Metal Semiconductor Field Effect Transistor (MESFET)

1. Theory

Definition: A metal-semiconductor field-effect transistor (MESFET) is a JFET whose PN gate is replaced by a Schottky (metal-semiconductor) gate on one side of a thin N-type active layer.
Same channel physics as the JFET: It uses the JFET depletion and Shockley current equations with a one-sided gate and $V_{bi}$ taken from the Schottky barrier height.
Why a Schottky gate: GaAs has no stable native oxide for a MOS gate, and a metal gate needs no extra junction doping step; the majority-carrier gate also stores no minority charge.
Threshold voltage: $V_{T} = V_{bi} - q N_{D} a^{2} /2 ε_{s}$ ; a thick or heavily doped channel gives depletion mode (normally on), a thin or lightly doped one gives enhancement mode (normally off).
Limited forward gate bias: The gate can only be forward biased to about the Schottky turn-on (a few tenths of a volt) before gate current flows.
Materials: GaAs gives high mobility for low-noise and small-signal circuits; 4H-SiC gives high critical field and thermal conductivity for RF power.

2. Working Principle

Gate control: The Schottky gate’s depletion region narrows the conducting channel as the gate becomes more negative.
Gradual-channel operation: In long gates, current saturates when the channel pinches off at the drain end.
Velocity saturation: In short gates (sub-micron) carriers reach $v_{s a t}$ before pinch-off, so $I_{D s a t}$ becomes linear in the undepleted thickness and $g_{m}$ is independent of $L$ .
High-frequency limit: The cutoff frequency $f_{T} \approx v_{s a t} /2 π L$ is set mainly by gate length and saturation velocity.
Power limit: Gate-drain breakdown and the knee voltage set the maximum RF output power, $P_{ma x} \approx I_{ma x} (B V - V_{k n ee}) /8$ in class A.
Trapping: Surface and buffer traps make the current respond slowly to the gate (dispersion), which the simple equations do not capture.

3. Applications

Current status: Largely superseded by GaAs pHEMTs for low-noise and mm-wave circuits, and by GaN HEMTs for RF power.
High-temperature and radiation-hard RF: SiC MESFETs still suit harsh-environment microwave circuits.
Historical role: GaAs MMIC amplifiers, satellite TV low-noise blocks, early cellular power amplifiers and GaAs digital logic.

