The linear stage of evolution of electron-hole avalanches in semiconductors

Journal Article · Tue Jan 15 04:00:00 EST 2008 · Semiconductors

DOI:https://doi.org/10.1134/S1063782608010028· OSTI ID:22004947

A complete analytical solution of the problem of the linear stage of evolution of electron-hole avalanches in the uniform time-independent electric field E{sub ext} is derived. The theory accounts for the drift, diffusion, and impact ionization of electrons and holes, thus providing a means for calculating the space-time distributions of fields and charges as well as all the basic parameters of the avalanches up to the onset of nonlinear effects at the time t{sub a}. Formulas for the group velocity of the avalanches and for the velocity of its leading fronts are derived. It is shown that the time t{sub a} must be determined from the condition that the impact ionization coefficient {alpha} in the center of the avalanche be reduced by a specified small quantity {eta}. A transcendent equation is derived, which allows the calculation of the time t{sub a} as a function of the quantity {eta}, the unperturbed coefficient {alpha}(E{sub ext}), and other parameters of the semiconductor. It is found that, when {alpha}(E{sub ext}) is increased by two orders of magnitude, the total number of electron-hole pairs generated up to the point t{sub a} decreases by nearly three orders of magnitude.

• OSTI ID: 22004947
• Journal Information: Semiconductors, Journal Name: Semiconductors Journal Issue: 1 Vol. 42; ISSN SMICES; ISSN 1063-7826
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
ANALYTICAL SOLUTION
DIFFUSION
DISTRIBUTION
ELECTRIC FIELDS
ELECTRONS
HOLES
IONIZATION
NONLINEAR PROBLEMS
SEMICONDUCTOR MATERIALS