MICROELECTRONICS TECHNOLOGY ECSE 2210
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Date Created: 10/19/15
Chapter 32 Diffusion and band bending We will learn two new topics today Diffusion a process whereby particles tend to spread out or redistribute as a result of their random thermal motion migrating on a macroscopic scale from regions of high particle concentration to region of low particle concentration Examples of diffusion Perfume in a room Ink drop in a bottle of water Hot point probe measurements Band bending resulting from the presence of electric field inside a semiconductor No band bending means the electric field is zero Hotpoint probe measurement This is a commonly used technique for determining Whether a semiconductor is p type or ntype Hot Cold Energetic holes Energetic electrons dlffuse away diffuse away a b Figure 313 Diffusion current For diffusion to occur there must be a concentration gradient Logically greater the concentration gradient greater the ux of particles diffusing from higher concentration region to lower concentration region If F is the ux ie the of particles cm2 s crossing a plane perpendicular to the particle ow then Ddn F dx Where D is called the diffusion coefficient The sign appears because for positive concentration gradient dndx the particles diffuse along the negative x direction Concentration n L r Particle diffusion Concentration gradient dndx positive Particles ow along x direction Diffusion current Electrons Holes O O O O O O C C C C C C C O C C C C C C C O C C O O O O O O O O O O O O x x hole ux 4 electron ux hole diffusion current electron diffusion current Jpldiffqudpdx Jnldiff2andndx What is the unit of diffusion coefficient D Total currents dp J p Jpdrift Jpdiff qupf qu a drift diffusion dn Jn JndriftJndiff anWE 6113113 The total current owing in semiconductor is given by J J nJ p Band bending Band diagram represents energies of electrons so far we have drawn it as independent of position When Efield is present EC and EV change with position called bandbending This is a way to represent that an E eld is present E C E EC E1 Ei EV EV No qs ezd indicates presence of Efield Band bending and electrostatic variables E Total E electron 6 Diagram represents total energy lg energy of electrons With x x a v KE E EC for electrons x PE EC Eref for electrons H RE Ev From elementary physics PE q Vfor electrons d x EC Eref i V x E dV dx 0quot lq dECdx Fiswew Band bending Crudely inverting EC in eV versus x diagram results in electrostatic potential Vin Volts versus x diagram Similar to potential energy V is relative with respect to some arbitrary reference 1 V gECEref We have to multiply EC Eref by 16 x 10 19 to convert from eV to Joules So values of V in Volts is numerically equal to Ec Eref expressed in eV The slope of EC energy in eV versus x diagram gives the Efield versus x plot idECld i qu qu qu E fz ela expressed in Vcm will be numerically equal to dEi dx if Ei is in eV and x in cm Example 1 Exercise 32 Plot electrostatic potential V and E eld E versus x for the case shown below 13 s g 2 3 8 0 EC 9 Lu 1 39 quot E 1 EF 0 51 E holes I 10 1 p qpup qnun Review Resistivity formula Jdrift JnldrjftJpdrift 61Hnnupp95 dn Jnldiff ana an d JP JD Jpldrift Jpdiff Jnldrift Jndiff Drift current density dp Jpl diff qu E Diffuszon current denszty d W qu 3p Total hole and d electron current an an 3 density Total current density BK 31 ECSE 2210 Microelectronic Technology Review Questions Problem l Consider a Si wafer doped with lO 6 cm 3 donors and 6x10395cm393 acceptors Assume that 7 the electron mobility is 200 cmZVs and hole mobility is 400 cmquotVs a This wafer is ptype intrinsic choose one 7 What is the ho nd39clectron concentration at 300 K in ihis semiconductor h mgu W39 X f I L 1 is r L 2 l 3 l n I I M P y 7 LJflr b Calculate Lhc resistivity ofthe above wafer at 300 K 3 l v 7 n it 7 f n I ll c Draw an energy band diagram showing the Fermilevel position Mark clearly EC Ev E and EF Indicate the numerical values ofEc vEVEc7 E andEiiE in the diagram d We would like to introduce additional impurities to this semiconductor such that the Fermi level is 04eV below the intrinsic level after the addition of additiona impurities How many additional impurities should be added What is the type donor or acceptor choose one if straw l NF A 1quot 370 