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

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

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+ -

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, 16 m*/me = 0.26, 0.067, 0.12

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) = 0.0259 eV and no ~ ND allowed ED + EV

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.

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- +

Acceptor Energy Levels EC - allowed EA + typically, EA – EV < 0.05 eV

Summary, p-type Semiconductor EC Eg EA - EV valence band with free holes po  NA

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

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

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

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

QUESTIONS?