**Photoconductive Mode**
Saturation behavior in the photoconductive mode can be understood by referring to the load-line analysis of Fig. 14-3. The load line has a slope *-1/R*_{L}, with an intercept on the voltage axis of *V*_{d} = -V_{B}. As the incident optical power increases, the operating point moves downward and to the right along the load line, decreasing the magnitude of reverse-bias voltage and increasing the magnitude of the current. Both the voltage and current change linearly with increasing optical power, until the operating point reaches the **Figure 14-7 **Diode voltage versus incident optical power for the photovoltaic mode. Smaller load resistance *R*_{L}gives a larger dynamic range but lower sensitivity. For *R*_{L} , the effective resistance reaches the upper limit of *R*_{sh}.
current axis *(V*_{d} = 0). At that point, the detector circuit saturates, and the output is no longer linear with the incident optical power. In the linear regime, we can obtain a simple analytical expression for the detector signal as follows. It is clear from Fig. 14-3 that *V*_{d} < 0 in the linear regime. Eq. (14-3) can then be written as Unless the operating point is close to saturation, it is a good approximation that
The exponential term above can then be neglected, giving The detector output in the photoconductive mode is generally taken to be the voltage *V*_{R}across the load resistor. Since this will always be negative, we define the output as *V*_{out}*-V*_{R}to give a positive number. Therefore, which can be written as using Eq. (14-2). The detector output is seen to have two components, one proportional to the incident optical power, and the other independent of power. The component that varies with *P*_{in}is identical to the expression obtained in Eq. (14-14) for the photovoltaic mode. In both cases, the output voltage arises from the photocurrent *i*_{ }flowing through load resistor *R*_{L}. The detector output can be expressed more compactly by defining the *responsivity *of the detector as which is similar to the definition given in Eq. (13-8) for emissive-type photodetectors.
The output in the photoconductive mode is then A similar expression applies to the photovoltaic mode, but without the* i*_{0} term. According to Eq. (14-17), the change in output voltage is linear with both *R*_{L}and *P*_{in}. However, this relation will only hold as long as *V*_{d} < 0, which requires that *V*_{out}* < V*_{B}. If *P*_{in} is increased above the point where *V*_{out} *V*_{B}, the output saturates, and becomes approximately independent of *P*_{in}*. *This behavior is illustrated in Fig. 14-8 for two values of *R*_{L}. Larger *R*_{L}makes the detector more sensitive, since there is a larger output for a small value of *P*_{in}*. *However, this reduces the range of *P*_{in} over which the response is linear. The result is a sensitivity-dynamic range trade-off similar to that of the photovoltaic mode. Although the photoconductive and photovoltaic modes have the similarities mentioned above, there are some significant differences. One difference is that saturation occurs at *V*_{out} *V*_{B } photoconductive mode, but at only *V*_{out} *V*_{T} in the photovoltaic mode. Since *V*_{T} 0.025 V at room temperature, whereas *V*_{B}is typically several volts, the detector output in the photoconductive mode can be approximately two orders of magnitude larger than in the photovoltaic mode. This means that for the same detector sensitivity (same *R*_{L}), the dynamic range is approximately two orders of magnitude larger in the photoconductive mode than in the photovoltaic mode. This improved dynamic range is an important advantage of the photoconductive mode. Another difference is that the photoconductive mode has a dark current, whereas the photovoltaic mode does not. The presence of dark current has two consequences. First, it contributes a constant background level that must be subtracted from the detector output in order to obtain the "true" signal (the signal arising from the incident light). Second, it contributes shot noise to the detector output, as discussed in Section 13-3. If the optical power is sufficiently large so that *i*_{ } i_{0}, then both of these effects become unimportant, in this large-signal regime, the photoconductive mode is the best choice for the detector circuit. However, if *i*_{ }*i*_{0}, then shot noise from the dark current can become a dominant source of detector noise. In this small-signal regime, the photovoltaic mode is a better choice, in order to obtain the best possible signal-to-noise ratio. The signal-to-noise properties of detector circuits are further discussed in Section 14-5. **Figure 14-8 **For a photodiode biased in the photoconductive mode, the detector response is linear for output voltages up to the reverse-bias voltage *V*_{B}. Larger load resistance *R*_{L}gives higher sensitivity but smaller dynamic range.
It should be emphasized that the dark current in a reverse-biased photodiode detector is much smaller and more well-defined than that in a photoconductive-type detector (one without a p-n junction). For example, a 1 cm^{2} silicon photodiode has a typical dark current *i*_{0} 1.5 × 10^{-8} A, independent of reverse-bias voltage. In contrast, a CdS photocell has a background current that depends on the applied voltage, a typical value being ~ 10^{-5 }A for a similar cross-sectional area and applied bias of 10 V. |