A Study of a-Si:H Absorption Edge Using Dunstan’s Model
Keywords:Dunstan model, Localized states, Mobility gap, Tauc model, Urbach model
The optical absorption data of Hydrogenated Amorphous Silicon was analyzed using a Dunstan model of optical absorption in amorphous semiconductors. This model introduces disorder into the band-band absorption through a linear exponential distribution of local energy gaps, and it accounts for both the Urbach and Tauc regions of the optical absorption edge.Compared to other models of similar bases, such as the O’Leary and Guerra models, it is simpler to understand mathematically and has a physical meaning. The optical absorption data of Jackson et al and Maurer et al were successfully interpreted using Dunstan’s model. Useful physical parameters are extracted especially the band to the band energy gap , which is the energy gap in the absence of disorder, that can be interpreted as the mobility gap of the material.
Published Online First 20/9/2022
Tauc J, Grigorovici R, Vancu A. Optical properties and electronic structure of amorphous germanium. Phys status solidi. 1966;15(2): 627–37.
Mullerova J, Sutta P. On some ambiguities of the absorption edge and optical band gaps of amorphous and polycrystalline semiconductors. Commun Lett Univ Zilina. 2017; 19(3): 9–15.
Pawlak J, Al-Ani SKJ. Inverse logarithmic derivative method for determining the energy gap and the type of electron transitions as an alternative to the Tauc method. Opt Mater (Amst). 2019; 88: 667–73.
Makuła P, Pacia M, Macyk W. How to correctly determine the band gap energy of modified semiconductor photocatalysts based on UV–Vis spectra. ACS Publications; 2018.
Zanatta AR. Revisiting the optical bandgap of semiconductors and the proposal of a unified methodology to its determination. Sci Rep. 2019; 9(1): 1–12.
Studenyak I, Kranjčec M, Kurik M. Urbach rule in solid state physics. Int J Opt Appl. 2014; 4(3): 76–83.
O’Leary SK, Johnson SR, Lim PK. The relationship between the distribution of electronic states and the optical absorption spectrum of an amorphous semiconductor: An empirical analysis. J Appl Phys. 1997; 82(7): 3334–40.
O’Leary SK, Malik SM. A simplified joint density of states analysis of hydrogenated amorphous silicon. J Appl Phys. 2002; 92(8): 4276–82.
O’Leary SK. An analytical density of states and joint density of states analysis of amorphous semiconductors. J Appl Phys. 2004; 96(7): 3680–6.
Thevaril JJ, O’Leary SK. A universal feature in the optical absorption spectrum associated with hydrogenated amorphous silicon: A dimensionless joint density of states analysis. J Appl Phys. 2016; 120(13): 135706.
Guerra JA, Tejada A, Korte L, Kegelmann L, Töfflinger JA, Albrecht S, et al. Determination of the complex refractive index and optical bandgap of CH3NH3PbI3 thin films. J Appl Phys. 2017; 121(17): 173104.
Guerra JA. Optical characterization and thermal activation of Tb doped amorphous SiC, AlN and SiN thin films. Ph. D. dissertation, PUCP, 2017 [Online]. Available: http://hdl.handle.net/20.500.12404/9187.
Guerra JA, Tejada A, Töfflinger JA, Grieseler R, Korte L. Band-fluctuations model for the fundamental absorption of crystalline and amorphous semiconductors: a dimensionless joint density of states analysis. J Phys D Appl Phys. 2019; 52(10): 105303.
Dunstan DJ. Evidence for a common origin of the Urbach tails in amorphous and crystalline semiconductors. J Phys C Solid State Phys. 1982; 15(13): L419.
Dunstan DJ. New evidence for a fluctuating band-gap in amorphous semiconductors. J Phys C Solid State Phys. 1983; 16(17): L567.
Frova A, Selloni A. The Optical Threshold of Hydrogenated Amorphous Silicon. In: Tetrahedrally-Bonded Amorphous Semiconductors. Springer; 1985. p. 271–85.
Skettrup T. Urbach’s rule derived from thermal fluctuations in the band-gap energy. Phys Rev B. 1978; 18(6): 2622.
Jackson WB, Kelso SM, Tsai CC, Allen JW, Oh S-J. Energy dependence of the optical matrix element in hydrogenated amorphous and crystalline silicon. Phys Rev B. 1985; 31(8): 5187.
Maurer C, Beyer W, Hülsbeck M, Breuer U, Rau U, Haas S. Impact of Laser Treatment on Hydrogenated Amorphous Silicon Properties. Adv Eng Mater. 2020; 22(6): 1901437.
Abbo AI. Analytical Study of near Mobility Edge Density of States of Hydrogenated Amorphous Silicon. Baghdad Sci J. 2014; 11(3).
Hussian AC. Analytical study of high absorption region of the absorption edge of a-Si: H using nonlinear regression method. Iraqi J Phys. 2018; 16(37): 88–97.
Cody GD, Brooks BG, Abeles B. Optical absorption above the optical gap of amorphous silicon hydride. Sol Energy Mater. 1982; 8(1–3): 231–40.
Minar SB, Moghaddam S, O’Leary SK. A re-examination of experimental evidence on the spectral dependence of the optical transition matrix element associated with thin-film silicon. J Mater Sci Mater Electron. 2019; 30(10): 9964–72.
Li Z, Lin SH, Qiu GM, Wang JY, Yu YP. A method for determining band parameters from the optical absorption edge of amorphous semiconductor: Application to a-Si: H. J Appl Phys. 2018; 124(2): 25702.
Orapunt F, O’Leary SK. Spectral variations in the optical transition matrix element and their impact on the optical properties associated with hydrogenated amorphous silicon. Solid State Commun. 2011; 151(5): 411–4.
Steffens J, Rinder J, Hahn G, Terheiden B. Correlation between the optical bandgap and the monohydride bond density of hydrogenated amorphous silicon. J Non-Crystalline Solids X. 2020; 5: 100044.
Jafari S, Steffens J, Wendt M, Terheiden B, Meyer S, Lausch D. Occurrence of Sharp Hydrogen Effusion Peaks of Hydrogenated Amorphous Silicon Film and Its Connection to Void Structures. Phys status solidi. 2020; 257(9): 2000097.
Schaefer ST, Gao S, Webster PT, Kosireddy RR, Johnson SR. Absorption edge characteristics of GaAs, GaSb, InAs, and InSb. J Appl Phys. 2020; 127(16): 165705.
Hakeem HS, Abbas NK. Preparing and Studying Structural and Optical Properties of Pb1-xCdxS Nanoparticles of Solar Cells Applications. Baghdad Sci J. 2021; 18(3): 640.
Morigaki K, Ogihara C. Amorphous semiconductors: Structure, optical, and electrical properties. In: Springer Handbook of Electronic and Photonic Materials. Springer; 2nd Ed, 2017. p. 1.
Sangiorgi N, Aversa L, Tatti R, Verucchi R, Sanson A. Spectrophotometric method for optical band gap and electronic transitions determination of semiconductor materials. Opt Mater (Amst). 2017; 64: 18–25.
Yuan L-D, Deng H-X, Li S-S, Wei S-H, Luo J-W. Unified theory of direct or indirect band-gap nature of conventional semiconductors. Phys Rev B. 2018; 98(24): 245203.
Capper P, Willoughby A, Kasap S. Optical Properties of Materials and Their Applications. 2nd EdJohn Wiley & Sons; 2020.
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