Intrinsic semiconductors and doping
In an intrinsic semiconductor, electron and hole concentrations are equal at ni. Doping with donors (n-type) increases electron concentration; doping with acceptors (p-type) increases hole concentration. The mass-action law np = ni² applies in thermal equilibrium, not under injection.
Check yourself: Are you applying the mass-action law under equilibrium conditions?
PN junction and diode characteristics
Under forward bias, the junction barrier decreases and current increases exponentially: I = Is(exp(V/(nVT)) − 1). Under reverse bias, current is approximately −Is until breakdown. The depletion width increases with reverse bias. The built-in potential depends on doping concentrations and temperature.
Check yourself: Is the diode forward biased, reverse biased, or in breakdown?
BJT operating regions
An NPN BJT is in active mode when the base-emitter junction is forward biased and the base-collector junction is reverse biased. In active mode, Ic ≈ βIb. In saturation, both junctions are forward biased and Vce,sat is small. Cutoff has both junctions off. Check voltages at all three terminals.
Check yourself: Which junctions are forward biased and which are reverse biased?
MOSFET regions
An enhancement NMOS turns on when Vgs > Vth. In the triode (linear) region, Vds < Vgs − Vth and Id = μnCox(W/L)[(Vgs − Vth)Vds − Vds²/2]. In saturation, Vds ≥ Vgs − Vth and Id = μnCox(W/L)(Vgs − Vth)²/2 without channel-length modulation. The threshold voltage is a device parameter, not a circuit variable.
Check yourself: Is Vds above or below (Vgs − Vth) for this bias point?
Device capacitances and switching
Junction capacitance depends on depletion width and varies with bias voltage. Gate capacitance in a MOSFET is approximately CoxWL in strong inversion. Switching speed depends on how quickly these capacitances charge and discharge through circuit resistances. Small-signal capacitance models apply near a specific bias point.
Check yourself: Are capacitance values evaluated at the correct operating point?