Predicting the performance of a photodetector

Transcription

1 Page 1 Predicting the perormance o a photodetector by Fred Perry, Boston Electronics Corporation, 91 Boylston Street, Brookline, MA USA. Comments and corrections and questions are welcome. The perormance o a photodetector system can be predicted rom the parameters * (detectivity), Responsivity, time constant and saturation level, and rom some knowledge about the noise in the system. No photodetector should be purchased until a prediction has been made. etectivity and NEP The principal issue usually acing the system designer is whether the system will have suicient sensitivity to detect the optical signal which is o interest. etector manuacturers assist in making this determination by publishing the igure o merit *. * is deined as ollows: * A Δ NEP (equation 1) where A is the detector area in cm 2 Δ is the signal bandwidth in hertz and NEP is an acronym or Noise Equivalent Power, the optical input power to the detector that produces a signal-to-noise ratio o unity (S/N=1). * is a igure o merit and is invaluable in comparing one device with another. The act that S/N varies in proportion to A and is a undamental property o inrared photodetectors.

2 Page 2 Active Area Consider a target about which we wish to measure some optical property. I the image o the target is larger than the photodetector, some energy rom the target alls outside the area o the detector and is lost. By increasing the detector size we can intercept more energy. Assuming the energy density at the ocal plane is constant in watts/cm 2, doubling the linear dimension o the detector means that the energy intercepted increases by 2 2 = 4 times. But NEP increases only as 4 = 2. Conversely, i the image o the target is small compared to the detector size, and i there are no pointing issues related to making the image o the target all on the photodetector, then halving the linear dimension o the photodetector will similarly double S/N, since the input optical signal S stays constant while the NEP ECREASES by a actor o 4 = 2. The moral o this story is: Neither throw away photons nor detector area. Know your system well enough to decide on an optimized active area. Bandwidth Error theory tells us that signal increases in a linear ashion but noise (i it is random) adds RMS. That is, Signal increases in proportion to the time we observe the phenomenon, but Noise according to the square root o the observation time. This means that i we observe or a microsecond and achieve signal-to-noise o β, in an integration time o 100 microseconds we can expect S/N o 100 β = 10β. Bandwidth is related to integration time by the ormula 1 = (equation 2) 2πτ where τ is the integration time or time constant o the system in seconds. Time constant τ is the time it takes or the detector (or the system) output to reach a 1 e value o 1 63% o its inal, steady state value. Signal Signal in all quantum photodetectors is constant versus requency at low requencies but begins to decline as the requency increases. The decline is a

3 Page 3 unction o the time constant. I Slow is the signal at low, a ew hertz, the signal at arbitrary requency» low is S low S = (equation 3) 2 1+ (2πτ ) This is graphically illustrated below. Frequency c is the point at which 1 S = Slow. 2 Noise Noise is not as simple as signal. Photoconductive devices like PbS, PbSe, and most HgCdTe exhibit licker or 1/ noise, which is excess noise at low requencies. Consequently, Signal-to-Noise ratio and * are degraded at these

4 Page 4 requencies. 1/ noise actually varies as 1 in voltage terms. At high requencies, the detector noise actually decreases according to the same relationship as signal decreases. However, the diiculty in constructing ollowing ampliier electronics that are signiicantly lower in noise than the photodetector results in system always having a noise at high requencies that is no better than noise at low requencies. The ollowing set o graphs illustrates this. To predict low requency perormance o a photoconductor, the extent to which * is degraded by 1/ noise must be estimated. Either o the ollowing ways is applicable: 1. use the manuacturer s published graphical data o * versus requency to determine the multiplication actor Nexcess to use to convert minimum guaranteed * at its measured requency to * at the requency o interest. 2. use the 1/ corner requency corner > low reported by the manuacturer to estimate the degradation actor at low as excess noise actor corner N excess = (equation 4) low In contrast to photoconductors, photovoltaic detectors normally have no 1/ noise. Signal is lat to or near C and thereore * is constant below the high requency roll-o region, so no low requency correction need be made.

5 Page 5 Spectral response correction The * o a quantum detector varies with wavelength. The detector manuacturer typically guarantees * at the wavelength o peak response, *(peak). When using the device at another wavelength, the * should be corrected by an appropriate actor: R = ( response at ) ( response at peak) = * R peak * (equation 5) where the relative response at wavelength is estimated by inspection o spectral response curves or other data supplied by the manuacturer. Thereore, the optical input power required to produce a signal-to-noise ration o 1:1 or a stated system response time and wavelength becomes: Case 1: Photoconductor at low requency: A NEP = * N excess (equation 6) Case 2: Photovoltaic detector at low to moderate requency:

