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A thermodynamic analysis of native point defect and dopant solubilities in zinc-blende III–V semiconductors
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10.1063/1.3386412
/content/aip/journal/jap/107/12/10.1063/1.3386412
http://aip.metastore.ingenta.com/content/aip/journal/jap/107/12/10.1063/1.3386412

Figures

Image of FIG. 1.
FIG. 1.

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.

Image of FIG. 2.
FIG. 2.

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

Image of FIG. 3.
FIG. 3.

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

Image of FIG. 4.
FIG. 4.

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

Image of FIG. 5.
FIG. 5.

Calculated GaSb solidus. Arrow marks the congruent point.

Image of FIG. 6.
FIG. 6.

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

Image of FIG. 7.
FIG. 7.

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

Image of FIG. 8.
FIG. 8.

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

Image of FIG. 9.
FIG. 9.

Calculated InSb solidus. Arrow marks the congruent point.

Image of FIG. 10.
FIG. 10.

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).

Image of FIG. 11.
FIG. 11.

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)].

Image of FIG. 12.
FIG. 12.

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).

Image of FIG. 13.
FIG. 13.

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.

Image of FIG. 14.
FIG. 14.

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.

Image of FIG. 15.
FIG. 15.

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.

Image of FIG. 16.
FIG. 16.

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.

Image of FIG. 17.
FIG. 17.

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) (◼).

Image of FIG. 18.
FIG. 18.

(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).]

Image of FIG. 19.
FIG. 19.

(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.

Image of FIG. 20.
FIG. 20.

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.

Image of FIG. 21.
FIG. 21.

(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.

Image of FIG. 22.
FIG. 22.

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.

Image of FIG. 23.
FIG. 23.

(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.

Image of FIG. 24.
FIG. 24.

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).]

Image of FIG. 25.
FIG. 25.

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).]

Image of FIG. 26.
FIG. 26.

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.

Image of FIG. 27.
FIG. 27.

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

Image of FIG. 28.
FIG. 28.

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

Image of FIG. 29.
FIG. 29.

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).]

Image of FIG. 30.
FIG. 30.

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.

Image of FIG. 31.
FIG. 31.

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.

Image of FIG. 32.
FIG. 32.

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).]

Image of FIG. 33.
FIG. 33.

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

Image of FIG. 34.
FIG. 34.

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

Image of FIG. 35.
FIG. 35.

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).]

Image of FIG. 36.
FIG. 36.

(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).]

Image of FIG. 37.
FIG. 37.

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).]

Image of FIG. 38.
FIG. 38.

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

Image of FIG. 39.
FIG. 39.

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

Image of FIG. 40.
FIG. 40.

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.

Image of FIG. 41.
FIG. 41.

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.

Image of FIG. 42.
FIG. 42.

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.

Image of FIG. 43.
FIG. 43.

(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).]

Image of FIG. 44.
FIG. 44.

(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).]

Image of FIG. 45.
FIG. 45.

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).]

Image of FIG. 46.
FIG. 46.

(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.

Image of FIG. 47.
FIG. 47.

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

Image of FIG. 48.
FIG. 48.

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).]

Image of FIG. 49.
FIG. 49.

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).]

Image of FIG. 50.
FIG. 50.

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).]

Image of FIG. 51.
FIG. 51.

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).]

Image of FIG. 52.
FIG. 52.

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)].

Image of FIG. 53.
FIG. 53.

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.

Image of FIG. 54.
FIG. 54.

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.

Image of FIG. 55.
FIG. 55.

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

Image of FIG. 56.
FIG. 56.

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.

Image of FIG. 57.
FIG. 57.

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

Generic image for table
Table I.

Defects incorporated into the thermodynamic model for each compound.

Generic image for table
Table II.

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.

Generic image for table
Table III.

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.

Generic image for table
Table IV.

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.)

Generic image for table
Table V.

Philips/van Vechten modified covalent radii.168

Generic image for table
Table VI.

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.)

Generic image for table
Table VII.

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.)

Generic image for table
Table VIII.

Electrophysical properties of the III–V compounds. (Coefficients of the Varshni equation179 .)

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/content/aip/journal/jap/107/12/10.1063/1.3386412
2010-06-21
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A thermodynamic analysis of native point defect and dopant solubilities in zinc-blende III–V semiconductors
http://aip.metastore.ingenta.com/content/aip/journal/jap/107/12/10.1063/1.3386412
10.1063/1.3386412
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