Lecture 7: High Electron Mobility Transistor
2014-01-30 1 Lecture 7, High Speed Devices 2014
• Modulation Doping
• HEMT/HFET/MODFET
• Device structure • Threshold voltage • Calculate the current using drift • Effect of velocity saturation
Fundamental MESFET Problems
2014-01-30 2 Lecture 7, High Speed Devices 2014
d
nN
1
Semi-insulating
Vgs (negative) Source Gate Drain
y
a Nd b
Depletion Region
00
1
gsbindm
V
L
aNg
2
002
aqN
s
d
High doping degrades mobility and causes gate leakage!
Depletion thickness (a-b) must be large (~ 50 nm) to avoid tunneling! Lg ≈≥ 3×a to avoid ”short channel effects”
gmmax,mesfet ~ 0.3 mS/µm gmmax,HEMT ~ 2.7 mS/µm High doping increases 00!
Heterostructure FET
2014-01-30 3 Lecture 7, High Speed Devices 2013
Nd
InAlAs AlGaAs AlSb
(In)GaAs
d Nd~0
Nd~0
Ef
Ec
Electrons accumulate in the (In)GaAs
Gate
tb
tb
+ µn can be very large – no channel doping + High electron concentration in channel + InGaAs channel – higher mobility + InAlAs barrier (Eg=1.5 eV) – large B
+ tb thin (5-10 nm!)– large bandgap ”barrier” limits tunneling leakage (Lg>3tb) - More advanced design – requires heterostructure growth ND is used to tune the threshold voltage/access resistance.
y
Two dimensional electron gas
2014-01-30 4 Lecture 7, High Speed Devices 2013
Nd WG
NG
d Nd~0
Nd~0
Ef
Ec
E1
E2
Part of wavefunction that penetrates into WG should also be kept away from any impurities d
y
• Electrons are confined in the y-direction
• Forms an quantum well! (Triangular or square) – 2-dimensional electron system system
• 2D density of states!
Modulation Doping II: 2D Density of states
2014-01-30 5 Lecture 11, High Speed Devices 2013
0
, fEEfEdEDn
DEEEE
mED
DEEmh
ED
DEmm
ED
n
n
n
D
n
nD
D
12
24
32
*
1
*
22
32
**
3
kT
EEDkT
kT
EEDkTn
ff
s
21exp1lnexp1ln
f(E,Ef) – Fermi-Dirac
32212
21
1
1
2
00
EEEEEDEED
EEE
EE
EEDn
ff
f
f
fs
*
2
4 m
hD
For T=0K – Fermi Dirac is a step function
E1 E2
D
2D
Ef
𝑛𝑆 = 𝑁2𝐷𝐹0(𝜂𝐹,𝑖)
𝑁2𝐷 =4𝜋𝑘𝑇
ℎ2𝑚Γ∗
2 minute excercise
2014-01-30 6 Lecture 11, High Speed Devices 2013
ns
Ef EC E1 E2
EC
E1
E2
Plot ns as Ef is varied in the quantum well T=0K
EF
Modulation Doping III: Energy Levels
2014-01-30 7 Lecture 11, High Speed Devices 2013
E1
E2
xqV i 2,~ s
si
qn
2,
3/2
2,*
2
4
1
2
3
28
nq
m
hE in
kT
nkEDkTn
sf
s
3/2
1exp1ln
Triangular Well: En depends of charge in well.
