Download presentation

Presentation is loading. Please wait.

Published byDamaris Ludgate Modified over 2 years ago

1
ECE 802-604: Nanoelectronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

2
VM Ayres, ECE802-604, F13 Lecture 11, 03 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability T(N) for multiple scatterers T(L) in terms of a “how far do you get length” L 0 How to correctly measure I = GV Landauer-Buttiker: all things equal 3-, 4-point probe experiments: set-up and read out

3
VM Ayres, ECE802-604, F13 Lec10: Scattering: Landauer formula for G

4
VM Ayres, ECE802-604, F13 Lec10: Scattering: Landauer formula for R … + ‘wire’ resistance: Dresselhaus

5
VM Ayres, ECE802-604, F13 E > barrier height V 0 E < barrier height V 0 Lec10: Modelled the scatterer X as a finite step potential in a certain region. Dresselhaus p. 144: static scattering, scattering by a potential in one dimension Modelled the wavelike e- as having energy E > or < V 0 and got a transmission probability T

6
VM Ayres, ECE802-604, F13 E > V 0 E < V 0 Point01: The phase and amplitude at electrode 2 can be obtained from the phase and amplitude at electrode 1 E > V 0 Phase and amplitude are the same E< V 0 Amplitude is reduced but phase is the same. 11 22 Phase: e- as wave is same at both contacts. This is the origin of the unchanged contact resistance G C - 1 = R C

7
VM Ayres, ECE802-604, F13 Point02: Everywhere: Transport is by occupying a discreet energy level, “channel”. Say that there are M channels in the 1-DEG. Dresselhaus Datta

8
VM Ayres, ECE802-604, F13 Point02: Everywhere: Transport is by occupying a discreet energy level, “channel”. Say that there are M channels in the 1-DEG. T is the transmission probability for a channel to go from electrode 1 to electrode 2, which is given by the sum of the sum of the transmission probability from the ith to the jth channel

9
VM Ayres, ECE802-604, F13 Point02: Everywhere: Transport is by occupying a discreet energy level, “channel”. Say that there are M channels in the 1-DEG. T is the transmission probability for a channel to go from electrode 1 to electrode 2, which is given by the sum of the sum of the transmission probability from the ith to the jth channel Clearly this e- didn’t make it. Reflections are the cause of resistance in the wire. … + ‘wire’ resistance: Dresselhaus

10
VM Ayres, ECE802-604, F13 Point02: Everywhere: Transport is by occupying a discreet energy level, “channel”. Say that there are M channels in the 1-DEG. T is the transmission probability for a channel to go from electrode 1 to electrode 2, which is given by the sum of the sum of the transmission probability from the ith to the jth channel Clearly this e- didn’t make it. Reflections are the cause of resistance in the wire. But don’t rule out scattering forward again. Versus

11
VM Ayres, ECE802-604, F13 Lecture 11, 03 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability T(N) for multiple scatterers T(L) in terms of a “how far do you get length” L 0 How to correctly measure I = GV Landauer-Buttiker: all things equal 3-, 4-point probe experiments: set-up and read out

12
VM Ayres, ECE802-604, F13 This is a representation of 2 scatterers. Go from 2 scatterers to N scatterers per unit length L. What happens to the transmission probability T: R1R1 R2R2

13
VM Ayres, ECE802-604, F13 Transmission probability for 2 scatterers: T = T 12 : Include the forward reflections that rein forces the transmission: 1 back- forth then out 2 back- forth then out

14
VM Ayres, ECE802-604, F13 Transmission probability for 2 scatterers: T = T 12 : Eliminate R 1 and R 2 :

15
VM Ayres, ECE802-604, F13 Transmission probability for 2 scatterers: T = T 12 : Ratio the Reflection to the Transmission probability:

16
VM Ayres, ECE802-604, F13 Transmission probability for 2 scatterers: T = T 12 : That’s interesting. That Ratio is additive: Assuming that the scatterers are identical:

17
VM Ayres, ECE802-604, F13 Transmission probability for N identical scatterers: You’ll get the same result for N identical scatterers:

