Urbach’s Rule states that the fundamental optical absorption edge exhibits an exponential shape: KA(ω) ∝ exp g(ħω-ħω0). The rule is valid for a variety of non-conducting materials, including semiconductors and alkali halides (with g=σ/kBT at high temperature, σ being nearly unity and weakly dependent on temperature). In the case of semiconductors, the origin of the Urbach edge is well established, largely as a result of a unification of early theoretical work by Redfield and by Dexter, and as a result of experiments by Redfield and Afromowitz and by Garrod and Bray. The semiconductor Urbach rule is attributable to ionization of the exciton by internal electric microfields. The extent to which the field-ionization mechanism is responsible for Urbach edges in all insulators is discussed with emphasis on recent experiments by Williams and Schnatterly. Finally it is suggested that in certain circumstances the shapes of multiphonon edges and Urbach edges should be related.
KeywordsAbsorption Edge Alkali Halide Fundamental Absorption Edge Longitudinal Optical Phonon Exponential Shape
Unable to display preview. Download preview PDF.
- 3.See, e.g., B. H. Winters, S. Silverman, and W. S. Benedict, J. Quant. Spectrosc. and Radiative Transfer 4, 527 (1964). The author thanks Dr. G. Birnbaum for bringing this reference to his attention.Google Scholar
- 4.Y. Toyozawa, Tech. Rept. ISSP (Univ. Tokyo) A119 (1964).Google Scholar
- 6.S. E. Schnatterly, Phys. Rev. Bl, 921 (1970).Google Scholar
- 7.R. T. Williams and S. E. Schnatterly (to be published), and these proceedings.Google Scholar
- 9.D. L. Dexter, Phys. Rev. Letters 19, 383 (1967).Google Scholar
- 10.J. D. Dow and D. Redfield, Phys. Rev. Bl, 3358 (1970); J. D. Dow, Comments on Sol. St. Phys. IV, 35 (1972).Google Scholar
- 11.D. K. Garrod and R. Bray, Proc. 11th Internati. Conf. Phys. Semiconductors, ( PWN-Polish Scientific, Warsaw, 1972 ), p. 1167.Google Scholar
- 14.Y. Brada and G. Yacobi, Proceed. 12th Internatl. Conf. Phys. Semicond. (M. H. Pilkuhn, ed., B. G. Teubner, Stuttgart, 1974 ), p. 1212.Google Scholar
- 15.D. Redfield and W. Burke, J. Appl. Phys. 45, 4566 (1974); S. H. Wemple, Phys. Rev. B2, 2679 (1970); M. DiDomenico and S. H. Wemple, Phys. Rev. 166, 565 (1968); A. Frova, Nuovo Cimento 55B, 1 (1968).Google Scholar
- 20.J. D. Dow (to be published).Google Scholar