GaAs InP High Electron Mobility Transistor (HEMT)

1. Theory

• Definition: A GaAs- or InP-based high electron mobility transistor (HEMT, MODFET or HFET) is a Schottky-gate FET whose channel is a two-dimensional electron gas (2DEG) at a heterojunction between a wide-gap barrier and a narrow-gap channel.
• Family: Covers the AlGaAs/GaAs HEMT, the pseudomorphic HEMT (pHEMT, strained InGaAs on GaAs), the metamorphic HEMT (mHEMT, high-indium channel on GaAs via a graded buffer) and the lattice-matched InGaAs/InAlAs HEMT on InP.
• Modulation doping: Donors sit in the wide-gap barrier, and their electrons fall across the conduction-band offset $\Delta E_C$ into the undoped channel, separated from their parent ions.
• No polarization charge: Unlike GaN, zinc-blende III-As and III-P materials have no large spontaneous polarization, so the 2DEG must be supplied by intentional doping.
• Spacer layer: An undoped spacer further separates electrons from donors, raising mobility but weakening gate control.
• High indium content: More indium lowers effective mass and raises velocity and band offset, but strained layers are limited by the Matthews-Blakeslee critical thickness.

2. Working Principle

• Charge control: The gate and 2DEG form a parallel-plate capacitor of spacing $d+\Delta d$, so the sheet density is $n_s={\epsilon }_b(V_{GS}-V_T)/q(d+\Delta d)$.
• High mobility: With remote-impurity scattering suppressed, mobility is limited mainly by phonons and rises sharply on cooling.
• Velocity-saturated operation: Short gates give $I_{Dsat}\approx Z{v}_{sat}{\epsilon }_b(V_{GS}-V_T)/(d+\Delta d)$ and $g_m$ independent of gate length.
• High transconductance: The thin barrier keeps the gate very close to the channel, giving much higher $g_m$ than a MESFET of the same gate length.
• Speed and noise: $f_T\approx v_{sat}/2\pi L_g$, and the high $g_m$ and low parasitic resistance give the lowest noise figures of any transistor (Fukui relation).
• Material trade-off: InP HEMTs reach the highest frequencies, pHEMTs are cheaper on GaAs, and mHEMTs approach InP performance on GaAs substrates.

3. Applications

• Cryogenic low-noise amplifiers: InP HEMTs are the standard first-stage amplifiers for radio astronomy and superconducting-qubit readout.
• Satellite and radio low-noise blocks: GaAs pHEMT LNAs in satellite TV receivers, GNSS and base stations.
• mm-wave and sub-THz amplifiers: InP and mHEMT MMICs above 100 GHz for radar, imaging and instrumentation.
• mm-wave 5G and point-to-point radio front ends: pHEMT power amplifiers and LNAs.

