Vol. 31
Latest Volume
All Volumes
PIERM 137 [2026] PIERM 136 [2025] PIERM 135 [2025] PIERM 134 [2025] PIERM 133 [2025] PIERM 132 [2025] PIERM 131 [2025] PIERM 130 [2024] PIERM 129 [2024] PIERM 128 [2024] PIERM 127 [2024] PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2013-06-30
Combined Method for Simulating Electron Spectrum of δ-Doped Quantum Wells in n-Si with Many-Body Corrections
By
Progress In Electromagnetics Research M, Vol. 31, 215-229, 2013
Abstract
The combined method to investigate the electron spectrum of single n-type d-doped quantum wells in silicon is proposed. It is based on computing the electron potential energy by means of the Thomas-Fermi method at finite temperatures; then the obtained electron potential energy is applied to the iteration procedure with solving the Schrodinger equations for the electron spectrum and the Poisson one for the potential energy. The many-body corrections to the electron spectrum in the quantum well also have been investigated. The combined method demonstrates a rapid convergence. It is shown that that the simple TF method gives a good approximation for the electron potential energy and for the total electron concentration within the well.
Citation
Christian Castrejon-Martinez, Volodymyr V. Grimalsky, Luis Manuel Gaggero-Sager, and Svetlana V. Koshevaya, "Combined Method for Simulating Electron Spectrum of δ-Doped Quantum Wells in n-Si with Many-Body Corrections," Progress In Electromagnetics Research M, Vol. 31, 215-229, 2013.
doi:10.2528/PIERM13041210
References

1. Yu, P. Y. and M. Cardona, Fundamentals of Semiconductors. Physics and Materials Properties, Springer, New York, 2010.
doi:10.1007/978-3-642-00710-1

2. Schubert, E. F., A. Fische, and K. Ploog, "The delta-doped field-effect transistor (δFET)," IEEE Trans. Electron. Devices, Vol. 33, No. 5, 625-630, 1986.
doi:10.1109/T-ED.1986.22543        Google Scholar

3. Ploog, K., "Delta- (δ-) doping in MBE-grown GaAs: Concept and device application," J. Cryst. Growth, Vol. 81, No. 4, 304-313, 1987.
doi:10.1016/0022-0248(87)90409-X        Google Scholar

4. Schubert, E. F., "Delta doping of III-V compound semiconductors: Fundamentals and device applications," J. Vac. Sci. Technol., Vol. A8, No. 3, 2980-2996, 1990.        Google Scholar

5. Nakagawa, K., A. A. van Gorkum, and Y. Shiraki, "Atomic layer doped field effect transistor fabricated using Si molecular beam epitaxy," Appl. Phys. Lett., Vol. 54, No. 19, 1869-1871, 1989.
doi:10.1063/1.101263        Google Scholar

6. Word, C. E. C., G. Metze, J. Berry, and L. F. Eastman, "Complex free-carrier profile synthesis by `atomic plane' doping of MBE GaAs," J. Appl. Phys., Vol. 51, No. 1, 383-387, 1980.
doi:10.1063/1.327383        Google Scholar

7. Nakazato, K., R. J. Blaikie, and H. Ahmed, "Single-electron memory," J. Appl. Phys., Vol. 75, No. 10, 5123-5136, 1994.
doi:10.1063/1.355758        Google Scholar

8. Zrenner, A., F. Koch, and K. Ploog, "Subband physics for a `realistic' δ-doping layer," Surf. Sci., Vol. 196, No. 1-3, 671-676, 1988.
doi:10.1016/0039-6028(88)90760-1        Google Scholar

9. Ullrich, B., C. Zhang, and K. V. Klitzing, "Quantum confined subband transitions of a GaAs sawtooth doping superlattice," Appl. Phys. Lett., Vol. 54, No. 12, 1133-1135, 1989.
doi:10.1063/1.100739        Google Scholar

