ee-612: nanoscale transistors fall 2006 mark lundstrom electrical
TRANSCRIPT
1
Electrical and Computer Engineering Network for Computational Nanotechnology
Birck Nanotechnology Center Purdue University, West Lafayette, Indiana USA
Lundstrom 5.3.2013 nanoHUB.org
EDS Mini-colloquium, Mexico City, May 3, 2014
From Lilienfeld to Landauer:
Understanding the nanoscale transistor:
Mark Lundstrom
2
history of the field-effect transistor
Lundstrom 5.3.2013
Lilienfeld, 1926 Heil, 1934
concept
Atalla and Dawon Kahng Bell Labs, 1959
demonstration
Intel IEDM, 2012
22 nm FinFET
3
NMOS-II
Hewlett-Packard Journal, Nov. 1977
NMOS II: 5 microns = 5000 nm
4
Moore’s Law
4
http://en.wikipedia.org/wiki/Moore's_law Micro- electronics
Nano- electronics
Lundstrom 5.3.2013
5
MOSFET IV characteristic
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007) S
D
G
circuit
symbol
gate-voltage controlled resistor
gate-voltage controlled
current source
Lundstrom 5.3.2013
6
MOSFET IV: low VDS
gate-voltage controlled resistor
Lundstrom 5.3.2013
7
velocity saturation
107
104 105
Lundstrom 5.3.2013
8
MOSFET IV: velocity saturation
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
Lundstrom 5.3.2013
textbook MOSFET model
9
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
gate-voltage controlled resistor
Lundstrom 5.3.2013
gate-voltage controlled current source
Velo
city
(cm
/s)
10
carrier transport nanoscale MOSFETs
D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.
quasi-ballistic
Lundstrom 5.3.2013
Ener
gy
11
MOSFET: IV (2-piece approximation)
Lundstrom 5.3.2013
12
current = charge times velocity
Lundstrom 5.3.2013
1) Low VDS:
2) High VDS:
13
model for ID(VG, VD)
If we can make the average velocity go smoothly from the low VD to the high VD limit, then we will have a smooth model for ID(VG, VD).
Lundstrom 5.3.2013
14
drain voltage dependent average velocity
Lundstrom 5.3.2013
15
empirical saturation function
✓
✓
Lundstrom 5.3.2013
16
“MIT Virtual Source” model
Lundstrom 5.3.2013
Only a few device-specific input parameters to this model: 1)
2)
3)
4)
5)
The parameter, β, is empirically adjusted to fit the IV. Typically, β ≈ 1.4 – 1.8 for both N- and P-MOSFETs.
17
MIT Virtual Source Model
32 nm technology
Lundstrom 5.3.2013
18
questions
Lundstrom 5.3.2013
1) Why does the traditional MOSFET model (based on transport physics that is not valid at the nanoscale) continue to describe the IV characteristics of nano-MOSFETs?
2) How does the velocity saturate in a ballistic or quasi-ballistic MOSFET?
3) What is the meaning of the “apparent mobility” and the “injection velocity.”
4) What will happen below 10 nm?
19
outline
1) Introduction
2) The MOSFET as a barrier-controlled device 3) The MOSFET as a nano-device
4) Connecting the traditional and Landauer models
5) What will happen below 10 nm?
6) Summary
Lundstrom 5.3.2013
energy band diagrams
20 Lundstrom 5.3.2013
source drain
SiO
2
silicon
S G D
(Texas Instruments, ~ 2000)
electron potential energy vs. position
the transistor as a barrier controlled device
21 Lundstrom 5.3.2013
source drain channel
low gate voltage
VD = VS = 0
the transistor as a barrier controlled device
22 Lundstrom 5.3.2013
low gate voltage
source drain channel
high drain voltage
the transistor as a barrier controlled device
23 Lundstrom 5.3.2013
high gate voltage
source high drain voltage
24
how transistors work
2007 N-MOSFET
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
E.O. Johnson, “The IGFET: A Bipolar Transistor in Disguise,” RCA Review, 1973
understanding MOSFET IV characteristics
25 Lundstrom 5.3.2013
electrostatics + transport
26
semiclassical transport in nanoscale MOSFETs
Lundstrom 5.3.2013
Velo
city
(cm
/s)
D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.
Ener
gy
27
quantum transport
Lundstrom 5.3.2013
L = 10 nm
n(x, E)
nanoMOS (www.nanoHUB.org)
28
outline
1) Introduction
2) The MOSFET as a barrier-controlled device
3) The MOSFET as a nano-device 4) Connecting the traditional and Landauer models
5) What will happen below 10 nm?
6) Summary
Lundstrom 5.3.2013
29
Landauer approach to transport
Lundstrom 5.3.2013
gate
nano-device
30
the DD equation for the 21st Century
Lundstrom 5.3.2013
nano-device
bulk semiconductor
31
“Lessons from Nanoscience”
Lundstrom 5.3.2013
http://nanohub.org/topics/LessonsfromNanoscience
32
i) small drain bias
Lundstrom 5.3.2013
nano-device
33
small drain bias
Lundstrom 5.3.2013
34
ballistic transport and quantized conductance
Lundstrom 5.3.2013
W --> B. J. van Wees, et al. Phys. Rev. Lett. 60, 848–851,1988.
