Unit 1: Semiconductor Physics

Comprehensive vocabulary flashcards covering energy band formation, intrinsic and extrinsic semiconductor physics, Fermi-Dirac statistics, p-n junction dynamics, and the Hall effect.

Valence Band

The last filled electron energy level or band at a temperature of $T = 0\,\text{K}$.

Conduction Band

The first unfilled electron energy level or band at $T = 0\,\text{K}$, in which electrons are free to conduct electricity once they access its states.

Degeneracy

A physical condition in which an enormous number of quantum states share the exact same energy level.

Work Function ($\phi_M$)

The electrostatic potential corresponding to the energy difference between the vacuum level and the Fermi energy level $E_F$, satisfying the relation $\Delta E = q\phi_M$.

Energy Gap ($E_g$)

The forbidden energy range separating the filled valence band from the empty conduction band where no allowed electron states exist; typically $5\,\text{eV}$ to $10\,\text{eV}$ in insulators, $1.1\,\text{eV}$ in silicon, and $0.68\,\text{eV}$ in germanium.

Intrinsic Semiconductor

A pure semiconductor crystal containing no impurities or lattice defects, possessing zero free charge carriers at $T = 0\,\text{K}$ because the valence band is completely full and the conduction band is completely empty.

Electron-Hole Pair (EHP)

The fundamental pair of charge carriers produced in an intrinsic semiconductor when a valence electron acquires sufficient thermal energy to break a covalent bond, exciting the electron into the conduction band and leaving behind a vacancy called a hole.

Recombination

The process in which a conduction-band electron transitions into an unoccupied state (hole) in the valence band, annihilating both charge carriers and releasing energy.

Doping

The controlled addition of impurity atoms into the crystal lattice of an intrinsic semiconductor to significantly enhance its electrical conductivity.

n-type Semiconductor

An extrinsic semiconductor created by doping pure Si or Ge with pentavalent donor impurities (such as P, As, or Sb), which introduce donor energy levels ($E_D$) located just below the conduction band edge.

p-type Semiconductor

An extrinsic semiconductor created by doping pure Si or Ge with trivalent acceptor impurities (such as B, Al, Ga, or In), which introduce acceptor energy levels ($E_A$) located just above the valence band edge.

Direct Gap Semiconductor

A semiconductor (such as GaAs) in which the conduction band minimum and valence band maximum align at the same wavevector value ($k = 0$), enabling direct electron-hole transitions with photon emission of energy $h\nu = E_g$.

Indirect Gap Semiconductor

A semiconductor (such as Si) in which the conduction band minimum and valence band maximum occur at different values of wavevector $k$, requiring both an energy change and a momentum change (typically dissipating energy to the lattice as heat via a defect state $E_t$).

Fermi-Dirac Distribution Function ($f(E)$)

A statistical distribution given by $f(E) = \frac{1}{1 + e^{(E - E_F)/kT}}$, specifying the probability that an available energy state at energy $E$ is occupied by an electron at absolute temperature $T$.

Fermi Level ($E_F$)

The energy level at which the probability of occupancy by an electron is exactly $\frac{1}{2}$; at $T = 0\,\text{K}$, it represents the maximum occupied electron energy state.

Intrinsic Fermi Level ($E_i$)

The Fermi level for a pure semiconductor, which lies in the middle of the band gap at $T = 0\,\text{K}$ according to $E_i = \frac{E_c + E_v}{2}$.

Invariance of the Fermi Level

The fundamental thermodynamic principle stating that at thermal equilibrium, no discontinuity or gradient can exist in the Fermi level ($E_{F1} = E_{F2}$) across materials in intimate contact.

Law of Mass Action

A principle stating that for a semiconductor at a constant temperature in thermal equilibrium, the product of electron and hole concentrations is constant and equals the square of the intrinsic carrier concentration: $n p = n_i^2$.

Drift Velocity ($v_d$)

The net average directed velocity acquired by mobile charge carriers under the influence of an applied electric field, which superimposes upon their random thermal motion.

Carrier Mobility ($\mu$)

The drift velocity acquired per unit applied electric field, defined mathematically as $\mu = \frac{v_d}{E}$ and measured in units of $\text{m}^2/\text{V}\cdot\text{s}$ or $\text{cm}^2/\text{V}\cdot\text{s}$.

Total Electrical Conductivity ($\sigma$)

The combined conductivity from electrons and holes in a semiconductor, expressed as $\sigma = q(n\mu_n + p\mu_p)$, which reduces to $\sigma = q n_i(\mu_n + \mu_p)$ for intrinsic semiconductors.

Depletion Region

The transition layer of width $W$ formed across a metallurgical p-n junction that is depleted of mobile charge carriers and consists solely of fixed, uncompensated ionized donor and acceptor atoms.

Built-in Potential Barrier ($V_0$)

The equilibrium electrostatic contact potential difference maintained across the depletion region of an unbiased p-n junction, expressed as $V_0 = \frac{kT}{q}\ln\left(\frac{N_A N_D}{n_i^2}\right)$.

Forward Bias

The external voltage condition where the battery positive terminal is applied to the p-side and the negative terminal to the n-side, reducing the potential barrier and depletion layer width to allow large current flow.

Reverse Bias

The external voltage condition where the battery positive terminal is applied to the n-side and the negative terminal to the p-side, increasing the potential barrier and depletion width and restricting current to a tiny minority-carrier leakage.

Hall Effect

The development of a transverse electric field ($E_y$) and a corresponding potential difference (Hall voltage $V_{AB}$) across a current-carrying conductor when subjected to a perpendicular magnetic field ($B_z$).

Hall Coefficient ($R_H$)

The proportionality constant between the induced transverse Hall field and the product of longitudinal current density and perpendicular magnetic flux density, defined as $R_H = \frac{1}{q p_0}$ for holes and $R_H = -\frac{1}{q n_0}$ for electrons.