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Unformatted text preview: ' $ ECE432 Junctions Chapter 3 & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 0 The Ohio State University % ' $ Lecture # 7 & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 1 The Ohio State University % ' $ Introduction I P N V Applications: & recti cation, ampli cation, switching, regulation, LED, lasers Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 2 The Ohio State University % ' $ Topic Covered Fabrication of pn junctions pn junction theory (equilibrium, steady-state, transiant) Metal-semiconductor diodes Heterojunctions Light emetting diodes & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 3 The Ohio State University % ' $ 5.1 Fabrication of p-n Junctions Processes involved in fabrication: Thermal oxidation Thermal di usion Rapid thermal processing Ion implantation Photolithography Chemical Vapor Deposition Etching Metallization & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 4 The Ohio State University % ' $ Thermal oxidation heating coils Silica tube O 2 or H2O SiO2 Si wafers Wafers are placed in a silica tube heated to 800-1000o C dry O2 or H2 O is owed in the silica tube Chemical reactions involved: Si + O2 ! SiO2 (dry oxidation) Si + 2 H2 O ! SiO2 + 2 H2 (wet oxidation) For every micron of oxide, 0.44 m of Silicon is consumed. & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 5 The Ohio State University % ' $ Di usion (Older Process) heating coils Impureties Silica tube Si −n Si −p SiO2 wafers Doping Na Nd Wafers are placed in a silica tube Dt Position heated to 800-1100o C (minutes to hours) to creates vacancies Dopants: B, P or As are owed in the silica tube using a dry or vapor source and di use in the silicon wafers & p The di usion length Dt is di cult to control as it is strongly temperature OHIO S ATE T sensitive: D = D0 exp ; EA =(kT )] ! supplanted by ion implantation Patrick Roblin T.H.E UNIVERSITY 6 The Ohio State University % ' $ Rapid Thermal Processing gold plated reflectors Tungsten−halogen infrared lamps Temperature Process 1000 oC Temp ramp ~100o C/s Quartz window Cool−down Gas flow Gas in Wafer 27 o C Gas out Gas flow stabilization Time (s) Low thermal mass provides fast heating and cooling (seconds) by IR radiation Used with oxidation, annealing after ion implantation, chemical vapor deposition & RTP reduces exposure time to high temperature for improved control of dopant OHIO di usion Patrick Roblin T.H.E S ATE T UNIVERSITY 7 The Ohio State University % ' $ Ion Implentation Doping Iionized Accelerated Mass separator Rp ΔRp High voltage source Magnet Wafer Gas source (Impureties) Distance from surface Impurities are ionized and accelerated to kinetic energies of several keV to MeV and directed to the semiconductor surface Concentration pro le: & N (x) = p Patrick Roblin 2 Rp 2 !23 exp 4; 1 x ; Rp 5 2 Rp T.H.E OHIO S ATE T UNIVERSITY 8 The Ohio State University % ' $ Advantages Advantages Low temperature process (avoid di usion of previously implanted dopants) Precise control of doping pro le High uniformity (beam scanning) across wafer Doping & Patrick Roblin Sum of gaussians T.H.E Distance from surface OHIO S ATE T UNIVERSITY 9 The Ohio State University % ' $ Other Issues with Impact Ionization Problem: damages