Statistics of charge carriers of quantum semiconductor film in the presence of strong lateral electrostatic field

Volodya Harutyunyan; Volodya Harutyunyan

doi:10.3934/matersci.2018.2.257

AIMS Materials Science

2018, Volume 5, Issue 2: 257-275. doi: 10.3934/matersci.2018.2.257

Previous Article Next Article

Research article Topical Sections

Statistics of charge carriers of quantum semiconductor film in the presence of strong lateral electrostatic field

Volodya Harutyunyan ^,

Department of general physics and quantum nanostructures, 0051, Hovsep Emin str. 123, Russian-Armenian University, Yerevan, Armenia

Received: 07 January 2018 Accepted: 28 February 2018 Published: 22 March 2018

Abstract
Full Text(HTML)
Download PDF

The influence of an external strong electrostatic field on the statistical characteristics of equilibrium free charge carriers in a quasi-two-dimensional structure is considered using an example of an InAs semiconductor quantum film. The analysis is carried out for the case when a strong quantization regime for charge carriers is realized in the film and only the first and second film sub-bands of their quantized motion are occupied. The general analytic expressions for the energy of the quantized motion of charge carriers in a film in the presence of a strong electrostatic field are given. An explicit dependence of the width of the band gap of the sample on the value of the external field is obtained. It is shown that with the increase in the external field, the width of band gap of the sample increases. The calculations and corresponding analytical expressions for the chemical potential, concentration, energy and heat capacity of free charge carriers of an InAs quantum film in the presence of a strong electrostatic field are also presented. It is shown that with an increase in the external electrostatic field, the chemical potential of the system retains its negative sign, but increases by the magnitude. For a given value of the external field, the chemical potential of the system increases linearly with the increase in temperature. It is shown that at a given temperature the carriers’ density decreases with the increase in the external field. At a fixed value of the field, the concentration increases with the increase in temperature. The behavior of the energy and heat capacity of the charge carriers is also determined by the same dependence on the temperature of the system and the magnitude of the external field. It is also shown that the main contribution to the indicated characteristics of the sample is made namely by the first filled sub-band of quantized motion of charge carriers. If the second sub-band is also filled, its contribution to the determination of the statistical characteristics of the sample is exponentially smaller than the contribution of the first filled sub-band.
- quantum film,
- strong field,
- charge carriers,
- concentration,
- chemical potential,
- energy,
- heat capacity
Citation: Volodya Harutyunyan. Statistics of charge carriers of quantum semiconductor film in the presence of strong lateral electrostatic field[J]. AIMS Materials Science, 2018, 5(2): 257-275. doi: 10.3934/matersci.2018.2.257

Related Papers:

Abstract

The influence of an external strong electrostatic field on the statistical characteristics of equilibrium free charge carriers in a quasi-two-dimensional structure is considered using an example of an InAs semiconductor quantum film. The analysis is carried out for the case when a strong quantization regime for charge carriers is realized in the film and only the first and second film sub-bands of their quantized motion are occupied. The general analytic expressions for the energy of the quantized motion of charge carriers in a film in the presence of a strong electrostatic field are given. An explicit dependence of the width of the band gap of the sample on the value of the external field is obtained. It is shown that with the increase in the external field, the width of band gap of the sample increases. The calculations and corresponding analytical expressions for the chemical potential, concentration, energy and heat capacity of free charge carriers of an InAs quantum film in the presence of a strong electrostatic field are also presented. It is shown that with an increase in the external electrostatic field, the chemical potential of the system retains its negative sign, but increases by the magnitude. For a given value of the external field, the chemical potential of the system increases linearly with the increase in temperature. It is shown that at a given temperature the carriers’ density decreases with the increase in the external field. At a fixed value of the field, the concentration increases with the increase in temperature. The behavior of the energy and heat capacity of the charge carriers is also determined by the same dependence on the temperature of the system and the magnitude of the external field. It is also shown that the main contribution to the indicated characteristics of the sample is made namely by the first filled sub-band of quantized motion of charge carriers. If the second sub-band is also filled, its contribution to the determination of the statistical characteristics of the sample is exponentially smaller than the contribution of the first filled sub-band.

