Doping, PN Junction & Diode Equation

Vocabulary flashcards covering semiconductor lattice structures, intrinsic and extrinsic doping, PN junction physics, carrier transport kinetics, and the ideal diode and solar cell equations.

Intrinsic semiconductor

A pure semiconductor without impurities or structural defects within its crystal matrix, characterized by relatively high electrical resistance.

N-type semiconductor

A semiconductor doped with electron donors (such as $N$, $P$, or $As$ substituting $Si$) or having missing nuclei, resulting in excessive conduction electrons in the crystal lattice.

P-type semiconductor

A semiconductor doped with electron acceptors (such as $B$ or $Al$ substituting $Si$), resulting in missing electrons in covalent bonds that produce mobile holes in the valence band.

Substitution doping

A process and methodology in semiconductor physics that replaces host crystal matrix atoms (both nuclei and electrons) with impurity dopant atoms.

Non-degenerated doping

Doping carried out at ultralow impurity levels such that the bandgap ($E_g$) of the doped semiconductor remains equal to the bandgap of the original intrinsic semiconductor.

Silicon diamond-like unit cell ($Si_2$)

The smallest non-cleavable representative unit of the silicon crystal structure, containing $2$ silicon atoms aligned in a tetrahedral matrix that minimizes system internal energy.

Silicon conventional crystal cell ($Si_8$)

A face-centered cubic structure composed of $4$ unit cells containing a net total of $8$ silicon atoms: $4$ interior atoms, $6$ face-centered surface atoms ($\frac{1}{2}$ each), and $8$ corner atoms ($\frac{1}{8}$ each).

Depletion region (DR)

An ultrathin boundary layer at a $p\text{-}n$ junction where mobile carriers are depleted; its edges carry charges opposite to the adjacent bulk while the overall region is neutral, creating an electric field ($V_{bi}$) that drives rapid charge transport.

Built-in potential ($V_{bi}$)

The internal electric potential difference formed across the depletion region at equilibrium, defined by $V_{bi} = \Delta(E_F) = E_{Fn} - E_{Fp} = \Delta\text{VBM} = \Delta\text{CBM}$.

Thermal voltage ($k_B T$)

The characteristic thermal energy per particle, approximately equal to $\frac{1}{40}\,eV$ ($25\,meV$) at $300\,K$, where the Boltzmann constant is $k_B = 1.381 \times 10^{-23}\,J/K = 8.617 \times 10^{-5}\,eV/K$.

Dark saturated current ($I_0$)

The small equilibrium exchange current across a $p\text{-}n$ junction climbing the energetic barrier in the dark, defined as $I_0 = C_1 \exp\left(-\frac{qV_{bi}}{k_B T}\right) = C_2 \exp\left(-\frac{E_g}{k_B T}\right)$, where $C_1 = q\omega_1$ and $C_2 = q\omega_2$.

Shockley diode equation (dark)

The net electrical current equation governing an unilluminated $p\text{-}n$ junction under an applied bias $V$: $I = I_0 \left[\exp\left(\frac{qV}{k_B T}\right) - 1\right]$.

Photogenerated current ($I_l$)

The additional electric current ($I_3$) generated in a $p\text{-}n$ junction when photons with energy $h\nu \ge E_g$ excite electron-hole pairs that are separated across the junction.

Ideal solar cell characteristic equation

The total current-voltage relationship of an illuminated $p\text{-}n$ junction ideal solar cell: $I = I_0 \left[\exp\left(\frac{qV}{k_B T}\right) - 1\right] - I_l$, or $I = I_l - I_0 \left[\exp\left(\frac{qV}{k_B T}\right) - 1\right]$ when mirrored into the first quadrant.

Thermalisation loss

The energy lost as heat when absorbed photons possess energy greater than the bandgap ($E > E_g$), causing photogenerated carriers to relax down to the conduction and valence band edges.