Native defects and self-diffusion in GaSb
Summary (2 min read)
Introduction
- This is an electronic reprint of the original article.
- The data supports the next-nearest-neighbor model for the self-diffusion, in which the migration occurs independently in the different sublattices.
- In this work the authors have studied the electronic structures and the formation energies of native defects in GaSb with ab initio methods.
- In Sec. III the authors present the results for the atomic and electronic structure of the stable native defects and study the concentrations of the defects, especially those of residual acceptors.
II. METHODS
- The structures and the total energies of the native defects are calculated within the density-functional theory12 and the local-density approximation ~LDA!.13.
- The formation energies of the defects are calculated following the formalism used by Zhang and Northrup.20.
- The atomic chemical potentials obtain values below their bulk precipitates: mGa<mGa(bulk) and mSb<mSb(bulk) .
- The electron chemical potential me is allowed to vary between zero and the experimental band gap value, 0 <me<Eg .
- The used supercell size and the k-point sampling may also induce errors in the formation [This article is copyrighted as indicated in the article.
A. Structures and energies
- The charge states, the symmetries and the formation energies for the native defects in GaSb are presented in Table I. charge states indicate that the partially occupied t2 level is split.
- This is a significantly different behavior from the anion antisite defects in GaAs.
- [This article is copyrighted as indicated in the article.
- Finally, in the Ta site Sb is stable in the charge state ~31!, which preserves the perfect Td symmetry.
B. Concentrations
- The p-type nature of GaSb is naturally explained by the calculations.
- The general trends for the residual hole concentrations are shown in Fig.
- In comparing GaSb against GaAs one also notes the absence of compensating electrically active defects.
- [This article is copyrighted as indicated in the article.
- Hence, experimental evidence indicates that there are two types of acceptors of which only one is present at Ga-rich conditions, while both are present in similar concentrations in the Sb-rich case.
A. Nearest-neighbor diffusion mechanism
- The nearest-neighbor diffusion mechanism by vacancies consists of successive atomic movements where a nearestneighbor atom moves to the vacancy.
- To the right, the Reaction ~8! is endothermic and involves electron transfer.
- The reaction energy, calculated for the most stable charge states, increases from 0.6 eV to 1.9 eV as the Fermi level is moved from the VBM to the conduction band minimum ~CBM!.
- Charge states, whereas VGaGaSb can be found in several negative charge states as shown in Table I. For GaSb this conclusion may not be valid since the diffusion experiments have been performed for intrinsic and p-type material.
B. Next-nearest-neighbor diffusion
- In the next-nearest-neighbor diffusion mechanism as suggested by Bracht et al.2,3 the Ga and Sb atoms diffuse independently of each other via either vacancies or interstitials.
- On the basis of the calculated concentrations the authors obtain a simple explanation for the large difference in the Ga and the Sb self-diffusion coefficients as found in experiments.
- [This article is copyrighted as indicated in the article.
- Therefore, if Reaction ~9! and the subsequent dissociation are assumed to be effective, the VGa concentration levels off as one moves toward Ga-rich conditions.
- Reaction ~12! could thus suppress the concentration of Sb interstitials in the presence of Ga vacancies.
C. Ga- and Sb-rich ambient conditions
- In the experiment by Bracht et al.2,3 diffusion measurements were performed for both Ga- and Sb-rich ambient conditions with the temperature varying between 571 and 708 °C.2,3.
- The main observations of these experiments were that the diffusion coefficient for Ga is identical under Sb-and Ga-rich ambient conditions, and that there is a lack of significant diffusion of Sb under Garich conditions.
- If the surface supply of the Gai defect would be responsible for Ga diffusion, the different surface conditions should produce differing diffusion coefficients.
- 2,3 For Ga-rich conditions the concentrations of Sb vacancies and interstitials in the as-grown material are very low, ;109 and ;0 cm23, respectively.
- [This article is copyrighted as indicated in the article.
