Semiconductor Diodes – Comprehensive Bullet-Point Notes

Chapter Objectives

• Become familiar with three key semiconductor materials (Si, Ge, GaAs)

  • General physical & electronic characteristics

• Understand charge conduction via electron‐hole theory

• Distinguish clearly between $n$-type and $p$-type substrates

• Master diode operation in

  • No-bias (equilibrium)

  • Forward-bias (conduction)

  • Reverse-bias (cut-off & breakdown)

• Calculate

  • $R<em>{DC}$, $r</em>d$ (AC/dynamic), $r<em>{av}$ (average AC) from the $I</em>D–V_D$ curve

• Apply and compare “ideal” versus “practical” equivalent-circuit models

• Analyse special diodes

  • Zener (regulation/breakdown)

  • LED (electroluminescence)

1.1 Introduction

• Fundamental device physics change very little over decades; fabrication & integration explode

  • 1930s vacuum-tube design rules still traceable in modern IC layouts

• Miniaturisation milestones

  • 1958 Kilby’s first IC (phase-shift oscillator)

  • 2020-era Intel Core i7 Extreme ≈ $7.31\times10^8$ transistors in $\approx1.67\,\text{in}^2$

• Moore’s Law (1965)

  • Transistor count doubles ~ every 2 yr; prediction still valid > 45 yr later

• Four shrinking limits

  1. Semiconductor purity

  2. Network/topology design skill

  3. Lithography / processing resolution

  4. Human ingenuity (R&D investment)

1.2 Semiconductor Materials: Ge, Si, GaAs

• Two classes

  • Single-crystal (elemental) ⇒ Ge, Si

  • Compound ⇒ GaAs, CdS, GaN, GaAsP …

• Early history

  • 1939 diode, 1947 transistor: both germanium ⇒ easier purification, abundant

  • Reliability problems (thermal sensitivity) led to switch to Si (1954 first Si BJT)

  • GaAs introduced 1970s for high-speed apps (carrier mobility ≈ 5×Si).

• Today

  • Ge still niche (RF mixers, IR detectors)

  • Si dominates IC industry (abundant, mature process)

  • GaAs & other III-V gaining in VLSI, optoelectronics

Intrinsic carrier data

• $n_i$ (carriers ⁄ $\text{cm}^3$)

  • Ge ≈$2.5\times10^{13}$

  • Si ≈$1.5\times10^{10}$

  • GaAs ≈$1.7\times10^{6}$

• Electron mobility $\mu_n\;(\text{cm}^2/\text{V·s})$

  • Ge 3900

  • Si 1500

  • GaAs 8500

1.3 Covalent Bonding & Intrinsic Material

• Atom review

  • Valence electrons: Ge, Si = 4 (tetravalent); Ga = 3 (trivalent); As = 5 (pentavalent)

• Covalent bond: valence electrons shared with four neighbours creating a rigid lattice

  • Pure crystal with almost no free carriers → intrinsic

• Thermal/optical excitation can break bond

  • Room-T intrinsic Si (1 cm³) ≈ $1.5\times10^{10}$ free e⁻ (15 billion!)

• Intrinsic ≡ chemically pure, impurity ≤$1\text{ part}/10^{10}$

1.4 Energy Levels & Bands

• Discrete atomic shells spread into bands in a crystal

  • Valence band ↔ Conduction band separated by band-gap $E_g$

• Typical $E_g$ values

  • Ge 0.67 eV

  • Si 1.1 eV

  • GaAs 1.43 eV

• Larger $E_g$ ⇒

  • Needs more energy to create carriers ⇒ lower intrinsic $n_i$, better high-T stability

  • Can radiate photons (LED/laser) instead of heat (GaAs)

• Energy unit conversion
  $1\,\text{eV}=1.6\times10^{-19}\,\text{J}$ (derived from $W=QV$)

1.5 n-Type & p-Type Extrinsic Materials

• Doping ≈ 1 impurity per $10^7$ host atoms changes conductivity drastically

n-Type

• Add pentavalent (Group V) donors (P, As, Sb)

  • 5ᵗʰ electron loosely bound → donor level just below conduction band

  • Electrically neutral overall; electrons majority, holes minority

p-Type

• Add trivalent (Group III) acceptors (B, Ga, In)

