Semiconductor Diode Detectors Electron energy diagram – (electrons fall downward) conduction band carrier density ED, donors → n-type (e’s conduct) EA, acceptors → p-type (holes conduct) valence band pn junction Egap ≅ 1.2 V (Si) “Fermi level” p-type n-type VEF (analogous to sea level) z C1Lec07- 1 DHS 12/27/00 open circuitConductivity of biased diodes trapped holes Egap +-E trapped electrons cannot cross junction holes Reversed-biased diode + -p-type n-type Forward-biased diode 0 i v If T = 300K, kT ≅ 26 mv electrons hf photo-excitation C2Lec07- 2 DHS 12/27/00Photodiodes Reverse current Forward biased behavior Increases with photo-excitation and T (therefore cooled photodetectors have less “dark current”) 0 0ve ~i av>−∝ -+ Quantum efficiency η≅ conduction electrons per photon if hf > Egap i RV -+ -+ hf (power = Ps) hf Piv s darko⎟ ⎠⎞⎜ ⎝⎛η += photodiode circuit i v vo C3Lec07- 3 DHS 12/27/00 for 1 0.8 – 0.95 R eAvalanche Photo Diodes, “APD” avalanche region breakdown APDs have current gain per photon i v 100 1 10 i(t) t L 0zj z cascaded ionizations produce “avalanche”photoexcitation hf collisionally excited electron E C4Lec07- 4 DHS 12/27/00Avalanche Photodiodes, “APD” 1 10 i(t) t 100 Simple model for avalanche current and noise: ioi th ei ≅ [ ]e 1dzeL 1G o L 0 ooio∆⎟⎠⎞⎜⎝⎛−=≅⎥⎦⎤ ⎢⎣⎡=∫ [] ⎥⎦⎤ ⎢⎣⎡−≅⎥⎦⎤ ⎢⎣⎡= 1e 1 o 2 oio ( )2 2 xG G ; x i l⎡ ⎤≅ ≅ = ⎢ ⎥⎣⎦ G ≅ 200 ± ~6 dB, for typical applications C5Lec07- 5 DHS 12/27/00 z g g gain has photon thickness junction L 1 L g e E L g z g z g L g2 e E g E L g2 z g2 In practice E g where x 0.25; 0.2-0.5 s typicaCarrier-to-Noise Ratio, “CNR” for photon detectors signal + shot dark + shot thermal 0 B Rd T°K i(t) RL = Rd 0°K Photodetector circuit model () [] () iand iwherei-iEtiCNR L s 22 s∆ ( ) Dsshot 2 n ii += ≅ constant for PMT ()ti ss signal power (W) E1 Only in/2 flows in RL from Rd noise (assume TL << Tdiode), ( ) dLL 2 n R2i =and L 2 niTherefore L = Lec07- 6 DHS 12/27/00 current total the is R through current signal the is t eG B2 hf eG P η = R diode to matched R since kTB R thermal R kTB4Carrier-to-Noise Ratio, “CNR” () [] () iand iwherei-iEtiCNR L s 22 s∆ ( ) Dsshot 2 n ii += ≅ constant for PMT ()ti ss signal power (W) L 2 ni L = ( ) ( )( ) ( )LDs 2 s PP CNR ++η η = for photo diodes or PMT with constant G 2 nshot i 2 nthermal i E2Lec07- 7 DHS 12/27/00 current total the is R through current signal the is t eG B2 hf eG P η = R thermal R kTB4 R kTB4 hf eG BeG2 hf eG PCNR for constant-G photodiodes, photomultipliers ( ) ( )( ) ( )LDs 2 s PP CNR ++η η = for photo diodes or PMT with constant G 2 nshot i 2 nthermal i ( )2 sLsD s eGPPP1 fPCNR η++ η = For PD = T =0, or Ps →∞; ideal quantum limit (denominator equals unity) In the quantum limit, we want large η and Ps, and small B Why not let RL →∞? Because