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Figure 11 shows what happens as the gain is raised to higher values. Notice that the secondary pulse develops an exponential tail, which gets longer as the gain is increased. In fact, the peak current tends to level off, with additional 172 AVALANCHE DIODES Bandwith (GHz) 6 5 Constant gain × bandwidth 4 3 2 1 1 2 3 4 6 8 10 Avalanche gain 20 30 40 Figure 12. Bandwidth of the avalanche diode in Fig. 1 as a function of gain. At high gains, the curve approaches a line with constant gain–bandwidth product.

Standard methods can be used to perform the numerical integration. The same approach is useful in calculating other quantities such as the excess noise and gain–bandwidth product. 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.

Since ͗Mi2͘ would equal ͗Mi͘2, the factor F(M) would be one and the noise spectral density would be larger than that of a conventional diode by a factor M2. This is exactly the shot noise that would be expected for a diode in which the individual ‘‘shots’’ are larger by a factor of M. For a real device with gain fluctuations, F(M) is always larger than one and represents the factor by which the noise is greater than shot noise. Appropriately, it is called the excess noise factor. Composition Law for Avalanche Regions In predicting the behavior of avalanche diodes, it is helpful to break the device into smaller regions that can be analyzed separately.

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20.Electron Devices by John G. Webster (Editor)

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