EE 232 Lightwave DevicesLecture 18: Photoconductors and pinLecture 18: Photoconductors and p-i-n PhotodiodesReading: Chuang, Chap. 14Instructor: Ming C. WuUniversity of California, BerkeleyElectrical Engineering and Computer Sciences DeptElectrical Engineering and Computer Sciences Dept.EE232 Lecture 18-1©2008. University of CaliforniaPhotoconductors()00 0 0Dark current:npJEnqpqEσμμ== +ωhLight illumination generate electron-hole pairs, increasing the conductivity:++--dx0increasing the conductivity:ndn nGdtδδτ=−Equivalent CircuitArea = wL×()0Steady state: d/dt --> 0nnGδτδ=ΔEquivalent Circuit()Photoconductor requires both contanpJnq EδμμΔ=⋅ +cts to be OhmicωhEE232 Lecture 18-2©2008. University of CaliforniaPhotoconductor requires both contacts to be OhmicPhotocarrier Generation RateLight Intensity xeα−∝(1 )PRωhxd(1 )optPR−(1 )deα−−++--dx11hi ioptPxdArea = wL×0311 : photocarrier generation rate [ ](1 )(1 )optdiGlwd cm sReαηωηη−==− −h: reflectivity of photoconductor surface: absorption coefficient: absorption lenghtRdαEE232 Lecture 18-3©2008. University of California: absorption lenght: fraction of light remains after abddeα−sorption length dPhotoconductive Gain()()()01nnptIlwJlwGq EPτμμΔ= Δ= +⎛⎞()()111optnnpoptPIlw q ElwdPqIqEPvητμμωητμη τ⎛⎞Δ= +⎜⎟⎝⎠Δ≈ =h() : transit timenn opt nntIqEPvdddvητμη τωωτΔ≈ ==hhnnopttvqIPτηωτ⎛⎞⎛⎞Δ=⎜⎟⎜⎟⎝⎠⎝⎠ht⎝⎠⎝⎠Photocurrent PhotoconductiveGainEE232 Lecture 18-4©2008. University of CaliforniaGainAnalogy to Current Gain in Bipolar TransistorCurrent gain in bipolar transistor:CIβECB=The current gain can also be expressed asCBIIβECB=:transittimerbtτβττ: transit time: carrier recombination lifetime in the basetrbττEE232 Lecture 18-5©2008. University of CaliforniaFrequency of Photoconductors1optnPdN Ndt lwdηωτ=−he (dB)01Small signal response: 1jtNN NePNω=+ Response/100ntττ=/1,000ntττ=/ 10,000ntττ=111111nPNjNlwdPNωηωτη=−=hconductive/1ntττ=/10ntττ=()()111 11/nnNlwd jIJlwNqvlwωωτ=+==⎛⎞⎛⎞hFrequency (Hz)Photoc()()1111DC Quantum Efficiency Photoconductive GainntnIqPjτηωτ ωτ⎛⎞⎛⎞=⎜⎟⎜⎟+⎝⎠⎝⎠=××hEE232 Lecture 18-6©2008. University of California()()DC Quantum Efficiency Photoconductive Gain Normalized Fre=××()quency ResponseP-i-n Photodiodehν• Reverse-biased p-i-n junction•Most of the voltage dropNihνPMost of the voltage drop across the i-region, the main absorption regionHigh field separates•High field separates photogenerated electron and hole0• Large bandgap materials are used for P and N if possible•Fast response21−Ec0iqEv0ihνFast response• Low noise•No gain (quantum efficiency3−2−qF0qEE232 Lecture 18-7©2008. University of CaliforniaNo gain (quantum efficiency < 100%)2− 107−× 1− 107−× 0 1107−× 2107−×4−xiI-V CurveI0Dark current: ( 1)BqVkTIIe=−Photocurrent: ph optqIPηω=hVQuantum efficiency: (1 )(1 )diReαωηη−=− −h0Total current: ( 1)BqVkTphIIe I=−+1phI2phIEE232 Lecture 18-8©2008. University of CaliforniaLoad Line for Biasing the PDAbsorption Coefficient• Light intensity decays exponentially in semiconductor:• Direct bandgap