Responsivity and Sensitivity

1. Responsivity and Sensitivity Responsivity, R(): Ratio of the signal output, x, to the incident radiant power,  (in Watts). (voltage, current, charge) Sensitivity, Q(): Slope of a plot of x vs. .

2. Spectral Response Short l limit – determined by window material Long l limit – determined by photocathode material Hamamatsu Catalogue

3. Transmittance of Window Materials Hamamatsu Catalogue

4. Response Speed Consider a sinusoidal input into a transducer with a finite response time. If the frequency, fc, of the sinusoidal input is high, the transducer response cannot keep up. The frequency where R() drops to 0.707 of the ideal is used to determine the time constant, .

5. Dark Signal Output in the absence of input radiation. Often limits S/N at low signal intensities. Hamamatsu catalog

6. Vacuum Phototube (“Vacuum Photodiode”) Photosensitive material: e.g. Cs3Sb, AgOCs Ingle and Crouch, Spectrochemical Analysis

7. Photoelectric Effect Photon must have some minimum energy to release an e-. Referred to as the work function. lt = hc/Ec = 1240/Ec For most metals the work function is ~2 – 5 eV. Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.

8. The Work Function Limits the Spectral Response 2-5 eV = 250-620 nm  Use materials with lower work functions, e.g., alkali metals. Hamamatsu Catalogue

9. Quantum Efficiency K() # of photoelectrons ejected for every incident photon. Typically K() < 0.5 Rate of electrons emitted from the cathode (rcp): rcp = pK() where p is the photon flux (photons / sec). Multiply by electron charge to get current. icp = ercp = eK()p Ingle and Crouch, Spectrochemical Analysis

10. Radiant Cathodic Responsivity (R()) Efficiency with which photon energy is converted to photo-electrons. Units: A / W Ingle and Crouch, Spectrochemical Analysis

11. Anodic Current Collection Efficiency () depends on the bias voltage (Eb). Arrival Rate at the Anode (collection rate): rap = rcp = pK() iap = icp = phR() p = photon flux Ingle and Crouch, Spectrochemical Analysis

12. Are you getting the concept? A vacuum phototube has radiant cathodic responsivity of 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 105 photons/sec, find the anodic pulse rate and the photoanodic current for a collection efficiency of 0.90.

13. Photomultiplier Tube 8–19 dynodes (9-10 is most common). Gain (m) is # e- emitted per incident e- () to the power of the # of dynodes (k). m = k E.g., 5 e- emitted / incident e-,10 dynodes. m = k = 510 1 x 107 Typical Gain = 104 - 107 Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.

14. Choosing a PMT • Average anodic current • Single photon counting Hamamatsu Catalog

15. Modes of Operations • Average anodic current • Single photon counting Hamamatsu Catalog

16. Single Photon Counting Single photons give bursts of e- The rise time of PMTs depends on the spread in the transit time of e- during the multiplication process. FWHM: Full Width at Half of Maximum Hamamatsu Catalogue

17. Single Photon Counting Improved S/N at low p Hamamatsu Catalogue

18. Thermionic Emission is Dependent on Bias Voltage Hamamatsu Catalogue

19. Sources of Dark Current: Glass Scintillation Brief flash of light when an e- strikes the glass envelope. Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992. Ingle and Crouch, Spectrochemical Analysis

20. Sources of Dark Current:Thermionic Emission Thermal energy releases e- from the cathode. Reduced by cooling Hamamatsu Catalogue