Detectors
Goal: Convert photons to an electronic signal
with as little accompanying noise as possible
ideally at the quantum limit enforced by the photons.
with as much conversion efficiency as possible
1 photon yields 1 electron (or ideally a bunch of electrons)
Primary Detection Methods
Bulk thermal response (bolometry)
incident radiation chages the temperature of the detector
electrical resistance changes with temperature
Conversion of photons to ''free'' electrons
quantum response
photoelectric or solid state detection
Coherent detection
sense wave nature (phase) of the photons
primarily through heterodyning to lower frequencies
Semiconductors play
a fundamental role
in all of these detection methods.
Detectors
Semiconductor Detectors
While the photoelectric effect creates free electrons
semiconductors provide an analog in the solid state.
Photoexcitation across the material's “insulating” bandgap produces
free carries.
cutoff =
1.24  m
E gap eV 
Resulting carriers produce a change in bulk material resistance
(photoconductors)
Carriers can also be directly detected as an electrical current in a
diode configuration (photovoltaics)
Photons can also change the bulk temperature of a small piece of
semiconductor changing the electrical resistance (bolometers)
Silicon
PbS
GaAs
InSb
Bandgap Cutoff (um)
1.11
1.12
0.37
3.35
1.43
0.87
0.18
6.89
Note cutoff is for room temperature.
Cutoffs change at cryogenic
temperature due to changing lattice
spacing (e.g. InSb detectors have a
5.5um cutoff at 77K).
Photoconduction in Intrinsic
Semiconductors
Pure elemental or compound (e.g. InSb) materials with small
bandgaps are “intrinsic” semiconductors.
Held near absolute zero temperature they will be insulators.
In this state photons can promote electrons to the conduction band
leaving a “hole” behind.
Both “particles” participate in conduction.
Conduction in Intrinsic Semiconductors
The details of the lattice interaction discussed previously will
determine the “mobility” of both the electrons and holes.
A charge in the lattice accelerating under the influence of an electric
field will experience frequent lattice scattering that sets a limit to
the mean drift velocity of the charge.
Conduction in an intrinsic semiconductor may be either hole or
electron dominated – note this has nothing to do with whether the
material is “p” or “n” type which involves “doped” semiconductors.
Conduction in Intrinsic Semiconductors
The details of the lattice interaction discussed previously will
determine the “mobility” of both the electrons and holes.
A charge in the lattice accelerating under the influence of an electric
field will experience frequent lattice scattering that sets a limit to
the mean drift velocity of the charge.
Conduction in an intrinsic semiconductor may be either hole or
electron dominated – note this has nothing to do with whether the
material is “p” or “n” type which involves “doped” semiconductors.
Photoconductors
A perfect insulator (e.g. an ideal
semiconductor at T=0K) has infinite
electrical resistance.
If photons create free carriers, the
electrical resistance becomes finite.
The net conductivity is an equilibrium
between electron/hole creation and
electron/hole recombination – lifetime = 
–
Greater photon rates produce greater
conductivity.
–
Short carrier lifetimes thwart sensitivity.
Resistance of the detector is measured
with Ohm's law and a voltage divider.
load resistor
detector
Quantitative Photoconductivity
Conductivity is proportional to the number of free
carriers and to their mobility
The number of free carriers depends on
photon flux (creation)
carrier lifetime (destruction)
Resistance then depends on the carrier mobility, ,
depends on the solid state properties of the material and will be
different for electrons and holes
Definition of conductivity – inverse resistance per unit
material cross section per unit material length.
Bulk resistance is then:
Quantitative Photoconductivity
Relate photoconductivity to the arrival rate of photons at the
detector.
express  in terms of the number of available carriers and their
mobility, 
 = nq
⟨v⟩
E
= nq 
where
 = −
⟨v⟩
E
there is a mobility term for both electrons and holes.
Define the carrier lifetime, . The equilibrium abundance
conductivity is the product of the creation rate and the
lifetime.
 photon =   qe  h 
where  is the photon flux,  is the quantum efficiency
for photon detection, and  is the carrier lifetime
Since R is inversely proportional to , by Ohm's
Law, the output current from a “biased”
photoconductor
is directly proportional
to photon
flux and to the applied voltage
Photocurrent and Photoconductive Gain
The resistance of a photoconductor is measured by applying a
voltage across the device to produce a current
Photon-generated carriers modulate the conductivity and thus the
current.