10. Ke, M. L., J. S. Rimmer, B. Hamilton, J. H. Evans, M. Missous, K. E. Singer, and P. Zalm, "Radiative transitions associated with hole confinement at Si δ-doped planes in GaAs," Phys. Rev., Vol. B45, No. 24, 14114-14121, 1992.        Google Scholar

11. Chang, C. Y., W. Lin, W. C. Hsu, T. S. Wu, S. Z. Chang, and C.Wang, "The δ-doped In0.25Ga0.75As/GaAs pseudomorphic high electron mobility transistor structures prepared by low-pressure metal organic chemical vapor deposition," Jpn. J. Appl. Phys., Vol. 30, No. 6, 1158-1163, 1991.
doi:10.1143/JJAP.30.1158        Google Scholar

12. Ni, W.-X., G. V. Hansson, J.-E. Sundgren, L. Hultman, L. R. Wallenberg, J.-Y. Yao, L. C. Markert, and J. E. Greene, "δ-function-shaped Sb-doping profiles in Si(001) obtained using a low-energy accelerated-ion source during molecular-beam epitaxy," Phys. Rev., Vol. B46, No. 12, 7551-7558, 1992.        Google Scholar

13. Kuo, T. Y., J. E. Cunningham, E. F. Schubert, W.T. Tsang, T. H. Chiu, F. Run, and C. G. Constad, "Selectively δ doped quantum well transistor grown by gas source molecular beam epitaxy," J. Appl. Phys., Vol. 64, No. 6, 3324-3327, 1988.
doi:10.1063/1.341513        Google Scholar

14. Gossmann, H.-J., C. S. Rafferty, A. M. Vredenberg, H. S. Luftman, F. C. Unterwald, D. J. Eaglesham, D. C. Jacobson, T. Boone, and J. M. Poate, "Time dependence of dopant diffusion in δ-doped Si films and properties of Si point defects," Appl. Phys. Lett., Vol. 64, No. 3, 312-314, 1994.
doi:10.1063/1.111189        Google Scholar

15. Schubert, E. F., J. E. Cunningham, and W. T. Tsang, "Electron-mobility enhancement and electron-concentration enhancement in δ-doped n-GaAs at T = 300 K," Solid State Commun., Vol. 63, No. 7, 591-594, 1987.
doi:10.1016/0038-1098(87)90859-3        Google Scholar

16. Liu, D. G., J. C. Fan, C. P. Lee, K. H. Chang, and D. C. Liou, "Transmission electron microscopy study of heavily delta-doped GaAs grown by molecular beam epitaxy," J. Appl. Phys., Vol. 73, No. 2, 608-614, 1993.
doi:10.1063/1.353370        Google Scholar

17. Headrick, R. L., B. E. Weir, A. F. J. Levi, D. J. Eaglesham, and L. C. Feldman, "Si(100) (2x1) boron reconstruction: Self-limiting monolayer doping," Appl. Phys. Lett., Vol. 57, No. 26, 2779-2781, 1990.
doi:10.1063/1.103785        Google Scholar

18. Zhu, J.-H., D.-W. Gong, B. Zhang, F. Lu, C. Sheng, H.-H. Sun, and X. Wang, "Admittance spectroscopy studies of boron δ-doped Si quantum wells," Phys. Rev., Vol. B52, No. 12, 8959-8963, 1995.        Google Scholar

19. Wang, Y., R. J. Hamers, and E. Kaxiras, "Atomic structure and bonding of boron-induced reconstructions on Si(001)," Phys. Rev. Lett., Vol. 74, No. 3, 403-406, 1995.
doi:10.1103/PhysRevLett.74.403        Google Scholar

20. Zheng, X., T. K. Carns, K. L. Wang, and B. Wu, "Electron mobility enhancement from coupled wells in delta-doped GaAs," Appl. Phys. Lett., Vol. 62, No. 5, 504-506, 1993.
doi:10.1063/1.108893        Google Scholar

