Sensitivity and Responsivity Sensitivity and Responsivity Responsivity, R( Responsivity, R( ): ): Ratio of the signal Ratio of the signal output, x, to the incident radiant output, x, to the incident radiant power, power, (in Watts). (in Watts). x R (voltage, current, charge (voltage, current, charge) Sensitivity, Q( Sensitivity, Q( ): ): Slope of a plot of x vs. Slope of a plot of x vs. . . d dx Q
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Transducers Converts one type of energy into another. Light Electrical (current, voltage, etc.) What characteristics should we look for in a transducer?
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Sensitivity and ResponsivitySensitivity and Responsivity
Responsivity, R(Responsivity, R():): Ratio of the signal output, x, to the Ratio of the signal output, x, to the incident radiant power, incident radiant power, (in Watts). (in Watts).
Sensitivity, Q(Sensitivity, Q():): Slope of a plot of x vs. Slope of a plot of x vs. ..
d
dx Q
d
dx Q
Spectral ResponseSpectral Response
Hamamatsu CatalogueHamamatsu Catalogue
Short Short limit – determined by window material limit – determined by window materialLong Long limit – determined by photocathode material limit – determined by photocathode material
Transmittance of Window MaterialsTransmittance of Window Materials
Hamamatsu CatalogueHamamatsu Catalogue
Response SpeedResponse Speed
Consider a sinusoidal input into a transducer with a Consider a sinusoidal input into a transducer with a finite response time.finite response time.
If the frequency, fIf the frequency, fcc, of the sinusoidal input is high, , of the sinusoidal input is high,
The frequency where R(The frequency where R() drops to 0.707 of the ) drops to 0.707 of the ideal is used to determine the time constant, ideal is used to determine the time constant, ..
cf2
1
cf2
1
Dark SignalDark Signal
Output in the absence ofOutput in the absence ofinput radiation.input radiation.
Often limits S/N at lowOften limits S/N at lowsignal intensities.signal intensities.
Douglas A. Skoog and James J. Leary, Principles of Instrumental Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.Analysis, Saunders College Publishing, Fort Worth, 1992.
Photon must have some Photon must have some minimum energy to release minimum energy to release an ean e--. Referred to as the . Referred to as the work function.work function.
tt = hc/E = hc/Ecc = 1240/E = 1240/Ecc
For most metals the work For most metals the work function is ~2 – 5 eV.function is ~2 – 5 eV.
The Work Function Limits the Spectral ResponseThe Work Function Limits the Spectral Response
Hamamatsu CatalogueHamamatsu Catalogue
2-5 eV = 250-620 nm2-5 eV = 250-620 nm
Use materials Use materials with lower work with lower work functions, e.g., alkali functions, e.g., alkali metals.metals.
Quantum Efficiency K(Quantum Efficiency K())# of photoelectrons ejected for # of photoelectrons ejected for every incident photon.every incident photon.
Typically K(Typically K() < 0.5) < 0.5
Rate of electrons emitted from Rate of electrons emitted from the cathode (rthe cathode (rcpcp):):
rrcpcp = = ppK(K())
where where pp is the photon flux is the photon flux
(photons / sec).(photons / sec).
Multiply by electron charge to Multiply by electron charge to get current.get current.
iicpcp = er = ercpcp = eK( = eK())ppIngle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Efficiency with which photon Efficiency with which photon energy is converted to photo-energy is converted to photo-electrons.electrons.
h
e K R
h
e K R
Units: A / WUnits: A / W
Anodic CurrentAnodic Current
Collection Efficiency (Collection Efficiency () depends ) depends on the bias voltage (Eon the bias voltage (Ebb).).
Arrival Rate at the AnodeArrival Rate at the Anode
(collection rate):(collection rate):
rrapap = = rrcpcp = = ppK(K())
iiapap = = iicpcp = = pphhR(R())
pp = photon flux = photon flux
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Are you getting the concept?Are you getting the concept?A vacuum phototube has radiant cathodic responsivity of A vacuum phototube has radiant cathodic responsivity of 0.08 A/W at 400 nm. (a) Find the quantum efficiency at 0.08 A/W at 400 nm. (a) Find the quantum efficiency at 400 nm. (b) If the incident photon flux at 400 nm is 2.75 x 400 nm. (b) If the incident photon flux at 400 nm is 2.75 x 101055 photons/sec, find the anodic pulse rate and the photons/sec, find the anodic pulse rate and the photoanodic current for a collection efficiency of 0.90.photoanodic current for a collection efficiency of 0.90.
