Unit 4: Fundamentals of semiconductor devices

I. Semiconductor Foundations — Charge carriers and device principles

Semiconductor devices control electrical current by manipulating electrons and holes in materials such as silicon (Si); their operation depends mainly on doping, junction formation, and externally applied electric fields.

A. Introduction to semiconductor devices

Semiconductor devices provide switching, amplification, rectification, regulation, and signal-processing functions in electrical and electronic circuits.

• Semiconductor conductivity: A semiconductor has conductivity between that of a conductor and an insulator; its conductivity generally increases with temperature.
• Charge carriers:
  • Electrons: Negatively charged mobile carriers in the conduction band.
  • Holes: Effective positive carriers created by missing valence electrons.
• Intrinsic semiconductor: Pure silicon or germanium has equal electron and hole concentrations.
• Extrinsic semiconductor: Controlled impurities are added through doping.
  • N-type: Pentavalent donor atoms produce majority electrons.
  • P-type: Trivalent acceptor atoms produce majority holes.
• Common devices: PN junction diodes, Zener diodes, varactor diodes, bipolar junction transistors (BJTs), and metal-oxide-semiconductor field-effect transistors (MOSFETs).
• Conventional current: Current is treated as flowing from positive to negative potential, opposite to electron motion.

II. PN Junction Diode — Unidirectional conduction

A PN junction diode is a two-terminal semiconductor device formed by joining P-type and N-type regions; its terminals are the anode and cathode.

A. Working and operation of PN junction diode

A PN junction conducts strongly in forward bias and blocks current, except for small leakage, in reverse bias.

• Junction formation: Electrons and holes diffuse across the junction and recombine, leaving fixed ions that form a carrier-free depletion region.
• Barrier potential: The internal electric field opposes further diffusion; typical room-temperature values are about (0.7\text{ V}) for silicon and (0.3\text{ V}) for germanium.
• Forward bias: Connecting P to positive and N to negative reduces the barrier and depletion width, allowing majority-carrier current.
• Reverse bias: Connecting P to negative and N to positive increases the barrier and depletion width; only a small reverse saturation current flows.
• Breakdown: Excessive reverse voltage causes a large current through Zener or avalanche mechanisms; an ordinary diode may be damaged unless current is limited.

B. Characteristics of PN junction diode

The diode characteristic describes the nonlinear relationship between diode voltage and current.

I_D = I_S[e^(V_D/(ηV_T)) − 1]

Here, (I_D) is diode current, (I_S) is reverse saturation current, (V_D) is diode voltage, (\eta) is the ideality factor, and (V_T) is thermal voltage, approximately (26\text{ mV}) at room temperature.

• Forward characteristic: Current remains small below the cut-in region and then rises rapidly; practical silicon calculations often use a constant (0.7\text{ V}) drop.
• Reverse characteristic: Current is approximately (-I_S) until breakdown voltage is reached.
• Static resistance: At an operating point, (R_D=V_D/I_D).
• Dynamic resistance: For small signal changes, (r_d=\Delta V_D/\Delta I_D).
• Temperature effect: Silicon forward voltage decreases by approximately (2\text{ mV}/^\circ\text{C}), while reverse leakage increases strongly with temperature.

III. Zener Diode — Controlled reverse breakdown

A Zener diode is a heavily doped PN junction designed to operate safely in reverse breakdown at a specified Zener voltage (V_Z).

A. Working and operation of Zener diode

A reverse-biased Zener diode maintains an approximately constant voltage when its current is kept within the rated operating range.

• Connection: The cathode is connected toward the positive supply and the anode toward the negative terminal.
• Below breakdown: Only a small leakage current flows when reverse voltage is less than (V_Z).
• At breakdown: Current rises sharply while diode voltage remains close to (V_Z).
• Current limiting: A series resistor prevents excessive power dissipation.

R_S = (V_S − V_Z)/I_Z
P_Z = V_Z I_Z

Here, (R_S) is series resistance, (V_S) is supply voltage, (I_Z) is Zener current, and (P_Z) is Zener power.

B. Characteristics of Zener diode

The Zener characteristic is similar to that of an ordinary diode in forward bias but has a well-defined reverse-breakdown region.

