Unit 4: Fundamentals of semiconductor devices

I. Orientation: Semiconductors and Device Physics

A semiconductor is a material whose conductivity lies between a conductor and an insulator (resistivity ≈ 10⁻⁴ to 0.5 Ω·m), and whose behaviour can be controlled by adding impurities. Silicon (Si) and germanium (Ge) are the dominant materials; devices built from them form the backbone of all modern electronics.

• Energy gap: The forbidden gap between valence and conduction bands — ≈ 1.1 eV for Si, ≈ 0.7 eV for Ge. Thermal energy promotes electrons across it, creating electron–hole pairs.
• Intrinsic semiconductor: Pure material; electron concentration n equals hole concentration p.
• Extrinsic semiconductor: Doped material:
  • N-type: Pentavalent dopant (P, As) adds free electrons; electrons are majority carriers.
  • P-type: Trivalent dopant (B, In) adds holes; holes are majority carriers.
• Charge carriers: Current flows by drift (under field) and diffusion (under concentration gradient).
• Convention: Conventional current is the direction of hole flow, opposite to electron flow.

II. PN Junction Diode — The Rectifying Junction

A PN junction diode is a single P-type and N-type crystal fused together, forming a two-terminal device (anode = P, cathode = N) that conducts in one direction only.

A. Working and operation of PN junction diode

When P and N regions join, majority carriers diffuse across the junction and recombine, leaving a depletion region of immobile ions and a barrier potential (≈ 0.7 V for Si, ≈ 0.3 V for Ge).

• Forward bias: P connected to +, N to −. The applied voltage opposes the barrier; once it exceeds the barrier potential, the depletion region narrows and large current flows.
• Reverse bias: P connected to −, N to +. The barrier widens; only a tiny reverse saturation current (I₀, due to minority carriers) flows.
• Breakdown: Beyond the reverse breakdown voltage, current rises sharply (avalanche/Zener effect).

B. Characteristics of PN junction diode

The V–I characteristic plots diode current against applied voltage.

• Forward region: Negligible current until the knee/cut-in voltage (0.7 V Si), then exponential rise.
• Reverse region: Constant small I₀ (nA–µA) until breakdown.
• Diode equation:

I = I₀ (e^(V/ηVT) − 1)

• I = diode current, I₀ = reverse saturation current
• V = applied voltage, VT = kT/q ≈ 26 mV at 300 K
• η = ideality factor (1 for Ge, 2 for Si)
  • Static resistance: R = V/I; dynamic resistance: rd = ΔV/ΔI.

III. Zener Diode — The Voltage Reference

A Zener diode is a heavily doped PN junction designed to operate continuously in the reverse breakdown region without damage, maintaining a near-constant voltage.

A. Working and operation of Zener diode

• Forward bias: Behaves like an ordinary diode (conducts above 0.7 V).
• Reverse bias below Vz: Blocks current.
• At Zener voltage (Vz): Breakdown mechanisms conduct heavily while voltage stays fixed:
  • Zener breakdown: Dominant below ≈ 5 V; strong field directly ruptures covalent bonds.
  • Avalanche breakdown: Dominant above ≈ 6 V; accelerated carriers ionise atoms in a chain.
• Series resistance: A resistor Rs limits current to prevent thermal destruction.

B. Characteristics of Zener diode

• Forward portion: Identical to a normal diode's V–I curve.
• Reverse portion: Flat vertical breakdown — voltage pinned at Vz while current varies widely.
• Key parameters: Vz (breakdown voltage), Izmin and Izmax (current limits), Pz = Vz × Iz (power rating).
• Regulation condition: Load voltage ≈ Vz as long as Izmin ≤ Iz ≤ Izmax.

IV. Varactor Diode — Voltage-Controlled Capacitance

A. Working and Operation of Varactor diode

A varactor (varicap) diode is a reverse-biased PN junction used as a voltage-variable capacitor, exploiting the depletion layer as a dielectric.

• Principle: The depletion region acts as an insulator between two conducting (P and N) plates — a parallel-plate capacitor.
• Reverse bias effect: Increasing reverse voltage widens the depletion layer, increasing plate separation and decreasing capacitance.
• Transition capacitance:

CT = ε A / W

• CT = junction capacitance, ε = permittivity, A = junction area, W = depletion width
  • Operation: Always reverse-biased; capacitance tuned electrically rather than mechanically.
  • Response: CT ∝ 1/√(VR) for an abrupt junction.

V. Logic Gates — Diode and Transistor Switching

A. Logic gates

Logic gates are circuits that implement Boolean functions, with semiconductor diodes and transistors acting as electronic switches producing binary outputs (0 = low, 1 = high).

