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.