ECE 802-604:Nanoelectronics

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

VM Ayres, ECE802-604, F13

Lectures 09 and 10, 26 Sep and 01 Oct 13

In Chapter 02 in Datta:

Transport: current I = GVV = IR => I = GV

VelocityEnergy levels M M(E)Conductance G = GC in a 1-DEG

Example Pr. 2.1: 2-DEG-1-DEG-2-DEGExample: 3-DEG-1-DEG-3-DEGTransmission probability: the new ‘resistance’

How to evaluate the Transmission/Reflection probability

How to correctly measure I = GVLandauer-Buttiker: all things equal

4-point probe experiments: set-up and read out

VM Ayres, ECE802-604, F13

Lecture 09 and 10, 26 Sep and 01 Oct 13

In Chapter 02 in Datta:

Transport: current I = GVV = IR => I = GV

VelocityEnergy levels M M(E)Conductance G = GC in a 1-DEG

Example Pr. 2.1: 2-DEG-1-DEG-2-DEGExample: 3-DEG-1-DEG-3-DEGTransmission probability: the new ‘resistance’

How to evaluate the Transmission/Reflection probability

How to correctly measure I = GVLandauer-Buttiker: all things equal

4-point probe experiments: set-up and read out

VM Ayres, ECE802-604, F13

M

N

Varies by edition:

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

Point 01: What are 1 and 2:

1 and 2 are being used as quasi Fermi levels

A quasi Fermi level is a Fermi energy level that exists as long as an external energy is supplied, e.g, E-field, light, etc.

In what follows, 1 F+ and 2 F-

1 and 2 are also chemical potentials

(2)

VM Ayres, ECE802-604, F13

Point 02: normal current versus unconventional e- current

Battery picture

VM Ayres, ECE802-604, F13

Lecture 09 and 10, 26 Sep and 01 Oct 13

In Chapter 02 in Datta:

Transport: current I = GVV = IR => I = GV

VelocityEnergy levels M M(E)Conductance G = GC in a 1-DEG

Example Pr. 2.1: 2-DEG-1-DEG-2-DEGExample: 3-DEG-1-DEG-3-DEGTransmission probability: the new ‘resistance’

How to evaluate the Transmission/Reflection probability

How to correctly measure I = GVLandauer-Buttiker: all things equal

4-point probe experiments: set-up and read out

VM Ayres, ECE802-604, F13

Point 02: normal current versus unconventional e- current

Note + terminal of battery versus electron I1

+

VM Ayres, ECE802-604, F13

Point 03: energy levels below Ef are filled in these diagrams:No current left to right

VM Ayres, ECE802-604, F13

Point 03: energy levels below Ef are filled in these diagrams:Even random motion back and forth requires holes below and e-s above Ef in both +kx and -kx : fluctuations in the e- and hole populations

VM Ayres, ECE802-604, F13

Point 04:(a) scattering in non-ideal quasi-1-DEGversus(b) transport in ideal 1-DEG

hbar0 + hbar0 +

X

W

t1: e-t2: e-

VM Ayres, ECE802-604, F13

Point 04:(a) scattering in non-ideal quasi-1-DEGversus(b) transport in ideal 1-DEG

hbar0 + hbar0 +

W

t1: e- t2: e-

VM Ayres, ECE802-604, F13

Ideal: no scattering: totally wavelike-transport: ballistic

Point 04: (b) transport in ideal 1-DEG

VM Ayres, ECE802-604, F13

Lecture 09 and 10, 26 Sep and 01 Oct 13

In Chapter 02 in Datta:

Transport: current I = GVV = IR => I = GV

VelocityEnergy levels M M(E)Conductance G = GC in a 1-DEG

Example Pr. 2.1: 2-DEG-1-DEG-2-DEGExample: 3-DEG-1-DEG-3-DEGTransmission probability: the new ‘resistance’

How to evaluate the Transmission/Reflection probability

How to correctly measure I = GVLandauer-Buttiker: all things equal

4-point probe experiments: set-up and read out

VM Ayres, ECE802-604, F13

Contact Conductance/Resistance

VDS

How do you step down:

VM Ayres, ECE802-604, F13

Contact Conductance/Resistance

VDS

How do you step down:

Have 1-2:What drives transport

VM Ayres, ECE802-604, F13

Lecture 09 and 10, 26 Sep and 01 Oct 13

In Chapter 02 in Datta:

Transport: current I = GVV = IR => I = GV

VelocityEnergy levels M M(E)Conductance G = GC in a 1-DEG

Example Pr. 2.1: 2-DEG-1-DEG-2-DEGExample: 3-DEG-1-DEG-3-DEGTransmission probability: the new ‘resistance’

How to evaluate the Transmission/Reflection probability

How to correctly measure I = GVLandauer-Buttiker: all things equal

4-point probe experiments: set-up and read out

VM Ayres, ECE802-604, F13

Have assumed: Reflectionless: RC comes from stepping down.

VDS

VM Ayres, ECE802-604, F13

With reflections:

VM Ayres, ECE802-604, F13

Within 1-DEG:

VM Ayres, ECE802-604, F13

Example:where does I1

- come from?

VM Ayres, ECE802-604, F13

Answer: Scattering

If T = 1, recover the previous reflectionless discussion.

VM Ayres, ECE802-604, F13

Answer: Scattering

VM Ayres, ECE802-604, F13

Landauer formula:

VM Ayres, ECE802-604, F13

Transmission probability example(Anderson, Quantum Mechanics)

Example: describe what this could be a model of.

Barrier height V0 is an energy in eV

VM Ayres, ECE802-604, F13

Transmission probability example(Anderson, Quantum Mechanics)

Answer:Modelling the scatterer X as a finite step potential in a certain region.

Modelling the e- as having energy E > V0

VM Ayres, ECE802-604, F13

Transmission probability example(Anderson, Quantum Mechanics)

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13Modelling the e- as having energy E > V0

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

E > barrier height V0

E < barrier height V0

VM Ayres, ECE802-604, F13

2

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13

VM Ayres, ECE802-604, F13