The carriers are created temporarily. Each contributes to the
photocurrent for a limited amount of time, .
The photoconductive gain, G, quantifies the probability that a
generated carrier will traverse the extent of the detector and reach an
electrode. The observed current is degraded by G.
t is the transit time for a carrier
from one electrode to the other
E
Photocurrent and Photoconductive Gain
Optimizing “G” involves
making the detector as thin as is feasible (at the risk of making the
detector transparent).
increasing the bias voltage/electric field to the limits of conductive
breakdown
maximizing carrier lifetime through the elimination of defects and
impurities.
E
Detector Opacity
In order to create an electron hole pair, a photon must be absorbed in
the active region of the detector.
A detector can be too thin and the photon will pass through
undetected
A detector can be too thick and the photon will be absorbed on the
surface of the detector without hope of reaching an electrode.
Optimizing the detector opacity (often requiring thick detectors)
and the photoconductive gain (requiring thin detectors) are often
competing goals.
 = 1 − R1 − e−a 
absorption efficiency can be improved by
placing
a reflective surface at the back of a
detector
Real-world Photoconductors
Leakage/Dark current
The ideal photoconductor has infinite resistance at zero
temperature.
In reality, materials are imperfect and free carriers exist
independent of the presence of photoelectrons. Imperfections arise
from
defects in the crystal lattice
impurities unintentionally incorporated into the crystal (extrinsic
contaminants)
These defects produce a finite resistance (free or weakly bound
carriers) even at cryogenic temperatures.
They also create recombination sites which reduce carrier
lifetimes.
Ignoring imperfections in readouts, Poisson statistics dominate the
noise.
If dark current >> signal then noise is dark current dominated.
Note that there is one such term for each
population
(intrinsic material,
contaminants, defects)
Noise in Photoconductors
Poisson noise from photon arrival is unavoidable.
Photoconductors exacerbate the issue because what is
observed is the current resulting from the generation (photons)
and recombination of carriers. Both are random events leading
to a  2 increase in Poisson noise.
Additional noise results from Brownian motion of carriers at finite
temperature.
A resistor or capacitor, unconnected to a circuit, will exhibit
voltage/current fluctuations at its terminals -- Johnson / kTC
noise
Detector Characterization
The performance of detectors can be characterized
in terms of:
Responsivity -- the number of amps (electrons)
out for a Watt of incident power
Noise Equivalent Power (NEP) -- The amount of
incident power needed to produce a signal equal
to the RMS noise.
Detectivity (D) - The inverse of NEP (for those
who don't golf).
Normalized Detectivity (D*) -- D divided by
sqrt(detector area)
this provides a more geometry independent
assessment of detector performance.
Conversion to Electronic Signals
To be practical, a photoconductor must be placed in a circuit
Because one must generate a current, a voltage bias
must be placed across the detector.
Ideally, the bias should not change as a function of
illumination.
Seemingly it must because shining light on the detector
changes its resistance and thus the voltage drop in the
circuit below.
Load Resistor
Detector
Conversion to Electronic Signals
An operational amplifier permits the best of both worlds.
An op amp has two differential inputs
It's purpose is to amplify infinitely the difference between
the two inputs. Doesn't sound interesting or practical,
but... consider the circuit below.
or at least its simplified
equivalent....
Conversion to Electronic Signals
An operational amplifier permits the best of both worlds.
An op amp has two differential inputs
It's purpose is to amplify infinitely the difference between
the two inputs. Doesn't sound interesting or practical,
but... consider the circuit below.
Conversion to Electronic Signals
An operational amplifier permits the best of both worlds.
An op amp has two differential inputs
It's purpose is to amplify infinitely the difference between
the two inputs. Doesn't sound interesting or practical,
but... consider the circuit below.
Load resistor
detector
Extrinsic Semiconductors
Introducing an impurity into an
intrinsic semiconductor can
introduce energy states with very
small bandgaps relative to the
intrinsic conduction and valence
bands.