Keith S. Champlin

Microwave free carrier Faraday effect in semiconductors--perturbation theory for guided waves

Abstract At frequencies approaching the electron-lattice collision frequency, the weak field Faraday effect can be used to study details of scattering mechanisms that are manifested in the complex Hall terms of the permittivity tensor. Plane wave theories that may apply to experiments using infrared or visible light do not apply rigorously to the guided wave experiments that have been performed in this frequency range. This paper describes a guided wave theory relating the real and imaginary parts of the weak field Hall terms to microwave measurements performed on a degenerate TE mode waveguide containing a longitudinally magnetized cubic semiconductor. The theory assumes only that the magnetic field is small and takes losses and reflections into consideration exactly.

TEMPERATURE DEPENDENCE OF THE MICROWAVE DIELECTRIC CONSTANT OF THE GaAs LATTICE

The relative dielectric constant er of high‐resistivity GaAs has been measured at 70.243 GHz as a function of temperature between 100 and 300°K. The measuring technique utilized a circular E field (TE°01) mode reflection‐coefficient bridge. Estimated relative and absolute accuracies of the measurements are ±0.2% and ±0.5%, respectively. The results are found to fit the equation er(T) = er(0){1 + αT} where er(0) = 12.73 ±.07 and α = (1.2 ± 0.1) × 10−4. At room temperature (295°K) the relative permittivity is er = 13.18 ±.07.

SEARCH FOR RESONANCE BEHAVIOR IN THE MICROWAVE DIELECTRIC CONSTANT OF GaAs

In a recent communication, Larrabee and Hicinbothem presented measurements of the dielectric constant of high‐resistivity GaAs showing a region of anomalous dispersion centered at 9.5 GHz. We have made similar measurements over the frequency range between 8.5 and 70 GHz but have not obtained their results. Our measurements indicate that the relative dielectric constant is independent of frequency in the microwave range and equal to 12.95 ± .10 at room temperature.

MICROWAVE PERMITTIVITY OF THE GaAs LATTICE AT TEMPERATURES BETWEEN 100°K AND 600°K

An earlier letter reported microwave (70.2 GHz) measurements of the relative permittivity er of high‐resistivity GaAs in the temperature range between 100° and 300°K. This letter extends the measurements to 600°K. Over the entire temperature range 100° < T < 600°K, the permittivity is observed to fit the expression er(T) = er(0){1 + αT}, where er(0) = 12.79 ± 0.10 and α = 1.0 × 10−4 deg−1.

On the influence of diffusion and surface recombination upon the GR noise spectrum of semiconductors

Abstract Several theories of generation-recombination (GR) noise in nearly intrinsic semi-conductors which consider the effects of diffusion and surface recombination are discussed. It is shown that the earlier eigenfunction treatments of Hyde and of van Vliet and van der Ziel do not allow for the fact that Fourier coefficients of different spatial modes are correlated. A proper treatment based on a transmission line analogy is presented and the result is examined for the cases arising when the recombination process is: 1) volume-limited; 2) surface-limited; and 3) diffusion-limited. For the diffusion-limited case, it is found that the spectrum varies as ω - 3 2 at high frequencies; at low frequencies, the noise determined from the turnover frequency is 5 6 that found for the volume- and surface-limited cases.

The Microwave Magneto‐Kerr Effect in Silicon and Germanium. I. Measurement of Complex Hall Factor

The complex conductivity and Hall factor of lightly doped n‐ and p‐type Si and Ge are measured at 8.6 GHz over the temperature range 77∘ [double-line equal to or less-than] T [double-line equal to or less-than] 300∘K. These phenomenological parameters are determined from observations of microwave reflectivity and low‐field magneto‐Kerr effect. The experimental analysis applies rigorously to guided waves and treats multiple reflections within the sample exactly. Both Hall and conductivity currents are found to lag the electric field at low temperature. These effects are attributed to the increased influence of the inertia of the charge carriers at low temperature.

Infrared response of lightly doped Schottky diodes

The traditional hf model of a Schottky diode has been extended to include skin effect, carrier inertia, and displacement current. Above the plasma frequency, results differ considerably from those of the traditional model. The extended model helps understand recently reported detection of 10.6‐μ radiation with Ge diodes doped to only 1016 cm−3.

Warm‐Carrier dc Transport in n Si

Measurements of the dc current density at 77 °K lattice temperature vs electric field for 26‐Ω cm n Si are presented and analyzed to determine the amount of repopulation when the field is applied in the 〈100〉 and 〈110〉 crystallographic directions. A relatively simple and straight‐forward technique for computing the energy‐relaxation‐time dependence on the electric field is proposed and applied to n Si. The electron temperatures vs electric field for several differently oriented conduction‐band minima are also calculated. An explanation for the previously observed but unexplained decrease in amount of repopulation above 400 V/cm is given. A new technique for computing the theoretical repopulation‐field dependence is also presented and found to give excellent agreement with the experimental results. A theory similar to that used in past literature, but more general, is used in the following experimental determination of the warm‐carrier repopulation in n Si.

The Microwave Magneto‐Kerr Effect in Silicon and Germanium. II. Determination of Relaxation Time and Effective Mass

This paper analyzes microwave (8.6 GHz) measurements of complex conductivity and Hall factor in order to investigate the temperature dependence of the momentum relaxation time and effective mass of majority carriers in near‐intrinsic n‐ and p‐type Si and Ge. The analysis uses scattering models which include ionized impurity scattering, intravalley acoustic‐ and optical‐mode scattering, and intervalley scattering. For n‐ and p‐type Ge and n‐type Si, the conductivity effective mass is found to be virtually independent of temperature in the range 77° < T < 160°K and to agree favorably with results calculated from microwave cyclotron resonance measurements at 4°K. Because of inadequancy of the model for p‐type silicon, the measurements do not yield an unambiguous value of the effective mass but do indicate constancy with temperature.

Waveguide Perturbation Techniques In Microwave Semi-Conductor Diagnostics

DC transport properties (e. g. , conductivity, Hall effect, magneto-conductivity) are proportional to various averages of the electron-lattice relaxation time ( , , , etc.) and hence give indirect information about the scattering mechanisms affecting the conduction process. With microwaves, the observation frequency can frequently be of the order of the scattering frequency 1/(2/spl pi ). Under these conditions, microwave transport properties are complex and contain potentially more information concerning detailed scattering mechanisms than the analogous dc properties.