Name	Formula	Related Formulae	Variables/Constants
Conduction band offset	$\Delta E_C=Q_c\Delta E_g$	$E_g^{\Gamma }(x)=1.424+1.247x({\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As},x\le 0.45)\text{(see Ternary Compound Semiconductors page)}$	$\begin{array}{r}\Delta E_C:conductionbanddiscontinuity\\ attheheterointerface\end{array}$ $\begin{array}{r}\Delta E_g:bandgapdifferencebetween\\ barrierandchannel\end{array}$ $\begin{array}{r}{Q}_c:fractionofthebandgapdifference\\ appearingintheconductionband(about\\ 0.6forAlGaAs/GaAs)\end{array}$
Threshold voltage	$V_T={\varphi }_b-\frac{\Delta E_C}{q}-\frac{q{N}_D{d}_d^2}{2{\epsilon }_b}-\frac{q{N}_D{d}_d{d}_i}{{\epsilon }_b}$	$\begin{array}{r}\text{(see}\text{Metal-Semiconductor}\text{Field-Effect}\\ \text{Transistor}\text{page}\text{for}\text{the}\text{Schottky-gate}\\ \text{analogue)}\end{array}$	$\begin{array}{r}{V}_T:gatevoltageatwhichthe2DEG\\ densitygoestozero\end{array}$ $\begin{array}{r}{\varphi }_b:Schottkybarrierheightofthe\\ gateonthebarrierlayer\end{array}$ $N_D:donordopingofthebarrier$ ${\epsilon }_b:barrierpermittivity$ $d_d,d_i:dopedlayerandspacerthicknesses$
2DEG sheet density (charge control)	$n_s=\frac{{\epsilon }_b\left(V_{GS}-V_T\right)}{q\left(d+\Delta d\right)}$	$d=d_d+d_i,\Delta d\approx 80\mathring{\mathrm{A}}$	$n_s:2DEGsheetcarrierdensity$ $\begin{array}{r}\Delta d:effectivedistanceofthe2DEG\\ centroidfromtheinterface\end{array}$ $\begin{array}{r}\text{(Delagebeaudeuf-Linh}\text{charge-control}\\ \text{model:}\text{the}\text{gate}\text{and}\text{2DEG}\text{form}\text{a}\\ \text{parallel-plate}\text{capacitor}\text{of}\text{spacing}\\ d+\Delta d\text{)}\end{array}$
Subband and Fermi energies	$E_0={\gamma }_0{n}_s^{2/3},E_F-E_0=\frac{\pi {\hslash }^2}{m^{\ast }}{n}_s$	${\gamma }_0={\left[\frac{9\pi \hslash q^2}{8{\epsilon }_s\sqrt{8m^{\ast }}}\right]}^{2/3}\text{(see GaN HEMT page)}$	$E_0:groundsubbandenergyinthetriangularwell$ $E_F:Fermienergy$ $m^{\ast }:channeleffectivemass$ $\hslash :reducedPlanckconstant$
Mobility (Matthiessen’s rule)	$\frac{1}{\mu }=\frac{1}{{\mu }_{lat}}+\frac{1}{{\mu }_{imp}}+\frac{1}{{\mu }_{int}}$	${\mu }_{imp}\uparrow \text{as}{d}_i\uparrow$	${\mu }_{lat}:lattice(phonon)limitedmobility$ ${\mu }_{imp}:remoteionizedimpuritylimitedmobility$ $\begin{array}{r}{\mu }_{int}:interfaceroughnessandalloy\\ limitedmobility\end{array}$
Drain current, gradual-channel region	$I_D=\frac{\mu {\epsilon }_{b}Z}{L\left(d+\Delta d\right)}\left[\left(V_{GS}-V_T\right)V_{DS}-\frac{V_{DS}^2}{2}\right]$	$V_{Dsat}=V_{GS}-V_T,I_{Dsat}=\frac{\mu {\epsilon }_{b}Z}{2L\left(d+\Delta d\right)}{\left(V_{GS}-V_T\right)}^2$	$Z,L:gatewidthandlength$ $\mu :2DEGelectronmobility$ $\text{(long-gate, mobility-limited regime)}$
Velocity-saturated current and transconductance	$I_{Dsat}=Z{v}_{sat}\frac{{\epsilon }_b\left(V_{GS}-V_T\right)}{d+\Delta d}$	$g_m=\frac{{\epsilon }_{b}Z{v}_{sat}}{d+\Delta d}$	$v_{sat}:electronsaturationvelocityinthechannel$ $\begin{array}{r}\text{(short-gate}\text{regime;}\text{the}\text{thin}\text{barrier}\\ d+\Delta d\text{gives}\text{much}\text{higher}{g}_m\text{than}\text{a}\\ \text{MESFET}\text{of}\text{the}\text{same}\text{gate}\text{length)}\end{array}$
Cutoff frequency	$f_T=\frac{g_m}{2\pi C_{gs}}\approx \frac{v_{sat}}{2\pi L_g}$	$C_{gs}\approx \frac{{\epsilon }_{b}Z{L}_g}{d+\Delta d}\text{(see Metal-Semiconductor Field-Effect Transistor page)}$	$f_T:intrinsiccurrent-gaincutofffrequency$ $L_g:gatelength$
Minimum noise figure (Fukui)	$N{F}_{min}=1+K_f\frac{f}{f_T}\sqrt{g_m\left(R_g+R_s\right)}$	$f_{max}\text{(see Metal-Semiconductor Field-Effect Transistor page)}$	$N{F}_{min}:minimumnoisefigure(linearratio)$ $K_f:empiricalfittingfactor$ $R_g,R_s:gateandsourceresistances$ $\begin{array}{r}\text{(empirical;}\text{the}\text{basis}\text{of}\text{HEMT}\\ \text{low-noise-amplifier}\text{design)}\end{array}$
Lattice mismatch (strained channel)	$f=\frac{a_{ch}-a_{sub}}{a_{sub}}$	$a(x)=(1-x)a_{\mathrm{GaAs}}+x{a}_{\mathrm{InAs}}\text{(see Ternary Compound Semiconductors page)}$	$\begin{array}{r}f:fractionallatticemismatch(about\\ 0.072xforI{n}_{x}G{a}_{1-x}AsonGaAs)\end{array}$ $\begin{array}{r}{a}_{ch},a_{sub}:latticeconstantsofthe\\ channelandsubstrate\end{array}$
Critical thickness (Matthews-Blakeslee)	$h_c=\frac{b\left(1-\nu {\cos }^2\theta \right)}{2\pi f\left(1+\nu \right)\cos \lambda }\left[\ln \left(\frac{h_c}{b}\right)+1\right]$	$b=\frac{a}{\sqrt{2}}\text{(zinc blende)}$	$\begin{array}{r}{h}_c:maximumthicknessofastrained\\ (pseudomorphic)layerbeforemisfit\\ dislocationsform(implicitequation)\end{array}$ $b:Burgersvectormagnitude$ $\nu :Poissonratio$ $\begin{array}{r}\theta ,\lambda :anglesbetweenthe\\ dislocationline,Burgersvector,and\\ slipplane\end{array}$
Lattice-matched composition on InP	$a\left({\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}\right)=a_{\mathrm{InP}}\Rightarrow x\approx 0.53$	$x\approx 0.52\text{for}{\mathrm{In}}_x{\mathrm{Al}}_{1-x}\mathrm{As}\text{(see Ternary Compound Semiconductors page)}$	$a_{\mathrm{InP}}=5.869\mathring{\mathrm{A}}$ $\begin{array}{r}{\text{(In}}_{0.53}{\text{Ga}}_{0.47}\text{As}\text{channel}\text{with}\text{an}\\ {\text{In}}_{0.52}{\text{Al}}_{0.48}\text{As}\text{barrier}\text{on}\text{InP)}\end{array}$

Important Questions

Ques: Why is the 2DEG mobility in a HEMT so much higher than in a doped MESFET channel?