References

[1]	Tavger BA, Demikhovskii VY (1969) Quantum size effects in semiconducting and semimetallic films. Sov Phys Usp 11: 644–658. doi: 10.1070/PU1969v011n05ABEH003739
[2]	Ando T, Fowler AB, Stern F (1982) Electronic properties of two-dimensional systems. Rev Mod Phys 54: 437–672. doi: 10.1103/RevModPhys.54.437
[3]	Yoffe AD (1993) Low-dimensional systems: quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems. Adv Phys 42: 173–262. doi: 10.1080/00018739300101484
[4]	Alivisatos AP (1996) Perspectives on the Physical Chemistry of Semiconductor Nanocrystals. J Phys Chem 100: 13226–13239. doi: 10.1021/jp9535506
[5]	Hodes G (2002) Chemical Solution Deposition Of Semiconductor Films, CRC Press.
[6]	Goh SM, Chen TP, Sun CQ, et al. (2010) Thickness effect on the band gap and optical properties of germanium thin films. J Appl Phys 107: 024305. doi: 10.1063/1.3291103
[7]	Eckertová L (2012) Physics of Thin Films, Springer Science & Business Media.
[8]	Ferry DK (2018) An Introduction to Quantum Transport in Semiconductors, CRC Press.
[9]	Wu J, Yuan H, Meng M, et al. (2017) High electron mobility and quantum oscillations in non-capsulated ultrathin semiconducting Bi₂O₂Se. Nat Nanotechnol 12: 530–534. doi: 10.1038/nnano.2017.43
[10]	Matveeva LA, Venger EF, Kolyadina EY, et al. (2017) Quantum-size effects in semiconductor heterosystems. Semicond Phys Quant Electron Optoelectron 20: 224–230. doi: 10.15407/spqeo20.02.224
[11]	Holloway H (1979) Quantum efficiencies of thin film IV–VI semiconductor photodiodes. J Appl Phys 50: 1386–1389. doi: 10.1063/1.326120
[12]	Popkirov G, Schindler RN (1987) Spectral dependence of the quantum efficiency of thin film semiconductor photoelectrodes: Reflection from either the back or the front side. Sol Energ Mat 15: 163–166. doi: 10.1016/0165-1633(87)90062-1
[13]	Xu JH, Ting CS (1993) Quantum size effect on optical absorption edge in thin antimony films. Appl Phys Lett 63: 129–132. doi: 10.1063/1.110376
[14]	Stradling RA (1996) The Electronic Properties and Applications of Quantum Wells and Superlattices of III-V Narrow Gap Semiconductors. Braz J Phys 26: 7–20.
[15]	Fox AM (1996) Optoelectronics in quantum well structures. Contemp Phys 37: 111–125. doi: 10.1080/00107519608230339
[16]	Sahu SN, Nanda KK (2001) Nanostructure Semiconductors: Physics and Applications. Proc Indian Natl Sci Acad Phys Sci 67: 103–130.
[17]	Dresselhaus MS, Lin YM, Koga T, et al. (2001) Low Dimensional Thermoelectricity, In: Tritt TM, Semiconductors and Semimetals: Recent Trends in Thermoelectric Materials Research III, San Diego, CA: Academic Press.
[18]	Rogacheva EI, Tavrina TV, Nashchekina ON, et al. (2002) Quantum size effects in PbSe quantum wells. App Phys Lett 80: 2690–2692. doi: 10.1063/1.1469677
[19]	Shur MS, Rumyantsev SL, Gska R (2002) Semiconductor thin films and thin film devices for electrotextiles. Int J Hi Spe Ele Syst 12: 371–390. doi: 10.1142/S0129156402001320
[20]	Ruyter A, O'Mahoney H (2010) Quantum Wells: Theory, Fabrication and Application, Nova Science Publishers.
[21]	Ramírez-Bon R, Espinoza-Beltrán FJ (2009) Deposition, Characterization and Applications of Semiconductor Thin Films, Research Signpost.
[22]	Chow GM, Ovid'ko IA, Tsakalakos T (2012) Nanostructured Films and Coatings, Springer Science & Business Media.
[23]	Khlyap H (2009) Physics and Technology of Semiconductor Thin Film-Based Active Elements and Devices, Bentham Science Publishers.
[24]	Suresh S (2013) Semiconductor Nanomaterials, Methods and Applications: A Review. Nanosci Nanotech 3: 62–74.
[25]	Chiu FC, Pan TM, Kundu TK, et al. (2014) Thin Film Applications in Advanced Electron Devices. Adv Mater Sci Eng 2014.
[26]	Seng S, Shinpei T, Yoshihiko I, et al. (2014) Development of a Handmade Conductivity Measurement Device for a Thin-Film Semiconductor and Its Application to Polypyrrole. J Chem Educ 91: 1971–1975. doi: 10.1021/ed500287q