semiconductor has a sharp absorption edgexeIxIα−=0)(has a sharp absorption edge• Si absorbs photons with hv > Eg= 1.1 eV, but the gabsorption coefficient is small– Sufficient for CCD•At higher energy ( 3eV)•At higher energy (~ 3 eV), absorption coefficient of Si becomes large again, due to directbandgaptransition toEE232 Lecture 18-9©2008. University of Californiadirect bandgaptransition to higher CBTwo Types of p-i-n PhotodiodesLdSurface-Illuminated p-i-nWaveguide p-i-nSurface Illuminated pin(1 )(1 ): internal quantum efficiencydiiReαηηη−=− −Waveguide pin(1 )(1 ): internal quantum efficiencyLiiReαηηη−Γ=− −: reflectivity: absorption layer thicknessRd: reflectivity: confinement factor: length of waveguide PDRLΓEE232 Lecture 18-10©2008. University of California: length of waveguide PDLRamo’s TheoremProof:Work done on the charge:dAWork done on the charge: Force DisplacementWVqEdx q dx=×==The current caused in external circuit AWork provided by power supply:()qEdx q dxdWitVdt===by a moving charge moving at a volocity ( ) in a parallel plate with a separation of and a voltage biasqvtd()()WitVdtVitVdt q dx⇒=a separation of and a voltage bias of V is()()dqv tit=()()()itVdt q dxdqdx qvtitddt d==EE232 Lecture 18-11©2008. University of California()itd=Response of One PhotogeneratedElectron-Hole Pair() () ()ehit i t i t=+()eit/eqv dNP()hit/hqv dxd0Timeedxv−hxvTimeElectronTrajectoryehTotal charge generated:() ()hQitdtitdt∞∞=+∫∫TimeHoleTrajectory00() ()ehehQitdtitdtqv qvdx xqdv dv+−=+=∫∫EE232 Lecture 18-12©2008. University of CaliforniaOne absorbed photon one charge detectedehdv dv→Transit Time() () ()it i t i t() () ()ehit i t i t=+()eitNP()e()hitTimeedvMany electron-hole pairsgeneratedhdvElectron current ends when the last electron generated near P-side reaches N-electrode: ldhhlhldetdv=Hole current ends when the last hole generated near N-side reaches P-electrode: htdv=dEE232 Lecture 18-13©2008. University of CaliforniaHole is usually slower A conservative estimate of the transit time: thdvτ→=Total Response Time of p-i-n(1) RC time:( : area of p-i-n)ARC R Aετ==Absorption layer thicknessfor optimum frequency response: (: area of p-i-n)(2) Transit time:RCRC R Addτ===RC thRA ddvεττ τ+= +⎛⎞⎛⎞Total response time:thdvτ=211hRAddvvετ⎛⎞⎛⎞≥⎜⎟⎜⎟⎝⎠⎝⎠3=12RC tdBfτττπτ+≈33,max1124Optimum bandwidth occurs whenhdB dBvffRAπτ π ε≈≤ =2πτhRA ddvdRAε=EE232 Lecture 18-14©2008. University of Californiaoptimum hdRAvε=More Rigorous Analysis ofp-i-n Response Time20Small-signal analysis: assume the input RC020 log H1 fi()()2⎡⎣⎤⎦⋅light is modulated at frequency ,the photocurrent is proportional toω⎛⎞Transit1106× 1107× 1108× 1109× 11010× 11011×40−20−fi2022sin12()1ttitjRCωτωωτ⎛⎞⎜⎟⎝⎠∝+⎛⎞⎜⎟TransitTime20020 log H2 fi()()2⎡⎣⎤⎦⋅2The first term is single-pole response from RC, hilt⎜⎟⎝⎠th d t i th h d l d t1106× 1107× 1108× 1109× 11010× 11011×40−20−fi20while the second term is the phase delay due totransit time response.Total020 log H3 fi()()2⎡⎣⎤⎦⋅EE232 Lecture 18-15©2008.