Quantum Transport: Atom to Transistor

Symbols

Fundamental Constants

q

electronic charge

1.602 10 ?19 C

h

Planck constant

6.626 10 ?34 Js

?

h/2 ?

1.055 10 ?34 Js

m

free electron mass

9.11 10 ?31 kg

? 0

permittivity of free space

8.854 10 ?12 F/m

a 0

Bohr radius, 4 ? ? 0 ? 2/ mq 2

0.0529 nm

G 0 = q 2/ h

conductance quantum

38.7 10 ?6 S (S = 1/ ? = A/V) = 1/(25.8 10 3 ?)

We will use rationalized MKS units throughout the book, with energy in electron-volts: 1 eV = 1.602 10 ?19 J.

E 0

q 2/8 ? ? 0 a 0

13.6 eV

Some of the Other Symbols Used

Units

I

current (external)

amperes (A)

J

current (internal)

amperes (A)

V

voltage

volts (V)

R

resistance

ohms ( ? = V/A)

G

conductance

siemens (S = A/V)

a

lattice constant

meters (m)

t 0

? 2/2 m* a 2

electron-volts (eV)

t

time

seconds (s)

m*

effective mass

kilograms (kg)

m c

conduction band effective mass

kilograms (kg)

? 1, 2, 3

Luttinger parameters

dimensionless

? r

relative permittivity

dimensionless

electric field

V/m

L

channel length

m

S

cross-sectional area

m 2

wavevector

/m

velocity

m/s

n S

electron density per unit area

/m 2

n L

electron density per unit length

/m

N

number of...

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