Topic 1: Review of Semiconductor Fundamentals Flashcards

Vocabulary flashcards covering semiconductor fundamentals including atomic structure, molecular orbitals, crystal structures, band theory, Bloch's theorem, thermal equilibrium, and carrier generation/recombination mechanisms.

Schrodinger Equation for Hydrogen Atom

The fundamental quantum differential equation $H\Psi(\mathbf{r}) = E\Psi(\mathbf{r})$, where $H \equiv -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r})$ and potential $V(\mathbf{r}) = -\frac{q^2}{4\pi\varepsilon_0 r}$, describing an electron in a potential well.

Hydrogen Atom Quantized Energy

The discrete energy levels of an electron in a Hydrogen atom given by the formula $E_H = -\frac{13.6}{n^2}\,\text{eV}$, where $n$ is the principal quantum number.

Quantum Numbers of Hydrogen Electron State

The set of four quantum numbers—principal ($n$), orbital angular momentum ($l$), magnetic ($m$), and spin ($s$)—that uniquely define the quantum state of an electron in a Hydrogen atom.

Bonding Molecular Orbital

The ground-state molecular orbital of an $H_2$ molecule formed by a linear combination of atomic orbitals (LCAO) with a symmetric spatial part and an antisymmetric spin part.

Anti-bonding Molecular Orbital

An excited-state molecular orbital of an $H_2$ molecule formed by a linear combination of atomic orbitals (LCAO) with an antisymmetric spatial part containing a node and a symmetric spin part.

Equilibrium Inter-atomic Distance ($d_0$)

The specific spacing between two atomic nuclei in a molecule where the total energy reaches a minimum ground state.

Core Electrons

Electrons in inner filled atomic orbitals (such as the 10 core electrons in Silicon with configuration $1s^2 2s^2 2p^6$) that are strongly bound to the nucleus and marginally interact with surroundings.

Valence Electrons

Electrons in the outermost shell (such as the 4 valence electrons in Silicon with configuration $3s^2 3p^2$) responsible for forming chemical bonds and determining crystal properties.

Crystalline Solid

A solid material in which constituent atoms are arranged in a highly ordered, periodic pattern exhibiting long-range order throughout the material.

Amorphous Solid

A solid material characterized by random spatial arrangements of atoms and a total absence of long-range periodic order.

Polycrystalline Solid

A solid material composed of localized orderly regions of atoms, exhibiting short-range order rather than continuous long-range order.

Bravais Lattice

An infinite periodic array of mathematical points in space where every point has identical surroundings.

Atomic Basis / Motif

A specific relative arrangement of one or more atoms attached identically to each point of a Bravais lattice to form a crystal structure.

Unit Cell

The smallest structural unit of a crystal lattice that, when translated continuously in three dimensions along lattice vector directions, builds the entire crystal.

Photoelectric Effect

The phenomenon where light incident on a material causes electron emission, described by the energy conservation equation $\frac{1}{2}mV^2 = h\nu - W = h(\nu - \nu_0)$, proving the particle nature of light.

Work-Function ($W$)

The minimum energy required to free an electron from a material, related to the threshold frequency $\nu_0$ by the relation $W = h\nu_0$.

Conduction Band

The higher-energy electronic band in a crystal containing $4N$ energy states ($0$ electrons at $0\,\text{K}$) where electrons are free to move throughout the crystal lattice.

Valence Band

The lower-energy electronic band in a crystal containing $4N$ states filled with $4N$ electrons at $0\,\text{K}$, where electrons are localized to specific atomic bonds.

Forbidden Gap / Band-Gap ($E_g$)

The energy region separating the valence band maximum ($E_V$) and conduction band minimum ($E_C$) in which no allowable electronic states exist.

Silicon Lattice Parameters

Physical dimensions of the Silicon crystal lattice, characterized by a lattice constant of $5.43\,\text{\AA}$ and an interatomic distance of $2.35\,\text{\AA}$.

Bloch's Theorem

A quantum mechanical theorem stating that for a periodic potential $V(\mathbf{x}) = V(\mathbf{x} + \mathbf{a})$, electron wave functions have the form $\Psi(\mathbf{x}) = e^{i\mathbf{k}\cdot\mathbf{x}} u(\mathbf{x})$, where $u(\mathbf{x}) = u(\mathbf{x} + \mathbf{a})$ matches the lattice periodicity.

Brillouin Zone

The primitive unit cell of a crystal lattice represented in reciprocal wave-vector space ($k_x, k_y, k_z$).

Crystal Momentum

The effective momentum quantity $\hbar\mathbf{k}$ assigned to an electron wave in a crystal, where wave vector $\mathbf{k}$ is restricted to the 1st Brillouin Zone.

Band ($E\text{-}k$) Structure

A plot showing the eigen-energies $E$ of electron quantum states plotted against wave vector $\mathbf{k}$ along high symmetry paths (such as $L \rightarrow \Gamma \rightarrow X \rightarrow K$) in the Brillouin Zone.

Comparative Band Structure ($E\text{-}k$) of Ge, Si, and GaAs

Comparative energy band diagrams for Germanium (Ge), Silicon (Si), and Gallium Arsenide (GaAs) plotting energy $E$ versus wave vector $\mathbf{k}$, highlighting direct versus indirect bandgap characteristics.

Direct Bandgap Semiconductor

A semiconductor material (such as GaAs) where the conduction band minimum (CBM) and valence band maximum (VBM) occur at the same wave vector $\mathbf{k}$-point.

Indirect Bandgap Semiconductor

A semiconductor material (such as Si or Ge) where the conduction band minimum (CBM) and valence band maximum (VBM) occur at different wave vector $\mathbf{k}$-points.

Thermal Equilibrium

A system state with no external excitations other than ambient temperature, where generation rate equals recombination rate and no net charge or energy flow occurs.

Principle of Detailed Balance

The principle stating that under thermal equilibrium, every fundamental forward micro-process is balanced by its exact reverse process occurring at the same rate.

Steady-State Condition

A non-equilibrium state where system parameters and carrier processes remain constant over time despite ongoing external excitation or carrier action.

Phonon

The particle equivalent or quantum of a lattice vibration / elastic wave in a crystal.

Hole ($h^+$)

A positively charged mobile carrier generated by the absence of a valence electron in a semiconductor lattice.

Electron-Hole Pair (EHP) Generation

The process where thermal energy or photon absorption excites a valence electron to the conduction band, creating a free electron and a hole.

Electron-Hole Pair (EHP) Recombination

The process where a free conduction electron transitions into an unoccupied valence state (hole), releasing energy to the crystal lattice or emitting light.

Auger Recombination

An EHP recombination process where the transition energy released by an electron-hole recombination is transferred to another free electron or hole in the lattice.

Photo-Generation and Radiative Recombination

EHP generation or recombination mechanisms driven by the direct absorption or emission of a photon ($h\nu$).