Semiconductor & PN-Junction Diode – Comprehensive Bullet-Point Notes

2.1 Introduction – Electrical vs Electronic Circuits

• Electronics = Control of charge flow; daily devices (mobile, TV, computer) rely on electron motion.
• Electrical circuit: only $R,L,C$ elements → no signal processing.
• Electronic circuit: $R,L,C$ + ≥ 1 semiconductor device (diode, transistor…) → amplify/rectify/attenuate.
• Charge carrier discovered by J.J. Thomson (1897): $q<em>e = -1.602\times10^{-19}\;\text{C},\; m</em>e = 9.11\times10^{-31}\;\text{kg}$.

2.2 Atomic Structure Evolution

• Thomson plum-pudding (1904): electrons embedded in positive “pudding”.
• Rutherford model (1911): α-scattering → small dense positive nucleus; atom mostly empty; nuclear radius $10^{-15}!\text{–}!10^{-14}\;\text{m},$ atomic radius $≈10^{-10}\;\text{m}$.
• Bohr model (1913/1922): electrons in quantised circular orbits (K,L,M…); $2n^2$ electrons/orbit; energy quantised.
• Chadwick neutron (1932) → modern nucleus composition.

2.3 Electron Energies

• Kinetic energy $KE = \frac12 m v_n^2$.
• Potential energy $PE = -\frac{Z e^2}{4\pi\varepsilon<em>0 r</em>n}$.
• Total orbit energy $E<em>n = -\frac{mZ^2e^4}{8\varepsilon</em>0^2 n^2 h^2}$ →
  $E_n = -\frac{13.6 Z^2}{n^2}\;\text{eV}$ (hydrogen ground state = –13.6 eV).
• Example: for H $KE = 13.6\;\text{eV},\; PE = -27.2\;\text{eV}$.

eV Unit

• $1\;\text{eV} = 1\;\text{V} \times 1\;\text{electron charge} = 1.602\times10^{-19}\;\text{J}$.

2.4 Valence Electrons & Periodic Trends

• Outer-shell electrons dictate chemical & electrical behaviour.
• Valence<4 → metals/conductors (e.g. Na, Mg, Al).
• Valence=4 → semiconductors (C, Si, Ge).
• Valence>4 → non-metals/insulators (N, S, Ne).

2.5 Energy Levels → Energy Bands

• In crystals, Pauli exclusion causes atomic levels to split → bands.
• Valence band = outermost filled band.
• Conduction band = energies of free electrons.
• Band-gap $E_g$ separates CB & VB.

2.6 Material Classification by $E_g$

• Insulator: E_g > 5\,\text{eV} (rubber, glass) → no carriers.
• Conductor: CB overlaps VB; many free electrons (Ag, Cu).
• Semiconductor: E_g < 5\,\text{eV}; Si 1.11 eV, Ge 0.67 eV, GaAs 1.43 eV.

2.7 Intrinsic Semiconductor

• Pure Si: $n<em>i = p</em>i$; at 300 K $n<em>i(Si)=1.5\times10^{10}\,\text{cm}^{-3}$, $n</em>i(Ge)=2.4\times10^{13}$.
• Temperature dependence: $n<em>i = B T^{3/2} e^{-E</em>g/2kT}$ (Table of B).

Fermi Level (intrinsic)

$E<em>{Fi}=\frac{E</em>C+E<em>V}{2} - \frac{kT}{2}\ln\frac{N</em>C}{N<em>V}$ → centred in mid-gap when $N</em>C=N_V$.

2.8 Extrinsic Semiconductor & Doping

N-type

• Add pentavalent donors (P, As, Sb) → extra electron; donor level $E_D$ ≈ 0.05 eV below CB.
• Majority carriers: electrons; minority: holes.

P-type

• Add trivalent acceptors (B, Ga, In) → hole generation; acceptor level $E_A$ ≈ 0.05 eV above VB.
• Majority carriers: holes.

Mass-action law

$n<em>e p</em>h = n_i^2$ (thermal equilibrium).

