Introduction | Mathematical
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- 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
- 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 ?
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.
- 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 the forward bias (ie, p-side more positive than the n-side),
use the "helper" button to display parameter definitions.
- 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).
Based on the above questions, do you understand the I-V equation for
an ideal diode ?
- 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
- 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 =
- np0 at a position deep inside the bulk, x = infinity.
- Using this boundary condition, solve the steady-state diffusion equation
= ( 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.