# 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) | ÷ ÷ | SCR edge | = | nen(U) | ÷ ÷ | SCR edge | · exp – | Vn + U kT
nep( U = 0) | = | ni2 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.
| Link to the solution

With frame

2.3.5 Junction Reconsidered

Solution to Exercise 2.1-1 Free Electron Gas with Constant Boundary Conditions

Solution to 2.3.5-1

© H. Föll (Semiconductors - Script)