Predicting The Performance of a Photodetector
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By Fred Perry, President, Boston Electronics Corp. When developing infrared (IR) systems or products implementing IR products, it is very important to predict and evaluate the performance of components in a system. In these systems, one of the most important components to evaluate is the photodetector. Photodetector performance can be predicted from the parameters detectivity, responsivity, time constant and saturation level. In addition, engineers need to have some knowledge about the noise in the system. A photodetector should not be purchased until a prediction has been made. Detectivity And NEP When evaluating the performance of a photodetector, the principal issue most frequently facing the system designer is whether the system will have sufficient sensitivity to detect the optical signal that is of interest. Detector manufacturers assist in making this determination by publishing the figure of merit detectivity, which is defined as:
where:
A is the detector area in cm2,
Detectivity is a figure of merit and is invaluable in comparing one device with another. The fact that SNR varies in proportion to Active Area
To evaluate performance, engineers need to start by establishing a target which will be used to measure an optical property. If the image of the target is larger than the photodetector, some energy from the target falls outside the area of the detector and is lost. By increasing the detector size more energy can be intercepted. Assuming the energy density at the focal plane is constant in watts/cm2, doubling the linear dimension of the detector means that the energy intercepted increases by
Conversely, if the image of the target is small compared to the detector size, and if there are no pointing issues related to making the image of the target fall on the photodetector, then halving the linear dimension of the photodetector will similarly double SNR. This occurs since the input optical signal stays constant while the NEP decreases by a factor of As a result, engineers should not throw away photon or detector areas. Instead, they should know their system well enough to decide on an optimized active area. Bandwidth
Error theory says that a signal increases in a linear fashion while noise (if it is random) adds root mean square (RMS). That is, signal increases in proportion to the observation time of the phenomenon, while noise increases at the square root of the observation time. For example, if engineers observe a signal for a microsecond and achieve signal to noise of
where t is the integration time or time constant of the system in seconds. Time constant t is the time it takes for the detector (or the system) output to reach a value of approximately 60 percent of its final steady-state value. Signal
Signal in all quantum photodetectors is constant versus frequency at low frequencies. But, as systems move up in frequency, signals begin to decline. This decline is a function of the time constant. If Slow is the signal at a few hertz, the signal at arbitrary frequency
Results from this equation can be graphically displayed (see figure).
In this figure, frequency is the point at which Sf = 0.5Slow. Noise
Evaluating noise is not as simple as examining a signal. Photoconductive devices like PbS, PbSe, and most HgCdTe exhibit flicker or 1/f noise, which is excess noise at low frequencies. Consequently, SNR and detectivity are degraded at these frequencies. Flicker actually varies as But, engineers experience difficulty in constructing following amplifier electronics which are significantly lower in noise than the photodetector. As a result, engineers can experience noise at higher frequencies that is no better than noise they experience with the same system at lower frequencies. To predict low frequency performance of a photoconductor, the extent to which detectivity degraded by 1/f noise must be estimated. These estimates can be conducted in two ways.
In contrast to photoconductors, photovoltaic detectors normally do not have 1/f noise. Signal is flat to or near DC and therefore detectivity is constant below the high frequency roll-off region, so low frequency correction does not need be made. Spectral Response Correction The detectivity of a quantum detector varies with wavelength l. Detector manufacturers typically guarantee detectivity at the wavelength of peak response. When using the photodetector at another wavelength l, the detectivity should be corrected by an appropriate factor:
where the relative response at wavelength l is estimated by inspection of spectral response curves or other data supplied by the manufacturer. Therefore, the optical input power required to produce an SNR of 1:1 for a stated system response time and wavelength becomes:
for a photoconductor at low frequency,
for a photovoltaic detector at low to moderate frequency and
for a photoconductor or photovoltaic detector at higher frequency. This yields an estimate of the input optical power to achieve a voltage output with SNR = 1. Upper Limits Another important question is the dynamic range of the system, expressed as the ratio of the maximum signal available to the NEP of the system. The upper limit of the system is typically set by the electrical gain of the preamplifier or the vertical gain of the oscilloscope used to display the signal, combined with the maximum output signal of the preamplifier or the maximum vertical deflection of the oscilloscope. The dynamic range of the system is then expressed in multiples of the system NEP. To illustrate, let the preamplifier gain be represented as G. In addition, let the responsivity of the detector in volts per watt (or volts per division in the case of an oscilloscope) at low frequency be Rlow and at frequency f let it be Rf where:
The voltage signal from the detector into the preamplifier or oscilloscope when SNR = 1 corresponding to this responsivity will be:
Then the output of the preamplifier at frequency f and SNR = 1 will be:
Let the maximum output of the system be
Preamp Dynamic Range Of course, with an oscilloscope it is usually possible to turn down the gain which in turn increases dynamic range. However, preamplifiers usually have fixed gain. In this case the input optical must be attenuated in order to keep the output from the preamp from saturating.
Sometimes the photodetector itself will saturate before the preamplifier. Some process, thermal or photonic, intrinsic to the photodetector may limit its output. In this case, the device manufacturer should specify the maximum available (saturation) output signal, typically as a not-to-exceed output voltage
for dynamic range limited by the preamplifier and
for dynamic range limited by the detector. This completes prediction of system performance. The input optical signal that corresponds to SNR equal to 1 has been calculated and the maximum output that can be extracted from the system in terms of a multiplier of the minimum input signal. The multiplier is dynamic range. System Options When designing a system using an IR photodetector, engineers also have some additional degree of freedom. They may increase the size of his optics in order to deliver more optical energy to the photodetector. They may also increase the efficiency of optics and increase the power of the source in a cooperative, active system (though not in a passive one). Finally, engineers can increase the time the signal is observes by decreasing bandwidth and increasing the time constant. Boston Electronics Corporation, 72 Kent Street, Brookline, MA 02146, (800)347-5445, FAX:(617)731-0935, e-mail boselec@world.std.com Edited by Robert Keenan |
is the signal bandwidth in Hz, and NEP is the noise equivalent power, which is defined as the optical input power to the detector that produces a signal-to-noise ratio of unity (SNR=1).
and 
is a fundamental property of IR photodetectors.
. But NEP increases only as 
.
.
in an integration time of 100 microseconds, they can expect an SNR of 
. Thus, bandwidth is related to integration time by the formula:
, is:
in voltage terms. At high frequencies, the detector noise actually decreases according to the same relationship as signal decreases.
, reported by the manufacturer to estimate the degradation factor at flow as excess noise factor.
volts (or 
vertical divisions in the case of an oscilloscope). The multiple of the NEP that corresponds to the maximum output 
will therefore be:
. This is expressed as:
