14.1    A photodiode with responsivity 0.3 A/W and dark current 2 nA is biased in the photoconductive mode, with a 9 V battery and 500 k resistor. Make a sketch like that of Fig. 14-3, showing the load line and the diode curves for incident powers from zero to 100 µW in steps of 20 µW. Circle the operating point for an incident power of 40 µW, and determine the approximate diode voltage from the graph.

14.2    For Problem 14.1, make a sketch of the output voltage (across the resistor) versus the incident optical power, for the range 0 to 100 µW. At what optical power does the detector response saturate?

14.3    The photodiode of Problem 14.1 is removed from the circuit and operated in the photovoltaic mode. (a) Determine the shunt resistance assuming ß = 2. (b) Under open circuit conditions (no load resistor), what incident optical power will result in saturation of the output voltage? (c) A load resistor is now added to increase the dynamic range. What value of load resistance is needed so that optical powers up to 20 µW can be detected without saturation?

14.4     Show that Eq. (14-13) can be obtained from the equivalent circuit model shown in Fig. 14-6.

14.5    A silicon solar cell has area 50 cm², reverse-saturation current 0.75 µA, ß = 2. The electrical power generated in the 0.4 load resistor is 894 mW. Determine (a) The circuit current i, (b) the photocurrent i , (c) the optical power incident on the cell, assuming that 80% is absorbed, and (d) the optical-to-electrical conversion efficiency of the cell. Assume the temperature remains near 300 K. Assume = 500 nm for the incident light.

14.6    Using Eq. (14-26) for an exponential voltage rise, show that the rise time (10% to 90% points) is given by t_r 2.2RC.

14.7    A silicon p-n junction photodiode has junction area 1 cm², and doping levels 10¹⁴ and 10¹⁶ cm^-3 on the n and p sides, respectively. It is reverse biased with 15 V and a 10 k load resistor is used. (a) Determine the 3 dB electrical bandwidth due to the RC time constant. (b) Determine the bandwidth due to the hole transit time. (c) What is the limiting bandwidth in this case?

14.8    Assume the total response time of a silicon photodiode can be taken as the sum of the transit time (limited by saturation velocity 10⁵ m/s) and the RC rise time t_r. Derive an expression for the optimum intrinsic region thickness d. If the load resistance is 50 and the detector area is 0.01 mm², calculate d and the resulting detector bandwidth.

14.9    A high-speed germanium PIN photodiode has a depletion width of 10 m and a reverse-bias voltage of 10 V. The hole mobility in Ge is 0.2 m²/(Vs), the saturation velocity is 7 × 10⁴ m/s, and the refractive index at 1300 nm is 4.3. (a) Determine the transit time limit to the response time, and calculate the corresponding 3 dB electrical bandwidth. (b) If light of wavelength 1300 nm is detected, determine the fraction of incident light that is absorbed in the depletion region (include the reflection loss from the air-Ge interface). (c) Repeat part b if the detected wavelength is 1600 nm. See Fig. 13-16 for Ge absorption coefficient.

14.10  A silicon APD has a responsivity of 20 A/W at the detection wavelength of 850 nm, and the absorption efficiency is 0.7. Determine the avalanche gain.

14.11  A silicon photodiode is configured as shown in Fig. 14-18 with a 90 V bias voltage. The light to be detected has intensity 20 W/cm² and wavelength 920 nm. Relevant material properties for the detector are: absorption efficiency = 0.18, dark current density at room temperature = 15 nA/cm², charge carrier mobility = 0.048 m²/Vs, and carrier saturation velocity = 10⁵ m/s. At the applied bias voltage, it is known that the width of the depletion region is 0.2 mm. (a) If the photocurrent is 150 nA, what is the area of the detector? (b) If the load resistor is 100 k , determine the RC time constant of the circuit, and the corresponding 3 dB bandwidth. Video requires a bandwidth of about 2 MHz. Will the circuit be suitable for video applications? (c) Determine the transit-time response for the circuit, and compare it with the RC time constant. Which is the primary limit to the bandwidth in this circuit? (d) Repeat part b assuming a load resistance of 10 k . Is the circuit now suitable for video applications?

14.12  In Problem 14.11, check to see that there is sufficient signal-to-noise (S/N) ratio. Using the results for the 10 k load resistor, determine the power S/N ratio, and also find the ratio of the rms deviation in signal voltage to the average signal voltage (express as a percentage).

14.13  The photodetector of Problem 14.11 is now used for low-level dc light-level measurements. Assume that in this application the effective bandwidth is 1 Hz. (a) Determine how large the load resistor must be in order for the noise to be dominated by dark current shot noise rather than by thermal noise. Take as the criterion that the shot noise power is five times the thermal noise power. (b) In the limiting case described in part a, determine the noise equivalent power (NEP) for the detector (in units of watts). (c) For the conditions described in part a, determine the minimum light intensity that can be detected with this detector, taking as the criterion that the signal voltage must be 10 times the rms noise voltage.

14.14  Consider the transimpedance amplifier optical receiver shown in Fig. 14-19. The feedback resistance is 10 k and the feedback capacitance is 0.2 pF. The diode's capacitance is 5 pF, and its responsivity is 0.5 A/W. The incident optical power is 0.5 mW. (a) Compute the signal current. (b) Compute the receiver's output voltage, (c) Compute the receiver's 3 dB electrical bandwidth. (d) Compute the rms thermal-noise current generated in the feedback resistor, assuming a temperature of 300K. (e) Assuming no dark current, and an ideal (noiseless) amplifier, compute the output SNR, expressed in dB. The actual SNR will be somewhat lower due to noise introduced by the amplifier.

14.15  Use the data in Fig. 14-17 to determine the following: (a) The minimum optical power at 900 nm that can be detected (SNR = 1) by a Si photodiode of area 0.02 cm² in a 1 Hz bandwidth, (b) the dark-current density of an InAs detector at 77 K, assuming that the absorption efficiency is near unity for = 2.8 m, and (c) the dark current and minimum detectable power for an InGaAs detector of area 0.02 cm², operating at 1550 nm in a 1 Hz bandwidth. Assume an absorption efficiency near unity at 1550 nm.