DetectorsClass 1 : Background

Bob Kremens

kremens@cis.rit.edu, 475-7286

Don Figer

Book

• Rieke , Detection of Light : From the Ultraviolet to the Submillimeter.– Chap 1, 2 3, 4, 5, 6, 7, 9, 10, 11– Radiometry & solid state physics review– Intrinsic photoconductors– Extrinsic photoconductors– Photodiodes, QWIP, STJ– Amplifiers and readouts– CCD, hybridized arrays– Photoemissive– Bolometers– Coherent receivers– Sub-millimeter

Class Expectations• Attend classes, read material provided.• Hand in homework. (30%)• Mid-term (35%)• Final (35%)

Light: preliminaries

• Light is the only thing we actually see – eg. When I “see” you, I am actually seeing light reflected off you.

• Light is a transverse wave, whose origin is accelerating electrons, eg in the sun

• Accelerating electrons not only can produce light, but also radio waves, microwaves, x-rays…. Grouped together as electromagnetic waves.

• Different types of electromagnetic waves differ in their frequency (and wavelength): light is just a small part of the electromagnetic spectrum with certain frequency range

Electromagnetic Waves• Origin is accelerating electron: how?

• Consider shaking a charged rod back and forth in space

i.e. You create a current (= moving charges) that varies in time. i.e. a changing electric field in space.

A changing electric field creates a changing magnetic field, that in turn creates a changing electric field, that in turn…

i.e. a propagating disturbance

• The EM wave moves outwards (emanates) from the vibrating charge.

• The vibrating (oscillating) electric and magnetic fields regenerate each other - this is the electromagnetic (EM) wave.

Maxwell’s Equations

/

0

BE E

t

EB B

t

where E is the electric field, B is the magnetic field,

ρ is the charge density, ε is the permittivity, and µ is the

permeability of the medium.

Electromagnetic Wave Velocity• An electromagnetic wave travels at one constant speed through space. Why?

Inherently due to wave nature (eg objects like spacecrafts can change speed, and go at different constant speeds); specifically, induction and energy conservation:

• The strength of the induced fields depends on the rate of change of the field that created it. So, if light traveled slower, then its electric field would be changing slower, so would generate a weaker magnetic field, that in turn generates a weaker electric field, etc….wave dies out.Similarly, if light sped up, would get stronger fields, with ever-increasing energy.

• Both cases violate energy conservation.

• What is the critical speed at which mutual induction sustains itself? Maxwell calculated this: 300 000 km/s = c

i.e. 3 x 108 m/s

• This is the speed in vacuum, and about the same in air. Slower in different media depending on n.

The Electromagnetic Spectrum• In vacuum, all electromagnetic waves move at the same speed c, but differ

in their frequency (and wavelength). Classified like:

• Visible light: 4.3 x 1014 Hz to 7 x 1014 Hz

i.e. red is at the low-freq end of light (next lowest is infrared)

violet is the high-freq end (next highest is ultraviolet)

and long-wavelength

short wavelength

recall c = f

The electromagnetic spectrum cont.

• frequency of wave = freq of vibrating source.

Applies to EM waves too, where source is oscillating electrons

• Note that EM waves are everywhere! Not just in air, but in interplanetary “empty space” - actually a dense sea of radiation. Vibrating electrons in sun put out EM waves of frequencies across the whole spectrum.

• Any body at any temperature other than absolute zero, have electrons that vibrate and (re-)emit in response to the EM radiation that permeates us, even if very low frequency.

Transparent materials• When light goes through matter, electrons in the matter are forced to

vibrate along with the light. • Response of material depends on how close the forced vibration is

to the natural frequency of the material. Same is true here with light.• First note that visible light has very high freq (~1014 Hz), so if

charged object is to respond to this freq, it has to have very little inertia ie mass. An electron does have tiny mass!

• Transparent materials – allow light to pass in straight lines

Simple model of atom: think of electrons attached to nucleus with springs. Light makes these springs oscillate.

• Different atoms/molecules have different “spring strengths” - so different natural frequencies.

• If this natural freq = that of impinging light, resonance occurs i.e. vibrations of electrons build up to high amplitudes, electrons hold on to the energy for “long” times, while passing it to other atoms via collisions, finally transferred to heat. Not transparent.

Transparent materials cont.• So materials that are opaque, or non-transparent, to visible light, have natural

frequencies in the range of visible light. (see more soon)

• Glass is transparent: its natural freqs are higher, in the ultraviolet range.

So glass is not transparent to ultraviolet.

