Lecture 10: P Junction & MOS Cpcitors Prof. iknej eprtment of EECS
Lecture Outline Review: P Junctions Therml Equilibrium P Junctions with Reverse Bis (3.3-3.6 MOS Cpcitors (3.7-3.9: Accumultion, epletion, Inversion Threshol oltge C Curve eprtment of EECS
Results of MT #1 Goo Job! AG MI MAX ST E 74 34 99 13 This is only 17% of your gre Homework 15% Lbortory 20% Miterm #1 17% Miterm #2 18% Finl 30% eprtment of EECS
P Junction in Therml Equilibrium Contct potentil evelops between P n region iffusion current blnce by rift current epletion region is spce-chrge region where the concentrtion of free crriers is low The epletion region is chrge ue to the immole bckgroun ions (onors n cceptors Use the epletion Approximtion to estimte the chrge ensity clculte the electric fiels n potentil vrition using electrosttics in 1 eprtment of EECS
Hve we invente bttery? Cn we hrness the P junction n turn it into bttery? n p A th ln ln ni n i th ln 2 ni A? umericl exmple: 15 A 10 10 26m ln 60m log 20 n 10 15 2 i 600m eprtment of EECS
Contct Potentil The contct between P junction cretes potentil ifference Likewise, the contct between two issimilr metls cretes potentil ifference (proportionl to the ifference between the work functions When metl semiconuctor junction is forme, contct potentil forms s well If we short P junction, the sum of the voltges roun the loop must be zero: mn pm n p 0 pm mn ( mn pm eprtment of EECS
P Junction Cpcitor Uner therml equilibrium, the P junction oes not rw ny current But notice tht P junction stores chrge in the spce chrge region (trnsition region Since the evice is storing chrge, it s cting like cpcitor Positive chrge is store in the n-region, n negtive chrge is in the p-region: q x q po x no eprtment of EECS
Reverse Bise P Junction Wht hppens if we reverse-s the P junction? < 0 Since no current is flowing, the entire reverse se potentil is roppe cross the trnsition region To ccommote the extr potentil, the chrge in these regions must increse If no current is flowing, the only wy for the chrge to increse is to grow (shrink the epletion regions eprtment of EECS
Current Uner Reverse Bis n p n E0 E0 n p p X X Uner therml equilibrium current is zero If we pply reverse s, we re incresing the brrier ginst iffusion current rift current is low since the fiel only moves minority crriers cross junction In fct, current is not zero but very smll since the minority crrier concentrtion is low. Minority crriers within one iffusion length of junction cn contribute to reverse s current. This is more or less inepenent of the pplie s 0 ( eprtment of EECS
eprtment of EECS EECS 105 Fll 2003, Lecture 10 oltge epenence of epletion With Cn reo the mth but in the en we relize tht the equtions re the sme except we replce the builtin potentil with the effective reverse s: s n p q x x X 1 1 ( 2 ( ( ( ε n s n x q x ε 1 ( 2 ( 0 p s p x q x ε 1 ( 2 ( 0 X X 1 ( 0
Chrge ersus Bis As we increse the reverse s, the epletion region grows to ccommote more chrge Q J ( qx p ( q 1 Chrge is not liner function of voltge This is non-liner cpcitor We cn efine smll signl cpcitnce for smll signls by breking up the chrge into two terms Q J ( v QJ ( q( v eprtment of EECS
eprtment of EECS EECS 105 Fll 2003, Lecture 10 erivtion of Smll Signl Cpcitnce From lst lecture we foun otice tht J J v Q Q v Q ( ( R p j j j x q Q C C 1 ( 0 j p j C x q C 1 1 2 0 0 s s p j q q q x q C ε ε 2 2 2 2 0 0
eprtment of EECS EECS 105 Fll 2003, Lecture 10 Physicl Interprettion of epletion Cp otice tht the expression on the right-hn-sie is just the epletion with in therml equilibrium This looks like prllel plte cpcitor! s j q C ε 2 0 0 1 0 1 1 2 s s s j X q C ε ε ε ( ( s j X C ε
A rible Cpcitor (rctor Cpcitnce vries versus s: C C j j0 Appliction: Rio Tuner eprtment of EECS