• Knee current: (I_{ZK}) is the minimum current required for effective regulation.
• Maximum current: It is limited by the power rating: (I{ZM}\approx P{ZM}/V_Z).
• Dynamic resistance: (r_Z=\Delta V_Z/\Delta I_Z); a smaller value gives better voltage regulation.
• Breakdown mechanisms: Zener tunnelling dominates at lower voltages, while avalanche multiplication dominates at higher voltages.
• Regulation range: Normal operation requires (I_{ZK}<IZ<I{ZM}).

IV. Digital Logic — Binary decision circuits

Logic gates implement Boolean operations using voltage levels interpreted as binary 0 and 1.

A. Logic gates

A logic gate produces a binary output determined by one or more binary inputs.

• NOT gate: Produces the complement, (Y=\overline{A}).
• AND gate: Produces 1 only when all inputs are 1, (Y=A\cdot B).
• OR gate: Produces 1 when at least one input is 1, (Y=A+B).
• NAND and NOR: Complement AND and OR respectively; both are universal gates because either can implement every Boolean function.
• XOR gate: Produces 1 when inputs differ, (Y=A\oplus B).
• XNOR gate: Produces 1 when inputs are equal.

V. Varactor Diode — Voltage-controlled capacitance

A varactor, or varicap, is a PN junction diode designed to act as a variable capacitor under reverse bias.

A. Working and operation of Varactor diode

A varactor changes junction capacitance by changing the reverse-bias voltage and hence the depletion width.

• Capacitor structure: P and N regions act as plates, while the depletion region acts as the dielectric.
• Voltage response: Increasing reverse voltage widens the depletion region and decreases capacitance.

C_j = εA/W

Here, (C_j) is junction capacitance, (\varepsilon) is semiconductor permittivity, (A) is junction area, and (W) is depletion width.

• Operating condition: Forward bias is avoided because conduction would destroy the intended capacitive action.
• Uses: Voltage-controlled oscillators, electronic tuning, phase-locked loops, frequency multipliers, and FM modulators.

VI. Device Testing — Identifying condition and terminals

Diodes and transistors can be checked with a digital multimeter using diode-test mode, preferably after isolating the device from the circuit.

A. Testing of diode and BJT

Testing verifies junction continuity, polarity, terminal identity, and common open- or short-circuit faults.

1. Diode testing:

   • Forward test: Red probe on anode and black probe on cathode should show approximately (0.5)–(0.8\text{ V}) for a silicon diode.
   • Reverse test: Reversing the probes should produce an over-range or open indication.
   • Faults: Low readings both ways indicate a short; open indications both ways suggest an open diode.

2. BJT testing:

   • Junction model: A BJT behaves like two PN junctions sharing the base: base-emitter and base-collector.
   • NPN identification: Both junctions conduct when the red probe is on the base.
   • PNP identification: Both junctions conduct when the black probe is on the base.
   • Collector-emitter check: It should normally read open in both directions when the base is unconnected.
   • Limitation: This test detects basic faults but does not accurately determine current gain (\beta) or performance under load.

VII. Rectifiers — AC-to-DC conversion

A rectifier uses diodes to convert alternating voltage into unidirectional pulsating voltage, which may then be smoothed by a filter.

A. Half-wave rectifier

A half-wave rectifier uses one diode to pass one AC half-cycle and block the other.

• Operation: The diode conducts during one polarity and remains reverse-biased during the opposite polarity.
• Average output: For an ideal diode and peak secondary voltage (V_m),

V_DC = V_m/π

• Performance: Ripple frequency equals supply frequency (f), maximum efficiency is about (40.6\%), and ripple factor is approximately (1.21).
• PIV: Peak inverse voltage across the diode is (V_m).
• Limitation: Poor transformer utilization and high ripple restrict it to low-power applications.

B. Full-wave rectifier

A centre-tapped full-wave rectifier uses two diodes alternately so that both AC half-cycles produce load current in the same direction.

• Operation: Each half of the centre-tapped secondary supplies one conducting diode on alternate half-cycles.
• Average output:

V_DC = 2V_m/π

Here, (V_m) is the peak voltage of each half-secondary.

• Performance: Ripple frequency is (2f), maximum efficiency is about (81.2\%), and ripple factor is approximately (0.482).
• PIV: Each diode must withstand approximately (2V_m).
• Limitation: It requires a centre-tapped transformer and uses only half the secondary winding at a time.