RLC = τ sec; C = detector capacitance ≅ 10 (say) Then RL ≅ 1000 Ω for τ = 10-9 (f ≅ 150 MHz) Also, generally: D < Ps set RLG2 large to contain thermal noise E3Lec07- 8 DHS 12/27/00 R kTB4 hf eG BeG2 hf eG P R kThf2 B2 h-12 set T so PCNR for variable-G avalanche photodiodes 0 δ i(t) t gie/δ gie Assume rectangular pulses to simplify analysis ( )Ds hf PP n +η = 0 δ-δ τ ()τφ ACi hf PPe g Ds 22 +ηδ ~1/δ hf PP eg Ds22 +η ( )f ACiΦ f shot noise 0 B E4Lec07- 9 DHS 12/27/00 1-s eventsCNR for variable-G avalanche photodiodes ( ) () ( ) hfPPeii Ds 22 B B i 22 i +η=Φ= ⎥⎦ ⎤ ⎢⎣ ⎡ −=σ ∫ − Therefore CNR (APD) = 0 δ-δ τ ()τφ ACi hf PPe g Ds 22 +ηδ ~1/δ hf PP eg Ds22 +η ( )f ACiΦ f shot noise 0 B ( ) ( ) LDs 22 2 s hfPPe ++η η 2 iσ thermali2 nshot E5Lec07- 10 DHS 12/27/00 g B2 df f R kTB4 g B2 hf eG PCNR for variable-G avalanche photodiodes Therefore CNR (APD) = ( ) ( ) LDs 22 2 s hfPPe ++η η 2 iσ thermali2 n In general, to maximize APD CNR we want G2 large to make thermal noise negligible, but small so Gx is still modest; e.g. Gx ≅ 4 is typical shot ( )2 sLs D 2 2 s eGPRP P1 G g fP η +⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + η = GGg x22 −≅≅Only change is E6Lec07- 11 DHS 12/27/00 R kTB4 g B2 hf eG P kThf2 B2 h(APD) CNR 5 . 0 2. 0 x ,Infrared Detection Types of electromagnetic detectors hf << kT “radio” hf >> kT “optical,” “visible,” etc. hf = kT “infrared” G1Lec07- 12 DHS 12/27/00Infrared Detection Bolometers (measure heat) -+ vout -+ RPs(W) Tbath Thermal conductance heat sink R(T) I = bias Signal power Ps raises T, changing R(T) and vo. Heat flows to heat sink and to bath; Tbath ~ ( ) TPowert 1 t ∆∆∆− donorskTd E z conduction band valence band whereR s TT o d≅ G2Lec07- 13 DHS 12/27/00 bias < 4 – 250K. WK G . P with increases Te RResponsivity S of a bolometer -+ vout -+ RPs(W) Tbath heat sink R(T) I = bias s 2 ss o PPwhereP P P RISP v += ∂ ∂ • ∂∂ =∆∂∂ ( )RRP RI11P P P RIP PThus bias 12 s 2 s >>⎟⎠⎞⎜⎝⎛ ∂∂−=+∂ ∂ ∂∂ = ∂ ∂− P T T R P RwhereP RI1P RI 2 ∂∂ • ∂∂ = ∂∂⎟⎠⎞⎜⎝⎛ ∂∂−∂∂ = ⎟ ⎠⎞⎜ ⎝⎛<< −≅⎟⎠⎞⎜⎝⎛ ∂ ∂ = 1T T TT d 2 doTT o d t = ⎟⎟ ⎠⎞ ⎜⎜ ⎝⎛ + − = 2 t d 2 2 t d 1S Td << T may not apply G3Lec07- 14 DHS 12/27/00 bias R I ty" responsivi " S Thus T R e R G 1 T G R T I T G R ITResponsivity S of a bolometer T1S d2 t d 2 2 t d <<⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − = Thus S → 0 and thermal noise in Rbias dominates as 0 biasI → ∞→ Thus there is optimum (near maximum S)[ ]2 tdbiasI = G4Lec07- 15 DHS 12/27/00 T If T G R T I T G R IT T G R T fBolometer noise sources bias (thermal) t traditional shot noise t t• carrier creations carrier recombinations (deaths) < × 2 shot noise ~ Recombination Noise H1Lec07- 16 DHS 12/27/00 1) Can be recombination noise 2) Johnson noise in R, R3) Phonon noise via G4) Photon noise (“radiation noise”)Johnson noise …