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P. A. Wolff, Theory of electron multiplication in silicon and germanium, Phys. , 95: 1415–1420, 1954. 9. W. , 2: 35–67, 1961. 10. G. A. Baraff, Distribution functions and ionization rates for hot electrons in semiconductors, Phys. , 128: 2507–2517, 1962. 11. S. M. Sze, Physics of Semiconductor Devices, New York: Wiley, 1981. 12. G. Chynoweth, Ionization rates for electrons and holes in silicon, Phys. , 109: 1537–1540, 1958. 13. B. K. Ridley, Lucky-drift mechanism for impact ionisation in semiconductors, J.
An analysis of the frequency response of an avalanche region with a uniform electric field and ionization ratio k has been done by Emmons (34). From his result, it is possible to derive a simple expression for the gain–bandwidth product: M f 3dB = (1 − k)2 ln k 4πkτ0 [2(1 − k) + (1 − k) ln k] and acceptor ions. At sufficiently high current, the mobile charge has to be included when integrating Poisson’s equation to obtain the electric field profile. In a one-sided diode in which most of the avalanche multiplication takes place at one side of the depletion layer, it is simple to show that the spacecharge of secondary carriers tends to lower the electric field just as if the voltage had been dropped by an amount ͳV given by ͳV ϭ IRs, where the space charge resistance Rs is just W2 /(2A⑀v), where v is the drift velocity of the secondary carriers (11).
Figure 8 shows the result for uniformly doped one-sided abrupt junctions in Breakdown voltage (V) 10 20 169 1000 n+p GaAs p+n InP 100 n+p Si 10 1015 1016 Carrier concentration (cm–3) 1017 Figure 8. Calculated breakdown voltage versus doping for one-sided abrupt diodes in Si, GaAs, and InP using the ionization coefficients of Fig. 2. The type of the low doped side was chosen so that the predominant carrier has the higher ionization coefficient. AVALANCHE DIODES Si, GaAs, and InP as a function of the doping level on the lower doped side.