Mark Cheung
Department of Electrical and Computer Engineering,
University of Virginia, Charlottesville, VA 22904, USA
1
This lecture will cover:
Field-effect transistor (FET) review
Motivation for TFET
Device design and simulation
Literature review
Simulation results
2
Field-effect transistor (FET)
review
 Switch
 On: ID is high
 Off: ID is low
Landauer Formula:
𝑞
𝛾1 𝛾2
𝐼𝐷 =
𝑑𝐸𝐷(𝐸 − 𝑈)(
)[𝑓 𝐸 − 𝑓2 𝐸 ]
ℎ −∞
𝛾1 + 𝛾2 1
∞
3
Motivation
"Intel," 2011. Available: http://www.carthrottle.com/why-chemistry-dictates-an-electric-vehiclefuture/
4
Current-voltage (IV) curve
 Subthreshold Swing SS (mV/dec):
 Power P=(1/2)C𝑉𝑑2 f+VdIloff
𝜕𝑉𝐺𝑆
𝜕log(𝐼𝐷 )
𝜕𝐼
= 𝑙𝑛 10 ∗ (𝜕𝑉 𝐷 ∗ 𝐼
𝐺𝑆
1
𝐷,𝑜𝑛
𝜕𝑉𝑔𝑠
𝜕log(𝐼𝑑 )
MOSFET IV Curve
)−1
Ion
≈ 60 mV/dec
~60 mV/dec
Ioff
5
Tunnel Field Effect Transistor (TFET)
6
Tunnel Field Effect Transistor (TFET)
2𝑒
𝐼𝑑 =
𝑊
ℎ
𝐸𝑣𝑐ℎ
𝐸𝑐𝑠
𝑇 𝐸 − 𝑈 𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
λ
On
𝐸𝑐
q∆𝑉𝐺
𝑓𝑠 𝐸
Source
Off
𝐸𝑣
Channel
Drain
7
Device design and simulation
Gate
Source
Drain
µ1
[𝛴]1
µ2
[H]
[𝛴]2
𝐼𝐷𝑆
𝑉𝐷𝑆
Green Function: 𝐺 = (𝐸𝐼 − 𝐻 − Σ 1 − Σ 2 ) −1
8
Graphene Nanoribbon (GNR)
Subbands
Transmission
9
Relevant Functions (analytical)
SS=
𝜕𝑉𝑔𝑠
𝜕log(𝐼𝑑 )

𝝏𝑰𝒅
𝝏𝑽𝒈𝒔
=
𝝏𝑰𝒅
𝒆 𝒄𝒉
𝝏𝑬𝒗
=
= 𝐥𝐧 𝟏𝟎 ∗ (
𝟐𝒆𝟐 𝝏𝑻𝑾𝑲𝑩
( 𝒄𝒉 𝑭
𝒉
𝑬𝒗
𝝏𝑰𝒅
𝝏𝑽𝒈𝒔
𝑬𝒄𝒉
𝒗
∗
𝟏
𝑰𝒅,𝒐𝒏
)−𝟏
𝝏𝑭(𝑬𝒄𝒉
𝒗 )
+ 𝑻𝑾𝑲𝑩
)
𝒄𝒉
𝝏𝑬𝒗
𝟑
∗
𝟒𝜦 𝟐𝒎 𝑬𝒈 𝟐
−
𝟑𝒉 ∆𝝓+𝑬𝒈
 𝑻𝑾𝑲𝑩 = 𝒆
F
𝑬𝒄𝒉
𝒗
=
𝐸𝑣𝑐ℎ
𝐸𝑐𝑠
𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
J. Knoch, S. Mantl and J. Appenzeller, "Impact of dimensionality on the performance of tunneling
FETs: Bulk versus one-dimensional devices," ScienceDirect, vol. 51, pp. 572-78, 2007.
10
Literature Review: MOSFET/TFET IV
of different material system
A. M. Ionescu and H. Riel, "Tunnel field-effect transistors as energy-efficient
electronics switches," Nature, vol. 479, pp. 329-337, 2011.