C. Full-wave bridge rectifier

A bridge rectifier uses four diodes and conducts through two diodes during each half-cycle.

• Current path: Alternate diode pairs reverse the negative half-cycle across the load, preserving one load-current direction.
• Output: Ideally, (V_{DC}=2V_m/\pi), with ripple frequency (2f).
• PIV: Each diode withstands approximately (V_m), lower than in the centre-tapped arrangement.
• Practical drop: Two conducting silicon diodes reduce instantaneous output by about (1.4\text{ V}).
• Advantage: No centre-tapped transformer is required, and transformer utilization is comparatively high.

VIII. MOSFET — Voltage-controlled switching and amplification

A MOSFET controls drain current by the electric field produced by an insulated gate, giving it very high input resistance.

A. MOSFET representation and characteristics

MOSFET representation identifies the gate (G), drain (D), source (S), and body (B), while its characteristics relate drain current to gate and drain voltages.

• Types: N-channel and P-channel devices may be enhancement-mode or depletion-mode; enhancement MOSFETs are normally off at zero gate-source voltage.
• Gate insulation: A thin oxide separates the gate from the semiconductor, so steady gate current is ideally zero.
• N-channel enhancement operation:
  • Cut-off: (V{GS}<V{TH}), so (I_D\approx0).
  • Ohmic region: The MOSFET behaves approximately as a voltage-controlled resistance.
  • Saturation region: (V{DS}\ge V{GS}-V{TH}), and current is mainly controlled by (V{GS}).
• Transfer characteristic:

I_D = K(V_GS − V_TH)²

Here, (ID) is drain current, (K) is a device constant, (V{GS}) is gate-source voltage, and (V_{TH}) is threshold voltage.

• Practical feature: Power MOSFETs contain an intrinsic body diode and require protection against excessive gate voltage and static electricity.

IX. Engineering Uses — Device selection by function

Semiconductor devices are selected according to voltage, current, switching speed, power dissipation, gain, and frequency requirements.

A. Applications of diodes

Diodes are primarily used wherever current direction, voltage level, or signal shape must be controlled.

• Rectification: Power diodes convert AC into pulsating DC.
• Protection: Flyback diodes suppress inductive voltage spikes across relays and motors.
• Wave shaping: Clippers limit signal amplitude, while clampers shift the DC level.
• Regulation: Zener diodes provide reference and regulated voltages.
• Detection: Signal diodes demodulate AM and other high-frequency signals.
• Optoelectronics: LEDs emit light, while photodiodes convert light into current.

B. Applications of transistors

Transistors provide amplification and controlled switching in analog, digital, and power circuits.

• Amplification: BJTs amplify voltage, current, or power in audio and sensor circuits.
• Switching: A transistor operates between cut-off and saturation to control relays, lamps, and digital loads.
• Oscillation: Transistors supply gain and feedback in waveform generators.
• Regulation: Pass transistors control load voltage or current in power supplies.
• Digital systems: Transistors form logic gates, memory cells, processors, and integrated circuits.

C. Applications of rectifiers

Rectifiers supply unidirectional power from AC sources.

• DC power supplies: Rectifier, filter, and regulator stages power electronic equipment.
• Battery charging: Controlled DC current restores electrochemical energy.
• Motor drives: Rectified DC feeds DC motors and inverter-based AC drives.
• Industrial processes: Rectifiers supply electroplating, electrolysis, and welding systems.
• Instrumentation: Rectifier circuits permit AC measurement using DC-sensitive meter movements.

D. Applications of MOSFET

MOSFETs are preferred for high-speed, voltage-controlled switching and densely integrated electronic systems.

• Power conversion: They switch current in switched-mode power supplies, DC–DC converters, and inverters.
• Motor control: Pulse-width-modulated MOSFET bridges regulate motor speed and direction.
• Digital integration: Complementary MOSFETs form low-power CMOS logic and memory.
• Amplification: MOSFETs serve in common-source, source-follower, audio, and radio-frequency amplifiers.
• Load control: Logic-level MOSFETs interface microcontrollers with LEDs, solenoids, heaters, and other high-current loads.