21. Gurtovoi, V. L., V. V. Valyaev, S. Y. Shapoval, and A. N. Pustovit, "Electron transport properties of double delta-doped GaAs structures grown by low-pressure metalorganic chemical vapor deposition," Appl. Phys. Lett., Vol. 72, No. 10, 1202-1204, 1998.
doi:10.1063/1.121013        Google Scholar

22. Kiunke, W., E. Hammerl, I. Eisele, D. Schulze, and G. Gobsch, "Electrical transport between delta layers in silicon," J. Appl. Phys., Vol. 72, No. 8, 3602-3605, 1992.
doi:10.1063/1.352300        Google Scholar

23. Sasagawa, R., H. Sugawara, Y. Ohno, H. Nakajima, S. Tsujino, H. Akiyama, and H. Sakaki, "Enhancement of intersubband transition energies in GaAs quantum wells by Si delta doping of high concentration," Appl. Phys. Lett., Vol. 72, No. 6, 719-721, 1998.
doi:10.1063/1.120856        Google Scholar

24. Shena, T.-C., J.-Y. Ji, M. A. Zudov, R.-R. Du, J. S. Kline, and J. R. Tucker, "Ultradense phosphorous delta layers grown into silicon from PH3 molecular precursors," Appl. Phys. Lett., Vol. 80, No. 9, 1580-1582, 2002.
doi:10.1063/1.1456949        Google Scholar

25. Oberbeck, L., N. J. Curson, M. Y. Simmons, R. Brenner, A. R. Hamilton, S. R. Schofield, and R. G. Clark, "Encapsulation of phosphorus dopants in silicon for the fabrication of a quantum computer," Appl. Phys. Lett., Vol. 81, No. 17, 3197-3199, 2002.
doi:10.1063/1.1516859        Google Scholar

26. Oberbeck, L., N. J. Curson, T. Hallam, M. Y. Simmons, G. Bilger, and R. G. Clark, "Measurement of phosphorus segregation in silicon at the atomic scale using scanning tunneling microscopy," Appl. Phys. Lett., Vol. 85, No. 8, 1359-1361, 2004.
doi:10.1063/1.1784881        Google Scholar

27. Kul'bachinskii, V. A., V. G. Kytin, R. A. Lunin, V. G. Mokerov, A. P. Senichkin, A. S. Bugaev, A. L. Karuzskii, A. V. Perestoronin, R. T. F. van Schaijk, and A. de Visser, "Transport and optical properties of tin delta-doped GaAs structures," Semiconductors, Vol. 33, No. 7, 771-778, 1999.
doi:10.1134/1.1187779        Google Scholar

28. Ahn, D., "Intersubband transitions in a δ-doped semiconductor with an applied electric field: Exact solutions," Phys. Rev., Vol. B48, No. 11, 7981-7985, 1993.        Google Scholar

29. Ozturk, E., "Optical intersubband transitions in double Si δ-doped GaAs under an applied magnetic field," Superlattices and Microstructures, Vol. 46, No. 5, 752-755, 2009.
doi:10.1016/j.spmi.2009.07.013        Google Scholar

30. Ozturk, E. and I. Sokmen, "The electric field effects on intersubband optical absorption of Si δ-doped GaAs layer," Solid-State Commun., Vol. 126, No. 11, 605-609, 2003.
doi:10.1016/S0038-1098(03)00301-6        Google Scholar

31. Ozturk, E. and I. Sokmen, "Intersubband transitions for single, double and triple Si δ-doped GaAs layers," 2003 J. Phys. D, Vol. 36, No. 20, 2457-2464, 2003.
doi:10.1088/0022-3727/36/20/006        Google Scholar

32. Kim, K. T., S. S. Lee, and S. L. Chiang, "Inter miniband optical absorption in a modulation doped AlxGa1-xAs/GaAs superlattice," J. Appl. Phys., Vol. 69, No. 9, 6617-6624, 1991.
doi:10.1063/1.348875        Google Scholar

