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Optical Properties of Defects

Semiconductor Physics

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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.

K. W. Böer: deceased

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Notes

  1. 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. 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. 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. 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. 5.

    The line-shape function enters into the absorption cross-section (Eq. 20); that is, (l/h)g(ν – νfi) replaces δ(Ef – Ei – hνfi) after introducing the damping term – see also Eq. 21.

  6. 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).

  7. 7.

    This is obtained from the lattice relaxation of 0.14 eV (=1.27–1.13 or = 0.62–0.48 eV) with breathing mode phonons of \( \hslash {\omega}_{\mathrm{char}}\cong 21\ \mathrm{meV} \) after capture of a hole or an electron, as indicated in Fig. 18a, b.

  8. 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. 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

    Article  Google Scholar 

  • Abram RA, Rees GJ, Wilson BLH (1978) Heavily doped semiconductors and devices. Adv Phys 27:799

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Baranowski JM (1979) unpublished. Work published in: Jaros M (1980) Deep levels in semiconductors. Adv Phys 29:409

    Google Scholar 

  • Barber HD (1967) Effective mass and intrinsic concentration in silicon. Solid State Electron 10:1039

    Article  ADS  Google Scholar 

  • Beaumont JH, Harmer AL, Hayes W (1972) The F3 centre in alkaline earth fluorides. J Phys C Solid State Phys 5:257

    Article  ADS  Google Scholar 

  • Berggren K-F, Sernelius BE (1981) Band-gap narrowing in heavily doped many-valley semiconductors. Phys Rev B 24:1971

    Article  ADS  Google Scholar 

  • Callaway J (1963) Transition processes in semiconductor lasers. J Phys Chem Solid 24:1063

    Article  ADS  Google Scholar 

  • Casey HC Jr, Stern F (1976) Concentration-dependent absorption and spontaneous emission of heavily doped GaAs. J Appl Phys 47:631

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Chakraborty PK, Biswas JC (1997) Conduction-band tailing in parabolic band semiconductors. J Appl Phys 82:3328

    Article  ADS  Google Scholar 

  • Condon EU, Morse PM (1929) Quantum mechanics. McGraw-Hill, New York

    MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Feynman RP, Hibbs AR (1965) Quantum mechanics and path integrals. McGraw-Hill, New York

    MATH  Google Scholar 

  • Fitchen D, Silsbee RH, Fulton TA, Wolf EL (1963) Zero-phonon transitions of color centers in Alkali Halides. Phys Rev Lett 11:275

    Article  ADS  Google Scholar 

  • Gebhardt W, Kuhnert H (1964) Temperature dependence of F-centre absorption and emission. Phys Lett 11:15

    Article  ADS  Google Scholar 

  • Ghazali A, Serre J (1982) Multiple-scattering approach to the formation of the impurity band in semiconductors. Phys Rev Lett 48:886

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • Grimmeiss HG, Ledebo L-Å (1975) Spectral distribution of photoionization cross sections by photoconductivity measurements. J Appl Phys 46:2155

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • Halperin BI, Lax M (1966) Impurity-band tails in the high-density limit. I. Minimum counting methods. Phys Rev 148:722

    Article  ADS  Google Scholar 

  • Halperin BI, Lax M (1967) Impurity-band tails in the high-density limit. II. Higher order corrections. Phys Rev 153:802

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Hayes W, Stoneham AM (1984) Defects and defect processes in nonmetallic solids. Wiley, New York

    Google Scholar 

  • Henry CH (1980) Large lattice relaxation processes in semiconductors. In: Kubo R, Hanamura E (eds) Relaxation of elementary excitation. Springer, Berlin, pp 19–33

    Chapter  Google Scholar 

  • Henry CH, Lang DV (1977) Nonradiative capture and recombination by multiphonon emission in GaAs and GaP. Phys Rev B 15:989

    Article  ADS  Google Scholar 

  • Huang K, Rhys A (1950) Theory of light absorption and non-radiative transitions in F centres. Proc R Soc London A204:406

    ADS  MATH  Google Scholar 

  • Huber MCE, Sandemann RJ (1986) The measurement of oscillator strengths. Rep Prog Phys 49:397

    Article  ADS  Google Scholar 

  • Hwang CJ, Brews JR (1971) Electron activity coefficients in heavily doped semiconductors with small effective mass. J Phys Chem Sol 32:837

    Article  ADS  Google Scholar 

  • Jagannath C, Grabowski ZW, Ramdas AK (1981) Linewidths of the electronic excitation spectra of donors in silicon. Phys Rev B 23:2082

    Article  ADS  Google Scholar 

  • 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

    Article  Google Scholar 

  • Kane EO (1963) Thomas-Fermi approach to impure semiconductor band structure. Phys Rev 131:79

    Article  ADS  MATH  Google Scholar 

  • Kayanuma Y, Fukuchi S (1984) Nonradiative transitions in deep impurities in semiconductors–study in a semiclassical model. J Phys Soc Jpn 53:1869

    Article  ADS  Google Scholar 

  • Keldysh LV, Proshko GP (1964) Infrared absorption in highly doped germanium. Sov Phys – Solid State 5:2481

    Google Scholar 

  • Kopylov AA, Pikhtin AN (1975) Effect of temperature on the optical absorption spectra of deep centers. Sov Phys Sol State 16:1200

