Quiz

1. 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.
2. 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.
3. 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).
4. 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 unhindered 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.
• Should Nn be equal to the concentration of the excess minority electron at the depletion boundary x = xp ?  ans) Yes, assuming no recombination loss in the depletion region.
• Show that
Nn = np(xp) - np0 = np0 [ exp(qV/kT) - 1].
where np0 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
• np(xp) at the p-side depletion boundary, x = xp, and
• np0 at a position deep inside the bulk, x = infinity.
• Using this boundary condition, solve the steady-state diffusion equation :
d2np(x)/dx2 = ( np(x) - np0 )/Ln2.
• The diffusion current density is found from
Jn(x) = qDn dnp(x)/dx.
Find the electron diffusion current at x = xp.
5. Based on the above questions, do you understand the I-V equation for an ideal diode ?