Transcript class1_BK - Center for Detectors

Detectors
Class 1 : Background
Bob Kremens
[email protected], 475-7286
Don Figer
Book
• Rieke , Detection of Light : From the Ultraviolet to the
Submillimeter.
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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
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Attend classes, read material provided.
Hand in homework. (30%)
Mid-term (35%)
Final (35%)
Light: preliminaries
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Light is the only thing we actually see – eg. When I “see” you, I am actually
seeing light reflected off you.
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Light is a transverse wave, whose origin is accelerating electrons, eg in the
sun
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Accelerating electrons not only can produce light, but also radio waves,
microwaves, x-rays…. Grouped together as electromagnetic waves.
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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
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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 vibrating (oscillating) electric and
magnetic fields regenerate each other this is the electromagnetic (EM) wave.
• The EM wave moves outwards (emanates) from the vibrating charge.
Maxwell’s Equations
E   /
B  0
B
 E  
t
E
  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
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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:
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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.
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Both cases violate energy conservation.
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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
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This is the speed in vacuum, and about the same in air. Slower in different
media depending on n.
The Electromagnetic Spectrum
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In vacuum, all electromagnetic waves move at the same speed c, but
differ in their frequency (and wavelength). Classified like:
recall c = f l
• 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)
and long-wavelength
violet is the high-freq end (next highest is ultraviolet)
short wavelength
The electromagnetic spectrum cont.
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frequency of wave = freq of vibrating source.
Applies to EM waves too, where source is oscillating electrons
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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.
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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.
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So materials that are opaque, or non-transparent, to visible light, have natural
frequencies in the range of visible light. (see more soon)
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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.
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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.
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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
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Have natural frequencies in the visible range, Eg books, you, tables, metals…
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So, they absorb light without re-emitting it.
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Light energy goes into random kinetic energy ie heat.
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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.
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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
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E = h=hc/l
h=6.626 x 10-34 Js
 in hertz
l 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 nm
UVB 320 nm - 290 nm
UVC 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.
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.
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)
X-Rays
Map with X-Rays
Gamma-Rays : at photon energies
above 100 million electron Volts
WMAP
Wilkinson Microwave Anisotropy Probe
33 GHz
9.1 mm
23 GHz
13.0 mm
61 GHz
4.9 mm
41 GHz
7.3 mm
94 GHz
3.2 mm
http://map.gsfc.nasa.gov/m_or.html
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 the absence of collisions,
molecules tend to remain
in the lowest energy state
available.
Collisions can knock a molecule
into a higher-energy state.
The higher the temperature,
the more this happens.
Low T
High T
N 2 exp   E2 / k BT 

N1 exp   E1 / k BT 
• In equilibrium, the ratio of the populations of two states is:
exp(–DE/kBT )
• As a result, higher-energy states are always less populated than
the ground state, and absorption is stronger than stimulated
emission.
Absorption
Spontaneous Emission
Stimulated
Emission
Einstein A and B coefficients
In 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 of
downward transitions:
B01 N0 I = A N1 + B10 N1 I
Recalling the MaxwellBoltzmann Distribution
Rearranging:
(B01 I ) / (A + B10 I ) = N1 / N0 = exp[–DE/kBT ]
Einstein A and B coefficients and
Blackbody Radiation
Now solve for the irradiance in: (B01 I ) / (A + B10 I ) = exp[-DE/kBT ]
Rearrange to:
or:
or:
B01 I exp[DE/kBT] = A + B10 I
I = A / {B01 exp[DE/kBT] – B10}
I = [A/B10] / { [B01 /B10] exp[DE/kBT] – 1 }
Now, when T  I should also. As T , exp[DE/kBT ]  1.
So:
B01 = B10  B
 Coeff up = coeff down!
And:
I = [A/B] / {exp[DE/kBT ] – 1}
Eliminating A/B and use DE = h:
I(,T)=2h³/{c²(exp[h/kBT]-1)}
Planck’s Equation
I(,T)=2h³/{c²(exp[h/kBT]-1)}
use  = c/l
I d = Il dl
 2 hc 2 / l 5 
Il 
exp  hc / lkBT  1
h = Planck’s constant = 6.6260755 x 10-34 Jsec
k = Boltzmann’s constant = 1/380658 x 10-23 J/K
c = 3 x 108 m/sec
T in Kelvin
I = spectral radiant excitance = f(l,T) = Wcm-2 m-1
Note
A/B 3
Remember
A = spontaneous rate
B = 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.
lT  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
 = emissivity
e.g.
Aluminum foil = 0.02
Red brick = 0.9
soot = 0.95
The Electromagnetic Spectrum
EM Spectrum
Atmospheric Transmission