2.9 Carrier Transport

Diffusion

• Flux due to concentration gradient: $J<em>n = q D</em>n \frac{dn}{dx},\; J<em>p = -q D</em>p \frac{dp}{dx}$.

Drift

• Motion under electric field: $v<em>{dn}= -\mu</em>n E,\; v<em>{dp}= \mu</em>p E$.
• Conductivity $\sigma = q (n\mu<em>n + p\mu</em>p)$.

2.10 PN Junction Formation

• At equilibrium: diffusion of majority carriers → depletion layer devoid of free carriers; fixed donor (+) & acceptor (–) ions create electric field.
• Built-in potential (barrier): $V<em>B = V</em>T \ln \frac{N<em>A N</em>D}{n<em>i^2}$ where $V</em>T = kT/q$ (≈26 mV at 300 K).

2.11 PN-Junction Currents

• Drift current of minority carriers vs. Diffusion current of majority carriers; at equilibrium they cancel (net I=0).

2.12 Diode I-V Characteristic

• Shockley equation: $I<em>D = I</em>S (e^{V<em>D/nV</em>T}-1)$.
• Forward region: knee at $\approx V_B$ (0.7 V Si, 0.3 V Ge).
• Reverse region: $I\approx -I<em>S$ until breakdown $V</em>{BR}$ (Zener/avalanche).

Temperature Effects

• $V_B$ decreases ≈2.5 mV/°C.
• $I_S$ doubles every 10 °C rise.

Resistances

• DC/static $R_D = V/I$.
• AC/dynamic $r<em>d = \frac{nV</em>T}{I<em>D}+r</em>B$.

Capacitances

• **Transition (junction) $C<em>T = \varepsilon A/W$ ∝ $1/\sqrt{V</em>R}$.
• **Diffusion $C<em>D = \tau I</em>D/V_T$ (dominant in forward bias).

Reverse Recovery

• $t<em>{rr}=t</em>s+t_t$ limits switching speed; Schottky/fast diodes minimise.

2.13 Ideal- vs Practical-Diode Models

1. Ideal: $V<em>B=0, I</em>S=0, r=0, C=0$ → perfect switch.
2. Piecewise-linear: ideal + barrier voltage + $r_{av}$.
3. High-freq model adds $C<em>T,C</em>D$.

2.14 Zener (Breakdown) Diode

• Heavily doped PN so $V_{Z}$ 2–200 V.
• Breakdown mechanisms:
  • Zener (field ionisation, $V<em>Z<5$ V, negative temp-coefficient). • Avalanche (VZ>5 V, positive TC).
• Equivalent: ideal source $V<em>Z$ in series with $r</em>Z$.
• Regulator condition: I{ZK}

2.15 Light-Emitting Diode (LED)

• Direct-band-gap alloys (GaAs, GaP, GaAsP, AlInGaP, GaN).
• Forward recombination → photons; $h\nu=E_g$ sets colour.
• Typical $V_F$: red 1.8 V, green 2.2 V, blue ≈3–5 V.
• Construction: P-layer upper (light escape), metal reflector cup (cathode), epoxy lens.

OLED

• Organic layers (HTL/EML/ETL) between ITO anode & metal cathode; electroluminescence; flexible displays & lighting.

2.16 Varactor (Varicap) Diode

• Operated in reverse bias; uses $C<em>T(V)$; $C(V)=C</em>0\left(1+\dfrac{V}{V_B}\right)^{-1/2}$.
• Applications: voltage-controlled tuning, FM modulators, PLLs.

2.17 Schottky Diode

• Metal–semiconductor (MS) junction (Au–Si, Pt–GaAs).
• Majority-carrier device → very low $t<em>{rr}$, $V</em>F\approx0.2–0.3\,\text{V}$.
• Used in high-speed switching, RF mixers, logic LS-TTL clamps.

2.18 Step-Recovery (Snap-Off) Diode

• Doping falls toward junction → abruptly clears stored charge → $t_{rr}\sim10\text{–}100\,\text{ns}$.
• Generates sharp pulses; harmonic multipliers, comb generators.

