Semiconductor Electronics: Materials, Devices and Simple Circuits — Formula Sheet

$E_g$: Energy band gap (eV) · $E_C$: Energy at the bottom of the conduction band (eV) · $E_V$: Energy at the top of the valence band (eV)

E_C is the bottom of the conduction band and E_V the top of the valence band. Conductor: bands overlap (no gap). Insulator: E_g > 3 eV. Semiconductor: E_g < 3 eV, e.g. Si ≈ 1.1 eV, Ge ≈ 0.7 eV.

$n_e$: Free-electron density (m⁻³) · $n_h$: Hole density (m⁻³) · $n_i$: Intrinsic carrier concentration (m⁻³)

In a pure semiconductor each electron freed by thermal energy leaves behind one hole, so the two densities are equal. n_i increases rapidly with temperature.

$I_e$: Current due to free electrons (A) · $I_h$: Current due to holes (A)

Electrons and holes move in opposite directions under an applied field, but both give current in the same direction, so the two currents add.

Holds in thermal equilibrium for both intrinsic and doped semiconductors. Raising one carrier density by doping lowers the other.

$N_D$: Donor atom concentration (m⁻³)

Doped with pentavalent donor atoms (As, Sb, P). Electrons are the majority carriers. The donor level lies just below the bottom of the conduction band.

$N_A$: Acceptor atom concentration (m⁻³)

Doped with trivalent acceptor atoms (In, B, Al). Holes are the majority carriers. The acceptor level lies just above the top of the valence band.

The acceptors take up electrons released by the donors, so the two dopings partly cancel. If N_A > N_D the material is p-type with n_h ≈ N_A − N_D. Valid when the difference is much larger than n_i.

$V_0$: Barrier potential at equilibrium (V) · $V$: Applied bias voltage (V)

V₀ is the barrier potential with no bias and V is the applied voltage. Forward bias lowers the barrier and narrows the depletion layer; reverse bias raises the barrier and widens the depletion layer.

In forward bias the current stays very small until the applied voltage reaches the threshold value; beyond it the current rises steeply (exponentially). These are the NCERT values; some other books quote about 0.3 V for Ge.

$r_d$: Dynamic resistance (Ω) · $\Delta V$: Small change in voltage (V) · $\Delta I$: Corresponding change in current (A)

The ratio of a small change in voltage to the resulting small change in current, read from the V–I curve at the operating point. Low (ohms to tens of ohms) in forward bias above threshold; very high in reverse bias.

$V$: Battery voltage (V) · $R$: Series resistance (Ω)

Kirchhoff's loop rule with the diode treated as a fixed forward drop V_th (≈ 0.7 V for Si). In reverse bias only a tiny reverse saturation current flows, so I ≈ 0.

A single diode conducts only during the half-cycle in which it is forward biased, so there is one output pulse per input cycle.

Two diodes with a centre-tapped transformer conduct on alternate half-cycles, giving two output pulses per input cycle: 100 Hz output from 50 Hz mains.