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3.46 PHOTONIC MATERIALS AND DEVICES Lecture 17: Detectors—Part 2 Notes Lecture Detector Attributes • efficiency • noise • speed • linearity “Digital” Sensitivity 1. Bit Error Rate • charge carriers are created by photons in a Poisson random process a) probability that a pair is generated in time interval dt = ρ(t) RP(t) dt q ηλ = P(t)dt hc ρ(t)dt = b) average # carriers generated ηλ t+T ∫ t P(t)dt hc ηλ E = hc Ν= energy in pulse of width T IL T t c) probability the N = n charges in time interval T (average value of N : N ) n Ν e-Ν P(Ν = n) = n! n = Ν exp (−ηλE hc ) n! 3.46 Photonic Materials and Devices Prof. Lionel C. Kimerling Lecture 17: Detectors—Part 2 Page 1 of 5 Lecture Notes Example What is E required such that P < 10-9 that a logical “0” will be detected when a logical “1” is transmitted? • logical “0” ≡ no e- h+ pairs ⎡ ηλΕ ⎤ ⎥ < 10−9 • P(N = 0) = exp ⎢− ⎢⎣ hc ⎦⎥ ⇒ Ε > 21 ⇒ hv η 21 photons required η d) Each bit is TB seconds long ⇒ required power at detector Pav = 21⋅ hν η 2TB • • assumes only shot noise quantum limit of the detection process ⎡ ηΕ ⎤ ∴ exp ⎢− ⎥ ≤ BER ⎢⎣ hν ⎥⎦ 2. Noise iS2 S Psignal = = 2 N Pnoise iN a) Shot Noise • quantization of charge q • quantization of light hν iN2 = 2qIB I = average diode current B = bandwidth of electronics 3.46 Photonic Materials and Devices Prof. Lionel C. Kimerling Lecture 17: Detectors—Part 2 Page 2 of 5 Notes Lecture • “white” noise o independent of center frequency • AC noise dependent on DC value of output current I = IL + Ibackground + Idark • RMS noise current ≡ • iN2 shot noise is multiplied by an APD b) Thermal Noise • attribute of any resistive load iN2 = 4k B TB R R = resistive load T = noise temperature of device • iN2 independent of signal Example M = ID = Ro = RL = T = B = PL = APD 50 10 nA 0.6 A/W (unamplified) 50 Ω 300 K 10 MHz 5 nW iS M=1 = RoPi = 3 nA = IL S = N iS2 M2 2q(IL +ID )M2B + 4k B TB RL 5.9 c) APD: shot noise dominates PIN: thermal noise dominates 3.46 Photonic Materials and Devices Prof. Lionel C. Kimerling Lecture 17: Detectors—Part 2 Page 3 of 5 Lecture Notes 3. Speed e− n+ + − p− h+ xj I, N a) drift transit time (in depletion region) Si: e− h+ 107 ln(vd) (cm/s) 105 JK ln E ( V cm) Δt = w s ≈ 10−7 ×w v d cm ⇒ 10 μm = w, Δt = 10-10 s 3.46 Photonic Materials and Devices Prof. Lionel C. Kimerling Lecture 17: Detectors—Part 2 Page 4 of 5 Lecture Notes b) diffusion time (outside w) Δt = x2 Dn,p ⎛k T ⎞ Dn,p = ⎜⎜ B ⎟⎟⎟ μ n,p ⎜⎝ q ⎠ Dn (Si) 30 c s (10 ) 2 −3 2 Δt ( x = 10 μm) = 30 = 3×10−8 s ● RC time constant εA C = ≤ 1 pF w Detector Design Rules a) η ↑ as w ↑ as C ↓ b) τ tr ↑ as w ↑ 2 α τ tr ≈ RC c) design for w ≈ PIN limit ≡ τ tr APD limit ≡ carriers drift to avalanche region + drift of multiplied carriers out + avalanche time 3.46 Photonic Materials and Devices Prof. Lionel C. Kimerling Lecture 17: Detectors—Part 2 Page 5 of 5