Detectors and System

Mar. 28, 2018

• Photodetection: Photoconductive effect is fast and used in communication.
Photovoltaic effect is slow and used in solar cells.
Exchange photons for electrons.
• Photo-current: `I_{ph} = ccR P_{"in"}` where `ccR` is responsivity ( A/W) and `P_{"in"}` is input optical power. Note - current `I = I_{ph} + I_d` where `I_d` is the dark current.
• Responsivity: `ccR = (eta q )/(h nu) = eta {lambda (mum)}/1.24`
Current is generated by excitation of electrons to upper level, i.e. `h nu > E_g ->` cut-off wavelength `lambda_{th} = 1.24/E_g`
Absorption of photons generates charges (electrons and holes)
Electron-hole generation animation
Photodiode: Reverse biased to photoconductive regime of a diode. Electrons need to travel across the depletion layer to be excited. Output voltage `V_{"out"} = I_{ph} R_L` where `R_L` is the load resistor.
• Modulation response: two factors control it.
Transit time - `Delta f = 0.35/tau_r` where `tau_r` is the rise time or the time to travel across depletion layer.
Circuit time - `tau_{"cr"} = 2.19 (R_L)_{eq} C_d` and `Delta f = 1/{2 pi (R_L)_{eq} C_d` where `C_d` is the junction capacitance.
Example on calculation with detector response time

• Mean square value of noise current: Shot noise `bar {i_S^2} = 2 q (bar{I_{ph}} + I_d) Delta f`
Note: noise is proportional to signal
Thermal noise `bar {i_T^2} = (4kT)/(R_L)_{eq} Delta f`
Note: noise increases as `R_L` decreases.
Example for SNR calculation with DC signal
Comment on SNR calculation with AC signal

• Overall bandwidth budget: total system delay `Delta tau_{sys} = sqrt(tau_r^2 + tau_t^2 + tau_f^2}` and `R_b = 1/(4 Delta tau_{sys})`
`tau_r` -- delay of detector, `tau_t` -- delay of source, `tau_f` -- delay of fiber.

Last Modified: March 27, 2018
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