Week 1B: Fermi Function and Conduction Mechanisms

Fermi Level

The energy level that has a 50% chance of being occupied by an electron.

False

There are multiple Fermi Levels in a system in thermal equilibrium.

up

Doping a semiconductor with n-type impurities causes the Fermi level of the semiconductor to shift (up, down) toward the conduction band.

down

Doping a semiconductor with p-type impurities causes the Fermi level of the semiconductor to shift (up, down) toward the conduction band.

Drift, Diffusion, Recombination-Generation

Conduction Mechanisms in Semiconductors

Drift

Movement of charged particles in the presence of an electric field.

Diffusion

Natural tendency of charged particles to seek uniform concentration.

Recombination-Generation

Particle motion due to recombination and generation processes.

opposite

Electrons move in the (opposite, same) direction of an electric field.

v = μE

Formula for average drift velocity. (Note: p-drift is positive, n-drift is negative.)

480 cm²/Vs

For intrinsic Si at room temperature, the hole mobility’s value is ____.

1350 cm²/Vs

For intrinsic Si at room temperature, the electron mobility’s value is ____.

decreases

Mobility (increases, decreases) when a semiconductor is doped due to increased scattering.

no. of holes = pAx

Formula for the number of holes.

Q_p = qpAx

Formula for total charge Q_p over a length x.

I_p-drift/n-drift = qpAμE

Formula for the hole drift current.

J_p-drift/n-drift = qpμE

Formula for the current density (current per unit area).

σ = q(pμ_p + nμ_n)

Formula for conductivity.

𝜌 = 1/σ (ohm-cm)

Formula for resistivity.

R = 𝜌(L/A)

Formula for resistance.

Diffusion

Tendency of carriers to spread themselves uniformly in a solid. Occurs when charge distribution is not uniform.

J_p-diff = -qD_p(dp(x)/dx)

Formula for hole current density due to diffusion.

J_n-diff = qD_n(dn(x)/dx)

Formula for electron current density due to diffusion.

D_p = 12 cm²/s, D_n = 35 cm²/s

Typical values of diffusion constants.

D/μ = kT/q

Formula for Einstein’s Relationship (relationship between diffusion constant and mobility).

26mV

Value of the thermal voltage at room temperature.

Band-to-Band Generation, Generation through R-G Centers, Impact Ionization

Enumerate the generation processes.

Direct Recombination, Recombination through R-G Centers, Auger Recombination

Enumerate the recombination processes.