Recitation 6 p-n junction under T.E. & reverse bias 6.012 Spring 2009 Recitation 6: p-n junctionToday’s agenda:1. p-n junction under thermal equilibrium (T.E.):• space charge region (depletion layer)• quasi-neutral region2. p-n junction under reverse bias3. depletion capacitancep-n junction under T.E.Yesterday we talked about p-n junction. We continue here:1. When we bring the p and n interface together, what will happen?Holes move from p-side to n-side and electrons diffuse from n-side to p-side, leavingbehind space charges. The result is an electric field counteracting diffusion.2. Space Charge Region (SCR): is a depletion region. xno,xpo,xno+ xpo= xdo.What is the charge density in SCR? qNa(−) and qNd(+) And qNa· xpo= qNd· xno=xpo=Nd. ⇒xnoNaQuasi-Neutral Region (QNR)1Recitation 6 p-n junction under T.E. & reverse bias 6.012 Spring 2009 3. Summaries of equations: 2sφBNaxno=q(Na+ Nd) Nd·2sφBNdxpo=q(Na+ Nd) Na·2 Recitation 6 p-n junction under T.E. & reverse bias 6.012 Spring 2009 xno,xpoare determined by doping on both sides!kT NaNdBuilt-in potential φB= φn− φp=ln2qni2sφB11xdo= xno+ xpo=+qNaNd2qφBMaximum field |Emax| = |Eo| =sNNaa+· NNddqNaqNd = xpo= xno ss 4. If strongly asymmetric, the lowly doped side controls the electrostatics.2sφB12qφBp+n : xpo xno xdo=qNd|Eo|sNdExamplesNow let us do some exercises before moving on to the next topic:Nd[cm−3]10161019Na[cm−3]10161016xno216 nm3.14˚Axpo216 nm341 nmEo[V/cm]3.3 ×104V/cm5.26 × 104V/cmφB720 mV900 mVφBis easier to calculate first.1. φn= 360 mV,φp= −360 mVφB= φn− φp= 720 mV2sφBxno=q(Na+ Nd)Na Nd =2 × 1 × 10−12(F/cm) × 0.72 (V)=√4.66 × 10−5cm = 216 nm1.6 × 10−19(C) × 2 × 1016(cm−3)xpo= xno(symmetric)2qφBNa· Nd|Eo| =sNa+ Nd1.6 × 10−19(C) × 0.72 (V) 1016× 1016(cm−3)2=2×1 × 10−12(F/cm)×2 × 1016(cm−3)=3.3 × 104V/cm3Recitation 6 p-n junction under T.E. & reverse bias 6.012 Spring 2009 2. φB= φn− φp= 540 mV + 360 mV = 900 mVxno=2sφBNa=3.41˚(really thin)Aq(Na+ Nd) Nd2sφBNdφB12sxpo= = = 344 nmq q(Na+ Nd)NaNa=qNa=1.6 × 10−19(C) · 1016(cm−3)× 3.41 × 10−7cm = 5.26 × 104(V/cm)|Eo|sxpo1 × 10−12(F/cm)Reverse BiasNow what happens when we apply a reverse bias?First: Bias convention for pn junction:use n-side as reference: V>0: forward biasV<0: reverse biasIn your weblab experiment, when you have V<0, what current do you measure? 6×10−15A(very small).With such a small current, the voltage drop across the QNRs will be really small, safely toignore.Then, where is the voltage drop? =⇒ across SCR4Recitation 6 p-n junction under T.E. & reverse bias 6.012 Spring 2009 Forward bias means V>0, moving “φp” up and reverse bias means V<0, moving “φp”down. Reverse bias V: barrier becomes φB− V>φB(V is negative, so barrier increases).Now, what happened to the electric field? Still zero in QNRs. Larger barriers means higherE-field, and ∴|Emax| increases. This will mean we need more space charges to support thelarger E-field. However, the charge density qNaor qNdcan not change, = xn,xpwidens.⇒5 Recitation 6 p-n junction under T.E. & reverse bias 6.012 Spring 2009 It turns out a straightforward way to do the new calculations is: replace φBwith φB− V .So:xn= xnoφrmB− VφB= xno1 −VφB=2s(φB− V )q(Na+ Nd)NaNdxp= xpo1 −VφBxd= xdo1 −VφBEmax= Eo1 −VφBThe concept of depletion capacitanceNow let us think about the junction region a bit further.1. It stores charges2. By changing the voltage (bias) across the junction, the amount of charges stored therechanges = Capacitor!⇒3. The charges that it stores:2qsNaNdQjo= |−qNa· xpo| = |qNd· xno| =Na+ Nd· φBAs voltage changes, Qjbecomes:Qj(V )= 2qsNaNd(φB− V )=Qjo1 −V.Na+ NdφB6 Recitation 6 p-n junction under T.E. & reverse bias 6.012 Spring 2009 Previously, we had C =Q, but that was for constant capacitance, a more rigorous definitionVshould be:dQC =dVTherefore,d(1−φVB)Cj= Cj(VD)= = QjodQjdV dV VDVD1 +qNaxpoVD·φB= 21− φB1qNaxpo=2φB·VD1 −φBqNaxpoCj(V =0) = Cjo=2φB2sqNaφBNdqsNaNd= = + Nd)×2φBq(NaNa2φBNa+ Nd∵ xdo= xno+ xpo=2sφBNa+ NdqNaNd= Cjo=s,Cj(VD)=⇒xdoCjo1 −VDφBssVDxdxdo1 −φBCj(VD)= = Can be considered as “parallel plate capacitor”. 7MIT OpenCourseWarehttp://ocw.mit.edu 6.012 Microelectronic Devices and CircuitsSpring 2009 For information about citing these materials or our Terms of Use, visit:
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