Detectors and System |
Mar. 28, 2018 |
• Photodetection: Photoconductive effect is
fast and used in communication.
Photovoltaic effect is slow and used in solar cells.
•
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)
•
:
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.
• 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.
• 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.