Herbert S. Bennett

Majority and minority electron and hole mobilities in heavily doped GaAs

The majority electron and minority hole mobilities have been calculated in GaAs for donor densities between 5×1016 and 1×1019 cm−3. Similarly, the majority hole and minority electron mobilities have been calculated for acceptor densities between 5×1016 and 1×1020 cm−3. All the important scattering mechanisms have been included. The ionized impurity and carrier–carrier scattering processes have been treated with a phase‐shift analysis. These calculations are the first to use a phase‐shift analysis for minority carriers scattering from majority carriers. The results are in good agreement with experiment, but predict that at high dopant densities minority mobilities should increase with increasing dopant density for a short range of densities. This effect occurs because of the reduction of plasmon scattering and the removal of carriers from carrier–carrier scattering because of the Pauli exclusion principle. Some recent experiments support this finding. These calculations do not treat the density‐of‐states m...

Hole and electron mobilities in heavily doped silicon: comparison of theory and experiment

Abstract Most device models for npn or pnp transistors assume that hole (electron) mobilities in n-type and p-type silicon are equal. Partial-wave phase shift calculations for the contributions of carrier-dopant ion scattering to the carrier mobilities lead to unequal minority hole (electron) and majority hole (electron) mobilities at the same doping density. These calculations are valid over the doping range of 2 x 1019 to 8 x 1019 cm−3 in n-type and p-type silicon and contain the assumptions that the holes and electrons move in isotropic parabolic energy bands and are scattered by the screened Coulomb potentials of the dopant ions. When the effects of carrier-acoustic phonon and carrier-carrier scatterings are included, these calculations agree to within the spread of experimental value for the majority mobilities reported in the literature. This agreement is a substantial improvement by factors of 2–4 over the results of earlier theories such as first order Born and nondegenerate theories. The results of this work, particularly the inequality of minority and majority carrier mobilities, have implications for the modeling of both bipolar and field effect transistors.

Models for heavy doping effects in gallium arsenide

Klauder’s self‐energy method is used in a self‐consistent calculation of the effects due to the interactions between carriers and dopant ions in GaAs at 300 K. The many‐body effects due to the interactions among the carriers themselves, exchange, and correlation, are estimated by evaluating expressions similar to those of Abram et al. at 300 K. When densities exceed about 5×1016 cm−3 in n‐type GaAs and 1018 cm−3 in p‐type GaAs, carrier‐dopant ion interactions and carrier‐carrier interactions become significant and should be included in calculations of band structure changes and of properties which depend on the density of states such as carrier transport, effective intrinsic carrier concentrations, and coefficients for optical absorption.

Internal field resonance structure: Implications for optical absorption and scattering by microscopic particles

Mie scattering theory is used to calculate the efficiency factors for absorption by microscopic dielectric spheres. Resonances in the efficiency factors for absorption and resonances in the amplitudes of the electric and magnetic multipoles which occur in an expansion of the fields inside the dielectric sphere are discussed. Several trends in the strengths and width of the various resonances as functions of the absorption coefficient of the sphere, size parameter, multipole order, and multipole resonance number are given. A formal solution for elastic (Mie) and inelastic (Raman) scattering by microscopic particles is derived from the extinction theorem. With this background, some implications of the resonances in the interpretation of absorption, fluorescence, and Raman scattering by microscopic particles are discussed.

Frequency dependence of photoacoustic spectroscopy: Surface‐ and bulk‐absorption coefficients

Researchers seek improved ways to measure separately the surface‐ and bulk‐absorption coefficients of highly transparent materials. The case in which a laser beam modulated at angular frequency ω passes through the weakly absorbing windows of a gas cell which contains a nonabsorbing gas is investigated in this paper. In particular, the frequency dependences of the acoustic stresses in the gas which arise from the surface and bulk absorption are derived. An intermediate range of frequencies exists for which the acoustic stress due to surface absorption varies as ω−1 and has a 90 ° phase shift relative to the modulated laser beam and for which the acoustic stress due to bulk absorption varies as ω−3/2 and has a 45 ° phase shift. In addition, expressions for the acoustic stress and phase shift which are valid for all frequencies are given. These expressions enable one to develop numerical procedures by which the surface‐ and bulk‐absorption coefficients may be determined separately. Numerical examples for a ...

