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 05, 12 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 Examples
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Lecture 05, 12 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) Convenient metrics lengths Lm and Lf
versus ldB and Lx,y,z 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 Examples
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Lz
ldB
e- ? Travelling wave
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Lz
ldB
e- ? Travelling wave
ldB Lz
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Lz
ldB
Result e- ? Standing wave(s) after initial
transient
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Lz
ldB
If ldB lt Lz happens due to momentum change e- ?
Travelling wave. Its the relative sizes that
matter not how small Lz is
e- ? Travelling wave
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• ldB is proportional to momentum (a vector)
• Momentum is changed by scattering
• Lm and Lf describe how much momentum is likely to
  change on average in terms of useful length(s)

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Use N(E) to get concentration nS
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Use N(E) to get concentration nS
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Fermi wavenumber kf
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Characteristic mean free path length Lm
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Corresponding Fermi velocity vf
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Example what is the mean free path Lm in this
HEMT 2-DEG if the momentum relaxation time tm is
reduced by a factor of 10?
Answer mean free path is also reduced by a
factor of 10 since Lm vf tm.
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Example what could cause a reduction in the
momentum relaxation time tm by a factor of 10?
Answer More scattering due to higher
concentration ns More scattering due to more
lattice vibrations at higher T
Which was it in the preceding example? Answer
it had to be higher T since in the answer the
class gave, you kept vf the same and
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Example these examples are based on the
assumption that the 2-DEG e- gas is degenerate.
Prove that it is by locating Ef relative to the
bottom of the conduction band.
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Lf Phase relaxation lengthStart with tf the
phase relaxation time.Experimental data 1/tf vs.
T
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Example what is the phase relaxation time tf for
the HEMT whose data is shown in the figure at T
0.5 K?
Answer
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vf and tm as appropriate for 2-DEG and
temperature (f ? cold)
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Lecture 05, 12 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 Examples
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Your Homework Pr 1.3 1 Deg in a semiconductor
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Your Homework Pr 1.3 1 Deg in a semiconductor
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2-DEG Energy
Special Schrödinger eqn (Con E) that
accommodates Electronic confinement band
bending due to space charge Useful external
B-field
Example ECE874, Pr. 3.5 with E-field determine
direction of motion. Datta 1.2.1 would be
correct way to continue the problem to get energy
levels
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2-DEG Energy
2-DEG wavefunction
Use this wave function in the special
Schroedinger eqn and it will separate into kz
and kx, ky parts. kz is a fixed quantized
number(s). kx, ky are continuous numbers
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2-DEG Energy
For the kx, ky part
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How do I write f(z)?
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Example write down the wave function for a 1-DEG
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Example write down the energy eigenvalues for a
1-DEG assuming an infinite square well potential
in the quantized directions