Lecture 6: III-V FET DC I - MESFETs
Metal-Semiconductor Junction
Basic MESFET Operation
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Lecture 6, High Speed Devices 2014
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Field Effect Transistors
Vg
Lg
W
Gate
Source
Drain
y
VDS
N+
N+
x
• The gate electrode controls the carrier concentration in the channel
• Source/Drain set the potential at the source/drain side
• Electrons flow from source to drain  IDS and n(x,y) depend on geometry
and transport properties.
• 2D problem (in x and y)
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Lecture 6, High Speed Devices 2014
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Field Effect Transistors
Bulk MOSFET
Metal
Vg=1V
SOI, Quantum Well MOSFET
VD=1V
Metal
Oxide
Oxide
n+
n+
p-type
n-
n+
n+
Oxide or wide bandgap Semicondudctor
p-type, S.I. Insulating
MESFET
Metal
n+
Vg=-1V
Depletion
region
n
n+
p-type, S.I. Insulating
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Metal
HEMT
Wide band
semiconductor
n+
n-
n+
Wide band
semiconductor
p-type, S.I. Insulating
Lecture 6, High Speed Devices 2014
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Si vs. III-V Field Effect Transistors (FETs)
• III-V MOSFETs are difficult to
fabricate
• Alternative: Semiconductor
to isolate the gate from the
channel
• Simple: MESFETs
• Better: HEMTs or III-V
MOSFETs
Si: µn≤ 1300 Vs/cm2. vsat ≈ 8×106 cm/s
InGaAs µn ≈ 14000 cm2/Vs! vsat ≈ 2×107 cm/s
SiO2-Si excellent interface
InGaAs- GaOxInOxAsOx – poor interface
SiO2/HfSiO2
Schottky
Barrier
n+
n+
n+
Si p-type
GaAs n
n+
GaAs Semi-Insulating
An Si MOSFET uses an oxide (SiO2,
SiHfO2) to isolate the gate
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A III-V Metal-Semiconductor
FET (MESFET)
Lecture 6, High Speed Devices 2014
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Metal-Semiconductor Junction
Similar to a p+N junction!
qcs
qfm
Fb
qfb  qfm  qc s
Fn
fbi  fb 
q
qfn
Fb
fbi
Schottky barrier height
Build in potential
Too simplistic!
However, now we ignored that we terminated the crystal and
created a lot of surface states....
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Lecture 6, High Speed Devices 2014
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Metal-Semiconductor Junction II
Experiments show only a very weak
dependence of fb as a function of metal
work function
fb
qfb
fm
Surface reconstruction and surface defects create a large
number of states in the bandgap, which “pins” the Fermienergy
The energy position of these surface states sets the
Schottky barrier height. For GaAs, fb≈0.7-0.8V
InP fb ≈ 0.3V, InAs fb ≈ -0.1V, In0.53Ga0.47As fb ≈ 0.1V
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Lecture 6, High Speed Devices 2014
Fn
fbi  fb 
q
fb is a material
parameter!
6
MESFET Structure – simplest FET transistor
Vgs (negative)
Source
Gate
Drain
x
Depletion
Region: n≈0
Nd
a
b
y
Semi-insulating
•Schottky depletion under gate modulates channel thickness b
•VDS causes current to flow from source to drain, which can be
modulated by Vgs
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Lecture 6, High Speed Devices 2014
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Metal-Semiconductor Junction III
d q
 Nd
dy  s
 y 
q
r
s
N d X dep  y 