IXIO 7 l l H iiiquot51739 to 3 N a L xi 1 quotW a c Suppose we dope GaAs with the same level of dopants namely lOm cm393 donors and 6x10 5em39J acceptors Calculate the electron and hole concentration in GaAs n value ofGaAs is 2x1060m IS elm i r cm LIL V L f Suppose we heat up the GaAs wafer of part e to 100C State whether the following statements are true or false The electron concentration will increase signi cantly T E The hole concentration will increase signi cantly F Problem 2 Abrupt ptn junction diode is made in silicon as shown below Answer the following at n ND 2x10396cm393 Dn25 cmZs Dle emZs r 0 7 s Draw the band diagram showing EC Ev E and BF Mark the numerical values For EE and EFE in the graph b Calculate the builtiiuoltage of the diode Slate which region is at a higher potential pfregion orn circle one A a a J39 Vb rugix 0393 7 k i 0 Calculate the reverse saturation current ofthe diode Assume it is ideali 39 i IL d Calculate current when 07V forward bias is applied 7 L L J vw f i2 L 11 e Calculate the diode capacitance for reverse bias of WV V i b I A 47 J A L l K Rikki1 1 r r L a w La i 1 Wquot u r U in 5 Suppose you make another diode with lhe same parameters like doping dif lsion coef cient etc but in Ge that has a band gap 0f07eV Which one will have higher reverse leakage eunenl e oiodelur Si diode Problem 3 A MOSFET made with nf poly silicon gate has he following characteristics Oxide thickness 500A Doping in Si N 1 x 10 cmquot Imerfacc oxide charges 64 x 10 q Coulcmbscm1 3 Calculate the at band voltage oflhis device 39 o L 39 3 71M 2 misnlvx LEV 7 ATquot i L 6 My a e r 2 I I39 gt cw1w axJ U39 Aquot l r 4 LI 7 quot I L39ler U s f 39 7 v 1 r 41 v39 be Calculate the lhmshold vollage of lhis devicc UT 7 Ts39v yr lfe uTl 1 7 g 4 b 2 v 33 a 5 139 9quot 7 w I Ly V C 1 H V 139 39Alzszv iquotiqu r 0 Plot he high frequency C VG charame stics for this device Mark important points in the graph Ignore the presence of SD for his case Ch 7 V 394 d Is this depletion mode device or enhancement mode device Plot the In VD characteristics qualitative for various values of V5 for this device far 3 ltVG 39 i lt3Vmstepsof1 U C A u lt E gt HE Wm 46 ample v lt lb yeVlLQ un 39r39W 3 quot 39 A i L 1h LLI 5H4 5L tileV V 1 7 A e Suppose we use ifr polysilieon as the gate instead of n polysilicon gate what will be the new V value W k c39 wD ji Li L5 quotI N we V5 ka 3N0 Hit Wm T31 Lt Ly391quot l L k mo 7 m t f Suppose Wm ease the substrate doping What will happen to the threshold voltage rtcelrdecrease remain the santez M5 quot gt upp e we increase the oxide thickness What will happen to the threshold voltage Increase decrease remains the same UV Wu 5 211 r39 v rv39ni L 539 Problem 4 Answer the following questions BC very brief a The gure 39below shows the electric eld in the depletion layer of a uniformly doped and abrupt silicon junction diode under a biased condition Which side is n type and which side is p type Which side is more heavily doped i an m 4 quotPquot a t I 412 0 L0 240 1pm b Two npn transistors are identical except that A has higher doping in the emitter than B Which one will have higher B Explain c Consider diodes made from Ge Si and GaAs Assume identical doping etc Which diode will have the highest reverse leakage current v F GalnSb is an alloy of GaSb and lush whose band gap can be varied from 0l7eV to 073 eV GaloSb with 20 InSb has a band gap of 055eV This particular material has been investigated at RPI as a candidate for converting heat energy to electricity Thc radiation spectrum From a 1500 C heat source is roughly drawn below Shade the region of the spectrum that can be converted to electrical power using diode cells made ofGalnSb Power WattscmzeV 0 c Draw a cross section of n well CMOS below and identify NMOS PMOS n and p regionst Also show the substrate and nwell contact and contact regions identify the eld region 9M 1 5 Crquot 1 L 351 m l 2 Lur39 r t 71L n it 7 u Low n Ti L311 Lilli n Chapter 63 Deviations from the ideal Mostly qualitative understanding of nonideal behavior of the diodes Reversebias breakdown Avalanching Zener process The RG current If VA gt Vbi then highcurrent phenomena result Series current Highlevel injection IV Characteristic of commercial Si diode at 300K 10 08 I mus 04 02 50 40 30 20 10 02 04 06 08 10 VA volts 04 06 08 10 Figure 69 