An analysis of the time dependence of avalanche processes encountered in silicon junctions, including the effects of different ionization rates and velocities of the two charge carriers, is presented. An earlier analysis of Read was restricted to equal ionization rates and velocities; that restriction has been removed but the frequency limitation of his analysis has been retained here. Various solutions of the generalized differential equation are obtained, including a steady-state solution to a sinusoidal perturbation of the avalanche-field maximum. The important features of this steady-state solution are that it describes the avalanche current for all explicit values of the multiplication M≥1, is valid for highly nonlinear responses to the sinusoidal perturbation, and contains both the in-phase and out-of-phase parts of the fundamental-frequency component of the avalanche response. The analysis is applied to solid-state photomultipliers, is used to explain an anomalous rectification observed in operating Read structures, and, lastly, the small-signal limit of the avalanche response is compared with susceptance measurements of a uniformly avalanching junction as a function of the multiplication and saturation current over a frequency range of 20 to 200 MHz.
Steady-state impurity distributions are produced when impurities are diffused into a piece of silicon, the surface of which is evaporating. The moving boundary condition results under steady state in an exponential impurity distribution. The silicon evaporation rate has been determined for temperatures between 1200 and 1325°C from weight loss measurements. No difference in the evaporation rate from various crystallographic planes could be observed from the diffusion technique but flat-bottomed etch pits which formed on surfaces closely orientated to the (111) plane indicated that this plane is probably the most stable. Single diffusions as well as simultaneous double diffusions of phosphorus and gallium into silicon have been studied.
Small area silicon p-n junctions have been made which are free from exposed edges and dislocations passing through the space-charge region. It is believed that the space-charge regions of these junctions more closely resemble plane parallel geometries than any studied similarly hitherto. The avalanche breakdown phenomena in these uniform junctions are shown to be drastically different from those occuring in junctions that contain many dislocations. A comparison is made between the uniform junctions and one that is similar except that it possesses two breakdown-inducing sites, probably dislocations. In the latter junction the reverse characteristic shows two slightly separated rapid increases in current which coincide, biaswise, with the formation of two isolated light-emitting microplasmas, the occurrence of characteristic microplasma noise, and two singularities in the charge-multiplication characteristics. The uniform junctions show no such phenomena at intermediate voltages, breakdown occurring at a voltage roughly twice that at which the microplasmas form and which was previously thought typical for the given material resistivity. The light emission pattern accompanying breakdown in the uniform junctions appears more diffuse (giving rise to the term—macroplasma) than in nonuniform junctions where it normally appears as an array of intense local spots (microplasmas). It is concluded that microplasmas are not a necessary accompaniment of avalanche breakdown in silicon, but that they tend to occur where there are field or lattice inhomogeneities.
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