1. Doping of Semiconductors
ECE G201
(Adapted from Prof. Hopwood)

2. Review intrinsic semiconductor: no= po= ni
conduction band
valence band EC EV + - x
E(x)
energy -

3. n-type doping in silicon Column V elements donate an electron to the conduction band
valence band EC EV x
E(x) - ED
The donor creates a small
variation in the lattice potential
resulting in an allowed state in
the bandgap. Si P+ -

4. What is the energy level, ED
What is the energy level, ED? We treat the ionized donor as a positive charge and consider the allowed energies of its extra valence electron using the Bohr model (an approximation!) EC EV ED +
E = Evac – mq2/2(4peonħ)2
= Evac – 13.6 eV/n2
But here the valence electron is free if E = EC. Also, the electron has an effective mass m* and the electron is in a semiconductor material with e = ereo.
So,
ED = EC – m*q2/2(4pereonħ)2
for Si, GaAs, Ge:
er = 11.8, 13.2, m*/me = 0.26, 0.067, 0.12

5. The lowest energy state (n=1) is most likely to be occupied, so…EC
EC-ED
~ 13.6 eV(m*/me)(er)-2 < 0.05 eV
This means that almost all donor atoms are ionized at room temperature since
Et = kT
= (8.63x10-5 eV/K)(300K)
= eV
and no ~ ND
allowed ED + EV

6. Assumption:
…the donor electron orbit (Y* Y) is big enough to encompass a large volume such that er represents the bulk material (not just a few atoms).
This is not always the case (for example, when the effective mass is large). Then the actual donor energy levels are greater than this Bohr model calculation.

7. p-type doping in silicon Column III elements accept an electron from the valence band
conduction band
valence band EC EV x
E(x) - EA
The acceptor creates a small
variation in the lattice potential
resulting in an allowed state in
the bandgap. Si B- +

8. Acceptor Energy LevelsEC -
allowed EA +
typically,
EA – EV < 0.05 eV

9. Summary, p-type SemiconductorEC Eg EA - EV
valence band with free holes
po  NA

10. Summary, n-type Semiconductor
conduction band with free electrons
no  ND EC - - - - ED Eg EV

11. Electron Current
Electrons move toward the positive potential (+) at a constant total energy (the kinetic energy increases but the potential energy decreases) until a collision with the an imperfection occurs. (EK0)
- V+ E
EC=EP EV
Fe = -dEp/dx = -dEC/dx, Fe 
-qV

12. “Band bending” E = (1/q)dEC/dx EC=EP -qV EV Fe = -dEp/dx = -dEC/dx
= -qE
-qV
E = (1/q)dEC/dx

13. Hole Current E
- V+
EC=EP(x)
-qV EV
Fh = +dEp/dx, Fh 

14. QUESTIONS?