Semiconductor explorer
Interactive lessons on how semiconductor devices work — carriers in the silicon lattice, doping and the Fermi level, drift and diffusion, the PN junction forming and under bias (Shockley, breakdown, capacitance, LEDs, solar cells), the BJT's injection and Ebers–Moll regions, the MOSFET's channel, square law and CMOS, power DMOS, and the JFET, Schottky, SCR/TRIAC and IGBT — every one a drawing you drag, with live numbers and a quiz.
Added
Works with
- Electronics handbook Electronicsthe formulas these lessons explain (the diode equation, BJT bias, MOSFET losses) as calculators
- Transistor and MOSFET switches Electronicsput the BJT saturation, MOSFET on-resistance and body diode from these lessons to work in real switch designs
- Circuit simulator Electronicssimulate the diodes and transistors explained here in circuits, and trace their curves with a DC sweep
- LED drivers Electronicsdrive the LEDs whose colour comes from the band gap here, with the right resistor or constant-current driver
- How a chip is made Electronicshow these devices are actually built — oxidation, lithography, implants, gates and wiring, step by step in 3-D
- CMOS gate designer Electronicsput the MOSFETs and CMOS inverter from these lessons to work in logic gates — transfer curve, sizing, layout
- Electronics course Electronicsthe course these lessons belong to — units 3 and 4 on diodes and transistors, with exercises and quizzes
- Curve tracer and load lines Electronicsreal parts’ diode, BJT and MOSFET curves with load lines and a Q point you can drag
How to use it
The device physics behind the parts in every circuit, from the silicon crystal up. Each lesson is a live drawing — a lattice of atoms with electrons breaking loose, a junction forming, a transistor with carriers flowing through it, a family of curves — that you drag with the mouse or a finger, with the numbers worked out as you go, a short explanation, a box with the equations to remember, and a small multiple-choice quiz that explains every answer.
The numbers are real: silicon’s band gap and carrier density against temperature, mobilities from the fits used in device simulators, the abrupt-junction depletion approximation, the Shockley, Ebers–Moll and square-law models, and the silicon limit for power devices. Where a picture would need a billion electrons, the drawing shows a log-scale handful and says so; the cards beside it give the real values.
How to use it
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Pick a section along the top — Silicon and doping, PN junction, BJT, MOSFET or Other devices — then a lesson in the row of buttons beneath it. Your place and every setting are remembered.
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Drag the orange handles in the drawings: the dot on a curve to move along it, the Fermi level up and down in a band diagram, the gate and drain of a MOSFET, the operating point on a family of curves, the point on the BJT’s region map. Sliders below each drawing change dopings, widths, temperatures and model parameters; preset buttons jump to typical cases.
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Play/Pause controls the animations (they start paused if your system asks for reduced motion).
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Read the cards for the numbers, and finish each lesson with its quiz.
What’s inside
Silicon and doping — a two-dimensional picture of the diamond lattice, its covalent bonds, and thermal generation and recombination of electron–hole pairs, with the intrinsic concentration nᵢ against temperature for silicon, germanium and gallium arsenide (drag along the curve); phosphorus and boron dopants with the majority and minority carriers from the mass-action law. The band diagram with a draggable Fermi level, the Fermi–Dirac occupancy, mobilities and the resistivity of silicon against doping (the Irvin curve). A drift-and-diffusion bar where you set the field and inject a pulse of carriers that drifts at μE and spreads as √(2Dt) — the Haynes–Shockley experiment.
PN junction — the junction forming: carriers diffusing, the depletion region and the uncovered ions, with the charge, field and potential profiles and a probe; the built-in potential and depletion widths from the dopings. Forward and reverse bias with the depletion width, the bent band diagram with the split quasi-Fermi levels, and the Shockley curve with the ideality factor and saturation current (1N4148 and 1N4007 presets). Zener and avalanche breakdown with their tempcos; junction capacitance against reverse voltage and a varactor tuning an LC tank; the temperature dependence of the forward voltage. LEDs: the band gap to the photon’s wavelength and colour, direct and indirect gaps, and the materials (GaAs, GaAsP, AlGaInP, GaP, InGaN, GaN). Photodiodes and solar cells: the IV curve shifted by the photocurrent, Voc, Isc, the maximum power point and fill factor.
BJT — an NPN with electrons injected from the emitter, crossing the base and collected, and the base current from recombination and back-injection in the real proportion 1/β; emitter injection efficiency, base transport factor, α, β and the Early voltage from the base width and dopings, with the collector characteristics. The four operating regions on a Vbe–Vbc map with the Ebers–Moll currents and the carrier flow in each.
MOSFET — a cross-section where the gate voltage takes the surface through accumulation, depletion and inversion, the threshold from the body doping and oxide thickness, and the channel tapering to pinch-off as Vds rises. The square law with its cutoff, triode and saturation regions, channel-length modulation, the body effect and subthreshold conduction on a log scale. N and P, enhancement and depletion devices side by side, and the CMOS inverter’s transfer curve and supply current. The vertical power MOSFET (DMOS): the current path, the blocking depletion region, the body diode, and the silicon limit Ron,sp ∝ BV2.5 against silicon carbide.
