More on detectors

Apr. 5, 2018

• Avalanche photodiode (APD): photodiode with internal gain, i.e. `I_{APD} = M ccR P_{"in"}`; `M` current gain through impact ionization by energetic electrons under high electric field, i.e. high reverse biasing voltage.
As temp increases, `M` decreases.
modulation bandwidth `(Delta f) = 1/(2 pi tau_{eff} M)`, `tau_{eff}` is the effective transit time.
• Noise in detection: the generation of each electron by photon is a random process `->` signal plus noise
amplifier introduces additional noise measured by noise figure F = SNR at input/ SNR at output; `F ge 1`
Shot noise of APD `bar {i_S^2} = 2q ( ccR bar {P_{"in"}} + I_d ) M^2 F_{apd} Delta f`
• Signal to noise ratio in analog system: SNR = average signal power / noise power `= {bar {I_{ph}^2}}/(bar {i_S^2} + bar {i_T^2})`
Note: dc `P_{"in"} -> bar {I_{ph}^2) = ccR^2 P_{"in"}^2`; ac sinusoidal modulated power `P_{"in"} = P_o (1+ m cos omega t ) -> bar {I_{ph}^2)= ccR^2 m^2 P_o^2/2` & ` bar {P_{"in"}} = P_o`; with APD, `bar {I_{ph}^2) -> M^2 bar {I_{ph}^2)` & `bar {i_S^2} -> M^2 bar {i_S^2}`
`SNR_{PIN} = {ccR^2 bar {P_{"in"}^2}} / (2q (ccR bar {P_{"in"}}+ I_d) Delta f+(4kTF}/(R_L)_{eq})`
`SNR_{apd} = {ccR^2 M^2 bar {P_{"in"}^2}} / (2q M^2 (ccR bar {P_{"in"}}+ I_d) F_{apd}Delta f+(4kTF}/(R_L)_{eq})`

• Thermal noise limited detection `bar{i_T^2}` >> `bar {i_S^2}`
• Shot noise limited (quantum-limited): `bar{i_T^2}` << `bar {i_S^2}`
fundamental limit under strong signal.

Last Modified: April 02, 2018
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