2.19 Small-Signal / Switching Diodes

• Very small junction area ⇒ $C<em>j\le1\,\text{pF}, t</em>{rr}\sim2\text{–}10\,\text{ns}$.
• Examples 1N4148 (Si), BAV99 (dual).

2.20 Point-Contact & TVS Diodes

• Point-contact: cat-whisker on N-type Ge; high-freq detectors.
• TVS: large-area Zener for surge/ESD suppression; uni- & bi-directional.

2.21 Tunnel (Esaki) Diode

• Heavily doped PN ⇒ depletion width ≈100 Å ⇒ quantum tunnelling.
• I-V shows negative resistance between $I<em>P, V</em>P$ and $I<em>V, V</em>V$.
• Equivalent: $-R<em>N\parallel C</em>D$; microwave oscillators, amplifiers.

2.22 Photonic Diodes

Photodiode

• Reverse-biased PIN; light generates $I_P \propto \text{illumination}$.
• Modes:
  • Photoconductive (reverse bias, fast).
  • Photovoltaic (zero bias, solar cell mode).
  • Avalanche (APD, internal gain).

PIN Diode

• Intrinsic layer ⇒ low $C_j$, high breakdown; used as RF attenuator, switch, photodetector.

2.23 Gunn Diode (Transferred-Electron)

• N-type GaAs; two-valley conduction band; above $E_{th}$ electrons transfer to high-mass valley ⇒ negative resistance.
• Formation of charge domain → microwave oscillations $f \approx v_d/2L$ (1–100 GHz).

2.24 Shockley (PNPN) Diode

• Four-layer two-terminal device; latches ON when $V<em>{BO}$ reached, OFF when $I<I</em>H$.
• Modelled as two coupled BJTs; used as trigger for SCR, relaxation oscillator.

2.25 Display & Opto-Energy Devices

Liquid-Crystal Display (LCD)

• Twisted-nematic field effect: crossed polarizers; no voltage → cell transparent; with voltage → alignment removes twist → segment dark.
• Dynamic scattering: ionic turbulence scatters light (no polarizers).

Solar Cell (Photovoltaic)

• Large-area PN (or PIN) junction; photon with $h\nu\ge E_g$ creates e-h pair; built-in field separates carriers.
• I-V: $I=I<em>P-I</em>S(e^{V/V_T}-1)$.
• Voc, Isc, MPP; Fill factor $FF = \dfrac{V<em>{mp}I</em>{mp}}{V<em>{oc}I</em>{sc}}$; efficiency $\eta = \dfrac{P<em>{out}}{P</em>{in}}$.
• Si efficiencies: mono-25 %, poly-18 %, a-Si 13 %.

2.26 Key Formulae Summary

• Barrier potential $V<em>B = V</em>T \ln\dfrac{N<em>A N</em>D}{n_i^2}$.
• Shockley diode $I = I<em>S( e^{V/nV</em>T}-1 )$.
• Dynamic resistance $r<em>d = \dfrac{n V</em>T}{I<em>D} + r</em>B$.
• Transition capacitance $C<em>T = C</em>{T0}\left(1+\dfrac{V<em>R}{V</em>B}\right)^{-1/2}$.
• Diffusion capacitance $C<em>D = \dfrac{\tau I</em>D}{V_T}$.
• Temperature coefficient of Zener $\alpha = \dfrac{\Delta V<em>Z}{V</em>Z\;\Delta T}$.

2.27 Practical Implications & Applications

• Rectification: bridge & half-wave power supplies.
• Voltage regulation: Zener + resistor.
• High-speed switching: Schottky, small-signal diodes.
• RF tuning & mixers: varactor, Schottky.
• Microwave generation: Gunn, tunnel diodes.
• Optoelectronics: LEDs, laser diodes (not covered), photodiodes, solar cells.
• Protection: TVS clamps, avalanche diodes.

These bullet-point notes collect every major and minor concept, formulas in $\LaTeX$, examples, device structures, characteristic behaviours, temperature effects, modelling equations, and real-world uses covered in the full transcript of Chapter 2: Semiconductor and PN-Junction Diodes.