Other devices — the JFET’s channel squeezed by its gate junctions; the Schottky barrier against a PN junction; the thyristor’s two-transistor latch with the gate pulse, holding current and the TRIAC; and the IGBT, a MOSFET driving a PNP, against a MOSFET of the same rating.
The physics
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Band gap (Varshni): Eg(T) = Eg(0) − αT² / (T + β); for silicon Eg(0) = 1.170 eV, α = 4.73 × 10⁻⁴ eV/K, β = 636 K (Thurmond 1975), so Eg = 1.12 eV at 300 K.
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Intrinsic carriers: nᵢ ∝ T1.5 · exp(−Eg/2kT), anchored to nᵢ(300 K) = 1.0 × 10¹⁰ cm⁻³ for silicon (Sproul and Green 1991; Altermatt 2003 gives 9.65 × 10⁹), 2.0 × 10¹³ for germanium and 2.1 × 10⁶ for GaAs (Sze).
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Doping: full ionisation, n − p = ND − NA and n·p = nᵢ²; EF − Eᵢ = kT·ln(n/nᵢ).
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Mobility (silicon, Caughey–Thomas form with the Masetti/Arora coefficients): μn = 68.5 + 1345.5 / (1 + (N / 9.2 × 10¹⁶)0.711), μp = 44.9 + 425.6 / (1 + (N / 2.23 × 10¹⁷)0.719) cm²/V·s; σ = q(nμn + pμp); the Einstein relation D = μkT/q.
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Abrupt junction (depletion approximation): Vbi = (kT/q)·ln(NAND/nᵢ²), W = √(2εs(Vbi − V)/q · (NA + ND)/(NAND)), NAxp = NDxn, Cj = εs/W.
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Diode: I = Is(exp(V/nVT) − 1), with Is = qAnᵢ²(Dp/(LpND) + Dn/(LnNA)) for a long diode and SPICE’s temperature scaling Is(T) = Is(T₀)(T/T₀)XTI/n expEg/nVT)(T/T₀ − 1.
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Breakdown: Sze and Gibbons' universal avalanche formula for a one-sided abrupt junction, BV ≈ 60(Eg/1.1)1.5(N/10¹⁶)−0.75 V; tunnelling below about 4Eg/q, avalanche above about 6Eg/q. The Zener tempcos are a fit to typical BZX55/1N47xx datasheet values.
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Light: λ = hc/E = 1239.84 nm·eV / E; colours from Dan Bruton’s wavelength-to-RGB fit. Solar cell: I = Iph − Is(exp(V/nVT) − 1), Voc = nVT ln(Iph/Is + 1), the maximum power point by search (it matches Green’s fill-factor formula).
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BJT: γ = 1/(1 + NBDEWB/(NE,effDBWE)) with Slotboom bandgap narrowing in the emitter (ΔEg = 9 mV·(ln(N/10¹⁷) + √(ln²(N/10¹⁷) + 0.5)), NE,eff = NE·exp(−ΔEg/kT)), αT = 1 − WB²/2LB², β = α/(1 − α), VA = qNBWB/Cjc. Ebers–Moll in the transport form used by SPICE, with an Early factor.
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MOSFET: Vth = VFB + 2φF + γ√(2φF + VSB) with an n⁺ polysilicon gate; the SPICE level-1 square law with λ; subthreshold from the EKV interpolation (scaled to meet the square law well above threshold), slope n·(kT/q)·ln 10. CMOS inverter by solving Idn = Idp.
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Power: Baliga’s silicon limit Ron,sp = 5.93 × 10⁻⁹·BV2.5 Ω·cm² and the optimum drift doping and width; 4H-SiC uses 2.97 × 10⁻¹² · BV2.5.
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Others: Shockley’s JFET equation ID = IDSS(1 − VGS/VP)²; thermionic emission J = AT² exp(−φB/VT) for a Schottky (A = 112 A/cm²K² for n-type silicon); the SCR’s two-transistor latch IA = (α₂IG + ICO)/(1 − (α₁ + α₂)).
Sources: S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (3rd ed., Wiley 2007); B. G. Streetman and S. Banerjee, Solid State Electronic Devices; R. F. Pierret, Semiconductor Device Fundamentals; B. J. Baliga, Fundamentals of Power Semiconductor Devices; M. A. Green, Solar Cells; the ngspice manual for the diode, BJT and MOSFET models.
These are the textbook long-channel, low-injection models: good for understanding and for estimates, not a substitute for a device’s datasheet. Real short-channel MOSFETs, high-current BJTs and modern LEDs deviate in ways a datasheet or a SPICE model captures better.
Want to measure the curves rather than read about them? Run the Sweep: examples in the circuit simulator, or use the curve tracer. For the formulas as calculators, see the electronics handbook; for using transistors as switches, transistor and MOSFET switches.
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