11
Literature Review: varying gate
overlap & differential voltage
Differential voltage between top and bottom gate
for a double gate TFET correlates positively with Ion/Ioff
Gate overlap improves SS
without degrading Ion and Ioff
Fiori, G.; Iannaccone, G., "Ultralow-Voltage Bilayer Graphene Tunnel FET," Electron Device Letters,
IEEE , vol.0, no.10, pp.1096,1098, Oct. 2009 doi: 10.1109/LED.2009.2028248
12
Literature Review: varying drainside gate underlap & drain doping
X. Yang, J. Chauhan, J. Guo, and K. Mohanram “Graphene tunneling FET and its applications in
low-power circuit design,” VLSI, pp. 263-268, 2010
Drain-side gate underlap and drain doping reduce the
ambipolar IV characteristics without sacrificing Ion/Ioff and SS
13
Result: varying channel width
2𝑒
𝐼𝑑 =
𝑊
ℎ
𝐸𝑣𝑐ℎ
𝐸𝑐𝑠
𝑇 𝐸 − 𝑈 𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
Channel width varies inversely with
SS and correlates negatively
(exponential) with Ion/Ioff
14
Result: varying channel width
250
1,000,000
100,000
y = 3E+08e-2.043x
R² = 0.979
200
150
1,000
100
100
y = 381.85e-0.554x
R² = 0.9697
50
10
0
ratio
SS(mV/dec)
10,000
SS (mV/dec)
Ion/Ioff
1
0
1
2
3
4
5
6
7
8
width (nm)
Channel width varies inversely with SS and
correlates negatively (exponential) with Ion/Ioff
15
Results: varying channel length
λ
On
𝐸𝑐
q∆𝑉𝐺
𝑓𝑠 𝐸
Source
Off
𝐸𝑣
Channel
Drain
16
Results varying channel length
180
100,000
160
y = 30782ln(x) - 70513
R² = 0.7531
140
10,000
1,000
100
Ratio
SS (mV/dec)
120
80
100
60
40
SS (mV/dec)
Ion/Ioff
10
20
0
1
0
20
40
60
80
100
120
140
160
180
length (nm)
Channel length varies inversely with SS and
correlates positively (logarithmic) with Ion/Ioff
17
Results: varying doping in contacts
λ
On
𝐸𝑐
q∆𝑉𝐺
𝑓𝑠 𝐸
Source
Off
𝐸𝑣
Channel
Drain
Channel doping correlates positively with SS (exponential) and
positively with Ion/Ioff (exponential) up until doping of around 0.28eV
18
Results: varying doping in contacts
70
1,000,000
60
100,000
y = 20.708e32.662x
R² = 0.9263
10,000
40
1,000
30
y = 0.1836e15.587x
R² = 0.8899
20
y = 3E+07e-33.01x
100
ratio
SS (mV/dec)
50
SS (mV/dec)
Ion/Ioff
10
10
0
1
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
doping (eV)
Channel doping correlates positively with SS (exponential) and
positively with Ion/Ioff (exponential) up until doping of around 0.28eV
19
Results: varying drain bias
λ
On
𝐸𝑐
q∆𝑉𝐺
𝑓𝑠 𝐸
Source
Off
𝐸𝑣
Channel
Drain
Drain bias correlates positively with SS (linear & weak)
and negatively with Ion/Ioff (exponential)
20
12
1,000,000
10
100,000
8
10,000
6
1,000
y = 366373e-26.58x
R² = 0.9464
4
ratio
SS (mV/dec)
Results: varying drain bias
100
2
SS (mV/dec)
Ion/Ioff
10
0
1
0
0.05
0.1
0.15
0.2
0.25
vd (V)
Drain bias correlates positively with SS (linear & weak)
and negatively with Ion/Ioff (exponential)
21
Conclusion
 SS of 6.4 mV/dec and Ion/Ioff of >25,000 were
obtained for length=40nm, width=5nm, vd=0.1 V, and
doping=0.24eV.
 Further analysis is required to balance the trade-offs
among size, power, and performance.
 In comparison to a MOSFET, high Ion/Ioff ratio and
steep SS over several decades indicate GNR TFET’s
superiority for ultra-low-voltage applications.