Detailed IV plots of commercial Si diode at 300K 100 Series resistance effect 10392 104 High level injection I amps 106 Ideal behavior 10398 GR part 1010 02 04 06 08 10 VA volts a 1012 0 VA volts 50 40 30 20 10 0 Breakdown b Figure 610 Reversebias breakdown A large reverse current ows when the voltage exceeds certain value Not destructive unless power dissipation causes excessive heating For a pn or pn diode VBR 0C NB 1 where VBR is the breakdown voltage and NB is the bulk doping on the lightly doped side Two processes Avalanching dominant process in lightly doped diodes Zener process more important in heavily doped diodes Avalanching Carrier multiplication due to impact ionization occurs at high reverse voltage when the electric eld reaches a critical value ECR These additional carriers are swept across the depletion layer due the high electric eld E eld K lt P 39 N lt VAltlt 0I 39 I The increase in current associated with the carrier multiplication is modeled by introducing a multiplication factor M I 0 and the multiplication factor can be empirically t to an equation 1 M m 1 VA VBR where m is between 3 and 6 Carrier activity Within a reversedbiased diode 1 Carrier multiplication 21 due to impact ionization a Small reverse bias 1 IVAI VBR Figure 612 Avalanching Ex O qND xn i p i n 8Si E 1 l 2 x 261 NAND Vbl VA SSi NA ND naX q q ND xne Breakdown occurs when O ECR and When Vbi VA gt Vbi VBR z VBR 2 N N 12 8sr AND For asymmetrically doped junctions Where NB is the bulk doping on lightly doped side Zener process P E I i I I I I i I i t VP yFiued states 7 Empty States 7 CIl vn lt Barner F W H Figure 614 Tunneling in a reverse biased diode occurs in heavily doped diodes The R G current reversebias case In an ideal diode the reverse current is 10 q A DppnLpl D11 npLn and this current is a constant The ideal diode equation was derived assuming no generation of carriers in the depletion layer In an actual device the thermal generation of carriers in the depletion layer should be taken into consideration The current due to thermal generation IRG increases with the volume of the depletion layer or W Volume or W increases with the applied reverse bias So IRG increases as reverse voltage is increased Detailed analysis shows that IRG for reverse bias can be written as A IRG W where 10 ftptntptn2 T0 The RG current forwardbias case Under forward bias some of the injected carriers may recombine while crossing the depletion layer This was neglected in the analysis of ideal diode Detailed analysis shows that amp RG 3 e ZkT 1 in the forward bias case Total forward current I diff IRG where diff is the current called diffusion current described by the ideal diode equation qVA 2 D 2 diff 10 e I 1 where 10 qA LJr PL diff increases more more rapidly with bias compared to IRG So diff dominates at higher forward voltage Relative values of LG and E In Si q A ni W 21 gtgt 10 and IRG current dominates at reverse bias and at small forward bias Since IRG oc W the reverse current never saturates but continually increases with reverse bias Since diff oc n12 and IRG oc ni the relative values of diff and IRG varies from semiconductor to semiconductor In Si and GaAs at 300 K q A ni W 21 gtgt I0 whereas in Ge 10 gtgt q A ni W 21 So Ge more closely follows ideal diode equation I 10 exp q VA k7 1 at 300K Since diff oc n12 and IRG oc ni diff increases at a faster rate with increasing temperature So even Si follows the ideal diode equation I 10 exp q VA k7 1 at higher temperature Zia Vm highcurrent phenomena As VA approaches Vbi a large current ows Two phenomena become important series resistance effect and highlevel injection Series resistance effect Some voltage drops in the quasineutral and ohmiccontact region reducing the actual voltage drop across the junction LVJ39 LVJ39 qVA IRS IzroekT 1 zloekT 10e kT when VA gtVbi Here is the actual voltage across the junction and VA is the applied voltage Some of the applied voltage is wasted so that larger applied voltage is necessary to achieve the same level of current compared to the ideal 12 Identi cation and determination of diode series resistance logI AV 1 Slope over region V VA gt1 b C Figure 616 13 High level injection When the forward voltage is within a few tenths of a volt below Vbi high current ows and the lowlevel injection assumption begins to fail High