6 Page 6 NEP A = (equation 7) * Case 3: Photoconductor or photovoltaic requency at higher requency: NEP S A = (equation 8) * This yields an estimate o the input optical power to achieve a voltage output with S/N=1. Upper Limits Another important question is the dynamic range o the system, e.g. the ratio o the maximum signal available to the NEP o the system. The upper limit o the system is typically set by the electrical gain o the preamp or the vertical gain o the oscilloscope used to display the signal, combined with the maximum output signal o the preamp or the maximum vertical delection o the oscilloscope. The dynamic range o the system is then expressed in multiples o the system NEP. Let the preamp gain be G. Let the responsivity o the detector in volts per watt (or volts per division in the case o an oscilloscope) at low requency be Rlow and at requency let it be R where R R S = (equation 10) low The voltage signal rom the detector into the preamp or oscilloscope when S/N=1 corresponding to this responsivity will be NEP = (equation 11) R Then the output o the preamp at requency and S/N=1 will be = G (equation 12) preamp

7 Page 7 Let the maximum output o the system be preamp volts (or vertical vertical divisions in the case o an oscilloscope). The multiple o the NEP that corresponds to the maximum output preamp will thereore be Preamp ynamic Range preamp = (equation 13) G O course, with an oscilloscope it is usually possible to turn down the gain and thus increase the dynamic range. However, preamps usually have ixed gain. In that case the input optical must be attenuated in order to keep the output rom the preamp rom saturating. Sometimes the photodetector itsel will saturate beore the preamp. Some process, thermal or photonic, intrinsic to the photodetector may limit it s output. In this case, the maximum available (saturation) output signal should be speciied by the device manuacturer, typically as a not-to-exceed output voltage detector.. Graphically the situation is illuatrated as ollows: Case 1: ynamic Range limited by the preamp preamp det ector = < (equation 14) G Case 2: ynamic Range limited by the detector < det ector preamp = (equation 15) G

8 Page 8 This completes our prediction o system perormance. We have calculated the input optical signal that corresponds to S/N=1, and the maximum output that can be extracted rom the system in terms o a multiplier o the minimum input signal. The multiplier is dynamic range. System options As the designer, you have the ollowing additional degrees o reedom in designing a system: 1. You may increase the size o his optics in order to deliver more optical energy to the photodetector. The key concept to remember is that throughput in any optical system, deined ast = A Ω, where A is area in cm 2 and Ω is solid angle ield o view in steradians, is a constant in the system. I A is detector area and Ω is detector FO, then collector area AC and collector FO ΩC are at best satisy A Ω = T = A Ω. Increasing the collector aperture decreases the FO. C C 2. You may increase the eiciency o his optics (transmittance and relectance optimization, etc). 3. You may increase the power o his source in a cooperative, active system (though not in a passive one). 4. You may increase the time he observes the signal, that is decrease the bandwidth and increase the time constant. =========================================================== Appendix: Sample Calculations See next page.

9 Boston Electronics Corporation Responsivity *(10.6 um) Ampliier 481-1X to 481- volts 10/9/ :42 PM E+07 20X saturates at 5 m/w cm.hz 1/2 /watt Assume detector saturation or CW signal is 20 m Assume detector saturation or single ast pulse is 600 mv Assume wavelength is 10.6 microns Assume active area is 1x1 mm Assume resistance is 50 ohms CW case Pulsed case System Time 3dB System Optical signal Electrical signal S/N at S/N at S/N at Elements Constant Frequency Gain (voltage) Responsivity or S/N=1 or S/N=1 etector etector Preamp (nsec) (MHz) (/W) (NEP, microwatts) (millivolts) Saturation Saturation Saturation PM-10.6 unampliied < no preamp PM-10.6 with 493A/40 < PM-10.6 with 493A < PM-10.6 with < PM-10.6 with PM-10.6 with PM-10.6 with PM-10.6 with PM-10.6 with PM-10.6 with PM-10.6 with PM-10.6 with Time constant τ BW o detector Square root o the Optical signal Saturation Saturation Clipping rom product lit and typical 50 Ω detector resistance and 3dB requency preamp responsivity detector area at S/N=1 times level or level or level or are related by indicated times gain times square root System CW signal Pulsed preamp =1/(2πτ) o the 3dB Responsivity divided by signal divided by - slower o requency divided Optical divided by electrical detector or preamp by the * rom signal at Optical signal or shown product lit S/N=1 signal at S/N=1 S/N= X saturates at.. 493A and 493A/40 saturates at Shading indicates saturation o detector or preamp or CW case This rather complicated chart is intended to illustrate how the perormance o our detectors (in this example the model PM-10.6 with 1x1 mm active area and typical values o responsivity and *) is aected by variously by (a) saturation o the detector itsel or (b) by saturation o a ollowing preamp. The shaded cells indicate the lower o S/N or CW signals and indicates whether it is the detector that saturates irst or the preamp that saturates irst. We loosely deine saturation in the detector as the point at which output deviates rom linearity by 20%; in the preamp we deine saturation as the output at which the signal is clipped. Notice that detector saturation is MUCH LOWER or the CW case. The most common signal is quasi-cw (or example an RF-modulated CO2 laser) and should be considered CW. Any pulsed laser with a duty cycle over 1% or pulse length longer than 10 microseconds is probably more like CW than pulsed. PM-10.6 saturation with preamps rev XLS Page 9