  • Creates holes (vacancies) in valence band

  • Holes majority, electrons minority

Carrier flow picture

• Electron motion opposite conventional current (hole flow)

• Majority/minority concept crucial for junction behaviour

1.6 The Semiconductor Diode (p–n Junction)

Regions of operation

1. No bias (equilibrium)

   • Diffusion of carriers ⇒ depletion region of fixed ions

   • Net external current $I_D=0$ (equal & opposite carrier flows cancel)

2. Reverse bias (V_D<0)

   • External field widens depletion; majority carrier flow stops

   • Minority carriers give tiny reverse saturation current $I_S$ (pA–nA range)

   • Shockley reverse current independent of |$V_D$| until breakdown

3. Forward bias (V_D>0)

   • Depletion narrows; majority carriers cross ⇒ exponential $I_D$ rise

   • Practical forward drop: Ge ≈0.3 V, Si ≈0.7 V, GaAs ≈1.2 V (knee $V_K$)

Shockley equation

$<br>I<em>D = I</em>S\left(e^{\Large \frac{V<em>D}{nV</em>T}}-1\right)<br>$

• $V_T = \dfrac{kT}{q}\;\,(\approx 26\,\text{mV at }27^{\circ}\text{C})$

• Ideality factor $n=1\text{–}2$ (assume 1 for high $I_D$, ~2 near knee)

Breakdown

• Excess reverse voltage ⇒ avalanche or Zener effect at $V_{BV}$

  • Defines PIV/PRV rating

Temperature effects

• Forward region: $\Delta V_F\approx -2.5\,\text{mV}/^{\circ}\text{C}$

• Reverse region: $I_S$ doubles every ≈10 °C

Material Comparisons (Ge vs Si vs GaAs)

• $V<em>K$, $I</em>S$, $V_{BV}$ differ (see Fig 1.18)

• GaAs: highest $\mu<em>n$, lowest $I</em>S$, largest $V<em>K$, higher $V</em>{BV}$

• Ge: lowest $V<em>K$ but high $I</em>S$, low $V_{BV}$

1.7 Ideal vs Practical Concepts

• Ideal diode ↔ perfect switch

  • Forward: $R_F=0\;\Omega$ (short)

  • Reverse: $R_R=\infty\;\Omega$ (open)

• Practical Si shifts right by $\approx0.7\,\text{V}$; reverse current finite

1.8 Resistance Definitions

• DC/Static: $R<em>D=\dfrac{V</em>D}{I_D}$ (point value)

• AC/Dynamic: $r<em>d=\dfrac{\Delta V</em>d}{\Delta I<em>d}\approx\dfrac{nV</em>T}{I_D}$

  • Include body/contact resistance $r<em>B$ ⇒ $r'</em>d=r<em>d+r</em>B$

• Average AC: $r<em>{av}=\dfrac{\Delta V</em>d}{\Delta I<em>d}\big|</em>{\text{pt-to-pt}}$ over large signal swing

Typical magnitudes (Si)

• $R_D$ 10 Ω – 80 Ω (on), MΩ (reverse)

• $r_d$ 1 Ω – 100 Ω (on)

1.9 Diode Equivalent-Circuit (Model) Hierarchy

1. Piecewise-Linear (PWL)

   • Ideal diode + $V<em>K$ battery + $r</em>{av}$

2. Simplified model

   • Ideal diode + $V<em>K$ (set $r</em>{av}\approx0$)

3. Ideal diode only (ignore $V_K$) — useful in power-supply, large-V networks

1.10 Capacitance Effects

• Transition/Barrier capacitance $C<em>T$ (reverse) $C</em>T=C(0)\,(1+V<em>R/V</em>K)^{-n}$ , $n=1/2$ or $1/3$

• Diffusion capacitance $C<em>D$ (forward) $C</em>D=\dfrac{\tau<em>T}{V</em>K}\,I<em>D$ (minority-carrier lifetime $\tau</em>T$)

• Total junction $C<em>j \approx C</em>T\;(\text{reverse}),\;C_D(\text{forward})$

• High-f: capacitive reactance $X_C=1/(2\pi f C)$ lowers, shorting diode

1.11 Reverse-Recovery Time $t_{rr}$

• Switching from forward to reverse bias

  • Storage phase $t_s$ (remove excess minority carriers)