y2 
fs  y   N d  X dep y  
s 
2 
q
dfs
( X dep )   ( X dep )  0
dy
fs (0)  0
Xdep a
Ref.
potential
y
X dep 
2 s
fbi  Va 
qN d
qN d 2
f00 
a
2 s
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Depletion thickness, maximum Xdep=a
Potential needed to fully
deplete down to a
Lecture 6, High Speed Devices 2014
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2 minute exercise – part 1
Depletion Edge
Vgs=0 Vgs=-1V
A
B
C
D
Black – Vg = 0V
Which green plot corresponds to Vgs=-1 V?
Remember: negative bias increases the potential energy of an electron!!
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Lecture 6, High Speed Devices 2014
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2 minute exercise – part 2
Vsub=1V
Vgs
Vgs=-1V
Vsub +
-
Depletion
egdes
Black plot – Vg and Vsub = 0V
Which red plot corresponds to Vgs=-1 V and
Vsub = 1V?
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Lecture 6, High Speed Devices 2014
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MESFET Operation
VDS +
-
Vgs
Id
Id
Vcs=0
Vcs(x)
Vcs=Vds
Resistive voltage drop along channel
DVgs
DVgs
DVgs
VDS
The potential under the gate is set by the channel-gate potential Vcs(x)
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Lecture 6, High Speed Devices 2014
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Calculation of the current
VDS +
-
Vgs
fs(x,0)=0
Id
𝐽𝑛 = 𝑞𝜇𝑛 𝑛𝛻𝑉
𝛻 ∙ 𝐽𝑛 = 0
𝜕2𝜙 𝜕2𝜙
−𝑞
+
= ∆𝑉 =
𝑁𝑑 − 𝑛
𝜕𝑥 2 𝜕𝑦 2
𝜀𝑠
Complicated 2D problem!
y
x
GCA – Gradual Channel approximation: d2f/dx2<<d2f/dy2
𝜕 2 𝜙 −𝑞
=
𝑁𝑑
𝜕𝑦 2
𝜀𝑠
𝜕𝜙(𝑥, 𝑏)
𝐽𝑛 = 𝑞𝜇𝑛 𝑛
𝜕𝑥
𝑑𝐽𝑛 (𝑥)/𝑑𝑥 = 0
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Xdep(x) varies slowly with x
Electric field in x-direction is ‘small’
Lecture 6, High Speed Devices 2014
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Drift Current
ich x   qWN d  n x bx 
Drift current
ich
 0  ich x    I D
x
Continuity
fs  x 
X dep  a
f00
bx   a  X dep
fs x   fbi  Vgs  Vcs (x)

fs x  

 a 1 
f00 

fs x 
 x   
x
Gradual channel approximation
b(x) varies slowly with x
b(x) is determined by solving fs(y)
Depletion
E-field

f L  
fs x   fs x  
fs 


x I D dx  qWN d n a x 1  f00  x dx  qWN d n a f  x  1  f00 dfs




L
L
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Lecture 6, High Speed Devices 2014
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Saturation Voltage, Pinch-off
Vds=0V
Vds>0>VDS,sat
Vds=VDS,sat
Vds>VDS,sat
At pinch-off, the depletion region reaches the S.I
region
Our 1D-decoupled model breaks down:
(d2f/dx2>>0) we need to solve 2D possion
equation, Dfs(x,y) (numerical solutions needed)
Result: Channel of finite thickness forms at
channel edge. Increased Vds drops inside this
region, or between channel-drain.
Current remains independent of Vds after Vds,sat
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VDS ,sat  f00  fbi  Vgs
Lecture 6, High Speed Devices 2014
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Current-Voltage Characteristics
fs  x 
fs 0
fs L 
u ( x) 
s
d
f00
f00
f00
ID 
s
fbi  Vgs
f 00
qWN d  n af00 
2 3/ 2 2 3/ 2 
d

s

d  s  d  fbi  Vgs  VDS V  V

DS
DS , sat
L
3
3


f
00
d
0.16
Vgs=0
0.14
qN d 2
f00 
a
2 s
VDS , sat  f00  fbi  Vgs
Ids - arb units
0.12
0.1
0.08
Vgs<0
0.06
0.04
VT  fbi  f00
0.02
0
0
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fbi  Vgs  VDS , sat
 1 VDS  VDS , sat
f 00
0.5
1
1.5
Vds
2
2.5
Pinch-off voltage
Threshold Voltage
3
Vgs=-|VT|
Lecture 6 High Speed Devices 2014
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MESFET limitations
I D , sat
gm 
qWN d  n af00  1
2 3/ 2 

 s s 
L
3
3

dI D , sat
dVgs
fbi  Vgs
qWN d  n a 

1

L
f00





• We want a high gm – but:
•
Positive gate-voltage – very high gate leakage!
• From electrostatics: a<L/3
• Increase ND – but this lowers µn due to impurity scattering and increases
gate leakage!
• Increase µn by material choice: Need to have a high Schottky barrier!
(InGaAs, InAs can’t be used!)
•
We can do better using heterostructures or MOSFETs!
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Lecture 6, High Speed Devices 2014
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