V. CONCLUSIONS
- The authors have made a comprehensive study of structures, formation energies, energy levels, and concentrations of native defects in undoped GaSb.
- The native defects show similarity in atomic and electronic structures with those in GaAs.
- A metastable state is found for the anion antisite SbGa .
- An important difference compared to GaAs is that in GaSb the anion antisite SbGa does not have ionization levels deep in the band gap, whereas in GaAs the ionization levels of the AsGa antisite cause the semi-insulating character of the asgrown material.
- The concentrations of the relevant defects estimated for typical experimental conditions are used to discuss the observed highly asymmetric self-diffusion of Ga and Sb in GaSb, i.e., the phenomenon that the diffusion of Ga is several orders in magnitude faster than that of Sb.
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Frequently Asked Questions (16)
Q2. Why is the material assumed to reach a thermal equilibrium state?
Due to the long diffusion times the material is actually assumed to reach a thermal equilibrium state which corresponds to Sb-rich growth conditions at ;700 °C.3
Q3. What is the effect of p-type doping on the formation of Sb defects?
For the Sb defects the formation energies of both vacancies and interstitials would decrease, but their concentration would still be small compared to that of Ga vacancies and interstitials.
Q4. What is the reaction energy for the complex to dissociate?
The reaction energy for the complex to dissociate decreases from 1.0 to 0.25 eV as the Fermi level is moved from the VBM to the CBM.
Q5. What is the effect of p-type doping on the formation of Ga defects?
The authors estimate that an extreme p-type doping would lower the formation energy of the Ga defect by ;0.1–0.3 eV ~at 450 °C! for stoichiometric or Ga-rich growth conditions thus increasing its concentration.
Q6. What is the vacancy mechanism for the diffusion of Sb?
In the case of the Sb diffusion, a high temperature and Sb-rich ambient conditions are found to increase the concentration of Sb interstitials and thereby the Sb self-diffusion.
Q7. How do you solve the atomistic diffusion mechanism?
In order to resolve the actual atomistic diffusion mechanism ~vacancy or interstitial! for both elements, it would be necessary to perform simulations for the diffusivities.
Q8. What are the mechanisms that have been neglected in these calculations?
The other mechanisms, such as the antisite exchange or the collective diffusive mechanisms, have been neglected in these calculations.
Q9. What is the effect of the increase of the GaSb acceptor concentration on the Ferm?
When moving toward Ga-rich conditions the increase of the GaSb acceptor concentration is seen to pull the Fermi level downward from its intrinsic value.
Q10. What is the Fermi level for the VSb defects?
For Ga-rich growth conditions at T5450 °C the Fermi level is at 0.15 eV ~Fig. 2!, which corresponds to the value ;20.3 eV for the reaction energy.
Q11. How do the authors determine the relative concentrations of the defects?
In showing the relative defect concentrations the authors use the temperature 450 °C, which corresponds to the growth temperature of the molecular beam epitaxy ~MBE!
Q12. What is the reaction that is proposed to explain the loss of Sb interstitials?
The recombination of Sb interstitials and Ga vacancies is a reaction which has been proposed to explain the loss of Sb interstitials:2,3SbGa VGa2Sbi .
Q13. What is the general trend for the residual hole concentrations?
3. There is a decrease in the hole concentration when moving from higher to lower temperatures and from Ga-rich to Sbrich conditions.
Q14. What is the entropy of states of the valence and conduction bands?
The effective densities of states of the valence and conduction bands are calculated from the effective masses of electrons and holes.
Q15. What is the entropy difference in the valence?
The entropy differences can be of the order of 3kB ,6 which corresponds to internal energies ;0.2 eV in the temperature range of 400 to 500 °C.
Q16. Why was the recombination of Sb interstitials performed under Ga-?
In contrast, due to the long diffusion times the Sb diffusion experiments performed under Sb-rich ambient conditions were considered to change the sample composition to correspond to Sb-rich growth conditions.