Semiconductor Physics - Video Notes

What happens to the discrete energy levels of isolated atoms when many atoms come together to form a solid?

They hybridize and split into N closely spaced levels that form a continuous energy band.

What is the valence band in a solid?

The highest occupied allowed energy band formed by valence electrons.

What is the conduction band?

The lowest unfilled (or partially filled) allowed energy band in which electrons can move freely.

What is the forbidden energy gap Eg?

The energy difference between the top of the valence band and the bottom of the conduction band; energy required to excite an electron across the gap.

How are solids classified based on the band gap Eg?

Insulators have large Eg, semiconductors have small Eg (~1 eV), and conductors have overlapping bands (no gap).

What are the defining features of insulators?

Full valence band, empty conduction band, large Eg (≈5–10 eV), very high resistivity.

What are the defining features of semiconductors?

Almost empty conduction band and filled valence band with a narrow energy gap (~1 eV); at room temperature some valence electrons cross the gap creating electrons and holes; resistivity is intermediate.

What are the defining features of conductors?

Overlapped valence and conduction bands with no gap; many free electrons; low resistivity.

What is a direct band gap semiconductor?

The top of the valence band and the bottom of the conduction band occur at the same momentum, so electron–hole recombination can emit a photon without a phonon.

What is an indirect band gap semiconductor?

The maximum of the valence band and the minimum of the conduction band occur at different momenta, requiring a phonon for momentum conservation during transitions.

Why are direct band gap semiconductors used for LEDs and lasers?

Electron–hole recombination is efficient and photon emission occurs directly without phonons.

What defines an intrinsic semiconductor?

A pure crystalline semiconductor with no impurities; at 0 K there are no charge carriers; at finite temperature electron–hole pairs are generated; n = p = ni.

What is intrinsic carrier concentration ni?

The equal concentration of electrons and holes in an intrinsic semiconductor.

What is an extrinsic semiconductor?

A doped semiconductor with added impurities to increase conductivity.

What is a donor impurity and what effect does it have?

A pentavalent impurity (e.g., As, P) that introduces energy levels just below the conduction band, providing extra electrons to create n-type material.

What is an acceptor impurity and what effect does it have?

A trivalent impurity (e.g., B) that introduces energy levels near the valence band, creating holes and producing p-type material.

In an n-type semiconductor, where is the Fermi level located?

In the band gap close to the conduction band, moving toward it as donor concentration increases.

In a p-type semiconductor, where is the Fermi level located?

In the band gap slightly above the top of the valence band ( Ev ), moving toward the center with temperature.

What is the Law of Mass Action for semiconductors?

In thermal equilibrium, np = ni^2; the product of electron and hole concentrations is constant and equals the square of the intrinsic concentration.

What is the Fermi-Dirac distribution function f(E)?

f(E) = 1 / [1 + exp((E − EF)/kT)], giving the probability that a state at energy E is occupied at temperature T.

Where is the Fermi level EF located in an intrinsic semiconductor at most temperatures?

Approximately in the middle of the band gap between Ev and Ec.

How does EF move with increasing donor concentration in an n-type semiconductor?

EF moves upward toward the conduction band and can become degenerate (enter the conduction band)