22
Future direction
 Link experimental results with analytical equations
 Adjust simulation to account for experimental
challenges
 Include scattering (inelastic & elastic)
 Alternative TFET designs
23
Appendix: Simulation Design
(continue)
 Tight-binding Hamiltonian model
 TFET setup:
 Channel doping
 Tri-gate
 Non-equilibrium green function (NEGF)
 Assumptions:
 Room temperature
 ballistic transport
 electrodes are infinite electron reservoir
 steady state
24
Appendix: NEGF
 𝐼𝑑 =
𝐸𝑣𝑐ℎ
2𝑒
𝑊 𝐸𝑠 𝑇
ℎ
𝑐
𝐸 − 𝑈 𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
 𝐺 = (𝐸𝐼 − 𝐻 − Σ 1 − Σ 2 )

−1
 E : energy matrices from the electronic band structure
 H : hamiltonian matrix
 Σ 1,2 : self energy matrices from the contacts
 Σ 1 =Γ1 𝑓1 , Σ 2 =Γ2 𝑓2
 Γ: broadening matrices due to coupling with contacts
 f: fermi functions describing number of electrons
𝐺 𝑛 = 𝐺 1 𝑓1 + 2 𝑓2 𝐺 +
 Electron density per unit energy
Γ
Γ
25
Appendix: NEGF (continue)
 T(E)=Trace(Γ1 𝐺 Γ2 𝐺 + )
 Average transmission at different energy
 U=𝑈𝐿 + 𝑈𝑁
 Potential energy effecting the DOS , and hence the transmission T
𝐶𝐺
𝐶
 𝑈𝐿 =
(−𝑞𝑉𝐺 )+ 𝐷 (−q𝑉𝐷 )
𝐶
𝐶
 𝑈𝑁 =
 𝑓(𝐸) =
𝐸
𝑞2
𝐶𝑒
𝐸
∆N
1
𝐸−µ
1+𝑒 𝑘𝑇
 Probability that an electron will be at an energy state E given the
fermi level µ, and temperature T
 𝐼𝑑 =
𝐸𝑣𝑐ℎ
2𝑒
𝑊 𝐸𝑠 𝑇
ℎ
𝑐
𝐸 − 𝑈 𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
26
Appendix: Relevant functions
(continue)
SS=
𝜕𝑉𝑔𝑠
𝜕log(𝐼𝑑 )

𝝏𝑰𝒅
𝝏𝑽𝒈𝒔
=
𝝏𝑰𝒅
𝒆 𝒄𝒉
𝝏𝑬𝒗
=
𝜦
 𝑻 𝑬 =
 𝑻
−𝟐
𝒆 𝟎
𝑬𝒄𝒉
𝒗
𝟐𝒆𝟐 𝝏𝑻𝑾𝑲𝑩
( 𝒄𝒉 𝑭
𝒉
𝑬𝒗
𝟐𝒎∗
𝒉𝟐
 𝑼
 𝑼
 F
𝑬𝒄𝒉
𝒗
= 𝑬𝒄𝒉
𝒗 + 𝑬𝒈
− 𝑬𝒔𝒄 = −𝒒𝝃𝒙
=
𝐸𝑣𝑐ℎ
𝐸𝑐𝑠
∗
𝟏
𝑰𝒅,𝒐𝒏
)−𝟏
𝝏𝑭(𝑬𝒄𝒉
𝒗 )
+ 𝑻𝑾𝑲𝑩
)
𝝏𝑬𝒄𝒉
𝒗
𝒒𝝃𝒙 𝒅𝒙
= 𝑻𝑾𝑲𝑩 = 𝒆
𝒔
 ∆𝝓 = 𝑬𝒄𝒉
𝒗 − 𝑬𝒄
𝑬𝒄𝒉
𝒗
𝝏𝑰𝒅
𝝏𝑽𝒈𝒔
= 𝐥𝐧 𝟏𝟎 ∗ (
−
𝟑
𝟒𝜦 𝟐𝒎∗ 𝑬𝒈 𝟐
𝟑𝒉 ∆𝝓+𝑬𝒈
J. Knoch, S. Mantl and J. Appenzeller, "Impact of dimensionality on the performance of tunneling
FETs: Bulk versus one-dimensional devices," ScienceDirect, vol. 51, pp. 572-78, 2007.
𝑓𝑠 𝐸 − 𝑓𝑑 𝐸 𝑑𝐸
27