level injection phenomena should be considered in deriving IV characteristics More detailed analysis shows that the current increases roughly as eXp q VA 2kT when VA gt Vbi n or p log scale logI A Highlevel injection Pp Caused by highlevel injection q2kT slope Jl llJllll I lllllllllll Ideal region 1 l l I 39 b Figure 617 14 Review log1 1 Photogeneration E D 2 Thermal recombination in the depletion legion Idefil 3 Avalanching andor reglon Zener process quotAVA C 4 Lowlevel injection VA 5 Depletion approximation 6 Thermal quot in te depletion region w gt l Band bending Z Series resistance VA gt Vbi 10 l quotgh 1mm injm tinn 0 S a Ed 23 58 EV Figure E69 Plot the IV characteristics for an ideal diode in the same graph above 15 Chapter 63 Deviations from the ideal Mostly qualitative understanding of nonideal behavior of the diodes Reversebias breakdown 7 Avalanching 7 Zener process The RG current If VA gt Vbi then highcurrent phenomena result 7 Series current 7 Highlevel injection IVCharacteristic of commercial Si diode at 300K Figure 69 Detailed I Vplots of commercial Si diode at 300 K Series resistance effect High level injection Forward bias W W Ideal behavior GR part Reverse bias GR part h Breakdown w riuuremn Reversebias breakdown A large reverse current ows when the voltage exceeds certain value Not destructive unless power dissipation causes excessive heating 39 71 For a p n or pn d10de VBR oc NB where VBR is the breakdown voltage and NB is the bulk doping on the lightly doped side Two processes Avalanching Dominant process in lightly doped diodes Zener process More important in heavily doped diodes Avalanching Carrier multiplication due to impact ionization occurs at high reverse voltage when the electric eld reaches a critical value ECR These additional carriers are swept across the depletion layer due the high electric eld E eld 7 lt P N VAltlt 039 The increase in current associated with the carrier multiplication is modeled by introducing a multiplication factor M I IO and the multiplication factor can be empirically fit to an equation 1 m 1 7 l VA l VBR Where m IS between 3 and 6 5 Carrier activity within a reversedbiased diode Carrier multiplication due to impact ionization b IVAl Van a Small reverse bias Figure 6 12 Avalanching u 851 a ijm SSi NAND Breakdown occurs when 0 ECR and When Vbi VA gt Vbi VBR VBR Nlquot Eq 53021 gm qNAxpS qNDxns 12 ECR EVER or VBR m m NAND Ssi NAND For asymmetrically doped junctions Where NB is the bulk doping on lightly doped side Zener process Empty states Tunneling in a reverse biased diode occurs in heaVily doped diodes The RG current reversebias case In an ideal diode the reverse current is I 0 qA DppnLp Dn ripLn and this current is a constant The ideal diode equation was derived assuming no generation of carriers in the depletion layer In an actual device the thermal generation of carriers in the depletion layer should be taken into consideration The current due to thermal generation IRG increases with the volume of the depletion layer or W Volume or W increases with the applied reverse bias So IRG increases as reverse voltage is increased Detailed analysis shows that IRG for reverse bias can be written as qAn RG T01W where to cp I m 1p Ira2 The RG current forwardbias case Under forward bias some of the injected carriers may recombine while crossing the depletion layer This was neglected in the analysis of ideal diode Detailed analysis shows that 39 2kT IR39G 10 e 1 in the forward bias case Total forward current I I diff IRG where I diff is the current called diffusion current described by the ideal diode equation WA 2 D 2 Idiff 10 e H l where 10 qA gIll 1 pn 1 Ln NA Lp ND dunf increases more more rapidly with bias compared to IRG So I diff dominates at higher forward voltage Relative values of IE and Iliff In Si qA ni W 239 gtgt 10 and IRG current dominates at reverse bias and at small forward bias Since IRG cx W the reverse current never saturates but continually increases with reverse bias Since I diff cx mi2 and IRG cx ni the relative values of I diff and IRG varies from semiconductor to semiconductor In Si and GaAs at 300 K qA niW21gtgt 10 whereas in Ge 10 gtgt qA ni W 2395 So Ge more closely follows ideal diode equation I 10 exp qVAkT 7 l at 300K Since I diff oc nil and IRG cx ni I diff increases at a faster rate with increasing