Electrons and Holes in Semiconductors

Chapter Objectives

• Understand basic concepts & terminology of semiconductors

• Focus on:

  • Energy band structure

  • Charge carriers: electrons & holes

  • Carrier concentrations & doping

  • Fermi distribution function and Fermi level

Silicon Crystal Structure

• Crystalline solids have repetitive atomic structures.

• Silicon atoms arranged in diamond cubic structure with a lattice constant of $5.43 ext{ Å}$.

• Each silicon atom has four nearest neighbors, forming covalent bonds.

Bond Model of Electrons and Holes

• At absolute zero, covalent electrons are not free; thermal energy causes some to become conduction electrons.

• Breaking a covalent bond results in a conduction electron and a hole.

• Creating mobile charge carriers in semiconductors requires about $1.1 ext{ eV}$ of energy.

• Doping introduces extra electrons (N-type) or holes (P-type).

Energy Band Model

• Electrons occupy discrete energy levels; levels merge to form energy bands in solids.

• Key bands:

  • Valence Band: Nearly full of electrons.

  • Conduction Band: Nearly empty; electrons here contribute to conduction.

• Band gap ($E_g$) in silicon is around $1.1 ext{ eV}$.

• Donor and acceptor levels in the band structure correspond to ionization energy.

Electron and Hole Concentrations

• Electron concentration ($n$) derived from the conduction band's density of states and Fermi level.

• Hole concentration ($p$) derived similarly from the valence band's density of states.

• The intrinsic carrier concentration for silicon is $n_i ext{ ~ } 10^{10} ext{ cm}^{-3}$.

• For semiconductors at thermal equilibrium, $np = n_i^2$.

Fermi Function and Thermal Equilibrium

• Describes the probability of occupation of energy states by electrons in thermal equilibrium.

• The Fermi level ($E_F$) is the energy at which the probability of occupancy is 1/2.

• At equilibrium, $E_F$ is determined by electron and hole concentrations and reflects material properties.

Doping and Carrier Concentrations

• Doping with group III (acceptors) or V (donors) elements affects carrier concentrations:

  • $n ext{ (N-type)} ext{ ~ } N_d$ (nearly all donors ionized).

  • $p ext{ (P-type)} ext{ ~ } N_a$ (nearly all acceptors ionized).

• Doping modifies the Fermi level, affecting electronic properties.

High and Low Temperature Effects

• At high temperatures, intrinsic behjavior can dominate as $n_i$ increases dramatically.

• Low temperatures may lead to