Name	Formula	Related Formulae	Variables/Constants
Schottky gate built-in potential	$V_{bi} = ϕ_{B n} - ϕ_{n}$	$ϕ_{n} = \frac{k _{B} T}{q} ln (\frac{N _{C}}{N _{D}}) (see Metal-Semiconductor Contacts page)$	$ϕ_{B n} : S c h o tt k y ba r r i er h e i g h t o f t h e g a t e m e t a l$ $ϕ_{n} : d e pt h o f E_{F} b e l o w E_{C} in t h e n e u t r a l c hann e l, d i v i d e d b y q$ $N_{D} : c hann e l d o n or co n ce n t r a t i o n$ $k_{B} : B o l t z mann co n s t an t$
Gate depletion width	$W (y) = \frac{2 ε _{s} [ V _{bi} - V _{GS} + V ( y ) ]}{q N _{D}}$	$(see Junction Field-Effect Transistor and Metal-Semiconductor Contacts pages)$	$W (y) : d e pl e t i o n w i d t h a t p os i t i o n y a l o n g t h e c hann e l$ $V (y) : c hann e l p o t e n t ia l (0 a t t h e so u r ce, V_{D S} a t t h e d r ain)$
Internal pinch-off voltage	$V_{P 0} = \frac{q N _{D} a ^{2}}{2 ε _{s}}$	$W = a at V_{bi} - V_{GS} + V (y) = V_{P 0}$	$V_{P 0} : j u n c t i o n v o l t a g e a t w hi c h t h e g a t e d e pl e t i o n r e g i o n r e a c h es t h e b o tt o m o f t h e a c t i v e l a y er$ $a : a c t i v e l a y er (c hann e l) t hi c k n ess$
Threshold voltage	$V_{T} = V_{bi} - V_{P 0} = ϕ_{B n} - ϕ_{n} - \frac{q N _{D} a ^{2}}{2 ε _{s}}$	$V_{T} < 0 : depletion mode (normally on); V_{T} > 0 : enhancement mode (normally off)$	$V_{T} : g a t e - so u r ce v o l t a g e a t w hi c h t h e c hann e l i s f u l l y d e pl e t e d$ $(thinner or more lightly doped channels shift V_{T} positive; enhancement mode is limited because the gate can be forward biased only to about the Schottky turn-on, a few tenths of a volt)$
Open channel conductance	$G_{0} = \frac{q μ _{n} N _{D} a Z}{L}$	$σ = q μ_{n} N_{D} (see Basic Semiconductor Equations page)$	$G_{0} : c hann e l co n d u c t an ce w i t h n o d e pl e t i o n$ $μ_{n} : e l ec t r o n m o bi l i t y$
Drain current, gradual-channel model	$I_{D} = G_{0} {V_{D S} - \frac{2}{3} \frac{( V _{D S} + V _{bi} - V _{GS} ) ^{3/2} - ( V _{bi} - V _{GS} ) ^{3/2}}{V _{P 0}^{1/2}}}$	$I_{D s a t} = G_{0} V_{P 0} [\frac{1}{3} - x + \frac{2}{3} x^{3/2}], x = \frac{V _{bi} - V _{GS}}{V _{P 0}}$	$(same form as the Junction Field-Effect Transistor page, with G_{0} for a single gate)$ $I_{D s a t} : s a t u r a t i o n c u r r e n t (c hann e l p in c h e d o f f a t t h e d r ain e n d)$
Square-law form near threshold	$I_{D s a t} \approx β (V_{GS} - V_{T})^{2}$	$β = \frac{G _{0}}{4 V _{P 0}} = \frac{μ _{n} ε _{s} Z}{2 a L}$	$β : t r an sco n d u c t an ce p a r am e t er (e x p an s i o n o f t h e e x a c t s a t u r a t i o n c u r r e n t f or s ma l l V_{GS} - V_{T})$ $g_{m} = 2 β (V_{GS} - V_{T})$
Velocity-saturated drain current	$I_{D s a t} = q N_{D} v_{s a t} Z (a - W_{s})$	$W_{s} = \frac{2 ε _{s} ( V _{bi} - V _{GS} )}{q N _{D}}$	$v_{s a t} : c a r r i er s a t u r a t i o n v e l oc i t y$ $W_{s} : d e pl e t i o n w i d t h a t t h e so u r ce e n d o f t h e g a t e$ $(applies to short gates, where the field exceeds E_{s} = v_{s a t} / μ_{n} so carriers saturate before the channel pinches off)$
Transconductance	$g_{m} = G_{0} [1 - \frac{V _{bi} - V _{GS}}{V _{P 0}}] (gradual channel)$	$g_{m} = \frac{ε _{s} v _{s a t} Z}{W _{s}} (velocity saturated)$	$g_{m} : \partial I_{D} / \partial V_{GS} in s a t u r a t i o n$ $(in the velocity-saturated regime g_{m} is independent of L)$
Cutoff frequency	$f_{T} = \frac{g _{m}}{2 π C _{g s}} \approx \frac{v _{s a t}}{2 π L}$	$C_{g s} \approx \frac{ε _{s} Z L}{W _{s}}$	$f_{T} : in t r in s i c c u r r e n t - g ain c u t o f f f r e q u e n cy$ $C_{g s} : g a t e - so u r ce c a p a c i t an ce$ $(ideal, ignores parasitics and velocity overshoot)$
Maximum oscillation frequency	$f_{ma x} \approx \frac{f _{T} /2}{\frac{R _{g} + R _{i} + R _{s}}{R _{d s}} + 2 π f _{T} R _{g} C _{g d}}$	$f_{ma x} (commonly used small signal estimate)$	$f_{ma x} : f r e q u e n cy a t w hi c h t h e u ni l a t er a l p o w er g ain f a l l s t o u ni t y$ $R_{g}, R_{i}, R_{s} : g a t e, in t r in s i c c hann e l, an d so u r ce r es i s t an ces$ $R_{d s} : o u tp u t r es i s t an ce$ $C_{g d} : g a t e - d r ain c a p a c i t an ce$
Gate-drain breakdown and maximum class A power	$B V_{G D} \approx \frac{ε _{s} E _{cr i t}^{2}}{2 q N _{D}}, P_{ma x} \approx \frac{I _{ma x} ( B V - V _{k n ee} )}{8}$	$(see PN Junction Diode / Avalanche Diode / SiC Schottky Diode pages)$	$B V_{G D} : g a t e - d r ain a v a l an c h e b r e ak d o w n v o l t a g e (g a t e S c h o tt k y j u n c t i o n)$ $I_{ma x} : ma x im u m c hann e l c u r r e n t$ $V_{k n ee} : d r ain k n ee v o l t a g e$ $P_{ma x} : t h eor e t i c a l ma x im u m c l a ss A R F o u tp u t p o w er$

