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 Detectors Semiconductors play a fundamental role in all of these detection methods.
Transcript
Goal: Convert photons to an electronic signal
with as little accompanying noise as possibleideally at the quantum limit enforced by the photons.
with as much conversion efficiency as possible1 photon yields 1 electron (or ideally a bunch of electrons)
Primary Detection Methods
Bulk thermal response (bolometry)incident radiation chages the temperature of the detectorelectrical resistance changes with temperature
Conversion of photons to ''free'' electronsquantum responsephotoelectric or solid state detection
Coherent detectionsense wave nature (phase) of the photons primarily through heterodyning to lower frequencies
Detectors
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.
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)
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 SemiconductorsThe 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 SemiconductorsThe 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.
load resistor
detector
PhotoconductorsA 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.
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,
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.
= −⟨v ⟩E
= nq ⟨v ⟩E
= nq
where is the photon flux, is the quantum efficiencyfor 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
where
photon = qe h
The resistance of a photoconductor is measured by applying a The resistance of a photoconductor is measured by applying a voltage across the device to produce avoltage 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.
E
Photocurrent and Photoconductive Gain
t is the transit time for a carrier from one electrode to the other
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 breakdownmaximizing carrier lifetime through the elimination of defects and impurities.
E
Photocurrent and Photoconductive Gain
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.
Detector Opacity
= 1 − R1 − e−a
absorption efficiency can be improved by placing a reflective surface at the back of a detector
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.
Real-world PhotoconductorsLeakage/Dark current
Note that there is one such term for each population (intrinsic material, contaminants, defects)
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 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
2
Noise in Photoconductors
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.
Detector Characterization
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 simplifiedequivalent....
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.
Conversion to Electronic Signals
detector
Load resistor
Introducing an impurity into an intrinsic semiconductor can introduce energy states with very small bandgaps relative to the intrinsic conduction and valence bands.
