Summary

Energy bands: In solids, discrete atomic levels broaden into bands — the valence band (filled with valence electrons) and the conduction band (empty or partially filled). The forbidden energy gap $E_g$ determines whether a material is an insulator ($E_g > 3\ \text{eV}$), a semiconductor ($E_g \approx 1\ \text{eV}$), or a conductor (bands overlap).

Intrinsic semiconductors: Pure Si or Ge have equal electron ($n_e$) and hole ($n_h$) concentrations: $n_e = n_h = n_i$. Conductivity is low and increases with temperature.

Extrinsic semiconductors: Doping introduces donor (pentavalent, e.g., P, As) or acceptor (trivalent, e.g., B, Al) impurities. n-type has electrons as majority carriers ($n_e \gg n_h$); p-type has holes as majority carriers ($n_h \gg n_e$).

p-n junction: Formed by joining p-type and n-type semiconductors. At equilibrium, a depletion region (with no mobile carriers) and a built-in potential barrier ($V_0$, about $0.7\ \text{V}$ for Si, $0.3\ \text{V}$ for Ge) appear.

Forward bias: p-side connected to positive terminal, n-side to negative. The barrier height reduces, and current flows once the applied voltage exceeds the knee voltage ($\approx 0.7\ \text{V}$ for Si). Current grows exponentially with voltage.

Reverse bias: p-side negative, n-side positive. The barrier height increases, and only a tiny reverse saturation current $I_0$ (due to minority carriers) flows until breakdown occurs at high reverse voltage.

Rectification: A p-n junction diode acts as a half-wave rectifier (conducts only during one half-cycle) or a full-wave rectifier (uses two diodes or a bridge to conduct both half-cycles). The output is pulsating DC, smoothed by a capacitor filter.

Zener diode: A heavily doped diode designed to operate in the reverse breakdown region (Zener voltage $V_Z$). It maintains a nearly constant voltage across it — used as a voltage regulator.

Optoelectronic devices:

• Light Emitting Diode (LED): Forward-biased p-n junction that emits light (wavelength $\lambda = hc/E_g$). Used in displays and indicators.
• Photodiode: Reverse-biased; current increases when light falls on it (due to generation of electron-hole pairs). Used as a light sensor.
• Solar cell: Converts light energy into electrical energy. The open-circuit voltage $V_{oc}$ and short-circuit current $I_{sc}$ define its performance.

Transistor (BJT): Three-layer device (npn or pnp) with three terminals: emitter (heavily doped), base (thin, lightly doped), collector (moderately doped). Operates in active region (emitter-base forward biased, collector-base reverse biased) for amplification.

Transistor as an amplifier: In common-emitter configuration, a small change in base current $\Delta I_B$ produces a large change in collector current $\Delta I_C$. The current gain $\beta = \Delta I_C / \Delta I_B$ (typically 50–300). Voltage gain $A_V = \beta \times (R_C / R_{in})$. …