solution interaction parameters for Group III and Group V atoms with dopant atoms. (Bracketed zero indicates default value. Interaction parameter .) (Asterisk “” denotes this work.)

Binary regular solution interaction parameters for Group III and Group V atoms with dopant atoms. (Bracketed zero indicates default value. Interaction parameter .) (Asterisk “” denotes this work.)

Philips/van Vechten modified covalent radii.^{168}

Philips/van Vechten modified covalent radii.^{168}

Ionization energies of native point defects. (Energies are in millielectron volt with donor states measured from the conduction band edge and acceptor states from the valence band edge. Bracketed values are estimates approximately scaled to energy gaps.)

Ionization energies of native point defects. (Energies are in millielectron volt with donor states measured from the conduction band edge and acceptor states from the valence band edge. Bracketed values are estimates approximately scaled to energy gaps.)

Dopant ionization energies. (Energies are in millielectron volt. Donor ionization energies are measured from conduction band edge and acceptor ionization energies from valence band edge. Subscripts A and B refer to Group III and Group V sites, respectively. Bracketed values are inferred from measured values for dopants of related type.)

Dopant ionization energies. (Energies are in millielectron volt. Donor ionization energies are measured from conduction band edge and acceptor ionization energies from valence band edge. Subscripts A and B refer to Group III and Group V sites, respectively. Bracketed values are inferred from measured values for dopants of related type.)

Electrophysical properties of the III–V compounds. (Coefficients of the Varshni equation^{179} .)

Electrophysical properties of the III–V compounds. (Coefficients of the Varshni equation^{179} .)

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