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Fundamentals of Nanoelectronics

ECE495 - Session 42, Dec 11, 2009

Thermoelectricity II

Professor Supriyo Datta

Class notes taken by: Mehdi Salmani

� = 2 �ℎ � �� ��� �

��� ����

��� − �� �����������

�� �!"����# $ ∆$

= &��' + &��∆

100 μm

10 μm

1 μm

0.1 μm

←

10 nm

1 nm

Heat current:

�)* = �+ , �� ��� �� − -� ��� − �� = &��' + &��∆

It carries �� − - energy before it was carry q charge.

DI

ee

e

Fundamentals of Nanoelectronics, Session 42

Dec 11, 2009

2

&�� = �!.+ , �� /− ��

��0 ���

&�� = 2�ℎ � �� ��� �� − -

�− 1�1�

&�� = 2�ℎ � �� ��� �� − - �− 1�

1�

2 &�� = &��

3� = &��' + &��∆ �) = &��' + &��∆ 4

I = 0 then Seebeck coefficient: 5 = "∆$ = 6*.

6**

f1=f2and ∆T=0 then Peltier Coefficient: Π = 898 = 6.*

6**

2 : = 5 ;<=>?@ A<=BC?D@

� = 2 �ℎ � �� ��� ��� − ��

��� = E�� ���� Semi-classical view

��� = ABF<[�&�&�] Full quantum view

E

µ µ1 2

E heatedcooled