iffusion Resistor -type iffusion Region Oxie P-type Si Substrte Resistor is cpcitively isoltion from substrte Must Reverse Bis P Junction! P Junction cretes istribute cpcitnce with substrte (RC trnsmission line eprtment of EECS
MOS Cpcitor Gte (n poly Boy (p-type substrte ε s 11.7ε 0 0 x Oxie (SiO 2 ε ox 3.9ε 0 ery Thin! t ox ~ 1nm MOS Metl Oxie Silicon Snwich of conuctors seprte by n insultor Metl is more commonly hevily ope polysilicon lyer n or p lyer MOS p-type substrte, PMOS n-type substrte eprtment of EECS
P-I- Junction Gte (n poly Boy (p-type substrte Uner therml equilibrium, the n-type poly gte is t higher potentil thn the p-type substrte kt p ln 550m n q n i o current cn flow becuse of the insultor but this potentil ifference is ccompnie with n electric fiel Fiels terminte on chrge! eprtment of EECS
Fiels n Chrge t Equilibrium ox B X 0 Boy (p-type substrte E ox At equilibrium there is n electric fiel from the gte to the boy. The chrges on the gte re positive. The negtive chrges in the boy come from epletion region eprtment of EECS
Goo Plce to Sleep: Flt Bn FB < 0 Q ( 0 G GB FB Boy (p-type substrte If we pply s, we cn compenste for this built-in potentil ( FB In this cse the chrge on the gte goes to zero n the epletion region isppers In soli-stte physics lingo, the energy bns re flt uner this conition n p eprtment of EECS
Accumultion Q C ( G ox GB FB GB < FB Q B Q G Boy (p-type substrte If we further ecrese the potentil beyon the flt-bn conition, we essentilly hve prllel plte cpcitor Plenty of holes n electrons re vilble to chrge up the pltes egtive s ttrcts holes uner gte eprtment of EECS
epletion GB > FB Boy (p-type substrte Q ( Q G GB B Q q X ( B GB Similr to equilibrium, the potentil in the gte is higher thn the boy Boy chrge is me up of the epletion region ions Potentil rop cross the boy n epletion region eprtment of EECS
Inversion GB T s Boy (p-type substrte As we further increse the gte voltge, eventully the surfce potentil increses to point where the electron ensity t the surfce equls the bckgroun ion ensity qs kt s i n ne s p At this point, the epletion region stops growing n the extr chrge is provie by the inversion chrge t surfce eprtment of EECS
Threshol oltge The threshol voltge is efine s the gte-boy voltge tht cuses the surfce to chnge from p- type to n-type For this conition, the surfce potentil hs to equl the negtive of the p-type potentil We ll erive tht this voltge is equl to: 1 Tn FB 2 p 2 qε s( 2 p C ox eprtment of EECS
Inversion Stops epletion A simple pproximtion is to ssume tht once inversion hppens, the epletion region stops growing This is goo ssumption since the inversion chrge is n exponentil function of the surfce potentil Uner this conition: Q ( Q G Tn B,mx Q ( C ( Q G GB ox GB Tn B,mx eprtment of EECS
Q- Curve for MOS Cpcitor Q G epletion inversion Q B,mx Q ( GB ccumultion FB Tn ( GB In ccumultion, the chrge is simply proportionl to the pplies gte-boy s In inversion, the sme is true In epletion, the chrge grows slower since the voltge is pplie over epletion region eprtment of EECS
umericl Exmple MOS Cpcitor with p-type substrte: t ox 20nm Clculte flt-bn: Clculte threshol voltge: 5 10 cm 16 3 ( (550 ( 402 0.95 FB n C ox p ε t ox ox 13 3.45 10 F/cm -6 2 10 cm 1 Tn FB 2 p 2 qε s ( 2 p C ox Tn 19 12 16 2 1.6 10 1.04 10 5 10 2 0.4.95 2( 0.4 0.52 C ox eprtment of EECS
um Exmple: Electric Fiel in Oxie Apply gte-to-boy voltge: GB 2.5 < FB evice is in ccumultion The entire voltge rop is cross the oxie: E ox GB ox n p 2.5 0.55 ( 0.4 8 10 t t ox ox 5 6 2 10 cm The chrge in the substrte (boy consist of holes: Q C ( 2.67 10 C/cm B ox GB FB 7 2 eprtment of EECS
umericl Exmple: epletion Region In inversion, wht s the epletion region with n chrge? B,mx s p p p 2p 0.8 B,mx 1 q 2 ε s X 2,mx X,mx 2ε s B,mx q 144nm Q,mx q X,mx 1.15 10 C/cm B 7 2 eprtment of EECS