The effect of surface charge self-organization on gate-induced electron and hole two-dimensional systems

A model is proposed for describing the self-organization of localized charges and quantum scattering in undoped GaAs/AlGaAs structures in which a two-dimensional gas of electrons or holes is created by the corresponding gate voltage. We assume that in such a metal-dielectric-undoped semiconductor structure carrier scattering on surface charges localized at the interface between GaAs and the dielectric dominates. Proposed model considers these charges and the corresponding image charges in the metal gate as a closed system in a thermostat. The electrostatic self-organization for this system in thermodynamic equilibrium is studied numerically using the Metropolis algorithm in a wide temperature range. It is shown that, at T > 100 K, a simple formula derived from the theory of two-dimensional one-component plasma gives almost the same behavior of the structural factor at low wave numbers as the Monte Carlo calculation. The scattering times of gate-induced carriers are described by formulas in which the structural factor characterizes the frozen disorder in the given system. In these formulas, the behavior of the structural factor at small wave numbers is decisive. A calculation using these formulas with disorder corresponding to infinite T gives two to three times shorter scattering times than in the corresponding experiments. We found that the theory is consistent with experiment at a freezing point of disorder T ≈ 1000 K for a sample with a two-dimensional electron gas and T ≈ 700 K for a sample with a two-dimensional hole gas. The found values are an upper estimate of the freezing temperature in the studied structures, since the model ignores sources of disorder other than temperature.

undoped structures, gate-induced two-dimensional systems, surface charge, disorder freezing temperature

1. Cowley A. M., Sze S. M. Surface states and barrier height of metal-semiconductor systems. J. Appl. Phys., 1965, vol. 36, no. 10, pp. 3212—3220. DOI: 10.1063/1.1702952

2. Sze S. M. Physics of semiconductor devices. New York: John Willey, 1981, 868 p.

3. Spicer W. E., Lindau I., Skeath P., Su C. Y. Unified defect model and beyond. J. Vac. Sci. Technol., 1980, vol. 17, no. 5, pp. 1019—1027. DOI: 10.1116/1.570583

4. Darling R. B. Defect-state occupation, Fermi-level pinning, and illumination effects on free semiconductor surfaces. Phys. Rev. B, 1991, vol. 43, no. 5, pp. 4071—4083. DOI: 10.1103/PhysRevB.43.4071

5. Harrell R. H., Pyshkin K. S., Simmons M. Y., Ritchie D. A., Ford C. J. B., Jones G. A. C., Pepper M. Fabrication of high-quality one- and two-dimensional electron gases in undoped GaAs/AlGaAs heterostructures. Appl. Phys. Lett., 1999, vol. 74, no. 16, pp. 2328—2330. DOI: 10.1063/1.123840

6. Tkachenko O. A., Tkachenko V. A., Baksheyev D. G., Pyshkin K. S., Harrell R. H., Linfield E. H., Ritchie D. A., Ford C. J. B. Electrostatic potential and quantum transport in a one-dimensional channel of an induced two-dimensional electron gas. J. Appl. Phys., 2001, vol. 89, no. 9, pp. 4993—5000. DOI: 10.1063/1.1352024

7. Chen J. C. H., Wang D. Q., Klochan O., Micolich A. P., Das Gupta K., Sfigakis F., Ritchie D. A., Reuter D., Wieck A. D., Hamilton A. R. Fabrication and characterization of ambipolar devices on an undoped AlGaAs/GaAs heterostructure. Appl. Phys. Lett., 2012, vol. 100, no. 5, p. 052101. DOI: 10.1063/1.3673837

8. Chen J. C. H., Klochan O., Micolich A. P., Das Gupta K., Sfigakis F., Ritchie D. A., Trunov K., Reuter D., Wieck A. D., Hamilton A. R. Fabrication and characterisation of gallium arsenide ambipolar quantum point contacts. Appl. Phys. Lett., 2015, vol. 106, no. 18, p. 183504. DOI: 10.1063/1.4918934

9. Taneja D., Sfigakis F., Croxall A. F., Das Gupta K., Narayan V., Waldie J., Farrer I., Ritchie D. A. N-type ohmic contacts to undoped GaAs/AlGaAs quantum wells using only front-sided processing: application to ambipolar FETs. Semicond. Sci. Technol., 2016, vol 31, no. 6, p. 065013. DOI: 10.1088/0268-1242/31/6/065013

10. Miserev D. S., Srinivasan A., Tkachenko O. A., Tka­chen­ko V. A., Farrer I., Ritchie D. A., Hamilton A. R., Sushkov O. P. Mechanisms for strong anisotropy of In-plane g-factors in hole based quantum point contacts. Phys. Rev. Lett., 2017, vol. 119, no. 11, p. 116803. DOI: 10.1103/PhysRevLett.119.116803

11. Mak W. Y., Das Gupta K., Beere H. E., Farrer I., Sfigakis F., Ritchie D. A. Distinguishing impurity concentrations in GaAs and AlGaAs using very shallow undoped heterostructures. Appl. Phys. Lett., 2010, vol. 97, no. 24, p. 242107. DOI: 10.1063/1.3522651

