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

2. Lecture 08, 24 Sep 13 In Chapter 02 in Datta:
Transport: current I = GV
V = IR => I = GV
Velocity
Energy levels M  M(E)
Conductance G in a 1-DEG
Scaling back up to 3-DEG using M
Transmission probability: the new ‘resistance’
How to evaluate the Transmission/Reflection probability
How to correctly measure I = GV
Landauer-Buttiker: all things equal
4-point probe experiments: set-up and read out
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3. Current I: basic idea:
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4. Current I: basic idea:
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5. Current I: basic idea:
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6. 1-Deg (no B) experiments: transport direction along kx:z y
px ny2 ħ2p nz2 ħ2p Ec
2m* m*Ly m*Lz2
E = x
Transport in x direction
Infinite square well (top) in y direction OR
Parabolic well (bottom) in y direction
Infinite square well in z direction
Well separated energy levels => nz = 1
px (ny + 1 )ħw nz2 ħ2p Ec
2m* m*Lz2
E =
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7. 1 Deg from parabolic U(y): energy eigenvalues:x x x x
Group velocity is ready
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8. Group velocity relationship: where from:
Conservation of Energy (special Sch eq’n):
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9. Current I: basic idea:
wrong:
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10. 1-DEG NT(E): just write down:
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11. 1-DEG NT(E): just write down:
Answer:
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12. 1-DEG NT(E) for parabolic U(y), B = 0:
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13. 1-DEG N(E) for parabolic U(y), B = 0:
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14. A finesse on N(E) in a transport situation:
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15. And can fill in the kx blank for group velocity:
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16. Calculate I: check Units first:
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17. Calculate I:
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18. Calculate I:
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19. What does ny do? It means e- has a choice of available energy levels, all of which have conductance G that become available as e- get more energy from applied V
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20. What does ny do? It means e- has a choice of available energy levels, all of which have conductance G that become available as e- get more energy from applied V. Sum Conductance G, just like nL in Pr. 1.3, and the result is:
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21. W Vsource to drain keep constant Vgate changes W
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22. What are m1 and m2:
Units: these are energies related to the applied potential.
note: eV / e = Volts
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23. 1 Deg + contacts and VDS: introduces a E-field vector potential in x: effect on transport pxz y
(px+pxE) ny2 ħ2p nz2 ħ2p Ec
2m* m*Ly m*Lz2
E = x
Transport in x direction
Infinite square well (top) in y direction OR
Parabolic well (bottom) in y direction
Infinite square well in z direction
Well separated energy levels => nz = 1
(px+pxE) (ny + 1 )ħw nz2 ħ2p Ec
2m* m*Lz2
E =
VM Ayres, ECE , F13