temperature So even Si follows the ideal diode equation I I 0 exp q VA kT 7 l at higher temperature Z gt Vbi highcurrent phenomena As VA approaches Vbi a large current ows Two phenomena become important series resistance effect and highlevel injection Sen39es resistance effect Some voltage drops in the quasineutral and ohmiccontact region reducing the actual voltage drop across the junction qVj qVj qVAeIRs 110 ekT i mIOekT 10e kT when VA gtVbi Here is the actual voltage across the junction and VA is the applied voltage Some of the applied voltage is wasted so that larger applied voltage is necessary to achieve the same level of current compared to the ideal 12 Identification and determination of diode series resistance 39 X I svwmm 39 I Slope RS qIltT slope Figure 515 13 High level injection When the forward voltage is within a few tenths of a volt below Vbi high current ows and the lowlevel injection assumption begins to fail High level injection phenomena should be considered in deriving I Vcharacteristics More detailed analysis shows that the current increases roughly as exp q VA 2kT when VA gt Vbi u or p log scale In I med by mghIzvel injection rlqure 611 14 Review 1 thogenemtmn u Thenml recombinmiun in me depletion region ener process g l wkch injection u nepmion Ippmximaliou o Thermal gcncmuon m the 4 nl v39 n moi n nauu mum 5 Series resistance 5 VA gt Vquot 3 Hi ghrlevel injection S a EC is 53 iv Figure 69 Plot the I Vcharacteristics for an ideal diode in the same graph above 15 Chapter 111 Detailed g Quantitative Analysis The goal is to relate transistor performance parameters y aT dc etc to doping lifetimes basewidths etc Assumptions pnp transistor steady state lowlevel injection Only drift and diffusion no external generations One dimensional etc General approach is to solve minority carrier diffusion equations for each of the three regions 2 2 622D mg 63sz Ak it p 3x2 1p 6 and L 6x2 In GL General Quantitative Analysis Under steady state and when GL 0 2 62m A Dp6Ap 0 and n0 n 6x2 11 6x2 In For the base in pnp we are interested only in holes 2 6 DP A2p g 0 6x 11 The rigorous analysis is carried out in chapter ll but we are going to take a more simplified approach Review Operational Parameters m 1c IEP L4 1 1BR E gt EN 4 7BE i IBR 1B Injection Efficiency 7 IEP IEP IEN Base transport factor aT 1c IEP Collector to emitter current gain aDc aT y Collector to base current gain Dc aDc l 7 am These parameters can be related to device parameters such as doping lifetimes diffusion lengths etc Review Indirect thermal recombinationgeneration 710 po 7 under thermal equilibrium n p 7 under arbitrary conditions functions of I An and Ap are deviations in carrier concentrations A 7 quot0 from their equilibrium values An and Ap can be both AP p p0 positive or negative An and Ap are termed excess carriers 7 excess above the equilibrium concentration Low level injection condition is assumed 7 Change in the majority carrier concentration is negligible For example in ntype material Ap ltlt n0 n u no in ptype material An ltlt p0 p m p0 Majority carriers are electrons in ntype material and holes in ptype material 4 Review Minority carrier concentration pro le under bias pside QVA An 0 np xp np0ek7 p np npo Anpx nside 124xquot p pnpr10 Apnx a VA 6 7 n0 u L Anpx Anp0 e 7L ApnOC A10e P Review of P N Junction Under Forward Bias VEB AnEm ptype emitter Area Qn Apno Area Qp ntype base Review of P N Junction Under Forward Bias cont In qADE dAnde 7 qADELE AnE0 1p qA DB dAPde 9A DBLB APB0 Total current I P 7 IN 7 because xE and xB point in opposite directions qA DBLB ApB0 qA DELE AnE 0 qADBLBpB0 exp 9 VEBkT 1 l qADELE quotE0 exp 9 VEB k 1 Z qA DBLB PBo exp 9 VEBkT qA DELE quotE0 exp 9 VEBkT Nate II and In can also be calculated based on the fact that Qp has to be replaced every TB seconds II Qp t39B and In QnTE and IE IP IN Simplified Analysis Consider the carrier distribution in a forward active pnp transistor Emitter Base Collector 11730 pBO Simplified Analysis cont Pl n P nEO pm and nco equ111br1um concentratlon of m1nor1ty carr1ers 1n emltter base and collector nE0 pB0 and nc0 minority carrier concentration under forward active conditions at the edge of the respective depletion layers AnE 0 ApB0 and Anc0 excess carrier concentration at the edge of the depletion layers Simplified Analysis