Heterostructures, HEMTs, HBTs & Microwave Devices

Semiconductor devices for GHz and beyond. Learn heterojunctions and band alignment (type I/II/III), modulation doping and the two-dimensional electron gas, HEMTs (GaAs pHEMT, InP, AlGaN/GaN), transconductance and f_T/f_max, noise figure and power density, HBTs (wide-gap emitter or SiGe graded base, high injection efficiency, f_T and f_max), MESFETs, RF MOSFETs/LDMOS, transferred-electron (Gunn) devices and negative differential mobility, IMPATT/TRAPATT avalanche transit-time diodes, RF Schottky, PIN and varactor diodes, and device selection for LNAs, PAs, mixers and oscillators — with Python computing transit-time f_T limits, g_m/C_gs f_T, HBT f_max, and Gunn/IMPATT frequencies.

At microwave and millimetre-wave frequencies, electrons must cross the active region in picoseconds. Heterostructures — junctions between different semiconductors — separate carriers from their dopants (high mobility) and decouple injection efficiency from doping, enabling transistors above 1 THz.

Some two-terminal devices even generate microwaves directly by exploiting negative differential resistance.

An analogy

A HEMT's 2DEG is like a smooth express lane built beside a bumpy road full of potholes (dopant atoms): the cars (electrons) come from the bumpy side but travel on the smooth lane, so they go much faster.

Heterojunctions

Joining semiconductors with different bandgaps creates band offsets. Type I (straddling, e.g. AlGaAs/GaAs) confines electrons and holes in the same layer — lasers, HEMTs; type II (staggered) separates them — photodetectors; type III (broken gap) enables tunnelling devices. Lattice matching or controlled strain (pseudomorphic layers) avoids dislocations.

HEMTs and HBTs

High-frequency transistors:

Other RF devices

MESFET: Schottky-gated GaAs FET (predecessor of the HEMT). LDMOS: silicon lateral MOSFET for base-station and broadcast PAs below ~4 GHz. RF CMOS: bulk/SOI for integrated radios and switches. Two-terminal sources: Gunn diodes (transferred-electron effect in GaAs/InP — electrons scatter into a heavier, slower valley creating negative differential mobility and travelling domains) and IMPATT diodes (avalanche + transit-time phase delay, high power but noisy); TRAPATT is a high-efficiency, lower-frequency variant. RF diodes: Schottky (mixers/detectors), PIN (switches, limiters), varactors (tuning).

Selection for RF functions

LNA: low NF_min and high gain — InP/GaAs HEMT, SiGe HBT, RF-SOI CMOS. PA: power density, efficiency, linearity, ruggedness — GaN HEMT (high power), GaAs HBT (handsets), LDMOS (sub-4 GHz infrastructure). Mixers/detectors: Schottky diodes, HEMTs. Oscillators: HBTs for low phase noise, Gunn/IMPATT for simple mm-wave sources. Thermal management and matching networks are as important as the device itself.

Formulas

Worked example: Transit time

Given: L_g 100 nm, v 1.5 × 10⁷ cm/s

Find: Transit time.

Answer: 0.67 ps

Worked example: HBT gain boost

Given: ΔE_g 0.1 eV

Find: Injection-efficiency factor.

Answer: ≈ 48×

Worked example: IMPATT

Given: Drift 5 µm

Find: f.

Answer: 10 GHz

AlGaAs/GaAs HEMT band diagram

  Gate │ n-AlGaAs (donors)  │ spacer │ undoped GaAs channel
  metal│  ╲___ E_c            │        │
       │      ╲______________ │ΔE_c    ▼ 2DEG triangular well (electrons, no dopants → high µ)
  E_F ─│───────────────────────────────▔▔▔▔▔▔▔▔▔ (E_F above E_c in the well)
  Gate voltage modulates n_s → drain current;  GaN: polarisation creates the 2DEG without donors

Electrons from donors in the wide-gap barrier fall into the lower conduction band of the narrow-gap channel, forming a thin sheet separated from the ionised donors by an undoped spacer — so impurity scattering is small and mobility high. GaN HEMTs get their 2DEG from polarisation charge instead.

Frequency limits of RF devices

import math
# RF device limits: HEMT fT from transit time, gm/Cgs, Gunn and IMPATT frequencies, HBT fmax
vsat = 1.5e7                                  # effective electron velocity in GaAs/GaN channels (cm/s)
for Lg_nm in (250, 100, 50):
    fT = vsat / (2 * math.pi * Lg_nm * 1e-7)
    print(f"HEMT Lg = {Lg_nm:3d} nm: intrinsic fT ~ v/(2*pi*Lg) = {fT/1e9:.0f} GHz (upper bound; parasitics cut it 2-3x)")
gm, Cgs = 0.4, 1.0e-12                         # 1 mm-wide GaN HEMT: 400 mS/mm, 1 pF/mm total gate capacitance
print(f"fT = gm/(2*pi*Cgs) = {gm/(2*math.pi*Cgs)/1e9:.0f} GHz for gm 0.4 S/mm and Cgs 1 pF/mm")
fT, rb, Cmu = 300e9, 50.0, 5e-15
print(f"SiGe HBT fmax = sqrt(fT/(8*pi*rb*Cmu)) = {math.sqrt(fT/(8*math.pi*rb*Cmu))/1e9:.0f} GHz")
for L_um in (10, 5):
    print(f"Gunn diode transit region {L_um} um: f ~ v_domain/L = {1e7/(L_um*1e-4)/1e9:.0f} GHz")
W = 3e-4
print(f"IMPATT drift region 3 um: f ~ vsat/(2W) = {1e7/(2*W)/1e9:.1f} GHz")
# HEMT Lg = 250 nm: intrinsic fT ~ v/(2*pi*Lg) = 95 GHz (upper bound; parasitics cut it 2-3x)
# HEMT Lg = 100 nm: intrinsic fT ~ v/(2*pi*Lg) = 239 GHz (upper bound; parasitics cut it 2-3x)
# HEMT Lg =  50 nm: intrinsic fT ~ v/(2*pi*Lg) = 477 GHz (upper bound; parasitics cut it 2-3x)
# fT = gm/(2*pi*Cgs) = 64 GHz for gm 0.4 S/mm and Cgs 1 pF/mm
# SiGe HBT fmax = sqrt(fT/(8*pi*rb*Cmu)) = 219 GHz
# Gunn diode transit region 10 um: f ~ v_domain/L = 10 GHz
# Gunn diode transit region 5 um: f ~ v_domain/L = 20 GHz
# IMPATT drift region 3 um: f ~ vsat/(2W) = 16.7 GHz

Shrinking the gate raises the intrinsic transit-time limit from ~95 GHz at 250 nm to ~480 GHz at 50 nm, though parasitic capacitances and resistances reduce practical f_T 2–3×. A typical GaN HEMT with 0.4 S/mm and 1 pF/mm reaches f_T ≈ 64 GHz. A SiGe HBT with f_T 300 GHz and low r_bC_µ reaches f_max ≈ 220 GHz. Gunn and IMPATT diodes generate 10–20 GHz from micrometre transit regions.

Common mistakes

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Key takeaways

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