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 07, 19 Sep 13
In Chapter 01 in Datta Two dimensional electron
gas (2-DEG) DEG goes down, mobility goes
up Define mobility Proportional to momentum
relaxation time tm Count carriers nS available
for current Pr. 1.3 (1-DEG) How nS influences
scattering in unexpected ways Pr 1.1
(2-DEG) 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 Finish Chp. 01
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Given z-dimension has a quantum confinement with
widely separated energy levels such that nz 1st
always is a good assumption.
Example if z-confinement can be modelled as an
infinite potential well
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2-DEG
1-DEG
1-DEG
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2-DEG
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1-DEG
1-DEG
n 0, 1, 2..
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1-DEG
Electric (confinement) sub-bands in units of E1
1-DEG
n 0, 1, 2..
Electric (confinement) sub-bands in units of
hbarw0
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electric ? U(y)
2-DEG U(x,y) 0, A 0
1-DEG U(x,y) U(y) ? 0 hardwall, A 0
1-DEG U(x,y) U(y) ? 0 parabolic, A 0
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Lec 06 Add useful B-field to 2-DEG
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Lec06 High B-field measurement of carrier
density
number of occupied Landau levels
Changes by 1 between any two levels
B1, etc. measured at maxima so there is a rest
of the oscillation Lec06 Spikes in N(E) gt
spikes in nS gt spikes/troughs in current What
you can do with a trough use a value of B to
turn the current OFF magnetic switch
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Lec06 High B-field measurement of carrier
density
number of occupied Landau levels
Changes by 1 between any two levels
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Lec06 High B-field measurement of carrier
density
number of occupied Landau levels
Changes by 1 between any two levels
B1, etc. measured at maxima so there is a rest
of the oscillation Lec06 Spikes in N(E) gt
spikes in nS gt spikes/troughs in current What
you could potentially do with a trough use a
value of B to turn the current OFF magnetic
switch
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Given z-dimension has a quantum confinement with
widely separated energy levels such that nz 1st
always is a good assumption.
Example if z-confinement can be modelled as an
infinite potential well
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Start here
2-DEG U(x,y) 0, A 0
Now add B-field
2-DEG U(x,y) 0, A ? 0
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U(y) 0
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x
x
You pulled B out in front but in terms of a
familiar function of B the cyclotron frequency wc
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Compare just the mathematical form to 1-DEG
parabolic electronic confinement form
2-DEG U(x,y) 0, A ? 0
1-DEG U(x,y) U(y) ? 0 parabolic, A 0
x
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Compare just the mathematical form to 1-DEG
parabolic electronic confinement form
2-DEG U(x,y) 0, A ? 0
1-DEG U(x,y) U(y) ? 0 parabolic, A 0
x
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Can write down the wavefunction and energy
eigenvalues by comparison to 1-DEG parabolic
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Compare just the mathematical form to 1-DEG
parabolic electronic confinement form
2-DEG U(x,y) 0, A ? 0
1-DEG U(x,y) U(y) ? 0 parabolic, A 0
x
Identical
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Compare just the mathematical form to 1-DEG
parabolic electronic confinement form
2-DEG U(x,y) 0, A ? 0
NO motion in current transport direction along kx
1-DEG U(x,y) U(y) ? 0 parabolic, A 0
x
Motion in current transport direction along kx
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1-DEG U(x,y) U(y) ? 0 parabolic, A 0
x
Motion in current transport direction along kx
n 0, 1, 2..
x
x
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2
1
0
x
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x
2
1
0
x
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y
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However no explicit kx dependence but there is
an implicit one
x
x
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ky
kx
y
x
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Magnetic switch in 2-DEG is not working out
Spikes in N(E) gt spikes in nS gt spikes/troughs
in current What you could do with a trough use
a value of B to turn the current OFF magnetic
switch
No group velocity gt no current. Lumps in nS but
no current.
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Try a Magnetic switch in 1-DEG (this does work)
1-DEG U(x,y) U(y) ? 0 parabolic, A ? 0
B-field out of page
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Mathematically similar type parabolic (y
something)2 ES py2/2m terms AND a yk2 ? kx2
term!
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Wavefunction
Energy eigenvalues
x
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0 1 2
group
The bigger the B-field (wc part) compared with
the electronic confinement w0 part), the flatter
that E-kx diagram. You can control the group
velocity.
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Even more effective you can control how many,
even if, those bands are occupied. Magnetic
switch in 1-DEG Pr. 1.4
OFF
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Fermi level is invariant throughout
device Ef2-Deg Ef1-DEG Ef
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First find
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Now find B-values that will make these 4 levels
inaccessible one by one
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