Abstract
The optical absorption spectrum of lattice defects provides the most direct information about their electronic properties; general characteristics are obtained from such spectra even without detailed knowledge about the defect structure. Two substantially different types of absorption spectra occur: line spectra near the fundamental band-to-band absorption originating from shallow-level defects and usually broad spectra from deep-level, tight-bonding defects. Shallow defects are described by a hydrogen-like model using a Rydberg energy modified by the effective mass and dielectric constant. Lattice coupling and relaxation of these centers is only weak. Deep centers show strong electron-lattice coupling described by the Huang-Rhys factor, which expresses the mean number of emitted phonons during lattice relaxation after electron capture. Electronic and vibronic properties of deep centers are described in a configuration-coordinate diagram, with optical excitation and emission processes represented by vertical transitions according to the Franck-Condon principle. Photoionization refers to an excitation from a defect center into a band and leads to edge-shaped absorption.
At high defect density, the localized wavefunctions overlap and form an impurity band, which at densities exceeding the Anderson-Mott limit merges with band states. such an extended density of states leads to an Urbach tail in the optical absoption near the band edge. In addition, the absorption edge of band-to-band transitions in heavily doped semiconductors is blueshifted due to the Burstein-Moss effect resulting from band filling.
Karl W. Böer: deceased.
Notes
- 1.
The quasi-hydrogen energy can be expressed as a function of the quasi-Bohr radius (for n = 1): \( {E}_{\mathrm{qH}}={\hslash}^2{k}_{\mathrm{r}}^2/\left(2{m}_n\right) \) for kr = 1/aqH. This is a familiar expression identifying the circling electron in a parabolic and isotropic conduction band.
- 2.
The basis for this analysis is the adiabatic approximation describd below. Here, the Hamiltonian is split into a part that deals with electrons and atoms at fixed lattice positions, multiplied by a function of displaced lattice atoms. The Hamiltonian can then be written as a sum of the electronic part and the interacting ionic part. This ionic part results in shifted, harmonic oscillations.
- 3.
This coupling is related to the depth of the electron levels. Centers with strong bonding (strong coupling) are more effective in “pushing the surrounding lattice atoms apart” when the electron is excited to a higher energy state. Eigenfunctions of shallow levels have the tendency to “slide over” the surrounding atoms when excited, by permitting the electron to circle within the surrounding lattice, thereby exerting comparatively little force on the surrounding atoms.
- 4.
In this chapter cross sections are identified with the commonly used σ. In later chapters treating of transport the symbol s is used instead to distinguish cross sections from conductivity.
- 5.
- 6.
Only in ultrapure semiconductors with vanishing internal stress and vanishing electric fields, the lines of isolated impurities have their natural width – see Jagannath et al. (1981) and Haller et al. (1987); also the natural isotope mixture contributes substantially to inhomogeneous broadening as demonstrated for isotopically pure 28Si – see Karaiskaj et al. (2003).
- 7.
- 8.
For a self-consistent determination of the screening, which depends on the carrier density, which in turn depends on the level density, which again is influenced by the screening length, see Hwang and Brews (1971).
- 9.
For instance, in InSb with mn = 0.0116, the effective density of states is Nc ≅ 3 · 1016 cm−3 ; hence doping with a shallow donor density in excess of 1017 cm−3 will cause a significant filling of conduction-band states.