First, convert First, convert to to →→ = 7.5 x 10 = 7.5 x 101414 s s-1-1
K(K() = R() = R()h)h/e = (0.08 As/J)(6.63 x 10/e = (0.08 As/J)(6.63 x 10-34-34 Js)(7.5 x 10 Js)(7.5 x 101414 s s-1-1)) 1.602 x 101.602 x 10-19-19 As As
K(K() = 0.248) = 0.248
rrapap = = ppK(K() = (0.90)(2.75 x 10) = (0.90)(2.75 x 1055 photons/s)(0.248) photons/s)(0.248)
rrapap = 6.15 x 10 = 6.15 x 1044 photons/s photons/s
iiapap = = pphhR(R() )
=(0.90)(2.75 x 10=(0.90)(2.75 x 1055 h h/s)(6.63 x 10/s)(6.63 x 10-34-34 Js)(7.5 x 10 Js)(7.5 x 101414 s s-1-1)(0.08 As/J) )(0.08 As/J)
iiapap = 9.7 x 10 = 9.7 x 10-15-15 A A
Photomultiplier TubePhotomultiplier Tube
Douglas A. Skoog and James J. Leary, Principles of Instrumental Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.Analysis, Saunders College Publishing, Fort Worth, 1992.
8–19 dynodes (9-10 is 8–19 dynodes (9-10 is most common).most common).
Gain (m) is # eGain (m) is # e-- emitted emitted per incident eper incident e-- ( () to the ) to the power of the # of power of the # of dynodes (k).dynodes (k).
1.1. Average anodic currentAverage anodic current2.2. Single photon countingSingle photon counting
Modes of OperationsModes of Operations
Hamamatsu CatalogHamamatsu Catalog
1.1. Average anodic currentAverage anodic current2.2. Single photon countingSingle photon counting
Single Photon CountingSingle Photon Counting
Hamamatsu CatalogueHamamatsu Catalogue
Single photons give Single photons give bursts of ebursts of e--
The rise time of PMTs The rise time of PMTs depends on the depends on the spread in the transit spread in the transit time of etime of e-- during the during the multiplication process.multiplication process.
FWHM: Full Width at Half of MaximumFWHM: Full Width at Half of Maximum
Single Photon CountingSingle Photon Counting
Improved S/N Improved S/N at low at low pp
Hamamatsu CatalogueHamamatsu Catalogue
Sources of Dark Current:Sources of Dark Current:Thermionic EmissionThermionic Emission
Thermal energy releases Thermal energy releases ee-- from the cathode. from the cathode.
Reduced by coolingReduced by cooling
Hamamatsu CatalogueHamamatsu Catalogue
Thermionic Emission is Thermionic Emission is Dependent on Bias VoltageDependent on Bias Voltage
Hamamatsu CatalogueHamamatsu Catalogue
Sources of Dark Current: Sources of Dark Current: Glass ScintillationGlass Scintillation
Brief flash of light when an eBrief flash of light when an e-- strikes the glass envelope.strikes the glass envelope.
Douglas A. Skoog and James J. Leary, Principles of Instrumental Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.Analysis, Saunders College Publishing, Fort Worth, 1992.
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
PhotodiodesPhotodiodes
Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis
Photons incident on the Photons incident on the depletion layer induce a depletion layer induce a current.current.
In most cases, best In most cases, best response in the NIR.response in the NIR.
Response is linear over 6 Response is linear over 6 – 7 orders of incident – 7 orders of incident radiant powerradiant power
Spectral Response of PhotodiodesSpectral Response of Photodiodes
Shinya Inoue and Kenneth Spring, Shinya Inoue and Kenneth Spring, Video MicroscopyVideo Microscopy, Plenum Press, New York, 1997., Plenum Press, New York, 1997.
Photodiode Arrays (PDA or DAD)Photodiode Arrays (PDA or DAD)
Douglas A. Skoog and James J. Leary, Principles of Instrumental Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.Analysis, Saunders College Publishing, Fort Worth, 1992.
Simultaneous Simultaneous detection detection in a spectrophotometer.in a spectrophotometer.
Incident photons excite electron-hole pairs,electrons gather in potential wells in each pixel
-V-V +V
CCD Rain Bucket AnalogyCCD Rain Bucket Analogy
Shinya Inoue and Kenneth Spring, Shinya Inoue and Kenneth Spring, Video MicroscopyVideo Microscopy, Plenum Press, New York, 1997., Plenum Press, New York, 1997.