1) conductance is quantized 2) upper limit to conductance
35
ii) large drain bias
Lundstrom 5.3.2013
nano-device
36
ballistic MOSFET: linear region
Lundstrom 5.3.2013
near-equilibrium
37
linear region with MB statistics
✔ Lundstrom 5.3.2013
38
ballistic MOSFET: linear region
Lundstrom 5.3.2013
near-equilibrium
ballistic MOSFET: saturated region
39 Lundstrom 5.3.2013
40
saturated region with MB statistics
✔ Lundstrom 5.3.2013
41
ballistic MOSFET:
Lundstrom 5.3.2013
42
the ballistic IV (Boltzmann statistics)
K. Natori, JAP, 76, 4879, 1994.
ballistic channel resistance
ballistic on-current
“velocity saturation”
Lundstrom 5.3.2013
43
velocity saturation in a ballistic MOSFET
Increasing VDS
-10 -5 0 5 10
ΕΧ vs. x for VGS = 0.5V 1) 2)
3) 4)
(Numerical simulations of an L = 10 nm double gate Si MOSFET from J.-H. Rhew and M.S. Lundstrom, Solid-State Electron., 46, 1899, 2002)
44
“velocity overshoot”
Lundstrom Fall 2012
Velo
city
(cm
/s)
D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.
45
comparison with experiment: Silicon
A. Majumdar, Z. B. Ren, S. J. Koester, and W. Haensch, "Undoped-Body Extremely Thin SOI MOSFETs With Back Gates," IEEE Transactions on Electron Devices, 56, pp. 2270-2276, 2009. Device characterization and simulation: Himadri Pal and Yang Liu, Purdue, 2010.
• Si MOSFETs deliver > one-half of the ballistic on-current. (Similar for the past 15 years.)
• MOSFETs operate closer to the ballistic limit under high VDS.
46
comparison with experiment: InGaAs HEMTs
Jesus del Alamo group (MIT)
47
scattering and transmission
X X X
λ0 is the mean-free-path for backscattering
Lundstrom 5.3.2013
48
the quasi-ballistic MOSFET
Lundstrom 5.3.2013
49
on-current and transmission
Lundstrom 5.3.2013
50
the quasi-ballistic MOSFET
Lundstrom 5.3.2013
51
scattering under high VDS
low VDS
high VDS
Lundstrom 5.3.2013
52
outline
1) Introduction
2) The MOSFET as a barrier-controlled device
3) The MOSFET as a nano-device
4) Connecting the traditional and Landauer models 5) What will happen below 10 nm?
6) Summary
Lundstrom 5.3.2013
53
MIT VS Model: why does it work?
32 nm technology
Lundstrom 5.3.2013
54
connection to traditional model (low VDS)
Lundstrom 5.3.2013
55
connection to traditional model (high VDS)
Lundstrom 5.3.2013
56
the MOSFET as a BJT
‘bottleneck’ “collector”
“base”
E.O. Johnson, “The IGFET: A Bipolar Transistor in Disguise,” RCA Review, 1973
Lundstrom 5.3.2013
Landauer VS model
57 Lundstrom 5.3.2013
58
outline
1) Introduction
2) The MOSFET as a barrier-controlled device
3) The MOSFET as a nano-device
4) Connecting the traditional and Landauer models
5) What will happen below 10 nm? 6) Summary
Lundstrom 5.3.2013
59
limits to barrier control: quantum tunneling
from M. Luisier, ETH Zurich / Purdue
1) 2)
3) 4)
Lundstrom 5.3.2013
60
5 nm MOSFETs?
Lundstrom 5.3.2013
Unpublished results from Saumitra Mehrotra, G. Klimeck group, Purdue University.
61
outline
1) Introduction
2) The MOSFET as a barrier-controlled device
3) The MOSFET as a nano-device
4) Connecting the traditional and Landauer models
5) What will happen below 10 nm?
6) Summary
Lundstrom 5.3.2013
62
top of the barrier / VS model
Lundstrom 5.3.2013
under strong control of gate with weak influence of the drain
For large VDS, most of the additional voltage drop occurs on the drain end of the channel.
In a “well-tempered” MOSFET, the height of the energy barrier is mostly controlled by the gate voltage and only weakly controlled by the drain voltage.
Current is controlled by a bottleneck near the beginning of the channel
63
the MIT VS model: Why does it work?
64
summary
• Understanding MOSFETs means understanding electrostatics and transport.
• The Landauer approach provides a clear, physical approach to transport at the nanoscale.
• 10 nm and below is still uncharted territory.
65
questions
For more information, take a nanoHUB-U short course: “Nanoscale transistors” on nanoHUB-U https://nanohub.org/groups/u/self_paced_nanoscale_transistors
This talk will be available soon at: www.nanoHUB.org