Institute of Solid State Physics
Technische Universität Graz
JFETs - MESFETs - MODFETs
Junction Field Effect Transistors (JFET)
Metal-Semiconductor Field Effect Transistors (MESFET)
Modulation Doped Field Effect Transistors (MODFET)
n
JFET
n-channel JFET
n
For NA >> ND
2ε (Vbi − V )
xn =
eN D
Depletion mode
Enhancement mode
h > xn =
2ε Vbi
eN D
2ε Vbi
h < xn =
eN D
conducting at Vg = 0
nonconducting at Vg = 0
n-channel JFET
drain
depletion region
p
n
p
gate
JFETs are often discrete devices
source
MESFET
Metal-Semiconductor Field Effect Transistors
n
Depletion layer created by Schottky barrier
xn =
2ε (Vbi − V )
eN D
Fast transistors can be realized in n-channel GaAs, however GaAs has
a low hole mobility making p-channel devices slower.
JFET
n
D
n-channel JFET
G
2ε (Vbi − V )
xn =
eN D
S
n-channel JFET
Pinch-off at h = xn
eN D h 2
Vp =
2ε
At Pinch-off, Vp = Vbi - V.
D
G
S
p-channel JFET
Vp = pinch-off voltage
Pinch-off at h = xn
eN D h 2
Vp =
2ε
JFET
JFET
xL
h
xn
xR
h
dV.
dV = I D dR = I D
ρ dy
Z (h − xn ( y ))
1
1
1
ρ= =
=
σ neμn N D eμn
dV = I D
ID is constant throughout the transistor
dy
eμn N D Z (h − xn ( y ))
I D dy = eμn N D Z (h − xn ( y ))dV
JFET
xL
h
xn
xR
h
VG is a forward bias
V(y) is a reverse bias.
dV.
depletion width is a function of position xn ( y ) =
differentiate
2ε (Vbi + V ( y ) − VG )
eN D
dxn ( y ) 1 ⎛ 2ε (Vbi + V ( y ) − VG ) ⎞
= 2⎜
⎟
dV
eN
D
⎝
⎠
dV =
eN D xn
ε
dxn
−1/ 2
2ε
ε
=
eN D eN D xn ( y )
JFET
xL
h
xn
h
xR
from last slides
I D dy = eμn N D Z (h − xn ( y ))dV
dV =
eN D xn
ε
dxn
I D dy = eμn N D Z (h − xn ( y ))
L
I D ∫ dy = eμn N D Z
0
eN D
ε
eN D
ε
xn dxn
xR
∫ (h − x ( y)) x dx
n
n
n
xL
μn N D2 Ze 2 ⎡
2
2
3
3
2
⎤
ID =
h
x
x
x
x
−
−
−
(
)
(
)
R
L
R
L
3
⎣
⎦
2 Lε
JFET
xn
xL
h
xR
h
μn N D2 Ze 2 ⎡
2
2
3
3
2
⎤
ID =
h
x
x
x
x
−
−
−
(
)
(
R
L
R
L )⎦
3
⎣
2 Lε
h=
2ε V p
eN D
2ε (Vbi − VG )
xL =
eN D
xR =
2ε (Vbi − VG + VD )
eN D
JFET - drain current
⎡V
2 ⎛ Vbi + VD − VG
D
⎢
ID = I p
− ⎜
Vp
⎢ V p 3 ⎜⎝
⎣
μn N D2 Ze 2 h3
Ip =
2 Lε
valid in the linear regime
(until pinch-off)
⎞
⎟⎟
⎠
3/ 2
2 ⎛ Vbi − VG
+ ⎜
3 ⎜⎝ V p
⎞
⎟⎟
⎠
3/ 2
⎤
⎥
⎥
⎦
Junction FET simulation
http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/jfet.html
JFET - Linear regime
⎡V
2 ⎛ Vbi + VD − VG
D
⎢
ID = I p
− ⎜
Vp
⎢ V p 3 ⎜⎝
⎣
⎞
⎟⎟
⎠
3/ 2
In the linear regime VD << Vsat.
