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*Quiz*

- In the depletion region (the white region), which way does the total
Electric Field point ?

ans) From the n-side to the p-side, because of the positively chanrged donor in n-side and negatively charged acceptor in p-side. From the energy band diagram, E-field points toward higher energy : Field = 1/q dE/dx. - At zero bias (click the "reset" button), you should see the electrons (blue dots) moving across the junction. Is the electron leakage current (from p to n) equal to the electron injection current (from n to p) ? Is it true for holes also ?
- I deliberately made the leakage electrons slide down the potential, where as the injection electrons move horizontally straight. Explain the physical significance of this seemingly different flow of electrons.
- Under a reverse bias (negative p-side voltage, relative to the n-side), change the doping level of the p-side by using the choice box at the bottom and observe the electron leakage current.
- is it clear that the leakage current is constant, independent of the applied bias ? Explain qualitatively why this is so (based on your observation of the applet).
- What controls the magnitude of the electron leakage current ? (Hint: The direction of electric field in the transition region, random thermal motion of minority electrons near the depletion boundary).
- Under the forward bias (ie, p-side more positive than the n-side), use the "helper" button to display parameter definitions.
- The amount of injected electrons is equal to the number which can go
to the p-side
by the potential barrier. From the band diagram, find the number of injected electrons, Nn, in terms of the donor doping level, Nd, and the potential, V0 - V, where V0 is the junction built-in potential and V is the applied bias.*unhindered* - Should Nn be equal to the concentration of the excess minority electron
at the depletion boundary x = x
_{p}? ans) Yes, assuming no recombination loss in the depletion region. - Show that

Nn = n_{p}(x_{p}) - n_{p0}= n_{p0}[ exp(qV/kT) - 1].

where n_{p0}is the minority electron concentration in p-side at equilibrium. - Do the above steps for the number of injected holes, Np.
- The boundary condition for the number of electrons in the p-side is
- n
_{p}(x_{p}) at the p-side depletion boundary, x = x_{p}, and - n
_{p0}at a position deep inside the bulk, x = infinity. - Using this boundary condition, solve the steady-state diffusion equation
:

d^{2}n_{p}(x)/dx^{2}= ( n_{p}(x) - n_{p0 })/L_{n}^{2}. - The diffusion current density is found from

J_{n}(x) = qD_{n}dn_{p}(x)/dx.

Find the electron diffusion current at x = x_{p}. - Based on the above questions, do you understand the I-V equation for an ideal diode ?