Quantum theory of the complex dielectric constant of free carriers in polar semiconductors

Journal Article · Wed Sep 01 04:00:00 EDT 1982 · IEEE J. Quant. Electron.; (United States)

DOI:https://doi.org/10.1109/JQE.1982.1071713· OSTI ID:6165963

Jensen, B

The optical constants and reflectivity of a semiconductor are known as functions of the real and imaginary parts of the complex dielectric constant. The imaginary part of the complex dielectric constant e/sub 2/ is proportional to the optical conductivity, which has recently been calculated from the quantum density matrix equation of motion. The expression obtained for e/sub 2/ reduces to the Drude result, as obtained from the quasi-classical Boltzmann transport equation, in the limit of low frequencies and elastic scattering mechanisms, and to the quantum result found using time dependent perturbation theory in the limit of high frequencies. This paper derives the real part of the complex dielectric constant e/sub 1/ for a III-V or II-VI semiconductor with the band structure of the Kane theory, using the quantum density matrix method. The relation of e/sub 1/ to the second order perturbation energy of the system is shown, and the reflectivity is a minimum when the second order perturbation energy vanishes. The quantum calculation for e/sub 1/ gives approximately the same result as the Drude theory, except near the fundamental absorption edge, and reduces to the Drude result at low frequencies. Using the complex dielectric constant, the real and imaginary parts of the complex refractive index, the skin depth, and surface impedance, and the reflectivity are found. The plasma resonance is examined. The surface impedance and the skin depth are shown to reduce to the usual classical result in the limit that e/sub 1/ = 0 and w tau << 1, where w is the angular frequency of the applied field and tau is the electron scattering time.

• Research Organization: Boston Univ., MA
• OSTI ID: 6165963
• Journal Information: IEEE J. Quant. Electron.; (United States), Journal Name: IEEE J. Quant. Electron.; (United States) Vol. QE-18:9; ISSN IEJQA
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360603* -- Materials-- Properties
ABSORPTION SPECTRA
ARSENIC COMPOUNDS
ARSENIDES
BOLTZMANN EQUATION
CADMIUM COMPOUNDS
CADMIUM TELLURIDES
CHALCOGENIDES
DENSITY MATRIX
DIELECTRIC PROPERTIES
DIFFERENTIAL EQUATIONS
ELECTRICAL PROPERTIES
ELECTRODYNAMICS
ELECTRONIC EQUIPMENT
ELECTRONS
ELEMENTARY PARTICLES
ENERGY LOSSES
EQUATIONS
EQUIPMENT
FERMIONS
GALLIUM ARSENIDES
GALLIUM COMPOUNDS
IMPEDANCE
INDIUM ARSENIDES
INDIUM COMPOUNDS
INDIUM PHOSPHIDES
LEPTONS
LOSSES
MATERIALS
MATRICES
MECHANICS
MICROWAVE EQUIPMENT
OPTICAL PROPERTIES
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
PHONONS
PHOSPHIDES
PHOSPHORUS COMPOUNDS
PHYSICAL PROPERTIES
PNICTIDES
QUANTUM MECHANICS
QUASI PARTICLES
REFLECTIVITY
REFRACTIVITY
SELENIDES
SELENIUM COMPOUNDS
SEMICONDUCTOR MATERIALS
SKIN EFFECT
SPECTRA
SURFACE PROPERTIES
TELLURIDES
TELLURIUM COMPOUNDS
ZINC COMPOUNDS
ZINC SELENIDES