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_Lgives 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_Racross the load resistor. Since this will always be negative, we define the output as V_out-V_Rto 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_inis 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 i₀ term.

According to Eq. (14-17), the change in output voltage is linear with both R_Land 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_Lmakes 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_Bis 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 i₀, 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 i₀, 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_Lgives 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 cm² silicon photodiode has a typical dark current i₀ 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.