Exercise 2.3.5-1

Show the equivalence of the two equations for the minority carrier density

The two equations for the minority carrier concentration (here the electrons at the p-side) at the edge of a junction were
nep(U) ÷
 =  nen(U) ÷
 · exp –   Vn + U

nep( U = 0)  =  ni 2
nhp(U = 0)
The first equation came from simply relating one kind of carriers on both sides of the junction including non-equilibrium (i.e. voltage U not zero), the second one is simple the mass action law valid for equlibium (i.e. U = 0).
Show that the two equations are equivalent.
Hint: Express nen in terms of nhp. Write down the equation for nh p and reshuffle the energies in the exponent so that nen and ni can be extracted.

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go to 2.3.5 Junction Reconsidered

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© H. Föll (Semiconductors - Script)