are created in the semiconductor crystal due to the collision. Solution: Annealing which is the self-repair of crystal at 1000o C Consequence: unintended di usion of the implanted dopants N (x) = p q 2 2 Rp + 2Dt & Patrick Roblin 3 20 2 12 1 (x ; R ) 5 4 exp 6; @ 2 p A 7 2 Rp + 2Dt T.H.E OHIO S ATE T UNIVERSITY 10 The Ohio State University % ' $ Chemical Vapor Deposition (CVD) heating coils Silica tube Gas flow SiO2 Si wafers Whereas oxidation consumes Si from the substrate and requires high temperatures, CVD uses low pressure and low temperature and does not consume Si from the substrate. In CVD a chemical reaction leads to the deposition of SiO2 on Si. Can be used to grow SiO2 , silicon nitride oxide (Si3 N4 ), polycrystaline and amorphous Si CVD can be plasma enhanced (PECVD) (plasma to be discussed later on) Di erent from VPE (MOCVD) which grows epitaxial crystal layer and isOHIO more challenging S ATE T & Patrick Roblin T.H.E UNIVERSITY 11 The Ohio State University % ' $ Photolithography Patterns used for devices and circuits are formed using photolithography. This involves the following key components: A reticle (mask) which is a transparent silica plate containing the pattern for a single chip (die). Opaque regions are realized using iron oxide A photosensistive (or electron beam sensitive) resist which is a material whose material properties changes when exposed to light. The following steps are used: The resist is spin-coated (3000 rpm) on the wafer to form a coat of (0.5 m) The resist is exposed using an optical stepper The exposed resist is etched away using NaOH (Sodium hydroxide). This transfers the patterns to the semiconductor. The resist is baked (125o C) to harden it and prepare it for subsequent processing (metal deposition, plasma etching, ion implantation). OHIO S ATE T Note: The reticle/mask is created itself using a resist. & Patrick Roblin T.H.E UNIVERSITY 12 The Ohio State University % ' & Patrick Roblin $ Optical Stepper T.H.E OHIO S ATE T UNIVERSITY 13 The Ohio State University % ' $ Limitation of Lithography Resolution is limited by di raction to the wavelength of the light used for the resist exposure This has pushed for the use of shorter wavelength from UV mercury lamp (0.365 m), to argon uoride (ArF) excimer lasers (0.193 m) or extreme UV (EUV) (0.154 m). Xray (0.01-1 nm) is been studied as an option. Improved resolution is obtained using Fourier optics (e.g., fuzzy edge) Depth of focus (DOF) decreases with decreasing wavelength and it is necessary to planarize circuits by chemical and mechanical polishing. Direct e-beam exposure of resists requires no mask and achieves down to 0.01 m=10 nm resolution which is ideal for nanotechnology research but is for IC production. too slow & OSU has recently acquired such an e-beam lithographic system: http://www.ece.osu.edu/%7Eberger/ebl.html/ Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 14 The Ohio State University % ' $ Etching In early days of Si technology selective etching of SiO2 was done with HF (hydro uoric) acid Wet etched is isotropic and is used now mostly for wafer cleaning Plasma etching is now prevalent as it is anisotropic (important for small geometry devices) The most popular plasma etching is reactive ion etching (RIE) as it is both anisotropic and selective (chemical etch by highly reactive radical) & What is a plasma? Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 15 The Ohio State University % ' $ Plasma State of Matter Plasma is a state of matter featuring ionized particles with high kinetic energy. It is often referred as the 4th state of matter but was really the rst state formed after the Big Bang (universe creation theory). Plasmas are conductive and screen radiation (skin depth). & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 16 The Ohio State University % ' & Patrick Roblin $ Ubiquitous Plasma T.H.E OHIO S ATE T UNIVERSITY 17 The Ohio State University % ' $ Plasma Etching Wafers Etch gas in Plasma Radicals & Ions out Anode (+) Cathode (−) RF gen Results from plasma physics: A high DC voltage (100-1000 V) develops near the cathode This builtin voltage accelerates positive ions toward the OHIO S T wafers and induces an etch normal to the surface (anisotropic)ATE & Patrick Roblin T.H.E UNIVERSITY 18 The Ohio State University % ' $ Metallization Al RF generator Al Al Cathode (−) Ar gas in Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al target Ar Plasma out Wafers 1111 0000 1111 0000 1111 0000 Al 1111 0000 1111 0000 11111 00000 11111 00000 11111 00000 Ar 11111 00000 11111 00000 Ar+ Anode (+) Devices needs to be connected together and with the IC package using metallization. Metal deposition techniques used include: Thermal or E-beam evaporation in vacuum (Au on GaAs) or sputtering with OHIO low-pressure Argon (Ar) plasma (Al and Cu on Si) S ATE T & Patrick Roblin T.H.E UNIVERSITY 19 The Ohio State University % ' $ PN Junction Fabrication http://jas.eng.buffalo.edu/education/fab/pn/diodeframe.html & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 20 The Ohio State University % ' $ Lecture # 8 & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 21 The Ohio State University % ' $ 5.2 Equilibrium Conditions P N P ε Concentration pp= Na hole diffusion φp nn= Nd Log scale electron diffusion np= & N Patrick Roblin n 2/ i pp pn= ni2/ n n φn Vn x Vp T.H.E OHIO S ATE T UNIVERSITY 22 The Ohio State University % ' $ Equilibrium Diode Band Diagram P N P N Energy Ec Ec Ecp EF Ecn EF Ev & Ev EFn Evn Fermi level is constant in equilibrium Patrick Roblin EFp Evp T.H.E OHIO S ATE T UNIVERSITY 23 The Ohio State University % ' $ Sailing, Biking (or Skying) on the Band Diagram Diffusion E cp * E cn Drift E Fn E Fp E vp Drift * & Patrick Roblin E vn Diffusion T.H.E OHIO S ATE T UNIVERSITY 24 The Ohio State University % ' & Patrick Roblin $ Sailing with a Laser T.H.E OHIO S ATE T UNIVERSITY 25 The Ohio State University % ' $ Built-in Contact Potential P N P N ε (electric field) Concentration pp= Na hole diffusion φp nn= Nd Log scale electron diffusion np= n 2/ p p i pn= ni2/ nn φn Vn V0 x Vp Energy Ec Ec Ecp EF Ecn & Patrick Roblin EF Ev Ev EFp Evp EFn T.H.E Evn OHIO S ATE T UNIVERSITY 26 The Ohio State University % ' $ Built-in Contact Potential In equilibrium there is no electron and hole currents: Jp = Jp(drift) + Jp(diffusion) = 0 Jn = Jn(drift) + Jn(diffusion) = 0 Using the holes's current we have dp J0 = 0 = q ppE ; qDp dx 0 = ; pp dV ; Dp dp dx dx 1 dp p dV ); Dp dx = p dx q dV = 1 dp ); kT p & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 27 The Ohio State University % ' $ Built-in