Important Questions

Ques: Why is the MESFET used in materials like GaAs and SiC, and what does a Schottky gate change compared with a JFET?

GaAs lacks a stable native oxide, so a MOSFET gate dielectric is hard to make, and forming a good p-n gate junction in a thin high-mobility channel is difficult; a metal deposited directly on the semiconductor forms a Schottky gate that needs no extra doping step. The Schottky gate is a majority-carrier device, so it injects and stores no minority carriers (see the Schottky Diode page), which keeps the gate fast. The costs are that the gate can only be forward biased up to the Schottky turn-on (a few tenths of a volt, set by $ϕ_{B n}$ ), and that the gate leakage follows the thermionic emission current of the Metal-Semiconductor Contacts page rather than a junction reverse-saturation current. The channel physics (pinch-off, saturation, transconductance) is otherwise the JFET model, with a one-sided gate. Reference: C.A. Mead, “Schottky barrier gate field effect transistor,” Proc. IEEE 54, 307 (1966); S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why do high-frequency MESFETs follow the velocity-saturated model rather than the pinch-off model?

High-frequency devices have short gates (often under a micron), so the lateral field in the channel exceeds the critical field $E_{s} = v_{s a t} / μ_{n}$ at modest drain voltages. Carriers reach $v_{s a t}$ before the channel is pinched off, and the current becomes $I_{D s a t} = q N_{D} v_{s a t} Z (a - W_{s})$ , which is linear in the depleted thickness instead of quadratic like the gradual-channel result. Differentiating gives $g_{m} = ε_{s} v_{s a t} Z / W_{s}$ , independent of gate length, and since $C_{g s} \approx ε_{s} Z L / W_{s}$ the cutoff frequency becomes $f_{T} \approx v_{s a t} / (2 π L)$ . The speed is then set only by the saturation velocity and gate length, which is why shrinking the gate is the main route to higher frequency. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: How do GaAs and SiC MESFETs differ in practice?

GaAs offers high low-field electron mobility and a small effective mass, which suit low-noise and small-signal microwave amplifiers, but it has a lower critical field and poorer thermal conductivity, which limit output power. 4H-SiC has a much higher critical field, bandgap (see the Material Constants page), saturation velocity and thermal conductivity (see the SiC Schottky Diode page), so with the class A estimate $P_{ma x} \approx I_{ma x} (B V - V_{k n ee}) /8$ it supports far higher drain voltages and power density at RF frequencies, at the cost of a lower mobility and therefore lower gain at the same gate length. SiC MESFETs are consequently found in microwave power amplifiers (for example S-band), while GaAs MESFETs are used in low-noise and moderate-power circuits. Both suffer from trapping effects (surface and buffer traps) that make the current respond slowly to the gate, an important practical effect that the simple equations on this page do not capture. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why is enhancement-mode MESFET operation limited?

An enhancement-mode device needs $V_{T} > 0$ , which requires a very thin or lightly doped channel so that the built-in depletion alone pinches off the channel at zero gate bias. At the same time, the gate cannot be forward biased much beyond about the Schottky turn-on without large gate current, so the usable gate swing is only a few tenths of a volt. This small swing limits the output current and noise margin of logic circuits built from enhancement-mode MESFETs, and it requires tight control of channel thickness and doping since $V_{T}$ depends on $a^{2} N_{D}$ . Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

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