In a MESFET the carriers move through the same material that contains the donors, so ionized-impurity scattering limits the mobility, especially at low temperature. In a HEMT the donors sit in the wide-gap barrier and the electrons fall across the heterointerface into the undoped narrow-gap channel, where they are spatially separated from their parent donors (modulation doping). The remaining scattering is described by Matthiessen’s rule, $1/\mu =1/{\mu }_{lat}+1/{\mu }_{imp}+1/{\mu }_{int}$: lattice scattering sets the room-temperature limit, while the remote-impurity term ${\mu }_{imp}$ is large because the electrons are separated from the donors, and grows further with the spacer thickness $d_i$. Cooling suppresses phonon scattering, so the 2DEG mobility rises sharply at low temperature, which is the basis of cryogenic low-noise amplifiers. Reference: R. Dingle, H.L. Störmer, A.C. Gossard, and W. Wiegmann, “Electron mobilities in modulation-doped semiconductor heterojunction superlattices,” Appl. Phys. Lett. 33, 665 (1978); S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: What is the trade-off in choosing the spacer thickness $d_i$?

A thicker spacer moves the donors further from the channel, which raises ${\mu }_{imp}$ and the 2DEG mobility. But it also increases the gate-to-channel distance $d+\Delta d$, which lowers the sheet density per volt, reduces $g_m={\epsilon }_{b}Z{v}_{sat}/(d+\Delta d)$ and $C_{gs}$, and shifts the threshold voltage through the $q{N}_D{d}_d{d}_i/{\epsilon }_b$ term. The result is a design compromise between mobility (low-field transport and noise) and charge control (gain and current drive), usually settled with spacers of a few nanometers. Reference: D. Delagebeaudeuf and N.T. Linh, “Metal-(n) AlGaAs-GaAs two-dimensional electron gas FET,” IEEE Trans. Electron Devices ED-29, 955 (1982).

Ques: How do the pHEMT, mHEMT, and InP HEMT differ, and why do they exist?

Raising the indium fraction of the InGaAs channel lowers the effective mass, raises the saturation velocity, and (with a suitable barrier) increases the conduction band offset, all of which raise $f_T$ and lower noise. But In${}_x$Ga${}_{1-x}$As on GaAs is lattice mismatched by about $0.072x$, so the channel can only be grown pseudomorphically (fully strained) up to the Matthews-Blakeslee critical thickness $h_c$; this limits a pHEMT to modest indium content (about $x\le 0.2$-$0.25$) and a thin channel. An InP substrate is lattice matched to In${}_{0.53}$Ga${}_{0.47}$As and can host higher-indium strained channels too, which is why InP HEMTs reach the highest frequencies. The mHEMT recovers much of the InP performance on a cheaper, larger GaAs substrate by inserting a thick graded metamorphic buffer that relaxes the lattice mismatch away from the active layers. Reference: J.W. Matthews and A.E. Blakeslee, “Defects in epitaxial multilayers I. Misfit dislocations,” J. Cryst. Growth 27, 118 (1974); S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: How does the 2DEG in an AlGaAs/GaAs HEMT differ from the one in the GaN HEMT?

In the GaN HEMT page the 2DEG density follows from the spontaneous and piezoelectric polarization sheet charge $\sigma (x)$ of the wurtzite AlGaN/GaN stack, so an undoped structure still forms a 2DEG. The zinc-blende AlGaAs/GaAs system has no comparable built-in polarization charge, so the electrons must be supplied by donors in the barrier, and the sheet density is set by the charge-control relation $n_s={\epsilon }_b(V_{GS}-V_T)/[q(d+\Delta d)]$ with a threshold that depends on $N_D$, $d_d$ and $d_i$. The subband energies ($E_0$, $E_F$) use the same triangular-well expressions in both materials, which is why that row cross-references the GaN HEMT page. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007; O. Ambacher et al., J. Appl. Phys. 85, 3222 (1999).

Related pages in this vault: GaN HEMT, Metal Semiconductor Field Effect Transistor (MESFET), Graphene Field Effect Transistor, Short Channel MOSFET, GaN HEMT (degradation), Junction Field Effect Transistor (JFET), Ternary Compound Semiconductor’s Material Values, GaAs and InP HEMT, MESFET and HBT, Angelov and Empirical FET Models.