Dielectric properties of metals

Ellipsometry

1 1 2 2sin sinn n

Ellipsometry

Ellipsometry measures the change of polarization upon reflection. The measured signal depends on the thickness and the dielectric constant.

http://en.wikipedia.org/wiki/Ellipsometry

Ellipsometry

The ratio of the two reflected polarizations is insensitive to instabilities of light source or atmospheric absorption.

Intraband transitions

( ) ( )c vE k E k

When the bands are parallel, there is a peak in the absorption (")

Ibac

h &

Luet

h

Intraband (d-band) absorption

1 R

y =

13.6

ev

Reflection Electron Energy Loss Spectroscopy

Fast electrons moving through the solid generate and a time dependent electric field. If the polarization moves out of phase with this field, energy will be lost. This is detected in the reflected electrons.

e-

Microwave engineering

Microwave frequencies are a few GHz

The wavelength is smaller than the circuit

Losses in metals increase with increasing frequency

Losses in dielectrics increase with increasing frequency

There is a characteristic length scale called the skin depth which tells us how far into a metal fields penetrate before they are reflected out.

Skin depth << 1

0B J

Ohm's law0J E

Take the curl0

1 dBJ Edt

0 0

1 dBBdt

Ampere's law

Faraday's law

2B B B

Vector identity0

2

0 0

1 dBBdt

02 2

11

ine ne

<< 1

Skin depth

0 0

2

2

0 0

1 dBBdt

2

0 0

k i

Assume harmonic dependence 0

i kx tB e

0 0 0 00 0 2 2

k i i

Exponential decaySkin depth

Light p is reflected out of a metal. The waves penetrate a length .

Skin depth

//0 ˆi x txB B e e z

//0

0 0

(1 )1 ˆi x txB iJ B B e e y

/ / 4/0

0 0 0

2 ˆi x txBJE e e y

/ / 4/0

0

2 ˆi x txBJ e e y

/ 41 2 ii e

The electric field lags behind the magnetic field by 45 degrees.

Surface resistance

0

Rw

wfor

0

1sR

Complex signal processing at high frequencies > 1 GHz is difficult because the losses increase with frequency.

Usually you mix down to a lower frequency as soon as possible.

At low frequencies: 0

Rwt wt

When < t :

Superconducting filter

Complex signal processing at high frequencies > 1 GHz is difficult because the losses increase with frequency.

Simulation