Please show all steps to the attached problem. Thank you. Inside a room temperat

Question

Please show all steps to the attached problem. Thank you.

Inside a room temperature Si PN diode, a region of width d has 4 times as many R-G centers as the neighboring regions. This special region is completely inside the depletion region when the diode is not under any bias. N_A= N_D=10^16/cm^3. Express the lifetime in the "d" region in terms of the lifetime in the neighboring regions. Derive an expression for I_R-G when the diode is reverse biased. If we move the "d" region to create a device like the diagram in Figure 2, what effect does this have on the R-G current under reverse bias? Under forward bias? Returning to Figure 1, we highly dope the P side material. Sketch minority carrier concentrations under reverse bias. Sketch the electron, hole and the total current densities under reverse bias.

Explanation / Answer

a) life time ,tp = wn2/2Dp

b)   IRG = Io * e(qV/kT - 1)

c) In forward biased mode, the electric current can easily flow through it. So it acts like a CLOSED SWITCH. However, in reverse biased mode, the current through it is practically zero and thus, it acts like an OPEN SWITCH.

d) At equilibrium, the product of the majority and minority carrier concentration is a constant .The number of carriers in the conduction and valence band with no externally applied bias is called the equilibrium carrier concentration. For majority carriers, the equilibrium carrier concentration is equal to the intrinsic carrier concentration plus the number of free carriers added by doping the semiconductor.

The number of minority carriers decreases as the doping level increases.

e) Applying a potential to the diode affects the current flowing through the diode. The potential hill varies with the applied voltage VA.   If VA = 0 the diode is in equilibrium, if VA > 0 it is forward biased, and if VA < 0 it is reverse biased. Drift current and diffusion current are present even though J = 0 in equilibrium. This is because for every electron that diffuses from the n-side to the p-side there is an electron that drifts from the p-side to the n-side. The same goes for holes. The two currents balance each other and the total current density J = 0.

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