But is transparent to lower freqs i.e. visible spectrum.

• What happens in this off-resonance case?

Atoms are forced into vibration but at less amplitude, so don’t hold on to the energy long enough to transfer much to other atoms through collisions. Less is transferred to heat; instead vibrating electrons re-emit it as light at same frequency of the impinging light.

• Infrared waves – frequencies lower than visible – can force vibrations of atoms/molecules as well as electrons in glass. Increases internal energy and temperature of glass. Often called heat waves.

• Glass is transparent to visible, but not to uv nor infrared.

Opaque materials• Have natural frequencies in the visible range, Eg books, you, tables, metals…

• So, they absorb light without re-emitting it.

• Light energy goes into random kinetic energy ie heat.

• Usually, not all the frequencies in the visible light spectrum are resonant - those that aren’t, get reflected: this gives the object color

Some cases of interest:• Earth’s atmosphere – transparent to some uv, all visible, some infrared. But is

(thankfully) opaque to high uv. - the small amount of uv that does get through causes dangerous sunburn. - clouds are semi-transparent to uv, so can still get sunburnt on a cloudy day.

• Water – transparent. This explains why objects look darker when wet:Light is absorbed and re-emitted, bouncing around inside wet region;

each bounce loses some energy to material. So less light enters your eye – looks darker.

Transparent materials cont.• So light-transparent materials (like glass) have natural frequencies that don’t coincide with those of light. The atoms re-emit after absorbing.

This re-emission is time-delayed:

• This leads to speed of light being different in different media:

In vacuum, it’s c

In air, only slightly less than c

In water, it’s 0.75c

In glass, 0.67c (but depends on type of glass)

When light emerges back into air, it travels again at original c

Radiometry

• E = h=hc/• h=6.626 x 10-34 Js in hertz is wavelength in meters

• c=2.998 x 108 m/s

(nu-bar) represents wavenumber, the number of wavelengths in 1 cm

EM Waves

1 eV = 1.6 x 10**-19 J

Questions

(1) Why in the sunlight is a black tar road hotter to the touch than a pane of window glass?

(2) Can you get sunburnt through a glass window?

Questions

(1) Why in the sunlight is a black tar road hotter to the touch than a pane of window glass?

Sunlight is absorbed and turned to internal energy in the road surface, but transmitted through the glass to somewhere else.

(2) Can you get sunburnt through a glass window?

Glass is opaque to ultraviolet light, so won’t transmit it, so you won’t get sunburnt (although you might get hot!).

http://www.edmundoptics.com/TechSupport/DisplayArticle.cfm?articleid=259

UVA 400 nm - 320 nmUVB 320 nm - 290 nmUVC 290 nm - 100 nm

http://www.fda.gov/fdac/features/2000/400_sun.html

Sunburn is caused by a type of UV light known as UVB. The thinking was if you prevent sunburn, you'd prevent skin cancer. In recent years, scientists have come to appreciate that UVA, may be just as, or even more, important in causing some skin disorders. Although experts still believe that UVB is responsible for much of the skin damage caused by sunlight UVA may be an important factor in other types of sun damage. Most sunscreens block UVB but fewer filter out most of the UVA.

I s it correct to say that in every case, without exception, any radio wave travels faster than any sound wave?

1. Yes2. No

1. Yes2. No

Is it correct to say that in every case, without exception, any radio wave travels faster than any sound wave?

Answer: 1

Yes, because any radio wave travels at the speed of light. A radio wave is an electromagnetic wave, like a low-freq light wave.A sound wave, on the other hand, is fundamentally different. A sound wave is a mechanical disturbance propagated through a material medium by material particles that vibrate against one another.

In air, the speed of sound is about 340 m/s, about one millionth the speed of a radio wave. Sound travels faster in other media, but in no case at the speed of light.

Which of these lamps is emitting electromagnetic radiation?

1. Lamp A2. Lamp B3. Both4. Neither

1. Lamp A2. Lamp B3. Both4. Neither

Which of these lamps is emitting electromagnetic radiation?

Answer: 3

All bodies with any temperature at all continually emit electromagnetic waves. The frequency of these waves varies with temperature. Lamp B is hot enough to emit visible light. Lamp A is cooler, and the radiation it emits is too low in frequency to be visible—it emits infrared waves, which aren’t seen with the eye. You emit waves as well. Even in a completely dark room your waves are there. Your friends may not be able to see you, but a rattlesnake can!