Statistical comparisons of data on band‐gap narrowing in heavily doped silicon: Electrical and optical measurements

A system of subroutines for iteratively reweighted least squares (IRLS) computations has been applied to the published measured and theoretical data on band‐gap narrowing in heavily doped silicon. The data include electrical and optical measurements at room temperature, photoluminescence and optical measurements for temperatures below 35 K, and theoretical calculations at 300 and 0 K. The IRLS procedure allows a clear graphical comparison of the various experimental and theoretical data in band‐gap narrowing to be made. The results are (1) band‐gap changes determined by the optical absorption are consistent at both 300 K and at temperatures below 35 K with recent theoretical calculations, (2) the electrical and optical measurements are not consistent with each other, and (3) the low temperature optical absorption data and the photoluminescence data are not consistent with each other.

Improved concepts for predicting the electrical behavior of bipolar structures in silicon

Most bipolar device models, based upon doping profiles and upon numerical solutions to coupled, nonlinear equations for semiconductor devices, contain empirical methods for computing the effective intrinsic carrier concentration niemobility, and lifetime. These methods usually are based upon electrical measurements, assume that the majority hole (electron) mobility equals the minority hole (electron) mobility at high doping densities, use Boltzmann statistics, and assume that the carrier lifetime is much greater than the carrier transit time. More physically correct concepts are reported in this paper and are applied to bipolar transistors in silicon. These concepts use the perturbed densities of states and nonparabolic bands which arise from a quantum mechanical description of bandgap narrowing to compute separately nieand the carrier mobility, use minority carrier lifetimes which agree much better with measured lifetimes in processed silicon, and use Fermi-Dirac statistics. When these concepts are incorporated into a device analysis code such as SEDAN1and then used to compute the dc common-emitter gain of two n-p-n transistors, the predicted gains agree very well with the measured gains. In addition, these concepts offer potential improvements in predicting the temperature dependence of the gain.

Effect of donor impurities on the conduction and valence bands of silicon

The energy shifts of valence and conduction band states in silicon due to the interaction of electrons and holes with ionized donors have been calculated by performing a partial wave analysis. The potential is modeled by the Yukawa form with the screening radius determined self‐consistently by the Friedel sum rule. The results show that this effect is an important part of the optically measured band‐gap narrowing. The variation of the Fermi energy due to this phenomenon is also calculated.

Photoacoustic methods for measuring surface and bulk absorption coefficients in highly transparent materials: theory of a gas cell

Researchers seek improved ways to measure the surface absorption and the bulk absorption coefficients of highly transparent materials. Procedures are presented here by which one may determine separately the surface absorption and the bulk absorption coefficients. For the case in which a laser beam modulated at angular frequency omega passes through the weakly absorbing windows of a gas cell containing a nonabsorbing gas, the temperature profiles in the cell windows and the temperature and acoustic pressure or stress profiles in the gas have been calculated. These calculations indicate that for sufficiently low frequencies and high ambient gas pressure, enough heat transfers from the cell windows to the gas to produce a detectable acoustic pressure signal at angular frequency omega in the gas. These calculations also enable us to state the necessary measurements for determining the surface and bulk absorption coefficients. Measuring the acoustic stress amplitude at the fundamental and higher harmonic frequencies and measuring the phase shifts of the frequency components of the acoustic stress with respect to the modulated laser beam give sufficient data by which one can determine the surface and bulk absorption coefficients. Numerical examples for a representative laser glass and air (nitrogen) are given.

Absorption coefficients of highly transparent solids: photoacoustic theory for cylindrical configurations.

The development of highly transparent solids for fiber optics, integrated optics, and high power lasers requires improved methods to measure very low absorption coefficients. For the case in which a laser beam, modulated at angular frequency omega, passes through a weakly absorbing solid which is surrounded by a confined, nonabsorbing gas, the temperature profiles in the solid and the temperature and pressure profiles in the gas have been calculated. The calculations suggest that for sufficiently low frequencies and high ambient gas pressures, enough heat transfers from the solid to the gas to produce a detectable acoustic-pressure signal at angular frequency omega in the gas. They also indicate that an absorbing layer at the solid-gas interface is not an essential mechanism for producing these detectable acoustic pressure signals. The model assumes that bulk absorption in the solid is the mechanism by which energy is transferred from the laser beam. Numerical examples for a typical laser glass are given.