12. Wang D. Q., Chen J. C. H., Klochan O., Das Gupta K., Reuter D., Wieck A. D., Ritchie D. A., Hamilton A. R. Influence of surface states on quantum and transport lifetimes in high-quality undoped heterostructures. Phys. Rev. B, 2013, vol. 87, no. 19, p. 195313. DOI: 10.1103/PhysRevB.87.195313

13. Tkachenko O. A., Tkachenko V. A., Terekhov I. S., Sushkov O. P. Effects of Coulomb screening and disorder on an artificial graphene based on nanopatterned semiconductor. 2D Mater., 2015, vol. 2, no. 1, p. 014010. DOI: 10.1088/2053-1583/2/1/014010

14. Tkachenko O. A., Baksheev D. G., Tkachenko V. A., Sushkov O. P. Modeling of localized charges self-organization at the boundary of a semiconductor with a gate dielectric. Proceedings of the International Conference “Advanced Mathematics, Computations and Applications 2019” (AMCA-2019). Novosibirsk: NSU, 2019, pp. 515—521 (In Russ.). DOI: 10.24411/9999-016A-2019-10082

15. Fetter A. L. Electrodynamics and thermodynamics of a classical electron surface layer. Phys. Rev. B, 1974, vol. 10, no. 9, pp. 3739—3745. DOI: 10.1103/PhysRevB.10.3739

16. Gann R. C., Chakravarty S., Chester G. V. Monte Carlo simulation of the classical two-dimensional one-component plasma. Phys. Rev. B, 1979, vol. 20, no. 1, pp. 326—344. DOI: 10.1103/PhysRevB.20.326

17. Efros A. L., Pikus F. G. Samsonidze G. G. Maximum low-temperature mobility of two-dimensional electrons in heterojunctions with a thick spacer layer. Phys. Rev. B, 1990, vol. 41, no. 12, pp. 8295—8301. DOI: 10.1103/PhysRevB.41.8295

18. Das Sarma S., Hwang E. H., Kodiyalam S., Pfeiffer L. N., West K. W. Transport in two-dimensional modulation-doped semiconductor structures. Phys. Rev. B, 2015, vol. 91, no. 20, p. 205304. DOI: 10.1103/PhysRevB.91.205304

19. Das Sarma S., Stern F. Single-particle relaxation time versus scattering time in an impure electron gas. Phys. Rev. B, 1985, vol. 32, no. 12, pp. 8442—8444. DOI: 10.1103/PhysRevB.32.8442

20. Chaplik A. V. Possible crystallization of charge carriers in low-density inversion layers. J. Experimental and Theoretical Physics, 1972, vol. 62, no. 2, pp. 395—398. URL: http://www.jetp.ac.ru/cgi-bin/dn/e_035_02_0395.pdf

21. Metropolis N., Rosenbluth A. W., Rosenbluth M. N., Teller A. H., Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys., 1953, vol. 21, no. 6, p. 1087. DOI: 10.1063/1.1699114

22. Rosenbluth M. N., Rosenbluth A. W. Further results on Monte Carlo equations of state. J. Chem. Phys., 1954, vol. 22, no. 5, p. 881. DOI: 10.1063/1.1740207

23. Chib S., Greenberg E. Understanding the Metropolis-Hastings algorithm. The American Statistician, 1995, vol. 49, no. 4, pp. 327—335. DOI: 10.2307/2684568

24. Kotkin G. L. Lectures on statistical physics. Moscow; Izhevsk: Regulyarnaya i khaoticheskaya dinamika, 2006, 190 p. (In Russ.)

25. Harrang J. P., Higgins R. J., Goodall R. K., Jay P. R., Laviron M., Delescluse P. Quantum and classical mobility determination of the dominant scattering mechanism in the two-dimensional electron gas of an AlGaAs/GaAs heterojunction. Phys. Rev. B, 1985, vol. 32, no. 12, pp. 8126—8135. DOI: 10.1103/PhysRevB.32.8126

26. Mani R. G., Anderson J. R. Study of the single-particle and transport lifetimes in GaAs/AlxGal-xAs. Phys. Rev. B, 1988, vol. 37, no. 8, pp. 4299—4302. DOI: 10.1103/PhysRevB.37.4299

27. Coleridge P. T., Stoner R., Fletcher R. Low-field transport coefficients in GaAs/Ga1-xAlxAs heterostructures. Phys. Rev. B, 1989, vol. 39, pp. 1120—1124. DOI: 10.1103/PhysRevB.39.1120

28. Bystrov S. D., Kreshchuk A. M., Tuan L., Novikov S. V., Polyanskaya T. A., Savelev I. G., Shik A. Y. Shubnikov-de Hass oscillations in a nonuniform 2D electron-gas. Semiconductors, 1994, vol. 28, no. 1, pp. 55—58.