Electromagnetic Properties Final

Location of Fermi energy in semiconductors

Halfway between conduction and valence bands, E_g/2

Intrinsic semiconductor conductivity

sigma = N_e*e*mu_e + N_h*e*mu_h

increasing temperature = _______ conductivity

increasing

Why are direct bandgap semiconductors used in optoelectronic devices?

direct = vertical/radiative recombination, indirect = nonradiative recombination

Radiative recombination reaction

electron + hole = photon (light)

Nonradiative recombination reaction

electron + hole = phonon (heat)

n-doped semiconductors

semiconductors doped with donors, extra electrons weakly bound to dopant atoms, extra negative charge

p-doped semiconductors

semiconductors doped with acceptors, available electron states, extra positive charge

What are the regions in this graph? (left to right, include region as T→0)

intrinsic region, extrinsic region, dopant ionization, freeze-out range

Freeze-out range

close to T=0, electrons/holes are bound to the donor/acceptor atoms

Dopant ionization

extra electrons/holes are available for conduction, dissociate from dopants

Extrinsic region

donors/acceptors are completely ionized, carrier concentration is relatively constant

Intrinsic region

thermally excited carriers are dominant

Why is the binding/ionization energy in semiconductors lower than that of the hydrogen Bohr model?

semiconductors have a small effective mass and large permittivity, so the binding energy is much lower

p-n junction

the interface between p-type and n-type doped semiconductors

depletion region

the region around the interface of a p-n junction where free carriers diffuse and recombine, creating a depletion of free carriers

contact potential

the built-in potential that stops further diffusion of particles at an interface, the difference in potentials/work functions in the materials

Schottky barrier

a potential barrier preventing electron flow from the metal to the n-type semiconductor

drift current

current induced by the drift of thermally-generated (minority) carriers

diffusion current

current induced by the diffusion of electrons and holes toward the interface in a p-n junction

forward/reverse bias

when a p-n junction is connected to a battery, the provided change in potential works against/with the built-in voltage, suppresses/improves drift, and improves/suppresses carrier diffusion

reverse breakdown

a phenomenon that occurs when a high reverse current is supplied, resulting in a high loss of energy from atom ionization or Si-Si bond rupture

rectifying contact

a semiconductor junction that allows current flow in only one direction due to a potential barrier

Ohmic contact

a semiconductor junction that allows current flow in both directions due to the lack of a potential barrier

work function

the energy required to remove an electron from the Fermi energy level to the vacuum level

electron affinity

the energy required to free electrons at the bottom of the conduction band to the vacuum level

pinning

defect states at the semiconductor interface introduce available energy levels, so the Fermi level at the semiconductor surface does not change with the addition/removal of electrons

how solar cells work

p-n junctions with narrow/heavily-doped n-sides, light waves are absorbed in the depletion and p regions, a charge difference is created in the diode and generates a current

how LEDs work

p-n junctions with a direct bandgap, radiative recombination emits a photon

rectification

limiting the direction of current by controlling free carrier diffusion with a potential barrier

how transistors work

3 differently-doped regions work as 2 diodes, the provided voltage controls the output current by affecting how many holes diffuse through the transistor without recombination

how MOSFETs work

metal-oxide semiconductor field-effect transistor, applied voltage through gate repels holes and creates a depletion region, high voltage creates an n-channel for electron flow

Ionic bonding

electron transfer between anions and cations in a solid

Covalent bonding

formation of bonds in which electrons are shared between adjacent atoms

Metallic bonding

valence electrons are donated to a “sea of electrons” in the average electrostatic potential of positively of positive charged atomic cores

Van Der Waals bonding

induced dipole moments produce attractive force between atoms

Type of bonding in metals (+ conductivity)

Metallic- high concentration of free carriers (conductor)

Type of bonding in ceramics (+ conductivity)

Ionic- localized and strongly bound nature of electrons (insulator)

Type of bonding in Group IV elements (C, Si, Ge) (+ conductivity)

Covalent- electrons can be released through thermal activation (semiconductor)

Type of bonding in polymers (+ conductivity)

Covalent/Van Der Waals (insulator)

Assumptions of classical theory of electrical conductivity (Drude model)

particle-like behavior, valence electrons donated to a sea of electrons, electrons are free except for scattering by defects and disturbances in the lattice, scattering produces frictional force and causes drift velocity

drift velocity

the terminal velocity of electrons

band

an allowed set of electron energy levels that span a range of energies

bandgap

a range of energies for which there are no allowed states separates allowed energy bands

Fermi Energy Level

the energy at which there is a 50% probability of electron occupation of the state, the energy of the highest occupied state at T=0K

Assumptions of quantum mechanical theory of electrical conductivity

wave-like behavior, scattering from perturbation of electrical potential, Pauli exclusion principle (only two electrons in each state), only electrons near Fermi energy contribute to conductivity

Wavevector

a vector in k-space that describes the magnitude and direction of the momentum of an electron wave

k-space

a reciprocal space coordinate system in which the vectors that span the space correspond to wavevectors

Work function

the energy required to remove an electron from the Fermi Energy in a metallic solid

Electron affinity

the energy required to remove an electron from the bottom of the conduction band in a semiconductor or insulator

Brillouin zone

the regions within k-space surrounded by boundaries in which electrons in a periodic potential are diffracted by the potential, defined by perpendicular bisectors of reciprocal lattice vectors

Density of states

the number of allowed states within a range of energy for electrons per unit volume

Effective mass

experienced by an electron, deviates from that of a free electron due to interactions with periodic potential in the lattice

Phase velocity

the velocity of a wave, w/k

Group velocity

the particle-like velocity of a wave packet, dw/dk

Degenerate states

states with identical energies and different quantum numbers

Why does the E-k relationship deviate from the parabolic prediction near Brillouin zone boundaries?

wavefunction is perturbed by periodic potential of lattice, satisfies condition for diffraction

Locations of Brillouin zone boundaries (1D)

x = +-n*pi/a

Band structure shape-band relations

flat bands below Fermi Energy = d-bands, parabolic bands near Fermi Energy = s-bands

Origin of k-space

Gamma point

Relationship between curvature and effective mass

effective mass inversely proportional to curvature

Refractive index (n)

ratio between the speed of light in a vacuum and the speed of light in a material

Complex refraction index

n-ik, characterizes damping of intensity of light due to energy losses

Why doesn’t information travel faster than the speed of light in metals?

n is less than 1, but it represents phase velocity and information is transferred in group velocity

Penetration depth (W)

the distance (z) at which intensity has decreased to 1/e (37%)

Refraction

change in propagation direction of light incident on an interface between two media