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3 shows the flow of current within the diode. A displacement current proportional to the drift velocity flows in the electrodes whenever there is a charge carrier moving within the depletion region. The area under the curve gives the total charge flow within Position 10 Avalanche region + – ;;; Current Ionization coefficient ( µ m–1) AVALANCHE DIODES Primary current Total current Time Figure 3. Space–time diagram for carrier multiplication in an avalanche diode like that in Fig. 1. The graph at the bottom shows the flow of primary and secondary current in the diode.
The procedure does not diverge, since the value of Jn simply integrates to zero at breakdown. A great simplification of the gain equation is obtained by assuming that the ratio of ionization coefficients (k ϭ Ͱ/ͱ) is constant throughout the avalanche region. While this is an oversimplification, it yields analytical results that are useful in developing an intuitive feeling for the device behavior. McIntyre (22) has analyzed this case in detail. The electron gain Mn is easily shown to be Mn = 1−k exp (k − 1) W 0 α dx − k (10) with a similar result for Mp.
The top part of the figure is a space–time diagram of the flow of carriers. The carriers are shown traveling at their saturated drift velocity, ignoring the acceleration and deceleration that occur under the influence of the electric field and scattering events. While not quantitatively accurate, this picture helps in understanding the essential physics. At the left side, a photon moves at high speed and produces an initial electron–hole pair. Under the influence of the electric field, holes travel toward the top edge of the depletion region, while electrons travel toward the bottom edge.
20.Electron Devices by John G. Webster (Editor)