Analytical Description of Avalanche Photodiode Characteristics. An Overview: Part II

This paper deals with the second part of the overview on analytical calculations of the characteristics of avalanche photodiodes (APDs) based predominantly on direct gap semiconductors. In the first part of the overview (JCTE 2017, vol. 62, no. 9, p. 1027), a general formulation of the problem is carried out and an approach to its solution is reported. The program for calculations of multiplication coefficientins is fulfilled. In the most typical situations, they are represented analytically. It is demonstrated that the obtained analytical results are in good quantitative agreement with previously published numerical calculations and experimental data. In the given part of the overview, the dependences between the interband tunnel current of the heterostructure with a p⁺–n junction in the “wide-gap” (wg) layer and the parameters of used semiconducting materials, layer-doping levels, and their thicknesses corresponding to avalanche breakdown voltages of a heterostructure are analyzed theoretically. It is demonstrated that, as a rule, the tunnel current depends nonmonotonically on the dopant concentration in the “high-resistance” region of a wg layer. There is an optimal concentration of the given dopant at which the tunnel current reaches its absolute minimum. Simple formula for determining the optimal concentration is derived. In addition, an analytical expression for determining the minimum tunnel current is obtained. In real cases, tunnel currents can vary by several orders of magnitude. It is found that, in many cases, an increase in the doping level of a “narrow gap” layer diminishes the tunnel current. It is shown that the tunnel current does not vanish with a decrease in the doping level of the high-resistance layers of a heterostructure but, beginning with a certain concentration, becomes independent of the doping level. An analogous effect is inherent to a homogeneous p⁺–n junction. Physical reasons of such behavior of tunnel currents, which are observed at an avalanche breakdown voltage, are discussed. A technique for the optimizing the parameters of the APD heterostructure with separate absorption and multiplication regions (SAMRs) is developed. As an example, specific calculations are carried out for a widely used InP–In_0.53Ga_0.47As–InP heterostructure. The opportunity of description of transient phenomena in p–i–n APDs is considered first of all in the case where the initial voltage V₀ is higher than the avalanche breakdown voltage V_BD. This problem is formulated because there is a need to know the explicit conditions whereby the Geiger mode is generated in APD operation. A formula describing the total time of progress in the avalanche Geiger process is derived. An analytical expression for the implementation of the Geiger mode is presented. At the end of the given paper, the advantages of avalanche heterophotodiodes with SAMRs of the low-high-low type over classical samples are demonstrated and discussed on the basis of analytical calculations. The numeration of formulas, figures, and references continues that used in Part I.