09 Heterojunction FET (HFET) principles
MOSFET and HFET devices are both very
similar to a plain capacitor
Metal
A
V
d
Semiconductor
Let the area of the capacitor plates be A.
The induced charge Q can be expressed as
Q = q × A × ∆nS,
where q = 1.6 ×10-19 C is the electron charge,
∆nS is the SURFACE CONCENTRATION of induced electrons, ∆nS = Q / (q × A);
What is the surface concentration?
The bulk charge density, n
the layer thickness, a;
then the surface concentration,
nS = n × a
1x1 cm2
a
Estimation of induced charge
Metal
V
A
d
Semiconductor
For the PLAIN CAPACITOR, C = ε ε0 ×A/d
Q = C × V = ε ε0 ×A×V/d,
The induced concentration of electrons (which are negatively charged) in
the top (metal) plate:
∆nSM = - ε ε0 ×V/(q×d) <0;
in the bottom (semiconductor) plate:
∆nS = ε ε0 ×V/(q×d) >0;
For a given voltage, V, the induced charge increases as we decrease d
The threshold voltage of FETs
Suppose the semiconductor plate is doped with donor concentration ND;
The equilibrium electron concentration in the semiconductor, n0 = ND;
For the layer thickness, a, the surface concentration nS0 = ND ×a;
The voltage needed to deplete the entire active layer ( the semiconductor plate) is
referred to as the THRESHOLD VOLTAGE of the FET
For the n-doped layer the threshold voltage is negative in order to repulse the electrons.
The induced concentration at the threshold has to compensate the equilibrium one:
∆nST = ε ε0 ×VT/(q×d) = - nS0
Therefore,
VT = - q×d ×nS0/ (ε ε0)
The charge control model of FETs
At the threshold the net concentration in the channel is zero:
∆nST – nS0 = 0, where ∆nST = ε ε0 ×VT/(q×d)
When the applied voltage is above the threshold, V > VT,
∆nS = ε ε0 ×V/(q×d)
nS = ∆nS – ∆nST = ε ε0 /(q×d) × (V – VT)
Note, ε ε0 /d = C1 the gap capacitance per unit area
Therefore,
nS = (C1/q) × (V – VT)
The above model is referred to as “charge control model” of FETs
FETs: general design considerations
Low drain bias
The gate length L
The current through the channel is
V0
I=
R
+
where V0 is the voltage applied
between the DRAIN and the SOURCE
V-
+
V0
G
S
D
Semiconductor
We are assuming that V0 << VT (we will see why, later on)
The channel resistance, R (Z is the device width):
R=
L
qnµ aZ
=
L
q ns µ Z
The channel current is then: I = V0 (q nS µ Z) /L = V0 q µ Z (C1/q) × (V – VT) /L
I = V0 µ Z C1 × (V – VT) /L
FETs: general design considerations
Low drain bias
The gate length L
I = V0 µ Z C1 × (V – VT) /L
The transconductance, gm = dI/dV;
The gm is the “responsivity” of FET.
In the linear mode under consideration
(V0 << V),
gm = V0 µ Z C1 /L
+
-
V-
+
V0
G
S
D
Semiconductor
The main factors affecting FET performance (for any FET type):
µ
I and gm
L
I and gm
Carrier mobility in the channel and the gate length are crucial parameters of any FET
Different types of FETs
Metal - Oxide - Semiconductor FET (MOSFET)
d
W
The gate-channel insulator is made out of dielectric (SiO2), ε = 3.9
Different types of FETs
Junction FET (JFET)
a0
W
a
The gate-channel insulator consists of the DEPLETION REGION,
i.e. the same material as the channel.
For GaAs, ε ~ 12; for GaN ε ~ 9.
Different types of FETs
Metal-Semiconductor FET (MESFET)
a0
a
The gate is formed by Schottky barrier to the semiconductor layer.
The gate-channel insulator consists of the DEPLETION REGION,
i.e. the same material as the channel. Very similar to the JFET
The Heterojunction Field-Effect Transistor (HFET)
The channel of HFETs is formed by 2D electron gas (2DEG)
Channel
induced channel (2DEG)
electrons
HFET
JFET, MOSFET, MESFET
Effects of high drain bias on FET characteristics
MOSFET
JFET
+
VG
Source
Gate
+
VD
The gate- to drain voltage difference depends on the position along the gate
So does the induced charge
Drain
Effects of high drain bias on FET characteristics
The particular range of the gate
voltage depends on the device
type
The channel narrowing at the drain edge of the gate causes current
saturation in the FETs
Effects of high drain bias on FET characteristics
Electron velocity saturation due to high electric field in the channel
Velocity saturation due to high
electric field in the channel also
results in the I-V saturation
The average electric field in the channel, Eav ~ V0 /L
Can be extremely high for small L
I = V0 µ Z C1 × (V – VT) /L
I = vS Z C1 × (V – VT)
v = µ × E ~ µ × V0 /L
The Heterojunction Field-Effect Transistor (HFET)
The channel of HFETs is formed by 2D electron gas (2DEG)
electrons
induced channel (2DEG)
after T.A. Fjeldly, T. Ytterdal and M. Shur, 1998
Undoped active layer
Very high NS;
very high µ;
very high vS (in sub-µ HFETs)
1960 - Accumulation layer prediction (Anderson)
1969 - Enhanced mobility of 2DEG prediction
(Esaki & Tsu)
1978 Enhanced mobility observed (Dingle et. al.)
1980 The first Heterojunction FET (HFET)
1991 The first GaN based HFET (A. Khan)
The Heterojunction Field-Effect Transistor (HFET)
A.k.a. High electron mobility FETs: why?
