Download E vac Space Charge - MSU College of Engineering

ECE 802-604:
Nanoelectronics
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University
[email protected]
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
VM Ayres, ECE802-604, F13
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 = ?
VM Ayres, ECE802-604, F13
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
VM Ayres, ECE802-604, F13
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
VM Ayres, ECE802-604, F13
VM Ayres, ECE802-604, F13
VM Ayres, ECE802-604, F13
Space Charge:
HEMT
VM Ayres, ECE802-604, F13
start
Space Charge:
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.
VM Ayres, ECE802-604, F13
Refer everything to Evac. When separated (starting condition) you have:
Evac
Type-I:
Material 01 (identified
by its smaller energy
bandgap) has lower
EC1 and higher EV1
Evac
Type-II:
Material 01 has lower
EC1 and lower EV1
Evac
Type-III:
Material 01 has EC1
that is close to
(“overlaps”) EV2
VM Ayres, ECE802-604, F13
When Materials 01 and 02 come together: what e-’s and o’s are most likely
to do first:
Evac
e-
Evac
Evac
e-
e-
o
Type-I:
e-’s are collected at
lower EC1 and o’s are
collected at higher EV1
o
Type-II:
e-’s collected at lower
EC1 and o’s collected
at higher EV2.
Therefore e-s and o’s
are confined in
different spaces
Type-III:
e-’s can be collected
at lower EC1but can
also recombine in the
nearby “overlapping”
EV2 levels
VM Ayres, ECE802-604, F13
Space Charge:
Compare: Datta and class examples were both Type I:
Evac
e-
o
Type-I:
e-’s are collected at
lower EC1 and o’s are
collected at higher EV1
VM Ayres, ECE802-604, F13
Space Charge:
Compare: Datta and class examples were both Type I:
Evac
e-
e-’s go into a triangular quantum
well region.
In HEMT, o’s go into EV1 : changed
by DEV but no quantum well
o
Type-I:
e-’s are collected at
lower EC1 and o’s are
collected at higher EV1
VM Ayres, ECE802-604, F13
Space Charge:
Contrast o’s for HEMT and for familiar infinite potential well:
Do also have
quantized
energy levels
for o’s in infinite
square potential
well. But not for
HEMT
VM Ayres, ECE802-604, F13
Expected transitions between EC and EV for, e.g. light
emission
J
Evac
q1
Evac
qm1
q2
DEC
EC1
EF1
EV1
qm2
Eg1
EC2
EF2
DEV
Eg2
EV2
VM Ayres, ECE802-604, F13
Back to current, not light:
Evac
q1
J
Evac
qm1
q2
DEC
EC1
EF1
EV1
qm2
Eg1
EC2
EF2
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
Eg2
EV2
VM Ayres, ECE802-604, F13
Space Charge:
J
Evac
q1
Evac
qm1
q2
EC1
EF1
EV1
Eg1
Lots of e-’s come here and stay here.
ND+
qm2
DEC
EC2
EF2
DEV
Eg2
They came from an n-type side.
They left behind ND+
Space charge region on both sides of
junction
EV2
VM Ayres, ECE802-604, F13
Space Charge:
J
Evac
q1
Evac
qm1
q2
EC1
EF1
EV1
Eg1
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
ND+
qm2
DEC
EC2
EF2
DEV
Eg2
EV2
VM Ayres, ECE802-604, F13
Space Charge:
J
Evac
q1
Evac
qm1
q2
EC1
EF1
EV1
Eg1
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.
ND+
qm2
DEC
EC2
EF2
DEV
Eg2
EV2
VM Ayres, ECE802-604, F13
How will you wire this up?
HEMT
VM Ayres, ECE802-604, F13
How will you wire this up?
Wire it up to use the triangular
quantum well region in GaAs
VM Ayres, ECE802-604, F13
Please! assign a consistent coordinate system;
Wire it up to use the triangular
quantum well region in GaAs
-z
y
x
y
z
VM Ayres, ECE802-604, F13
Please! assign a consistent coordinate system;
Wire it up to use the triangular
quantum well region in GaAs
-z
y
Ey
nx
= (-|e |)(-|E y|)
y
z
Seems correct for e-’s with Drain = +
Note: current I is IDS
VM Ayres, ECE802-604, F13
Why do this: increase in Mobility
mobility
931C: 3D Scattering
Sweet spot
at 300K
T = cold:
Impurity =
ND+, NAscattering
T = hot:
Phonon
lattice
scattering
VM Ayres, ECE802-604, F13
Why do this: increase in Mobility
Compare 3-DEG (dotted
lines) and 2-DEG (shaded
area). 2-DEG is better
especially at low T.
VM Ayres, ECE802-604, F13
Datta explanation:
When tm is long, m is high
VM Ayres, ECE802-604, F13
Streetman explanation brings out scattering and group
aspects better:
Drain
Source
VM Ayres, ECE802-604, F13
Streetman explanation:
VM Ayres, ECE802-604, F13
Streetman explanation:
VM Ayres, ECE802-604, F13
Streetman explanation:
VM Ayres, ECE802-604, F13
Streetman explanation:
VM Ayres, ECE802-604, F13
Streetman explanation:
1) Direction of electron drift velocity is opposite to direction of E-field.
2) Could stop here with <vx> = vd = m E. Mind the vectors/directions.
3) Next slide relates mobility to current, which can be measured not <vx>
which can’t.
VM Ayres, ECE802-604, F13
Streetman explanation:
VM Ayres, ECE802-604, F13
Streetman explanation:
Key:
1) When number of e’s that have not scattered N(t) goes up => 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.
VM Ayres, ECE802-604, F13