cont AquotE 0 quot150 quotE0 quotE0 exp 9 VEB kT 1l APB 0 PB 0 PBo PBo exp 1 VEB kT 1l By taking the slopes of these minority carrier distribution at the depletion layer edges and multiplying it by qA Dnyp we can get hole and electron currents Note that In qA Dn dndx and 1p 7 qA Dp dpdx Calculation of Currents Collector current I C c q A DB slope must be taken at end ofbase qADB pB0 0l WB 9 4 DB PB0 WB 1c qA DBWE PBo eXP qVEB kT quotquot A only hole current if we neglect the small reverse saturation current of reverse biased CB junction Calculation of Currents cont Emitter Current I E IE is made up of two components namely IEP and IEN IEP 1c current lost in base due to recombination 1c excess charge stored in base139B Ic qA WE ApB0 2rB 914 D BWB PBo exp qVEB k7 l th WE2713 PBo exp qVEBkml B Assuming exp q VEBkT 7 l m exp q VEBkT when VEB is positive ie forward biased Calculation of Currents cont Emitter Current c0nt JEN corresponds to electron current injection from base to emitter since EB junction is forward biased IEN qA DELE quotE0 exp 9 VEBkT 1 qA DE LE quotE0 exp 9 VEBkTH quotquot C Calculation of Currents cont Base Current I B supplies electrons for recombination in base supplies electrons for injection to emitter 1B qA PBO WE27B exp WEB167 qA DELE quotE0 eXP qVEBkT recombination electron injection to emitter Now we can find transistor parameter easily Calculation of Currents cont Base transport factor a T 1 13 5911 5 same as eq 1142 in text Emitter injection ef ciency 7 7 EPIEPIEN 11IENIEP 11CB 1 1 DE quotEnLE DB PBOWB 15 Calculation of Currents cont Eq 1141 in textbook ni 2NE doping in emitter pB0 71 2NB doping in base Chapter 7 Smallsignal admittance We will study the small signal response of the pn junction diode A small ac signal Va is superimposed on the dc bias This results in ac current 239 Then admittance Y is given by YivaGj03C Speci cally the following parameters will be studied Reverse bias junction or depletion layer capacitance Forward bias diffusion or charge storage capacitance Forward and reverse bias conductance Ca acitance measurements Idc Y admittance L G ij Vac i and va depends on the applied dc bias I I I I I I I l I I I I YijG Model for a diode under ac Reverse bias iunction capacitance pn junction under reverse bias behaves like a capacitor Such capacitors are used in ICs as voltagecontrolled capacitors Depletion layer Width under small ac superimposed on DC bias voltage Looks similar to a parallel plate capacitor 83114 Where Wis the depletion layer Width J W under dc bias Reverse bias iunction capacitance 12 28 N N W A M Vbi VA For pn junction 6 N A ND 1 2 Z 2881 Vb VA For pn or pn junction Where NB is qNB 1 the doping on the lightly doped side 1 2 8A 8 qN CJ 2 W 14m For asymmetrically doped junction CJ increases with NB 2 CJ decreases with applied reverse bias Parameter extractionpro ling CV data from a pn junction is routinely used to determine the doping pro le on the lightly doped side of the junction 12 C A Slopez J N 3 AZ W 2Vbi VA q B s1 2 l 2 Vbi VA CJ2 AZQNBESi 1 1Cj2 1 If the doping on the lightly I I doped side is uniform a plot 10 5 o 0 of lCJ2 versus VA should be VA Volts i a straight line with a slope inversely proportional to NB and an extrapolated lCJ2 O intercept equal to Vbi Intercept Vbi Forward bias diffusion capacitance C2 CD is also called the charge storage capacitance Minority carrier charge uctuation results in diffusion capacitance Both CJ and CD are always present but for forward biased case CD becomes dominant p i origin of diffusion lt gt pno capac1tance p0 x I l For a pn junction I QpTp where Qp is total excess charge in nside D T amp Q hp qA p p pno expf Aj ll qALp pno e W Lp kT dQ 6 qV 6 C p AL eX A C D dV qu ppm pi CT kT P 6 Forward bias conductance qVA GDZEZML 6H 11 dV Lp dV kT Assumes D Cp ltlt1 Complicated at higher frequencies Equivalent circuit for a diode Example Consider a pn junction forward biased such that the forward current is 1 mA Assume the lifetime of holes is 10 7 s Calculate the diffusion capacitance and the diffusion resistance Review question The current through the depletion layer will mostly be carried by holes electrons choose one Plot the current carried by the holes and electrons through the ntype region assuming that the diffusion length of holes is l um Answer CD 386 nF rd lGD 259 Ohms