References
Abram RA (1993) Effects of heavy doping and high excitation on the band structure of gallium arsenide. Semicond Semimetals 39:259
Abram RA, Rees GJ, Wilson BLH (1978) Heavily doped semiconductors and devices. Adv Phys 27:799
Aleksandrov IA, Zhuravlev KS (2020) Luminescence line shapes of band to deep centre and donor–acceptor transitions in AlN. J Phys Condens Matter 32:435501
Alkauskas A, Lyons JL, Steiauf D, Van de Walle CG (2012) First-principles calculations of luminescence spectrum line shapes for defects in semiconductors: the example of GaN and ZnO. Phys Rev Lett 109:267401
Alkauskas A, Yan Q, Van de Walle CG (2014) First-principles theory of nonradiative carrier capture via multiphonon emission. Phys Rev B 90:075202
Alkauskas A, Dreyer CE, Lyons JL, Van de Walle CG (2016) Role of excited states in Shockley-Read-Hall recombination in wide-band-gap semiconductors. Phys Rev B 93:201304
Baranovskii SD, Doerr U, Thomas P, Naumov A, Gebhardt W (1994) Exciton line broadening by compositional disorder in ZnSexTe1−x quantum wells. Solid State Commun 89:5
Baranowski JM (1979) unpublished. Work published in: Jaros M (1980) Deep levels in semiconductors. Adv Phys 29:409
Barber HD (1967) Effective mass and intrinsic concentration in silicon. Solid State Electron 10:1039
Beaumont JH, Harmer AL, Hayes W (1972) The F3 centre in alkaline earth fluorides. J Phys C Solid State Phys 5:257
Berggren K-F, Sernelius BE (1981) Band-gap narrowing in heavily doped many-valley semiconductors. Phys Rev B 24:1971
Bhattacharya R, Mondal R, Khatua P, Rudra A, Kapon E, Malzer S, Döhler G, Pal B, Bansal B (2015) Measurements of the electric field of zero-point optical phonons in GaAs quantum wells support the Urbach rule for zero-temperature lifetime broadening. Phys Rev Lett 114:047402
Callaway J (1963) Transition processes in semiconductor lasers. J Phys Chem Solid 24:1063
Casey HC Jr, Stern F (1976) Concentration-dependent absorption and spontaneous emission of heavily doped GaAs. J Appl Phys 47:631
Casey HC Jr, Sell DD, Wecht KW (1975) Concentration dependence of the absorption coefficient for n- and p-type GaAs between 1.3 and 1.6 eV. J Appl Phys 46:250
Chakraborty PK, Biswas JC (1997) Conduction-band tailing in parabolic band semiconductors. J Appl Phys 82:3328
Condon EU, Morse PM (1929) Quantum mechanics. McGraw-Hill, New York
Davydov VYu, Klochikhin AA, Emtsev VV, Ivanov SV, Vekshin VV, Bechstedt F, Furthmüller J, Harima H, Mudryi AV, Hashimoto A, Yamamoto A, Aderhold J, Graul J, Haller EE (2002) Band gap of InN and In-rich InxGa1–xN alloys (0.36 < x < 1). Phys Status Solid B 230:R4
Dexter DL (1958) Theory of the optical properties of imperfections in nonmetals. In: Seitz F, Turnbull D (eds) Solid state physics, vol 6. Academic, New York, pp 353–411
Eagles DM (1960) Optical absorption and recombination radiation in semiconductors due to transitions between hydrogen-like acceptor impurity levels and the conduction band. J Phys Chem Solid 16:76
Feneberg M, Osterburg S, Lange K, Lidig C, Garke B, Goldhahn R, Richter E, Netzel C, Neumann MD, Esser N, Fritze S, Witte H, Bläsing J, Dadgar A, Krost A (2014) Band gap renormalization and Burstein-Moss effect in silicon- and germanium-doped wurtzite GaN up to 1020 cm−3. Phys Rev B 90:075203
Feynman RP, Hibbs AR (1965) Quantum mechanics and path integrals. McGraw-Hill, New York
Fitchen D, Silsbee RH, Fulton TA, Wolf EL (1963) Zero-phonon transitions of color centers in Alkali Halides. Phys Rev Lett 11:275
Gebhardt W, Kuhnert H (1964) Temperature dependence of F-centre absorption and emission. Phys Lett 11:15
Ghazali A, Serre J (1982) Multiple-scattering approach to the formation of the impurity band in semiconductors. Phys Rev Lett 48:886
Goede O, John L, Hennig D (1978) Compositional disorder-induced broadening for free excitons in II-VI semiconducting mixed crystals. Phys Stat Solid B 89:K183
Grimmeiss HG (1985) Deep energy levels in semiconductors. In: Chadi JD, Harrison WA (eds) Proceeding of the 17th international conference on the physics of semiconductors, San Francisco 1984, pp 589–600. Springer, New York
Grimmeiss HG, Ledebo L-Å (1975) Spectral distribution of photoionization cross sections by photoconductivity measurements. J Appl Phys 46:2155
Haller EE, Navarro H, Keilmann F (1987) Intrinsic linewidth of 1S → nP donor transitions in ultrapure germanium. In: O Engström (ed) Proceedings of the 18th international conferences on the physics of semiconductors, Stockholm 1986, pp 837–840. World Scientific, Singapore