Square well: En almost independent of ns
AlGaAs
AlGaAs
InGaAs
E1
E2
tw
2
22
*8 w
ntm
nhE Infinite square well
kT
EEDkTn
f
s
1exp1ln
Ef
Ef vs ns for a QW
2014-01-30 8 Lecture 11, High Speed Devices 2011
0 1 2 3 4 5 6 7
x 1016
0
0.05
0.1
0.15
0.2
0.25
ns (m-2)
E f (eV
)
T=300K
T=10K
1st subband
2nd subband Ef
Ef0
Ef(ns)-Ec=Ef0+ans
01 fss
f ED
nE
D
nE 2D QW
Electron concentration: ns(Vg)
2014-01-30 9 Lecture 7, High Speed Devices 2013
AlGaAs
GaAs
d
tb
qB
-qVGB
qG,1
DEc Ef
y
tb
d
Charge
Nd,1
Nd,1 Nd,2≈0
y
s
dqN
x
1,
ns
s
si
qn
bt
G dxxqq0
1,
fGBBcG EqVqEq D 1,
D BGB
sfc
b
s
d
b
ss V
q
nEEt
qN
tqn d
)(
2
21,
0 (ref. level)
EC
-field
Channel Charge Equation
2014-01-30 10 Lecture 7, High Speed Devices 2014
D
D B
fc
b
s
d
GB
bb
ss
q
EEt
qNV
ttqn d
021,
2
Ef –Ec0needs to change as ns changes
01 fss
f ED
nE
D
nE Quantum well, T=0K
D BGB
sfc
b
s
d
b
ss V
q
nEEt
qN
tqn d
21,
2
*
2
2 4 m
h
qt sb
D
Triangular well needs numerical approximation, Dtb~68Å for GaAs, Ef0 ~ 0.058 eV
2Å (Si) 24Å (GaAs) 74Å (InAs)
TGBoxs VVCqn '
Identical to that of an MOSFET!
A HEMT without doping in the barrier is essential equivivalent to a FD-SOI Si MOSFET
Dtb ? - Semiconductor (Quantum) Capacitance
2014-01-30 11 Lecture 7, High Speed Devices 2014
Triangular well needs numerical approximation, Dtb~68Å for GaAs, Ef0 ~ 0.058 eV
MIM Capacitor:
VCn oxs DDSemiconductor quantum well
DqC
Dqn
EEqDn
q
fs
fs
2
2
1
DD
Cox
Cq
There must be a voltage drop over the oxide and the semiconductor!
𝐶𝑜𝑥′ =
𝜖𝑠𝑡𝑏 + Δ𝑡𝑏
𝐶𝑜𝑥′ =𝜖𝑠𝑡𝑏
Ordinary parallell-plate capacitor MOS capacitor
HEMT Structure – IV Calculation
2014-01-30 12 Lecture 7, High Speed Devices 2014
Wide bandgap Nd
Wide bandgap intrinsic
Wide bandgap, S.I or intrinsic
Vgs Source Drain
Small bandgap, triangular or square well
VDS
),()(,' ' txvVtvCtxq csTGSoxch
x
x=0 x=L
x
Charge (cm-2)
Total potential difference over wide bandgap region: (Vgs-VT)-Vchannel(x)
This is the same fundamental equation as for an ordinary
MOSFET!
HEMT on-Current – drift only
2014-01-30 13 Lecture 11, High Speed Devices 2013
),()(,' txvVtvtt
txq csTGS
bb
sch
D
D '
00
0
q
EEV
fc
BT
21,'
002
d
b
s
dt
qN'
oxC
2
2
2'
,
2'
)(
)0(
'
0
TGSnoxsatD
DSDSTGS
noxD
LV
V
cscsTGSnox
L
D
VV
L
WCI
VVVV
L
WCI
dVVVVL
WCdxI
cs
cs
satDSDS
satDSDS
VV
VV
,
,
satDSDS
satDSDS
satDS
DS
satDD
VV
VVV
V
II
,
,
,
2
,
0
11
TGSsatDS VVV ,
Long channel current saturates when qch(L)=0
Written using saturation index
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
Voltage (V)
Cu
rre
nt (m
A)
Vgs-VT=2V
Vgs-VT=1.33V
Vgs-VT=0.67V
Channel potential - DC
2014-01-30 14 Lecture 7, High Speed Devices 2014
),(
),()(),(
txuxU
txvVtvtxu
chch
csTGSch
2
0
2
22'22' LUU
L
WCLUxU
xL
WCI CHCHnoxCHCHnox
D
0
0
CHCH
TGSCH
ULU
VVU
2110 L
xUxU CHCH
We will use this extensively for the AC-analysis of the HEMT
x
xUx
xUCtxq
chch
choxch
','
Assuming drift only – simple analytical expressions for qch and ch is obtained!
Short Channel Effects – Velocity Saturation
2014-01-30 15 Lecture 7, High Speed Devices 2014
TGSnox
m VVL
WCg
'
High gm: Decrease L!
