Suppose that $N_A(x) = N_0 \exp(-x/L)$ in a region of silicon extending from $x = 0$ to $x = 15 \mu m$, where $N_0$ is a constant. Assume that $p(x) = N_A(x)$. Assuming that $j_p$ must be zero in thermal equilibrium, show that a built-in electric field must exist and find its value for $L = 1 \mu m$ and $N_0 = 10^{18}/cm^3$.
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We are given that the doping concentration, N, is a constant. This means that the concentration of holes, p(x), is proportional to the position x, with a constant of proportionality A. Therefore, we can write p(x) = N(Ax). Show more…
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