33. Ozturk, E. and I. Sokmen, "Effect of magnetic fields on the linear and nonlinear intersubband optical absorption coefficients and refractive index changes in square and graded quantum wells," Superlattices and Microstructures, Vol. 48, No. 3, 312-320, 2010.
doi:10.1016/j.spmi.2010.06.015        Google Scholar

34. Schubert, E. F., "Delta-doping of semiconductors: Electronic, optical, and structural properties of materials and devices," Semiconductors and Semimetals, Vol. 40, Chapter 1, 1-151, Elsevier, Amsterdam, 1994.        Google Scholar

35. Fu, Y. and M. Willander, "Physical Models of Semiconductor Quantum Devices," Kluwer, Dordrecht, NL, 1999.        Google Scholar

36. Zeindl, H. P., T. Wegehaupt, I. Eisele, H. Oppolzer, H. Reisinger, G. Tempel, and F. Koch, "Growth and characterization of a delta-function doping layer in Si," Appl. Phys. Lett., Vol. 50, 1164-1166, 1987.
doi:10.1063/1.97950        Google Scholar

37. Li, H.-M., K.-F. Berggren, W.-X. Ni, B. E. Sernelius, M. Willander, and G. V. Hansson, "Tunneling current spectroscopy of electron subbands in n-type δ-doped silicon structures grown by molecular beam epitaxy," J. Appl. Phys., Vol. 67, No. 4, 1962-1968, 1990.
doi:10.1063/1.345575        Google Scholar

38. Ramdas Ram-Mohan, L., Finite Element and Boundary Element Applications in Quantum Mechanics, Oxford University Press, New York, Oxford, 2002.

39. Hurkx, G. A. M. and A. van Haeringen, "Self-consistent calculations on GaAs-AlxGa1-xAs heterojunctions," J. Phys. C: Solid State Phys, Vol. 18, No. 29, 5617-5628, 1985.
doi:10.1088/0022-3719/18/29/012        Google Scholar

40. Simserides, C. D. and G. P. Triberis, "A systematic study of electronic states in n-AlxGa1-xAs/GaAs/n-AlxGa1-xAs selectively doped double-heterojunction structures," J. Phys.: Condens. Matter, Vol. 5, No. 35, 6437-6446, 1993.
doi:10.1088/0953-8984/5/35/009        Google Scholar

41. Xu, W. and J. Mahanty, "The influence of Si delta doping on the electronic structure of AlGaAs-GaAs-AlGaAs single quantum wells," J. Phys.: Condens. Matter, Vol. 6, No. 25, 4745-4762, 1994.
doi:10.1088/0953-8984/6/25/013        Google Scholar

42. Simserides, C. D. and G. P. Triberis, "Looking for the maximum low-temperature conductivity in selectively doped AlxGa1-xAs-GaAs-AlxGa1-xAs double heterojunctions," J. Phys.: Condens. Matter, Vol. 8, No. 30, L421-L430, 1996.
doi:10.1088/0953-8984/8/30/002        Google Scholar

43. Xu, W., "Self-consistent electronic subband structure in terahertz-driven two-dimensional electron gases," Europhys. Lett., Vol. 40, No. 4, 411-416, 1997.
doi:10.1209/epl/i1997-00480-8        Google Scholar

44. Green, T. J. and W. Xu, "Population inversion in an optically pumped single quantum well," J. Appl. Phys., Vol. 88, No. 6, 3166-3169, 2000.
doi:10.1063/1.1287604        Google Scholar

45. Xu, W., P. A. Folkes, and G. Gumbs, "Self-consistent electronic subband structure of undoped InAs/GaSb-based type II and broken-gap quantum well systems," J. Appl. Phys., Vol. 102, No. 3, 033703-9, 2007.        Google Scholar