Contact Potential q dV = 1 dp ; kT p q Z Vn dV = Z pn 1 dp ); pp p kT Vp q ) ; (Vn ; Vp ) = Ln(pn) ; Ln(pp) kT q V = Ln pp ! ) kT 0 pn The built-in contact voltage is: ! kT 0 n 1 kT 0 N N 1 p a V0 = kT Ln pp = q Ln @ nn A = q Ln @ n2 d A q n p i using nppp = nnpn = n2. i & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 28 The Ohio State University % ' $ Built-in Contact Voltage 0 1 kT Ln @ NaNd A V0 = 2 q cannot be measured. Why? ni Diffusion E cp * E cn Drift E Fn E Fp E vp & Patrick Roblin Drift * E vn Diffusion T.H.E OHIO S ATE T UNIVERSITY 29 The Ohio State University % ' $ Non-Measurable Contact Potential The voltage VD across the diode in equilibrium is 0. Only di erence in Fermi levels can be measured as voltage ;qVD . 0 1 EF = Ec(0) ; qV (x) + kT Ln @ n(x) A | {z } {z Nc } | electrostatic potential energy = n (x) ; qV (x) = constant chemical potential The variation in electrostatic potential is compensated by variation in chemical potential: & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 30 The Ohio State University % ' $ Non-Measurable Contact Potential Diffusion E cp * E cn Drift E Fn E Fp E vp Drift * E vn Diffusion The variations in electrostatic potential energy is compensated by the variations in chemical potential energy: & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 31 The Ohio State University % ' $ Proof P V0 = ) eqV0=(kT ) = = & = = )1 = Patrick Roblin ) kT Ln pp ! q pn Ecp pp pn EFp Nv e(Evp;EF p)=(kT ) Evp (Evn ;EF n )=(kT ) Nv e e(Evp;Evn)=(kT ) e(EF n;EF p)=(kT ) eqV =(kT )e(EF n;EF p)=(kT ) e(EF n;EF p)=(kT ) EFn = EFp N qV0 Ecn E Fn Evn 0 T.H.E OHIO S ATE T UNIVERSITY 32 The Ohio State University % ' $ Space Charge at a Junction Equations to solve: dE = (x) with dx (x) = q p(x) + Nd(x) ; n(x) ; Na(x)] P N Ecp qV0 Ecn & Patrick Roblin EFp Evp E Fn T.H.E Evn 33 OHIO S ATE T UNIVERSITY The Ohio State University % ' $ Depletion Approximation P ρ=0 E cp N A ρ= ρ= ρ=0 −qN a qNd qV0 E cn EFp E vp E Fn E vn & −x p0 0 Macroscopic space charge neutrality: qAxp0Na = qAxn0Nd Patrick Roblin 34 xn0 x T.H.E OHIO S ATE T UNIVERSITY The Ohio State University % ' $ Depletion width W P ρ=0 N A ρ= ρ=0 ρ= −qN a qNd −x p0 0 xn0 x W & xp0 ! = x 1 + Nd ! W = xn0 + xp0 = xn0 1 + x n0 Na n0 W = Na W ) xn0 = Nd Na + Nd 1 + Na Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 35 The Ohio State University % ' $ Charge, Electric Field, Potential P N A ρ qNd −x p0 xn0 0 −qN a dE = qNd dx Z0 qNd Z xn dx dE = E 0 qNd x ;E = −x p0 ε xn0 0 V 0 & Patrick Roblin x ε0 0 0 x n0 qV0 T.H.E −x p0 0 xn0 x OHIO S ATE T UNIVERSITY 36 The Ohio State University % ' $ V0 = & ; Z xn0 ;xp0 Contact Potential and Depletion Width E (x)dx ! 1 1 = ; xp0E0 + xn0E0 2 2 1E W =; 0 2 = 1 qNd xn0W 2 1 q NaNd W 2 = 2 Na + Nd v u 2 (N + N ) u a W = t qN N d V0 ad Patrick Roblin P N A ρ qNd −x p0 xn0 0 x −qN a −x p0 ε xn0 0 x ε0 V T.H.E qV0 −x p0 37 0 xn0 OHIO S ATE Tx UNIVERSITY The Ohio State University % ' $ PN Junction Formation http://jas.eng.buffalo.edu/ & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 38 The Ohio State University % ' $ Lecture # 9 Forward & Reverse Biased Junctions & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 39 The Ohio State University % ' Charge and Band Diagram when a Voltage is Applied V +− P −+ V −+ N P −+ −+ P N −+ Ec Ec −qV E F Ev & $ Forward Biased Patrick Roblin E F Ev N Ec E F Ev − − ++ −− ++ −− ++ E F Equilibrium −qV E F T.H.E Reverse Biased OHIO S ATE T UNIVERSITY 40 The Ohio State University % ' $ Band Diagram in Equilibrium Diffusion E cp * E cn Drift E Fn E Fp E vp Drift * & E vn Diffusion Drift and di usion currents are cancelling each other. Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 41 The Ohio State University % ' $ Band Diagram in Forward Bias Diffusion E cp Drift E Fp E vp E cn E Fn −qV Drift E vn & Diffusion Di usion currents dominate over drift currents. Patrick Roblin 42 T.H.E OHIO S ATE T UNIVERSITY The Ohio State University % ' $ Band Diagram in Reverse Bias E cp Diffusion Drift E Fp E vp −qV E cn E Fn Drift Diffusion & E vn Drift currents dominate over di usion currents but both are neglegible. Only the rare Olympic electrons doing the high jump can make it over the increased OHIO S ATE T potential barrier. Patrick Roblin T.H.E UNIVERSITY 43 The Ohio State University % ' $ All Biases Diffusion Drift E Fp E vp Diffusion E cp E cp E cn E Fn −qV E vn Diffusion Diffusion * Drift E cn Drift E Fp E vp Drift E cp Drift E Fn E Fp E vp −qV E cn E Fn * E vn Diffusion Drift Diffusion Forward Bias & Patrick Roblin Equilibrium E vn Reverse Bias T.H.E OHIO S ATE T UNIVERSITY 44 The Ohio State University % ' $ Carrier Injection In equilibrium there is no electron and hole currents: Jp = Jp(drift) + Jp(diffusion) = 0 Jn = Jn(drift) + Jn(diffusion) = 0 Using the holes's current we have dp J0 = 0 = q ppE ; qDp dx Let us evaluate the magnitude of the di usion/drift currents dp Jp(diffusion) = qDp dx 19 5 ;3 ;19 (C) 10(cm2 /s) 10 ; 10 (cm ) = 1:6 10 4 10;{zcm | } 1m OHIO = 1:6 105A/cm2 Very Large! S ATE T & Patrick Roblin T.H.E UNIVERSITY 45 The Ohio State University % ' $ Assumption Since Jp(diffusion) = 1:6 105A/cm2 is very large we can safely assume that when a bias is applied Jp = Jp(drift) + Jp(diffusion) << Jp(diffusion) or equivalently Jp = Jp(drift) + Jp(diffusion) ' 0 like in equilibrium. & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 46 The Ohio State University % ' $ Carrier Injection So like in equilibrium we start from: Jp = Jp(drift) + Jp(diffusion) = 0 Using the holes's current we have dp Jp = 0 = q ppE ; qDp dx 0 = ; pp dV ; Dp dp dx dx 1 dp p dV ); Dp dx = p dx q dV = 1 dp ); kT p & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 47 The Ohio State University % ' $ Carrier Injection q dV = 1 dp ; kT p q Z Vn dV = Z p(xn ) 1 dp ); p(;xp ) p kT Vp q (V ; V ) = Ln p(;x )] ; Ln p(x )] ) p0 n0 kT n p 2 3 q (V ; V ) = Ln 4 p(;xp0) 5 ) kT 0 p(xn0) Resulting in: 2 3 p(;xp0) = exp 4 q(V0 ; V ) 5 p(xn0) kT 0 0 & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 48 The Ohio State University % ' $ Range of Integration P ρ=0 E cp N A ρ= ρ= ρ=0 −qN a qNd qV0 E cn EFp E vp E Fn E vn & Patrick Roblin −x p0 0 xn0 x T.H.E OHIO S ATE T UNIVERSITY 49 The Ohio State University % ' $ Electrostatic Potential when Diode is Biased V>0 +− P V<0 +− N −+ P −+ −+ −+ N P − − ++ −− ++ −− ++ N Vn Vn Electrostatic Potential Vn V0 −V Vp with V>0 Vp Vp −q(V 0−V) with V0 −V V0 −qV 0 −q(V 0−V) V>0 with −qV V<0 −qV & Patrick Roblin T.H.E Forward Bias Equilibrium 50 Reverse Bias OHIO S ATE T UNIVERSITY The Ohio State University % ' $ Carrier Injection We have found that when