  • Transition phase $t<em>t$ ⇒ $t</em>{rr}=t<em>s+t</em>t$

• Typical fast-switching diodes $t_{rr}\sim$ ns; standard rectifiers μs

1.12 Reading Diode Datasheets (example: 125 V HV rectifier)

Key parameters usually supplied

1. $V<em>F$ @ specified $I</em>F$, $T$

2. $I_{F(max)}$ vs $T$

3. $I<em>R$ vs $V</em>R$, $T$

4. Reverse-voltage rating: PIV/PRV or $V_{BR}$

5. $P<em>D_{max}$ with derating curve $P</em>D(T)=P_{25}-\theta(T-25)$

6. $C<em>T$ vs $V</em>R$ (1 MHz test)

7. $t_{rr}$

8. Operating $T_{j}$ range

Graph reading tips

• Semi-log: one axis log, other linear (expansive current range)

• Log-log: both axes log (slope ⇒ power law)

Power check using simplified model
$P_{diss}\approx (0.7\text{ V})I_D\quad(\text{Si})$

1.13 Diode Notations & Physical Packages

• Cathode often marked by band, dot, or tab (matches bar in symbol)

• Anode ↔ arrow side (triangle for schematic LED)

• Packages: axial-lead signal, surface-mount chip, power stud, puck, planar, beam-lead PIN etc.

1.14 Testing Diodes

1. DMM “diode” mode

   • Forward-bias reading ≈ $V_F$ (0.6–0.8 V Si)

   • Reverse reading “OL” ⇒ healthy

2. Multimeter ohmmeter

   • Low R forward, very high reverse

3. Curve tracer — plots $I–V$ directly for diagnosis

1.15 Zener Diodes

• Utilise sharp reverse breakdown $V_Z$ (Zener + avalanche)

• Equivalent PWL: ideal diode (reverse orientation) + $V<em>Z$ battery + $r</em>Z$ (slope resistance)

  • $r<em>Z\,(I</em>ZT)$ tabulated at test current (e.g.
    $I<em>{ZT}=12.5\,\text{mA},\;V</em>Z=10\,\text{V},\;r_Z=8.5\;\Omega$)

• Temperature coefficient $TC=\dfrac{\Delta V<em>Z}{V</em>Z}\dfrac{100\%}{\Delta T}$

  • Can be +ve (> ≈5 V) or –ve (< ≈5 V)

• Power rating
  $P<em>{Z\,max}=V</em>Z I<em>{ZT}$ (¼ power point) or continuous $I</em>{ZM}$ limit

1.16 Light-Emitting Diodes (LEDs)

• Recombination in certain III-V semiconductors releases photons (electroluminescence)

• Colours/materials & typical $V_F$ (~20 mA)

  • Red GaAsP $\approx2.0\,\text{V}$

  • Green GaP $\approx2.2\,\text{V}$

  • Blue GaN $\approx5.0\,\text{V}$

  • White (Blue GaN + YAG phosphor) $\approx4.1\,\text{V}$

• Wavelength ↔ bandgap
  $\lambda=\dfrac{c}{f}=\dfrac{hc}{E_g}$

• Human eye response peaks ≈ 550 nm (green) — LEDs must be brighter in red/blue for equal visual perception

• Reverse breakdown very low (3–5 V) ⇒ must protect against reverse bias

• Seven-segment display

  • Common-cathode/-anode wiring; 5-V logic drives individual LED segments

1.17 Key Take-Away Principles

• Device physics centred on band theory, doping & junction electrostatics

• Shockley exponential governs ideal diode behaviour; practicalities (series R, $I<em>S$, $V</em>K$, $t<em>{rr}$, $C</em>j$) tailor real devices

• Temperature strongly influences $V<em>F$ (-2.5 mV/°C) and $I</em>S$(×2 per 10 °C)

• Multiple resistance definitions exist; choose according to signal type (DC, small-signal, large-signal)

• Equivalent-circuit modelling (ideal ↔ PWL) turns nonlinear diodes into solvable linear pieces

• Zener & LED are specialised p-n junctions exploiting breakdown and radiative recombination respectively