𝜀 𝑥 =𝑈𝐶𝐻 0
𝐿1 − 𝛼2
1
1 −𝑥𝐿 1 − 𝛼
2
Channel Electric Field
Dri
ft V
elo
city
(V
/cm
)
Vsat
Epeak ~ 4x103 V/cm
(x)>c! Electron velocity does not increase. Very important correction for modern devices.
Velocity Saturation II
2014-01-30 16 Lecture 7, High Speed Devices 2014
Short channel transistors (Lg < 1µm) Modern FETs – Lg=16-50 nm – => c
Analytical modeling starts to become tricky
𝑣𝑑 =𝜇𝑛𝜀
1 +𝜀𝜀𝑐
𝐼𝑑 =𝑊𝐶𝑜𝑥′ 𝜇𝑛
1 +𝑉𝐷𝑆𝜀𝑐𝐿𝐿𝑉𝐺𝑆 − 𝑉𝑇 𝑉𝐷𝑆 −
𝑉𝐷𝑆2
2
2
2'
,TGSnox
satD
VV
L
WCI
𝑉𝐷𝑆,𝑠𝑎𝑡 = 𝑉𝐺𝑆 − 𝑉𝑇
1
1 + 1 +𝑉𝐺𝑆 − 𝑉𝑇𝐿𝜀𝑐
𝐼𝑑𝑠 ≈ 𝑊𝐶𝑜𝑥′ 𝜀𝑐𝜇𝑛 𝑉𝐺𝑆 − 𝑉𝑇 = 𝑊𝐶𝑜𝑥
′ 𝑣𝑠𝑎𝑡 𝑉𝐺𝑆 − 𝑉𝑇
2
2'
DSDSTGS
noxD
VVVV
L
WCI
TGSsatDS VVV ,
No velocity saturation – unphysical for Lg < 1 µm!
Triode Region
L0
Saturation Voltage
Velocity Saturation III
2014-01-30 17 Lecture 7, High Speed Devices 2013
10-2
10-1
100
101
102
10-5
10-4
10-3
10-2
10-1
100
Gate Length (µm)
Curr
ent (m
A)
TGSsatoxD VVvWCI '
𝑣𝑑 =𝜇𝑛𝜀
1 +𝜀𝜀𝑐
VDS=2V VGS-VT=1V W = 1µm Cox’=1 µF/cm2
c= 4kV/cm µn=10000 cm2/Vs
Current at saturation
For gate lengths below ~ 1µm – velocity saturation is very important! For very short gate-lengths – quasi-ballistic transport!
Channel Length Modulation
2014-01-30 18 Lecture 7, High Speed Devices 2014
Velocity saturarion occurs approximately when =dU/dx>sat
Vds=Vds,sat
VDS
IDS
1
vdrift
-field sat
vsat
𝜀 𝑥 =𝑈𝐶𝐻 0
𝐿1 − 𝛼2
1
1 −𝑥𝐿1 − 𝛼2
(x) < crit
qch(x)
x
qch(x)
x x
2 3
L L L
qch(x)
D
2
2
,
,
'satDS
satDSTGSnox
D
VVVV
LL
WCI
=sat at x=L DL
Low-field Velocity saturation
=sat at x=L-DL
Channel Length Modulation II
2014-01-30 19 Lecture 7, High Speed Devices 2014
VDS
IDS
1 2 3 𝑔𝑑 =
𝑑𝐼𝐷𝑆𝑑𝑉𝐷𝑆
D
2)(
2
,
,
'satDS
satDSTGS
ds
noxD
VVVV
VLL
WCI
• Channel Length modulation causes output conductance!
• 2D electrostatic effects also gives a similar
• Very Important for short channel FETs!
Modern HEMT with Lg=30-50 nm Signs of velocity saturation: IDS almost independent of Lg
IDS ~ VGS-VT
gm/gd ~ 5-50
However – these devices are quasi ballistic
MESFET / HEMT Breakdown
2014-01-30 20 Lecture 7, High Speed Devices 2014
Lateral FETs breakdown is due to high field in the gate-drain region. The high field causes impact ionization / tunneling breakdown. This limits the maximum VDS of the device Scales with band gap (Eg,channel & Eg,barrier)
Sou
rce
Dra
in
Ec
Ev
Vdg=Vds-Vgs
Impact Ionization Impact Ionization
Tunneling causes large gate leakage