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Low-temperature electron mobility in doped semiconductors with high dielectric constant
by Khachatur G. Nazaryan, Mikhail Feigel'man
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Submission summary
| Authors (as registered SciPost users): | Mikhail V. Feigel'man · Khachatur G. Nazaryan |
| Submission information | |
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| Preprint Link: | scipost_202209_00051v1 (pdf) |
| Date submitted: | Sept. 23, 2022, 7:22 p.m. |
| Submitted by: | Khachatur G. Nazaryan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We propose and study theoretically a new mechanism of electron-impurity scattering in doped seminconductors with large dielectric constant. It is based upon the idea of \textit{vector} character of deformations caused in the crystalline lattice by any point defects siting asymmetrically in the unit cell. In result, local lattice compression due to the elastic deformations decay as $1/r^2$ with distance from impurity. Electron scattering (due to standard deformation potential) on such defects leads to low-temperature mobility $\mu(n)$ scaling with electron density $n$ of the form $\mu(n) \propto n^{-2/3}$ that is close to experimental observations on a number of relevant materials.
Current status:
Has been resubmitted
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-10-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202209_00051v1, delivered 2022-10-17, doi: 10.21468/SciPost.Report.5915
Report
In the manuscript, the electron mobility dependence on impurity concentration in doped semiconductors with high dielectric constant is examined. The aim of this work is to explain the power-law dependence of the mobility observed in a number of recent experiments. Due to large dielectric constants of the studied materials, the Coulomb impurity scattering is irrelevant, and some other scattering mechanism should dominate. According to the experimental data, this mechanism results in the correct concentration dependence if the scattering potential behaves as 1/r^2. The author’s proposal is that such a potential can be caused by a deformation induced by the point-like defects asymmetrically located in the elementary cell. The latter is large and complicated in the studied materials, which supports the author’s idea.
The proposed idea is formulated in Eqs. (1)-(3). Then, in Eqs. (4)-(8), authors make standard textbook transformations which can be found, e.g., in [A.A. Abrikosov, Fundamentals of the theory of metals, 1988. United States: Elsevier Science Pub Co Inc.] and obtain the transport relaxation time and the mobility. The scattering potential ~1/r^2 does not allow for description of the experimental data, and the authors take into account that, not only the transport relaxation time, but also the effective mass of carriers depends on the concentration, as it follows from independent measurements. The effective mass varies up to the factor of 5 according to Fig. 1. Account for this strong mass variation allows for explaining the mobility dependence on the concentration for a few materials in a wide concentration window, Fig. 3. The authors also check that the fitting parameter corresponds to reasonable deformation values.
The manuscript looks scientific and convincing, and it can be published after clarifying the following points.
1. If there are some independent witnesses for the defects asymmetrically positioned in the unit cells? Is it possible to find them by, e.g., AFM technique? If there are relevant publications on this issue?
2. Why do these scatterers not scatter electrons like defects with a short-range potential? The authors exclude this mechanism because it results in an incorrect dependence of the mobility, but why this it is excluded physically? It should be much stronger than the proposed deformation-potential mechanism requiring an asymmetrical position of a defect in the unit cell.
3. What is the reason for the effective mass dependence on concentration? This strong dependence means a sufficient nonparabolicity of the energy spectrum. In this case the density-of-states mass is defined as m=p/(dE/dp). How does it correspond to Eq. (11)?
The proposed idea is formulated in Eqs. (1)-(3). Then, in Eqs. (4)-(8), authors make standard textbook transformations which can be found, e.g., in [A.A. Abrikosov, Fundamentals of the theory of metals, 1988. United States: Elsevier Science Pub Co Inc.] and obtain the transport relaxation time and the mobility. The scattering potential ~1/r^2 does not allow for description of the experimental data, and the authors take into account that, not only the transport relaxation time, but also the effective mass of carriers depends on the concentration, as it follows from independent measurements. The effective mass varies up to the factor of 5 according to Fig. 1. Account for this strong mass variation allows for explaining the mobility dependence on the concentration for a few materials in a wide concentration window, Fig. 3. The authors also check that the fitting parameter corresponds to reasonable deformation values.
The manuscript looks scientific and convincing, and it can be published after clarifying the following points.
1. If there are some independent witnesses for the defects asymmetrically positioned in the unit cells? Is it possible to find them by, e.g., AFM technique? If there are relevant publications on this issue?
2. Why do these scatterers not scatter electrons like defects with a short-range potential? The authors exclude this mechanism because it results in an incorrect dependence of the mobility, but why this it is excluded physically? It should be much stronger than the proposed deformation-potential mechanism requiring an asymmetrical position of a defect in the unit cell.
3. What is the reason for the effective mass dependence on concentration? This strong dependence means a sufficient nonparabolicity of the energy spectrum. In this case the density-of-states mass is defined as m=p/(dE/dp). How does it correspond to Eq. (11)?
Report #1 by Anonymous (Referee 1) on 2022-10-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202209_00051v1, delivered 2022-10-12, doi: 10.21468/SciPost.Report.5880
Strengths
1-Originality 2-Timeliness 3- Relevance to experimental data
Weaknesses
1- The physical meaning of the force F is barely discussed. 2- Comparison with the experimental data is somewhat selective and the discrepancies not sufficiently presented.
Report
See the attached file.
Requested changes
See the attached.