Visible Light (hand drawn using 7000 stars)

Galactic Center

COBE Image - IR

The Sky : 408 MHz

cosmic radio waves are generated by high energy electrons spiraling along magnetic fields. & pulsars

Ultra-Violet (IUE)

Map with X-RaysX-Rays

Gamma-Rays : at photon energies above 100 million electron Volts

23 GHz13.0 mm

33 GHz9.1 mm

41 GHz7.3 mm

61 GHz4.9 mm

94 GHz3.2 mm

http://map.gsfc.nasa.gov/m_or.html

Wilkinson Microwave Anisotropy ProbeWMAP

The Electromagnetic Spectrum

Radio & microwave regions (3 kHz – 300 GHz)

Synchrotron Radiation

Synchrotron X-ray source and uses at LBL

X-rays for photo-lithography

You can only focus light to a spot size depending on the light’s wavelength. So x-rays are necessary for integrated-circuit applications with structure a small fraction of a micron.

1 keV photons from a synchrotron:

2 micron lines over a base of 0.5 micron lines.

Blackbody Radiation

A black body is a theoretical object that absorbs 100% of the radiation that hits it. Therefore it reflects no radiation and appears perfectly black.

Blackbody

• In practice no material has been found to absorb all incoming radiation, but carbon in its graphite form absorbs all but about 3%. It is also a perfect emitter of radiation. At a particular temperature the black body would emit the maximum amount of energy possible for that temperature. This value is known as the black body radiation. It would emit at every wavelength of light as it must be able to absorb every wavelength to be sure of absorbing all incoming radiation. The maximum wavelength emitted by a black body radiator is infinite. It also emits a definite amount of energy at each wavelength for a particular temperature, so standard blackbody curves can be drawn for each temperature, showing the energy radiated at each wavelength. All objects emit radiation above absolute zero.

The Maxwell-Boltzman Distribution

• In equilibrium, the ratio of the populations of two states is:

exp(–E/kBT )• As a result, higher-energy states are always less populated than

the ground state, and absorption is stronger than stimulated emission.

In the absence of collisions,molecules tend to remainin the lowest energy stateavailable.

Collisions can knock a molecule into a higher-energy state.The higher the temperature, the more this happens.

22

1 1

exp /

exp /B

B

E k TN

N E k T

Low T High T

Absorption

Spontaneous Emission

Stimulated Emission

Einstein A and B coefficientsIn 1916, Einstein considered the various transition rates between molecular states (say, 0 and 1) involving light of irradiance, I:

Absorption rate = B01 N0 I

Spontaneous emission rate = A N1

Stimulated emission rate = B10 N1 I

In equilibrium, the rate of upward transitions equals the rate ofdownward transitions:

B01 N0 I = A N1 + B10 N1 I

Rearranging: (B01 I ) / (A + B10 I ) = N1 / N0 = exp[–E/kBT ]

Recalling the Maxwell-Boltzmann Distribution

Einstein A and B coefficients and Blackbody Radiation

Now solve for the irradiance in: (B01 I ) / (A + B10 I ) = exp[-E/kBT ]

Rearrange to: B01 I exp[E/kBT] = A + B10 I

or: I = A / {B01 exp[E/kBT] – B10}

or: I = [A/B10] / { [B01 /B10] exp[E/kBT] – 1 }

Now, when T I should also. As T , exp[E/kBT ] 1.

So: B01 = B10 B Coeff up = coeff down!

And: I = [A/B] / {exp[E/kBT ] – 1}

Eliminating A/B and use E = h

I(,T)=2h³/{c²(exp[h/kBT]-1)}

Planck’s Equation

2 52 /

exp / 1B

hcI

hc k T

use = c/I d = I d

h = Planck’s constant = 6.6260755 x 10-34 Jseck = Boltzmann’s constant = 1/380658 x 10-23 J/Kc = 3 x 108 m/secT in Kelvin

I = spectral radiant excitance = f(,T) = Wcm-2 m-1

I(,T)=2h³/{c²(exp[h/kBT]-1)}

Note

A/B 3

Remember A = spontaneous rateB = stimulated rate

X-ray lasers hard to make (need lots of B).

Blackbody Emission

The higher the temperature, the more the emission and the shorter the average

wavelength.

Wien's Law: Blackbody peak wavelength scales as 1/Temperature.

T 3000 m K (2898 actually)

Stefan Boltzmann Law

P = AT4 For blackbodies

= 5.67033 x 10-8 W/K4 m2

P = AT4 For real objects

= emissivitye.g. Aluminum foil = 0.02

Red brick = 0.9soot = 0.95

EM SpectrumThe Electromagnetic Spectrum

Atmospheric Transmission