Halperin BI, Lax M (1966) Impurity-band tails in the high-density limit. I. Minimum counting methods. Phys Rev 148:722
Halperin BI, Lax M (1967) Impurity-band tails in the high-density limit. II. Higher order corrections. Phys Rev 153:802
Haufe A, Schwabe R, Feiseler H, Ilegems M (1988) The luminescence lineshape of highly doped direct-gap III-V compounds. J Phys C 21:2951
Hayes W, Stoneham AM (1984) Defects and defect processes in nonmetallic solids. Wiley, New York
Henry CH (1980) Large lattice relaxation processes in semiconductors. In: Kubo R, Hanamura E (eds) Relaxation of elementary excitation. Springer, Berlin, pp 19–33
Henry CH, Lang DV (1977) Nonradiative capture and recombination by multiphonon emission in GaAs and GaP. Phys Rev B 15:989
Huang K, Rhys A (1950) Theory of light absorption and non-radiative transitions in F centres. Proc R Soc London A204:406
Huber MCE, Sandemann RJ (1986) The measurement of oscillator strengths. Rep Prog Phys 49:397
Hwang CJ, Brews JR (1971) Electron activity coefficients in heavily doped semiconductors with small effective mass. J Phys Chem Sol 32:837
Jagannath C, Grabowski ZW, Ramdas AK (1981) Linewidths of the electronic excitation spectra of donors in silicon. Phys Rev B 23:2082
Jain SC, Mertens RP, Van Overstraeten RJ (1991) Bandgap narrowing and its effects on the properties of moderately and heavily doped germanium and silicon. Adv Electronics Electron Phys 82:197
Jin Y, Govoni M, Wolfowicz G, Sullivan SE, Heremans FJ, Awschalom DD, Galli G (2021) Photoluminescence spectra of point defects in semiconductors: validation of first-principles calculations. Phys Rev Mater 5:084603
Kane EO (1963) Thomas-Fermi approach to impure semiconductor band structure. Phys Rev 131:79
Karaiskaj D, Stotz JAH, Meyer T, Thewalt MLW, Cardona M (2003) Impurity absorption spectroscopy in 28Si: the importance of inhomogeneous isotope broadening. Phys Rev Lett 90:186402
Kayanuma Y, Fukuchi S (1984) Nonradiative transitions in deep impurities in semiconductors–study in a semiclassical model. J Phys Soc Jpn 53:1869
Keldysh LV, Proshko GP (1964) Infrared absorption in highly doped germanium. Sov Phys – Solid State 5:2481
Kim S, Hood SN, Walsh A (2019) Anharmonic lattice relaxation during nonradiative carrier capture. Phys Rev B 100:041202
Klauder JR, Anderson PW (1962) Spectral diffusion decay in spin resonance experiments. Phys Rev 125:912
Kopylov AA, Pikhtin AN (1975) Effect of temperature on the optical absorption spectra of deep centers. Sov Phys Sol State 16:1200
Kubo R (1952) Thermal ionization of trapped electrons. Phys Rev 86:929
Larsen DM (1976) Inhomogeneous broadening of the Lyman-series absorption of simple hydrogenic donors. Phys Rev B 13:1681
Lasher G, Stern F (1964) Spontaneous and stimulated recombination radiation in semiconductors. Phys Rev 133:A553
Lax M (1952) The Franck-Condon principle and its application to crystals. J Chem Phys 20:1752
Lifshitz IM (1964) The energy spectrum of disordered systems. Adv Phys 13:483
Lucovsky G (1965) On the photoionization of deep impurity centers in semiconductors. Sol State Commun 3:299
Markham JJ (1956) Electron-nuclear wave functions in multiphonon processes. Phys Rev 103:588
Moss TS (1961) Optical properties of semiconductors. Butterworths Scientific Publications, London
Mott NF (1974) Metal-insulator transitions. Barnes and Noble, New York
Mott NF, Davis EA (1979) Electronic processes in noncrystalline materials. Claredon Press, Oxford, UK
Noras JM (1980) Photoionisation and phonon coupling. J Phys C 13:4779
Onton A (1971) Donor-electron transitions between states associated with the X1c and X3c conduction-band minima in GaP. Phys Rev B 4:4449
O’Rourke RC (1953) Absorption of light by trapped electrons. Phys Rev 91:265
Pekar SI (1953) On the effect of lattice deformations by electrons on optical and electrical properties of crystals. Uspekhi Fiz Nauk 50:197
Peuker K, Enderlein R, Schenk A, Gutsche E (1982) Theory of non-radiative multiphonon capture processes; solution of old controversies. Phys Status Solid B 109:599
Sadigh B, Erhart P, Åberg D, Trave A, Schwegler E, Bude J (2011) First-principles calculations of the urbach tail in the optical absorption spectra of silica glass. Phys Rev Lett 106:027401
Sallen G, Tribu A, Aichele T, André R, Besombes L, Bougerol C, Richard M, Tatarenko S, Kheng K, Poizat J-Ph (2011) Subnanosecond spectral diffusion of a single quantum dot in a nanowire. Phys Rev B 84:041405