• AND gate: Output 1 only if all inputs 1; Y = A·B. Diode AND: output pulled low unless every diode is off.
• OR gate: Output 1 if any input 1; Y = A + B. Diode OR: any forward-biased diode raises output.
• NOT gate: Inverter using a transistor in saturation/cut-off; Y = Ā.
• NAND / NOR: AND/OR followed by inversion — universal gates (any function realisable from them).
• Diode action: A forward-biased diode ≈ closed switch; reverse-biased ≈ open switch.

VI. Testing of Diode and BJT

A. Testing of diode and BJT

Testing uses a digital multimeter (DMM) in diode mode to confirm junction health via forward/reverse resistance.

1. Diode test:
   • Good diode: Forward (red on anode) reads ≈ 0.6–0.7 V (Si); reverse reads OL (open).
   • Faulty: Short (≈ 0 both ways) or open (OL both ways).
2. BJT test (two back-to-back junctions):
   • NPN: Base = common P... (treated as two diodes with common base).
   • NPN: Place red on base — both B–E and B–C read ≈ 0.7 V; reverse reads OL.
   • PNP: Place black on base for the ≈ 0.7 V readings.
   • Collector–emitter: Should read OL both directions in a healthy transistor.

VII. Rectifiers — AC to DC Conversion

A rectifier converts alternating current to unidirectional (DC) current using the one-way conduction of diodes.

A. Half wave rectifier

Uses a single diode conducting only during one half-cycle of the AC input.

• Operation: Diode conducts on the positive half; blocks the negative half, so output is pulsating DC with gaps.
• Formulae:

Vdc = Vm / π        Idc = Im / π
Ripple factor γ = 1.21     Efficiency η = 40.6%

• Vm = peak input voltage, Im = peak current
  • Drawback: Half the input wasted; high ripple.

B. Full wave rectifier

Uses two diodes with a centre-tapped transformer, conducting on both half-cycles.

• Operation: D1 conducts on the positive half, D2 on the negative half; both drive current the same way through the load.
• Formulae:

Vdc = 2Vm / π       Idc = 2Im / π
Ripple factor γ = 0.48     Efficiency η = 81.2%

• Advantage: Output frequency = 2f; lower ripple than half wave.

C. Full wave bridge rectifier

Uses four diodes in a bridge, removing the need for a centre-tapped transformer.

• Operation: On each half-cycle, two diagonally opposite diodes conduct, steering current one way through the load.
• Formulae: Same Vdc = 2Vm/π, γ = 0.48, η = 81.2%.
• Comparison with centre-tap:
  1. Bridge: 4 diodes, no centre tap, PIV = Vm, better transformer use.
  2. Centre-tap: 2 diodes, needs centre tap, PIV = 2Vm.

VIII. MOSFET — The Voltage-Controlled Transistor

A MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) is a three-terminal (gate, drain, source) device where gate voltage controls drain current through a thin oxide-insulated gate.

A. MOSFET representation and characteristics

• Types:
  1. Enhancement MOSFET: No channel at VGS = 0; channel induced only when VGS exceeds threshold VT. Normally OFF.
  2. Depletion MOSFET: Channel exists at VGS = 0; gate voltage depletes/enhances it. Normally ON.
• Symbol: Gate separated by a gap (insulated); arrow on substrate indicates N-channel (inward) or P-channel (outward); broken channel line = enhancement, solid = depletion.
• Transfer characteristic: ID vs VGS — current begins past VT (enhancement).
• Drain (output) characteristic: ID vs VDS, with regions:
  • Ohmic/triode region: ID rises with VDS (acts as resistor).
  • Saturation/active region: ID nearly constant, set by VGS (used for amplification).
  • Cut-off: VGS < VT, ID ≈ 0.
• Saturation current:

ID = k (VGS − VT)²

• k = device constant, VT = threshold voltage
  • Advantage: Very high input impedance (insulated gate draws no DC gate current).

IX. Applications of Semiconductor Devices

A. Application of diodes, transistors, rectifiers and MOSFET

• Diodes: Rectification, clipping and clamping circuits, freewheeling (flyback protection), voltage multipliers; Zener for voltage regulation and reference; varactor for tuning in radios, TVs and VCOs.
• Transistors (BJT): Switching, amplification (audio/RF), oscillators, and as the base element of logic gates.
• Rectifiers: DC power supplies, battery chargers, adapters, and DC links in inverters.
• MOSFET: Digital logic (CMOS ICs, microprocessors, memory), power switching (SMPS, motor drives), and RF/audio amplification — chosen for high input impedance and fast switching.