1) Mobility depends on the interactions between electrons and phonons and impurities.
For the phonon scattering, the dependence of mobility on temperature:
For the impurity scattering, the dependence of mobility on impurity concentration, N:
When the dependence on both temperature and impurities is taken into account,
The Heterojunction Field-Effect Transistor (HFET)
Concentration dependence of electron mobility
T = 300 K
The Heterojunction Field-Effect Transistor (HFET)
Electron Drift velocity
The electron accelerates in the electric field until it gains enough energy to excite lattice
vibrations:
m n v n2 max
= E n − E o ≈ hω l
2
where vnmax is the maximum electron drift velocity. Then the scattering
process occurs, and the electron loses all the excess energy and all the drift
velocity. Hence, the electron drift velocity varies between zero and vnmax,
and average electron drift velocity (vn = vnmax/2) becomes nearly
independent of the electric field:
vn ≈
hω l
= v sn
2m n
Typically, vsn ≈ 105 m/s. Indeed, the measured drift
velocity becomes nearly constant in high electric fields
The Heterojunction Field-Effect Transistor (HFET)
Electron Drift velocity
3
InGaAs
electron velocity (100,000 m/s)
InP
GaAs
2
1
Heavily doped
Si
T = 300 K
0
0
5
10
15
20
electric field (kV/cm)
In the heavily doped materials the peak electron velocity is lower
The HFET basics
metal
AlGaAs
GaAs
qVN
∆E c
qφb
Ec
Ec
qVFB
qϕb
E Fi
E Fp
di
Ev
Considering first the band diagram of an AlGaAs/GaAs HFET with flat bands in the
GaAs buffer. As can be seen from this figure, the flat-band voltage is given by
VFB = φ b − V N − (∆Ec + ∆E F ) / q
The HFET basics
The HFET basics
qVN
F
Fi
Charge and field profiles
Band diagram
From the Poisson equation,
Fi =
qns
ε 0ε s
At the threshold, ns~0 --> Fi ~0
The HFET basics
HFET threshold voltage
When ns is close to zero, the Fermi level in the
GaAs is close to the bottom of the conductance
band. Therefore,
qN d di2
− ∆Ec / q
VT ≈ φ b −
2ε i
For non-uniform doping profile,
di
N d (x)
x dx
VN = q ∫
ε (x)
0 i
For the “delta-doped” barrier layer,
VT ≈ φ b − qnδ dδ / ε i − ∆Ec / q
The HFET basics
HFET I-V characteristics
Above the threshold the HFET is similar to MOSFET, i.e.
qns = ci [VGT − V ( x )]
where VGT = VG - VT
The drain current:
Id = Wµ n qns F = Wµ nc i (VGT − V )
[
]
dV
dx
⎧ V V − V 2 / 2 , for V ≤ V
DS
SAT
Wµ n ci ⎪ GT DS
DS
Id =
×⎨
L
2
⎪⎩VGT
/ 2,
for VDS > VSAT
where VSAT = VGT
The HFET basics
HFET I-V characteristics
The transconductance,
gm =
⎧⎪βV
,
DS
gm = ⎨
⎪⎩βVGT ,
dId
dVGS V DS
for VDS ≤ VSAT
for V
DS
>V
SAT
where β = Wµnci /L is called the transconductance parameter.
The HFET basics
HFET I-V characteristics
Velocity saturation in HFETs
A two-piece model is a simple, first approximation to a realistic velocity-field
relationship:
⎧ µF , F < Fs
v ( F) = ⎨
⎩ vs , F ≥ Fs
1.2
m=
More realistic velocity-field relationships :
v ( F) =
m=2
0.8
µF
[1+ (µF / vs ) ]
m=1
m 1/m
where m = 1….2
0.4
0.0
0
1
2
Normalized Field
3
The HFET basics
HFET I-V characteristics
Velocity saturation in HFETs
[
]
⎧ V V −V2 / 2 ,
GT DS
DS
Wµ n ci ⎪
×⎨
Id =
L
⎪VL2 ⎡ 1 + (VGT V L )2 − 1⎤ ,
⎥⎦
⎩ ⎢⎣
for VDS ≤ VSAT
for VDS > VSAT
⎡
⎤
2
VSAT = VGT − VL ⎢ 1+ (VGT / V L ) − 1⎥
⎣
⎦
where VL = Fs L.
For VL >> VGT, we arrive to the same expression as with the constant mobility case.
The HFET basics
HFET I-V characteristics
Velocity saturation in HFETs
[
]
⎧ V V −V2 / 2 ,
GT DS
DS
Wµ n ci ⎪
×⎨
Id =
L
⎪VL2 ⎡ 1 + (VGT V L )2 − 1⎤ ,
⎥⎦
⎩ ⎢⎣
for VDS ≤ VSAT
for VDS > VSAT
⎡
⎤
2
VSAT = VGT − VL ⎢ 1+ (VGT / V L ) − 1⎥
⎣
⎦
where VL = Fs L.
In the opposite limit, when VL << VGT, we obtain
VSAT ≈ VL
Isat ≈ βVLVGT
where β = Wµnci /L is the transconductance parameter.