⎡1
dI D
1 ⎛ Vbi + VD − VG
⎢
= Ip
− ⎜
dVD
Vp
⎢V p V p ⎝⎜
⎣
⎞
⎟⎟
⎠
Ip ⎡
V −V
dI D
ID ≈
VD =
⎢1 − bi G
dVD
V p ⎢⎣
Vp
⎤
⎥ VD
⎥⎦
variable resistor
1/ 2
⎤
⎥
⎥
⎦
2 ⎛ Vbi − VG
+ ⎜
3 ⎜⎝ V p
⎞
⎟⎟
⎠
3/ 2
⎤
⎥
⎥
⎦
JFET - Saturation regime
⎡V
2 ⎛ Vbi + VD − VG
D
⎢
ID = I p
− ⎜
Vp
⎢ V p 3 ⎜⎝
⎣
⎡1
dI D
1 ⎛ Vbi + VD − VG
⎢
= Ip
− ⎜
dVD
Vp
⎢V p V p ⎜⎝
⎣
1/ 2
⎞
⎟⎟
⎠
⎞
⎟⎟
⎠
3/ 2
⎤
⎥=0
⎥
⎦
set dID/dVD = 0 to find Vsat
Vsat = V p − Vbi + VG
I sat
⎡1 V −V
2 ⎛ Vbi − VG
bi
G
⎢
= Ip −
+ ⎜
3 ⎜⎝ V p
Vp
⎢3
⎣
⎞
⎟⎟
⎠
2 ⎛ Vbi − VG
+ ⎜
3 ⎜⎝ V p
3/ 2
⎤
⎥
⎥
⎦
⎞
⎟⎟
⎠
3/ 2
⎤
⎥
⎥
⎦
JFET - transconductance
In the saturation regime,
I sat
⎡1 V −V
⎛ Vbi − VG
2
bi
G
= Ip ⎢ −
+ ⎜
3
3 ⎜⎝ V p
V
⎢
p
⎣
transconductance
dI sat I p ⎛
Vbi − VG
gm =
= ⎜1 −
dVG V p ⎜⎝
Vp
⎞
⎟
⎟
⎠
dI sat 2 Z μn eN D h ⎛
Vbi − VG
gm =
1
=
−
⎜
⎜
dVG
L
Vp
⎝
⎞
⎟
⎟
⎠
⎞
⎟⎟
⎠
3/ 2
⎤
⎥
⎥
⎦
JFET
High frequencies
iin = 2π fCG vG
iout = g m vG
iin < iout
for gain:
f <
average capacitance:
gm
= fT
2π CG
CG = ZL
ε
xn
μn eN D h 2
fT =
2πε L2
fT is the frequency
where the gain drops
below 1
For velocity saturation, the approximation dV = I D
Ohm's law assumes vd = μE
fT ≈
vs
L
ρ dy
Z (h − xn ( y ))
is not valid
JFET/MESFET
JFET: small gate current (reverse leakage of the gate-to-channel junction)
More gate leakage than MOSFET, less than bipolar.
JFET has higher transconductance than the MOSFET.
Used in low-noise, high input-impedance op-amps and sometimes used in
switching applications.
MESFET: usually constructed in compound semiconductor technologies
lacking high quality surface passivation such as GaAs, InP, or SiC, and are
faster but more expensive than silicon-based JFETs or MOSFETs.
Production MESFETs are operated up to approximately 30 GHz, and are
commonly used for microwave frequency communications and radar.
Majority carrier device (like Schottky diode).
MODFET (HEMT)
Modulation doped field effect transistor (MODFET)
High electron mobility transistor (HEMT)
Modulation doped field effect transistor
High electron mobility transistor
VT = Threshold voltage = voltage where charge is depleted
Heterostructure
pn junction formed from two semiconductors with different band gaps
undoped channel
PhD Thesis Sergey Smirnov
http://www.iue.tuwien.ac.at/phd/smirnov/node71.html
MODFET (HEMT)
j = nevd = neμn E y
I = jZt = Zeμn ns E y
ns
n=
t
t is the thickness of the 2DEG
ns is the sheet charge at the interface in C/cm2.
VG − V ( y ) is the voltage between the gate and the 2DEG
q = CV
−ens ( y ) = Cg (VG − V ( y ) − VT ) is the charge on the 2DEG
The charge is zero when
VG − V ( y ) = VT
solve for ns
ns ( y ) =
−Cg (VG − V ( y ) − VT )
e
MODFET (HEMT)
I = jZt = Zeμn ns E y
ns ( y ) =
−Cg (VG − V ( y ) − VT )
e
substitute ns in the top equation and substitute
dV ( y )
I = Z μnC (VG − VT − V ( y ) )
dy
integrate along the length of the channel
L
VD
∫ Idy = ∫ Z μ C (V
n
0
G
− VT − V ( y ) ) dV
0
⎡
VD2 ⎤
Z
I D = μnC ⎢(VG − VT ) VD − ⎥
2 ⎦
L
⎣
− dV ( y )
Ey =
dy
MODFET (HEMT)
⎡
VD2 ⎤
Z
I = μnC ⎢(VG − VT ) VD − ⎥
2 ⎦
L
⎣
dI
Z
= μnC ⎡⎣(VG − VT ) − VD ⎤⎦ = 0
dVD L
Set the derivative = 0 to find
saturation voltage
Vsat = (VG − VT )
Substitute the saturation voltage into the formula at the top to find
saturation current
Z
2
I sat =
2L
μnC (VG − VT )
MODFET/HEMT
HEMT: HEMT devices are found in many types of equipment ranging from
cell phones and DBS receivers to electronic warfare systems, microwave
and millimeter wave communications, radar, and radio astronomy. 600 GHz