Question #109529

Given a forward biased si diode with I = 1mA. If the diffusion capacitance is Cd =1microferad , what is the diffusion Length Lp? Assume that the doping of the P-side is much greater than that of the n-side . Use Dp = 13metersquare second.

Expert's answer

In this problem, we will need the following:

"L_p" - diffusion length for holes, m;

"D_p" - diffusion constant for holes, "\\text{m}^2\/\\text{s}";

"C_D" - diffusion capacitance, μF;

"\\tau_p" - meal life time for holes, s;

"V_T" - volt equivalent of temperature "T" (26 mV for 300 K);

"\\eta=1" for Ge and "\\eta=2" for SI - a constant, "\\eta=I_0(e^{V\/\\eta V_T}-1)."

The diffusion length is

Therefore, combining all this, we get

"L_P=\\sqrt{\\frac{D_pC_D\\eta V_T}{I}}=\\\\ \\space\\\\\n=\\sqrt{\\frac{13\\cdot(1\\cdot10^{-6})\\cdot2\\cdot(300\/11600)}{(1\\cdot10^{-3})}}=0.0259\\text{ m}."

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