[27]	Ma N, Jena D (2015) Carrier statistics and quantum capacitance effects on mobility extraction in two-dimensional crystal semiconductor field-effect transistors. 2D Mater 2: 015003. doi: 10.1088/2053-1583/2/1/015003
[28]	Odoh EO, Njapba AS (2015) A Review of Semiconductor Quantum Well Devices. Adv Phys Theor Appl 46: 26–33.
[29]	Powell RC, Jayamaha U, Abken A, et al. (2016) Photovoltaic devices including doped semiconductor films. U.S. Patent 9,263,608. 2016-2-16.
[30]	Bezák V (1966) The degenerate semiconductor thin films. I-The Fermi energy. J Phys Chem Solids 27: 815–820. doi: 10.1016/0022-3697(66)90255-1
[31]	Halpern V (1968) Electron statistics in thin films of semiconductor. Phys Lett A 26: 236–237.
[32]	Mancini NA, Pennisi A (1971) Fermi level dependence on thickness in degenerate semiconductor films. Phys Lett A 35: 245–246. doi: 10.1016/0375-9601(71)90363-X
[33]	Gokhfeld VM (2005) On the thermodynamics of quasi-2D electron gas. Fizika Nizkikh Temperatur 31: 769–773.
[34]	Panda S, Panda BK (2010) Chemical potential and internal energy of the noninteracting Fermi gas in fractional-dimensional space. Pramana-J Phys 75: 393–402. doi: 10.1007/s12043-010-0125-5
[35]	Sokolova ES, Sokolov SS, Studart N (2010) Chemical potential of the low-dimensional multisubband Fermi gas. J Phys-Condens Mat 22: 465304. doi: 10.1088/0953-8984/22/46/465304
[36]	Böer KW (2014) Handbook of the Physics of Thin-Film Solar Cells, Springer Science & Business.
[37]	Fenech K (2016) Kinematics and Thermodynamics of a Two-Dimensional Fermi Gas [PhD Thesis]. Centre for Quantum and Optical Science Faculty of Science, Engineering and Technology Swinburne University of technology Melbourne, Australia.
[38]	Sevilla FJ (2017) Thermodynamics of low-dimensional trapped Fermi gases. J Thermodyn 2017.
[39]	Lee K, Shur MS (1983) Impedance of thin semiconductor films in low electric field. J Appl Phys 54: 4028–4034. doi: 10.1063/1.332584
[40]	Haroutyunian VA, Haroutyunian SL, Kazarian EM (1998) Electric field effect on exciton absorption in size-quantized semiconductor film. Thin Solid Films 323: 209–211. doi: 10.1016/S0040-6090(97)01198-X
[41]	Sandomirsky V, Butenko AV, Levin R, et al. (2001) Electric-field-effect thermoelectrics. J Appl Phys 90: 2370–2379. doi: 10.1063/1.1389074
[42]	Cassidy A, Plekan O, Balog R, et al. (2014) Electric Field Structures in Thin Films: Formation and Properties.J Phys Chem A 118: 6615–6621. 43. Harutyunyan VA (2015) Effect of Static Electric Fields on The Electronic And Optical Properties of Layered Semiconductor Nanostructures. PART I: Effect of Static Electric Fields on The Electronic Properties of Layered Semiconductor Nanostructures, Bentham Science Publishers.
[43]	44. Kuznetsova IA, Romanov DN, Savenko OV, et al. (2017) Calculating the High-Frequency Electrical Conductivity of a Thin Semiconductor Film for Different Specular Reflection Coefficients of Its Surface. Russ Microelectron 46: 252–260. doi: 10.1134/S1063739717040059
[44]	45. Adaci S (1992) Physical properties of III–V Semiconductor Compounds, John Wiley & Sons.
[45]	46. Abrikosov NK (2013) Semiconducting II–IV, IV–VI, and V–VI Compounds, Springer.
[46]	47. Madelung O (2012) Semiconductors: Data Handbook, Springer Science &Business Media.
[47]	48. Landau LD, Lifshitz EM (1981) Quantum Mechanics: Non-Relativistic Theory (Volume 3 of Course of Theoretical Physics), Pergamon Press.
[48]	49. Takei K, Fang H, Kumar SB, et al. (2011) Quantum Confinement Effects in Nanoscale-Thickness InAs Membranes. Nano Lett 11: 5008–5012. doi: 10.1021/nl2030322
[49]	50. Alcotte R, Martin M, Moeyaert J, et al. (2018) Low temperature growth and physical properties of InAs thin films grown on Si, GaAs and In_0.53Ga_0.47As template. Thin Solid Films 654: 119–123.

Reader Comments

your name:*

Email:*
© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)