the 3 diode is under a bias we have: 2 p(;xp0) = exp 4 q(V0 ; V ) 5 p(xn0) kT Using the equilibrium relation we have: pp = exp " qV0 # ) p(;xp0) = pp exp ;qV ! pn kT p(xn0) pn kT Low injection approximation: p(xn0) = pn + pn minority carrier p(;xp0) = pp + pp ' pp majority carrier It results that: qV ! ) p = p "exp qV ! ; 1# p(xn0) = pn exp kT n n kT & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 51 The Ohio State University % ' $ Minority Carrier We derived that the excess minority carrier is: " q V ! ; 1# pn = pn exp kT Variation of the excess minority carriers: 8 >V =0 > pn = 0 > < for > V >> 0 pn ' pn exp qV kT > > : V << 0 pn = ;pn & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 52 The Ohio State University % ' $ Lecture # 10 Carrier Injection and Current & Patrick Roblin T.H.E OHIO S ATE T UNIVERSITY 53 The Ohio State University % ' $ Band Diagram and Excess Carriers 1.5 1 Energy (eV) 0.5 0 −0.5 V=0.5 V V=0 V −1 E v E V=−0.5 V c & −1.5 −1.5 −1 −0.5 0 position qV ! ; 1# and pn = pn exp kT Patrick Roblin " 54 0.5 1 " 1.5 qV ! ; 1#OHIO np = np exp kT S ATE T −7 x 10 T.H.E UNIVERSITY The Ohio State University % ' $ Doping Concentration 25 10 20 10 hole concentration p Concentration (cm−3) electron concentration n 15 V=0.5 V V=0.5 V V=0 V V=0 V V=−0.5 V 10 V=−0.5 V 10 10 5 10 & Patrick Roblin T.H.E 0 10 −1 −0.5 0 position 0.5 1 −7 x 10 OHIO S ATE T UNIVERSITY 55 The Ohio State University % ' Excess Carriers Concentration Δ np Δ pn diffusion & recombination Ln P diffusion & recombination −x p0 − x n0 0 − + neutral − + depletion +− np(x) = npe(x+xp )=Ln and 0 & qV ! ; 1# and np = np exp kT Patrick Roblin Lp " 56 Position + Qn Qd Qd Qp − with $ N + neutral pn(x) = pne;(x;xn )=Lp 0 " qV ! ; 1#OHIO pn = pn exp kT S ATE T T.H.E UNIVERSITY The Ohio State University % ' $ Current Distribution Current total current I Ip diffusion & recombination diffusion & recombination In Ln −x p0 0 x n0 − + Qn − + Qp − + Position + − P − Lp + N +− & We shall rst assume that there is neglegible recombination in the depletion region. Patrick Roblin 57 T.H.E OHIO S ATE T UNIVERSITY The Ohio State University % ' Diode Forward Biased Ln P Neutral W Space Charge 1 0 Excess electrons 1 0 Diffusion 1 0 1 0 1 0 In 1 0 1 0 1 0 1 0 1 0 1 0 Recombination 1 0 1 0 1 0−qv Di 1 0 1 0 1 0 1 0 E cp −qvD= EFp E vp & Patrick Roblin $ vD Ohmic loss Drift In +Ip Diffusion Ip + R 58 E Lp Neutral 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 N 1 0 1 0 1 0 I +I 1 0 np 1 0 Drift 1 0 1 0 1 0 1 0 1 0 E cn 1 0 1 0 1 0 1 0Ohmic loss E Fn 1 0 1 0 1 0 Recombination 1 0 1 0 1 0 1 0 1 0 E vn 1 0 Excess holes − A T.H.E OHIO S ATE T UNIVERSITY The Ohio State University % ' $ Current Calculation Using pn(x) = pne;(x;xp0)=Lp and np(x) = npe(x+xn0 )=Ln with " qV ! ; 1# and n = n "exp qV ! ; 1# pn = pn exp kT p p kT the total diode current is evaluated from: Ip = AJp(xn0) = ;AqDp dp(x) = AqDp Lpn dx xn0 p np dn(x) = AqDn In = AJn(;xp0) = AqDn dx Ln ;xp0 0 1" Dn n + Dp p A exp qV ! ; 1# I = In + Ip = Aq @ L p L n kT n {z p} | & Patrick Roblin I0 T.H.E OHIO S ATE T UNIVERSITY 59 The Ohio State University % ' $ Diode I-V Characteristic " q V ! ; 1# I = I0 exp kT I0 is the leakage current (very small): 1 0 I0 = Aq @ Dn np + Dp pnA Ln Lp For...
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