Sarangapani P, Chu Y, Charles J, Klimeck G, Kubis T (2019) Band-tail formation and band-gap narrowing driven by polar optical phonons and charged impurities in atomically resolved III–V semiconductors and nanodevices. Phys Rev Appl 12:044045
Sa-yakanit V (1979) Electron density of states in a Gaussian random potential: path-integral approach. Phys Rev B 19:2266
Sa-yakanit V, Glyde HR (1980) Impurity-band density of states in heavily doped semiconductors: a variational calculation. Phys Rev B 22:6222
Sa-yakanit V, Sritrakool W, Glyde HR (1982) Impurity-band density of states in heavily doped semiconductors: numerical results. Phys Rev B 25:2776
Shklovskii BI, Efros AL (1984) Electronic properties of doped semiconductors. Springer, Berlin
Singh J, Bajaj KK (1986) Quantum mechanical theory of linewidths of localized radiative transitions in semiconductor alloys. Appl Phys Let 48:1077
Smakula A (1930) Über Erregung und Entfärbung lichtelektrisch leitender Alkalihalogenide. Z Phys 59:603 (On excitation and decoloration of photoconducting alkali halides, in German)
Sritrakool W, Sa-yakanit V, Glyde HR (1985) Absorption near band edges in heavily doped GaAs. Phys Rev B 32:1090
Sritrakool W, Sa-yakanit V, Glyde HR (1986) Band tails in disordered systems. Phys Rev B 33:1199
Stoneham AM (1969) Shapes of inhomogeneously broadened resonance lines in solids. Rev Mod Phys 41:82
Stradling RA (1984) Studies of the free and bound magneto-polaron and associated transport experiments in n-InSb and other semiconductors. In: Devreese JT, Peeters FM (eds) Polarons and excitons in polar semiconductors and ionic crystals. Plenum Press, New York
Sumi H (1983) Nonradiative multiphonon capture of free carriers by deep-level defects in semiconductors: adiabatic and nonadiabatic limits. Phys Rev B 27:2374
Takebe T, Saraie J, Matsunami H (1982) Detailed characterization of deep centers in CdTe: photoionization and thermal ionization properties. J Appl Phys 53:457
Toyozawa Y, Inoue M, Inui T, Okazaki M, Hanamura E (1967) Coexistence of local and band characters in the absorption spectra of solids I. Formulation. J Phys Soc Jpn 22:1337; Okazaki M, Inoue M, Toyozawa Y, Inui T, Hanamura E (1967) II. Calculations for the simple cubic lattice. J Phys Soc Jpn 22:1349
Türck V, Rodt S, Stier O, Heitz R, Engelhardt R, Pohl UW, Bimberg D, Steingrüber R (2000) Effect of random field fluctuations on excitonic transitions of individual CdSe quantum dots. Phys Rev B 61:9944.
Urbach F (1953) The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids. Phys Rev 92:1324
Van Mieghem P (1992) Theory of band tails in heavily doped semiconductors. Rev Mod Phys 64:755
Velický B, Sak J (1966) Excitonic effects in the interband absorption of semiconductors. Phys Status Solid 16:147
Vérié C (1967) Electronic properties of CdxHg1-xTe alloys in the vicinity of the semimetal-semiconductor transition. In: Thomas DC (ed) II-VI semiconductor compounds. Benjamin, New York, p 1124
Wagner J (1985) Heavily doped silicon studied by luminescence and selective absorption. Sol State Electron 28:25
Walsh A, Da Silva JLF, Wei SH (2008) Origins of band-gap renormalization in degenerately doped semiconductors. Phys Rev B 78:075211
Zeiger HJ (1964) Impurity states in semiconducting masers. J Appl Phys 35:1657
Zhao GY, Ishikawa H, Jiang H, Egawa T, Jimbo T, Umeno M (1999) Optical absorption and photoluminescence studies of n-type GaN. Jpn J Appl Phys 38:L993
Zheng J, Allen JW (1994) Photoionization of a deep centre in zinc selenide giving information about the conduction band structure. J Cryst Growth 138:504
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this entry
Cite this entry
Böer, K.W., Pohl, U.W. (2022). Optical Properties of Defects. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_17-4
Download citation
DOI: https://doi.org/10.1007/978-3-319-06540-3_17-4
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06540-3
Online ISBN: 978-3-319-06540-3
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics
Publish with us
Chapter history
-
Latest
Optical Properties of Defects- Published:
- 21 June 2022
DOI: https://doi.org/10.1007/978-3-319-06540-3_17-4
-
Optical Properties of Defects
- Published:
- 04 April 2020
DOI: https://doi.org/10.1007/978-3-319-06540-3_17-3
-
Optical Properties of Defects
- Published:
- 27 September 2017
DOI: https://doi.org/10.1007/978-3-319-06540-3_17-2
-
Original
Optical Properties of Defects- Published:
- 21 May 2016
DOI: https://doi.org/10.1007/978-3-319-06540-3_17-1