46. Ozturk, E., "Effect of magnetic field on a p-type δ-doped GaAs layer," Chinese Phys. Lett., Vol. 27, No. 7, 077302-5, 2010.
doi:10.1088/0256-307X/27/7/077302        Google Scholar

47. Shpatakovskaya, G. V., "Semiclassical model of the structure of matter," Phys. Usp., Vol. 55, No. 5, 429-464, 2012.
doi:10.3367/UFNe.0182.201205a.0457        Google Scholar

48. Ioriatti, L., "Thomas-Fermi theory of δ-doped semiconductor structures: Exact analytical results in the high-density limit," Phys. Rev., Vol. B41, No. 12, 8340-8344, 1990.        Google Scholar

49. Rodriguez-Vargas, I. and L. M. Gaggero-Sager, "Subband structure comparison between n- and p-type double delta-doped GaAs quantum wells," Revista Mexicana de Fisica, Vol. 50, No. 6, 614-619, 2004.        Google Scholar

50. Gaggero-Sager, L. M., "Exchange and correlation via functional of Thomas-Fermi in delta-doped quantum wells," Modelling Simul. Mater. Sci. Eng., Vol. 9, No. 1, 1-6, 2001.
doi:10.1088/0965-0393/9/1/301        Google Scholar

51. Oubram, O., O. Navarro, L. M. Gaggero-Sager, J. C. Martinez-Orozco, and I. Rodrguez-Vargas, "The hydrostatic pressure effects on intersubband optical absorption of n-type δ-doped quantum well in GaAs," Solid State Sciences, Vol. 14, No. 4, 440-444, 2012.
doi:10.1016/j.solidstatesciences.2012.01.020        Google Scholar

52. Gulveren, B., "Quantum dot with N interacting electrons confined in a power-law external potential," Solid State Sciences, Vol. 14, No. 1, 94-99, 2012.
doi:10.1016/j.solidstatesciences.2011.11.001        Google Scholar

53. Drumm, D. W., A. Budi, M. C. Per, S. P. Russo, and L. C. L. Hollenberg, "Ab initio calculation of valley splitting in monolayer δ-doped phosphorus in silicon," Nanoscale Research Letters, Vol. 8, No. 1, 111-121, 2013.
doi:10.1186/1556-276X-8-111        Google Scholar

54. Carter, D. J., N. A. Marks, O. Warschkow, and D. R. McKenzie, "Phosphorus δ-doped silicon: Mixed-atom pseudopotentials and dopant disorder effects," Nanotechnology, Vol. 22, No. 6, 065701-10, 2011.
doi:10.1088/0957-4484/22/6/065701        Google Scholar

55. Brennan, K. F., The Physics of Semiconductors, Cambridge Univ. Press, Cambridge, 1999.

56. Grimalsky, V., L. M. Gaggero-Sager, and S. Koshevaya, "Electron spectrum of delta-doped quantum wells by the Thomas-Fermi method at finite temperatures," Physica B, Vol. 406, No. 2, 2218-2222, 2011.
doi:10.1016/j.physb.2011.03.034        Google Scholar

57. Gummel, H. K., "A self-consistent iterative scheme for one-dimensional steady state transistor calculations," IEEE Trans. Electron. Dev., Vol. 11, No. 10, 455-465, 1964.
doi:10.1109/T-ED.1964.15364        Google Scholar

58. Rodriguez-Vargas, I., M. L. Gaggero-Sager, V. V. Grimalsky, M. E. Mora-Ramos, and R. Perez-Alvarez, "Electron spectrum of single n-type delta-doped quantum wells in Si," PIERS Proceedings, 248-251, Beijing, China, Mar. 26-30, 2007.        Google Scholar

59. Grimalsky, V., L. M. Gaggero-Sager, S. Koshevaya, and M. C. Castrejon, "Combined method for simulating electron spectrum of δ-doped quantum wells in n-Si," Proc. 28th Internat. Conference on Microelectronics (MIEL 2012), 305-308, Nis, Serbia, May 13-16, 2012.        Google Scholar