18
VM Ayres, ECE802-604, F13 Transmission probability for N identical scatterers: Now solve for transmission probability T(N):

19
VM Ayres, ECE802-604, F13 Transmission probability T(N) => T(L): Re-write N in terms of = N/L: Define a “how far do you get length” L 0 : L 0 is similar to a mean free path L m but in terms of T versus lots/few R

20
VM Ayres, ECE802-604, F13 Transmission probability T(N) => T(L): Therefore: with:

21
VM Ayres, ECE802-604, F13 Transmission probability T(N) => T(L):

22
VM Ayres, ECE802-604, F13 Lecture 11, 03 Oct 13 In Chapter 02 in Datta: Transport: current I = GV V = IR => I = GV Velocity Energy levels M M(E) Conductance G = G C in a 1-DEG Example Pr. 2.1: 2-DEG-1-DEG-2-DEG Example: 3-DEG-1-DEG-3-DEG Transmission probability: the new ‘resistance’ How to evaluate the Transmission/Reflection probability T(N) for multiple scatterers T(L) in terms of a “how far do you get length” L 0 How to correctly measure I = GV Landauer-Buttiker: all things equal 3-, 4-point probe experiments: set-up and read out

23
VM Ayres, ECE802-604, F13 Now relate the transmission probability T(N) or T(L) to an e- current I using Landauer’s formula for G:

24
VM Ayres, ECE802-604, F13 Add probes: 3-point configurations:

25
VM Ayres, ECE802-604, F13 Add probes: 4-point configurations:

26
VM Ayres, ECE802-604, F13 h Landauer-Buttiker formalism: Very briefly: why:

27
VM Ayres, ECE802-604, F13 Landauer-Buttiker formalism: Very briefly: why: 2/ Due to a physical bending, probe P1 couples preferentially to -k x states, while probe P2 couples preferentially to +k x states. You could read normal, very low or negative resistance depending on T. 3/ How close is your probe to a scatterer: e- wave interference zero reading?

28
VM Ayres, ECE802-604, F13 Landauer-Buttiker formalism: Very briefly: why:

29
VM Ayres, ECE802-604, F13 Landauer-Buttiker formalism: how: q <- p is from p to q, where p and q are any of the terminals.

30
VM Ayres, ECE802-604, F13 Landauer-Buttiker formalism: how:

31
VM Ayres, ECE802-604, F13 Landauer-Buttiker formalism: how:

32
VM Ayres, ECE802-604, F13 Landauer-Buttiker formalism: how:

33
VM Ayres, ECE802-604, F13 Landauer-Buttiker formalism: how: GOAL: Find resistance R

34
VM Ayres, ECE802-604, F13 Example: 3 point probe-a Find R for this circuit!

35
VM Ayres, ECE802-604, F13 qqq

36
qqq

37
qqq

38
Landauer-Buttiker set-up is complete

39
VM Ayres, ECE802-604, F13

47
In V 1 eq’n ?

48
VM Ayres, ECE802-604, F13

54
= R 21 R 3terminal = R 3t

55
VM Ayres, ECE802-604, F13 Example: 3 point probe-b Question: How would you find R for this configuration? Answer: a/ Choose: V 3 = 0 b/ Choose: ideal I 1 = 0 c/ From I-V 2x2 matrix equations, identify the R that you want as:

56
VM Ayres, ECE802-604, F13 Example: 3 point probe-b Question: How would you find R for this configuration? Answer: a/ Choose: V 3 = 0 b/ Choose: ideal I 1 = 0 c/ From I-V 2x2 matrix equations, identify the R that you want as: From: V’ = V 1 – V 3 =R 11 I 1 + R 12 I 2

Similar presentations

OK

ECE 802-604: Nanoelectronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University

ECE 802-604: Nanoelectronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on sea level rise map Ppt on grease lubrication training Free ppt on autism Ppt on interview etiquettes Ppt on 555 timer schematic Ppt on building construction in india Ppt on different types of dance forms computer Download ppt on civil disobedience movement martin Ppt on induced abortion Ppt on brain computer interface