ECE 802-604: Nanoelectronics

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ECE 802-604Nanoelectronics

• Prof. Virginia Ayres
• Electrical Computer Engineering
• Michigan State University
• ayresv_at_msu.edu

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Lecture 03, 05 Sep 13
In Chapter 01 in Datta Two dimensional electron
gas (2-DEG) DEG goes down, mobility goes
up Define mobility (and momentum
relaxation) One dimensional electron gas
(1-DEG) Special Schrödinger eqn (Con E) that
accommodates Electronic confinement band
bending due to space charge Useful external
B-field Experimental measure for mobility
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n 0 for 1st m meff for conduction band e- in
GaAs. At 300K this is 0.067 m0 a ?
U(z) a z
z
Expected Units of a ?
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n 0 for 1st m meff for conduction band e- in
GaAs. At 300K this is 0.067 m0 a ?
U(z) a z
z
Expected Units of a eV/m or eV/nm
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Another way to ballpark an answer Equate the
first triangular well energy level to the first
energy level of a 10 nm GaAs infinite square well
(familiar problem) and then solve for asymmetry a
Set Triangular well Ec1 infinite square well
Ec1
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Space Charge
HEMT
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Space Charge
start
finish
ECE 875 Sze Classification of heterojunctions
into types I, II, and III. Look at the
opportunities for e- and o movement as EF is
established.
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Refer everything to Evac. When separated
(starting condition) you have
Evac
Evac
Evac
Type-I Material 01 (identified by its smaller
energy bandgap) has lower EC1 and higher EV1
Type-II Material 01 has lower EC1 and lower EV1
Type-III Material 01 has EC1 that is close to
(overlaps) EV2
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When Materials 01 and 02 come together what e-s
and os are most likely to do first
Evac
Evac
Evac
e-
e-
e-
o
o
Type-I e-s are collected at lower EC1 and os
are collected at higher EV1
Type-II e-s collected at lower EC1 and os
collected at higher EV2. Therefore e-s and os
are confined in different spaces
Type-III e-s can be collected at lower EC1but
can also recombine in the nearby overlapping
EV2 levels
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Space Charge
Compare Datta and class examples were both Type
I
Evac
e-
o
Type-I e-s are collected at lower EC1 and os
are collected at higher EV1
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Space Charge
Compare Datta and class examples were both Type
I
Evac
e-
e-s go into a triangular quantum well
region. In HEMT, os go into EV1 changed by
DEV but no quantum well
o
Type-I e-s are collected at lower EC1 and os
are collected at higher EV1
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Space Charge
Contrast os for HEMT and for familiar infinite
potential well
Do also have quantized energy levels for os in
infinite square potential well. But not for HEMT
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Expected transitions between EC and EV for, e.g.
light emission
J
DEC
DEV
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Back to current, not light
J
DEC
DEV
Note e-s likely to be stuck in 1st energy level
because of the amount DE it takes to physically
move on to further location
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Space Charge
J
DEC
ND
Lots of e-s come here and stay here. They came
from an n-type side. They left behind ND Space
charge region on both sides of junction
DEV
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Space Charge
J
DEC
ND
DEV
Band bending ? due to space charge Have a local
E-field and potential U(z) here that are
different from periodic lattice potential of GaAs
and AlGaAs
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Space Charge
J
DEC
ND
DEV
This is why we will use Eqn 1.2.1 where U(r ) is
the potential energy due to space charge not the
Bloch lattice potential.
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How will you wire this up?
HEMT
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How will you wire this up?
Wire it up to use the triangular quantum well
region in GaAs
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Please! assign a consistent coordinate system
Wire it up to use the triangular quantum well
region in GaAs
-z
y
x
y
z
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Please! assign a consistent coordinate system
Wire it up to use the triangular quantum well
region in GaAs
-z
y
n-
E y
x
(-e )(-E y)
y
z
Seems correct for e-s with Drain Note
current I is IDS
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Why do this increase in Mobility
931C 3D Scattering
Sweet spot at 300K
mobility
T hot Phonon lattice scattering
T cold Impurity ND, NA- scattering
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Why do this increase in Mobility
Compare 3-DEG (dotted lines) and 2-DEG (shaded
area). 2-DEG is better especially at low T.
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Datta explanation
When tm is long, m is high
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Streetman explanation brings out scattering and
group aspects better
Drain
Source
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Streetman explanation
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Streetman explanation
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Streetman explanation
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Streetman explanation
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Streetman explanation
1) Direction of electron drift velocity is
opposite to direction of E-field. 2) Could stop
here with ltvxgt vd m E. Mind the
vectors/directions. 3) Next slide relates
mobility to current, which can be measured not
ltvxgt which cant.
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Streetman explanation
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Streetman explanation
Key
1) When number of es that have not scattered
N(t) goes up gt t must go up 2) Then m goes up 3)
Scattering involves energy and momentum
conserving interactions. Putting quantum
restrictions on these interactions means that
fewer can occur.