Advanced: Device Models and Semiconductor Behavior
BJT exponential law
In forward-active operation, a simplified BJT model relates collector current to base-emitter voltage:
This is closely related to the diode equation because the base-emitter junction is a PN junction. The transistor adds carrier transport across the thin base.
Transconductance
The BJT small-signal transconductance at a bias current is:
At room temperature, VT is about 25.9 mV, so a BJT operating at 1 mA has a transconductance of roughly 38.6 mS.
Small-signal emitter resistance
This internal dynamic resistance helps explain emitter-degeneration gain and the relationship between bias current and amplifier transconductance.
Early effect
Collector current in a real BJT changes somewhat with collector-emitter voltage even at fixed base-emitter voltage. This finite output resistance is associated with base-width modulation and is modeled by the Early effect.
MOSFET square-law model
For a long-channel enhancement MOSFET in saturation, a simplified teaching model is:
Modern short-channel MOSFETs depart substantially from this simple square-law model because of velocity saturation, mobility reduction, channel-length modulation, and other effects.
MOS transconductance
For the same simple long-channel model:
The denominator is often called overdrive voltage.
Channel-length modulation
A MOSFET in saturation does not behave as an ideal current source. Drain current increases somewhat as drain voltage rises. Small-signal models represent this with an output resistance ro.
Capacitances
Every transistor contains capacitance. BJT base-emitter and base-collector junction capacitances limit high-frequency gain. MOSFET gate-source, gate-drain, and drain-body capacitances determine drive energy and switching behavior.
Miller effect
Capacitance between an amplifier's input and output can appear much larger at the input when voltage gain exists between the two nodes. This Miller effect strongly influences transistor amplifier bandwidth.
Frequency response
BJT transition frequency fT and FET gain-bandwidth-related figures help indicate how quickly a device can amplify. RF transistors are optimized for small capacitances, short carrier transit times, low parasitic inductance, and suitable package geometry.
Noise
Transistors produce several forms of noise:
- Shot noise associated with junction current.
- Thermal noise from resistive elements and channel resistance.
- Flicker or 1/f noise that becomes important at low frequencies.
- Generation-recombination and other device-specific noise mechanisms.
The best device for a low-noise amplifier depends on source impedance, frequency, bias current, and required gain—not on one headline noise number.
Thermal behavior
Transistor parameters change with junction temperature. Power dissipation raises junction temperature according to the thermal path from silicon to ambient. Thermal impedance is dynamic during short pulses, so transient thermal curves are important for power-device pulse operation.
Breakdown mechanisms
BJTs and FETs have several maximum-voltage limits associated with junction breakdown, oxide fields, punch-through, and parasitic structures. A datasheet may specify different limits depending on how unused terminals are connected.
Secondary breakdown
Power BJTs can develop localized hot spots in high-voltage, high-current linear operation. This phenomenon creates a safe-operating-area limit below the simple power-dissipation boundary. MOSFETs generally avoid classic BJT secondary breakdown, but modern devices still have thermal and SOA constraints.
Device matching
Discrete transistors vary considerably in beta, threshold voltage, leakage, and other parameters. Transistors fabricated close together on the same IC die often match much better because they share process and temperature. Analog IC design uses this matching to build accurate differential pairs, current mirrors, and bias networks.