    Google Scholar 

  • Kubo R (1952) Thermal ionization of trapped electrons. Phys Rev 86:929

    Article  ADS  MATH  Google Scholar 

  • Larsen DM (1976) Inhomogeneous broadening of the Lyman-series absorption of simple hydrogenic donors. Phys Rev B 13:1681

    Article  ADS  Google Scholar 

  • Lasher G, Stern F (1964) Spontaneous and stimulated recombination radiation in semiconductors. Phys Rev 133:A553

    Article  ADS  Google Scholar 

  • Lax M (1952) The Franck-Condon principle and its application to crystals. J Chem Phys 20:1752

    Article  ADS  Google Scholar 

  • Lifshitz IM (1964) The energy spectrum of disordered systems. Adv Phys 13:483

    Article  ADS  MATH  Google Scholar 

  • Lucovsky G (1965) On the photoionization of deep impurity centers in semiconductors. Sol State Commun 3:299

    Article  ADS  Google Scholar 

  • Markham JJ (1956) Electron-nuclear wave functions in multiphonon processes. Phys Rev 103:588

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Moss TS (1961) Optical properties of semiconductors. Butterworths Scientific Publications, London

    Google Scholar 

  • Mott NF (1974) Metal-insulator transitions. Barnes and Noble, New York

    Google Scholar 

  • Mott NF, Davis EA (1979) Electronic processes in noncrystalline materials. Claredon Press, Oxford, UK

    Google Scholar 

  • Noras JM (1980) Photoionisation and phonon coupling. J Phys C 13:4779

    Article  ADS  Google Scholar 

  • Onton A (1971) Donor-electron transitions between states associated with the X1c and X3c conduction-band minima in GaP. Phys Rev B 4:4449

    Article  ADS  Google Scholar 

  • O’Rourke RC (1953) Absorption of light by trapped electrons. Phys Rev 91:265

    Article  ADS  MATH  Google Scholar 

  • Pekar SI (1953) Uspekhi Fiz Nauk 50:193

    Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Sa-yakanit V (1979) Electron density of states in a Gaussian random potential: path-integral approach. Phys Rev B 19:2266

    Article  ADS  Google Scholar 

  • Sa-yakanit V, Glyde HR (1980) Impurity-band density of states in heavily doped semiconductors: a variational calculation. Phys Rev B 22:6222

    Article  ADS  Google Scholar 

  • Sa-yakanit V, Sritrakool W, Glyde HR (1982) Impurity-band density of states in heavily doped semiconductors: numerical results. Phys Rev B 25:2776

    Article  ADS  Google Scholar 

  • Shklovskii BI, Efros AL (1984) Electronic properties of doped semiconductors. Springer, Berlin

    Book  Google Scholar 

  • Singh J, Bajaj KK (1986) Quantum mechanical theory of linewidths of localized radiative transitions in semiconductor alloys. Appl Phys Let 48:1077

    Article  ADS  Google Scholar 

  • Smakula A (1930) Über Erregung und Entfärbung lichtelektrisch leitender Alkalihalogenide. Z Phys 59:603 (On excitation and decoloration of photoconducting alkali halides, in German)

    Article  ADS  Google Scholar 

  • Sritrakool W, Sa-yakanit V, Glyde HR (1985) Absorption near band edges in heavily doped GaAs. Phys Rev B 32:1090

    Article  ADS  Google Scholar 

  • Sritrakool W, Sa-yakanit V, Glyde HR (1986) Band tails in disordered systems. Phys Rev B 33:1199

    Article  ADS  Google Scholar 

  • Stoneham AM (1969) Shapes of inhomogeneously broadened resonance lines in solids. Rev Mod Phys 41:82

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • Sumi H (1983) Nonradiative multiphonon capture of free carriers by deep-level defects in semiconductors: adiabatic and nonadiabatic limits. Phys Rev B 27:2374

    Article  ADS  Google Scholar 

  • Takebe T, Saraie J, Matsunami H (1982) Detailed characterization of deep centers in CdTe: photoionization and thermal ionization properties. J Appl Phys 53:457

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • Urbach F (1953) The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids. Phys Rev 92:1324

    Article  ADS  Google Scholar 

  • Van Mieghem P (1992) Theory of band tails in heavily doped semiconductors. Rev Mod Phys 64:755

    Article  ADS  Google Scholar 

  • Velický B, Sak J (1966) Excitonic effects in the interband absorption of semiconductors. Phys Status Solid 16:147

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • Wagner J (1985) Heavily doped silicon studied by luminescence and selective absorption. Sol State Electron 28:25

    Article  ADS  Google Scholar 

  • Zeiger HJ (1964) Impurity states in semiconducting masers. J Appl Phys 35:1657

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Naples, FL, USA

    Karl W. Böer

  2. Institut für Festkörperphysik, EW5-1, Technische Universität Berlin, Berlin, Germany

    Udo W. Pohl

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  1. Karl W. Böer
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Böer, K.W., Pohl, U.W. (2020). Optical Properties of Defects. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_17-3

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  1. Latest

    Optical Properties of Defects
    Published:
    21 June 2022

    DOI: https://doi.org/10.1007/978-3-319-06540-3_17-4

  2. Optical Properties of Defects
    Published:
    04 April 2020

    DOI: https://doi.org/10.1007/978-3-319-06540-3_17-3

  3. Optical Properties of Defects
    Published:
    27 September 2017

    DOI: https://doi.org/10.1007/978-3-319-06540-3_17-2

  4. Original

    Optical Properties of Defects
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    21 May 2016

    DOI: https://doi.org/10.1007/978-3-319-06540-3_17-1

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