MOS Capacitors Prof. Ali M. Niknejad Prof. Rikky Muller

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1 EECS 105 Spring 2017, Modue 3 MOS Capacitors Prof. Ai M. Niknejad Prof. Rikky Muer Department of EECS University of Caifornia, Berkeey

2 Announcements Prof. Rikky Muer Wecome to the second haf of EE105! Professor Muer wi be ecturing Midterm 1 handed back today Mean = Median = Standard Dev = Midterm 2 on Thursday, March 23 in ecture Attend discussion sessions! They are hepfu for homework, exam reviews and topics not covered in ecture. 2 University of Caifornia, Berkeey

3 MOS Capacitor Prof. Rikky Muer Gate (n + poy) Body (p-type substrate) εs = 11.7ε 0 0 x Oxide (SiO 2 ) ε = 3.9ε 0 ery Thin! t ~1nm 3 MOS = Meta Oxide Semiconductor Sandwich of conductors separated by an insuator Meta is more commony a heaviy doped poysiicon (poy-si) ayer n + or p + ayer Was meta (e.g. A) unti ~1970 but changed to poy-si due to high temperature processing. After 2008, meta gates have been reintroduced! Learn more about MOS process technoogy in EE130 & EE143 NMOS à p-type substrate, PMOS à n-type substrate University of Caifornia, Berkeey

4 Meta-Oxide-Semi Junction Prof. Rikky Muer Gate (n + poy) Body (p-type substrate) 4 Under therma equiibrium, the n-type poy gate is at a higher potentia than the p-type substrate φ p = kt q n N a φ n poy,n + = kt i q n N d,poy n 550m i No current can fow because of the insuator but this potentia difference is accompanied with an eectric fied Fieds terminate on charge! University of Caifornia, Berkeey

5 Fieds and Charge at Equiibrium Prof. Rikky Muer + + B X d 0 Body (p-type substrate) E 5 At equiibrium there is an eectric fied from the gate to the body Need a positive charge on the gate, negative charge in substrate Since body is p-type, negative charges in the body come from a depetion region University of Caifornia, Berkeey

6 Prof. Rikky Muer Fat Band otage, GB = FB FB < 0 + Q ( = ) = 0 G GB FB Body (p-type substrate) 6 If we appy a bias, we can compensate for this buit-in potentia = ( φ φ ) FB In this case the charge on the gate goes to zero and the depetion region disappears In soid-state physics ingo, the energy bands are fat under this condition n + p University of Caifornia, Berkeey

7 Prof. Rikky Muer Fat Band otage, GB = FB 7 University of Caifornia, Berkeey

8 Prof. Rikky Muer Accumuation, GB < FB Q = C ( ) G GB FB GB < FB Q B = Q G Body (p-type substrate) If we further decrease the potentia beyond the fat-band condition, we essentiay have a parae pate capacitor Penty of hoes and eectrons are avaiabe to charge up the pates Negative bias attracts hoes under gate 8 University of Caifornia, Berkeey

9 Prof. Rikky Muer Accumuation, GB < FB 9 University of Caifornia, Berkeey

10 Prof. Rikky Muer Depetion, GB > FB GB > FB Body (p-type substrate) Q ( ) = Q G GB B Q = qn X ( ) B a d GB Simiar to equiibrium, the potentia in the gate is higher than the body Body charge is made up of the depetion region ions Potentia drop across the body and depetion region 10 University of Caifornia, Berkeey

11 Prof. Rikky Muer Depetion, GB > FB 11 University of Caifornia, Berkeey

12 Prof. Rikky Muer Inversion, GB > T GB = T φ s Body (p-type substrate) 12 As we further increase the gate votage, eventuay the surface potentia increases to a point where the eectron density at the surface equas the background ion density qφs kt s i a n = ne = N φs = φp At this point, the depetion region stops growing and the extra charge is provided by the inversion charge at surface Inversion meaning that the surface is effectivey n-type University of Caifornia, Berkeey

13 Prof. Rikky Muer Inversion, GB > T 13 University of Caifornia, Berkeey

14 Threshod otage Prof. Rikky Muer The threshod votage is defined as the gate-body votage that causes the surface to change from p- type to n-type For this condition, the surface potentia has to equa the negative of the p-type potentia We can derive that this votage is equa to: 1 Tn = FB 2φp + 2 qεs Na( 2 φp) C 14 University of Caifornia, Berkeey

15 Prof. Rikky Muer Recap Accumuation: GB < FB Q = C ( ) G GB FB GB < FB + Q B = Q G Body (p-type substrate) Essentiay a parae pate capacitor Capacitance is determined by ide thickness 15 University of Caifornia, Berkeey

16 Prof. Rikky Muer Recap Depetion: FB < GB < T GB > + FB Q ( ) = Q G GB B Body (p-type substrate) Q = qn X ( ) B a d GB Positive charge on gate terminates on negative charges in depetion region Potentia drop across the ide and depetion region Charge has a square-root dependence on appied bias 16 University of Caifornia, Berkeey

17 Prof. Rikky Muer Recap Inversion: GB > T φ s GB = T Body (p-type substrate) qφs kt s = i = a n ne N 17 The surface potentia increases to a point where the eectron density at the surface equas the background ion density At this point, the depetion region stops growing and the extra charge is provided by the inversion charge (eectrons) at the surface University of Caifornia, Berkeey

18 Q- Curve for MOS Capacitor Prof. Rikky Muer Q G depetion Q B,max Q ( ) N GB FB Tn ( ) GB In accumuation, the charge is simpy proportiona to the appies gate-body bias In inversion, the same is true In depetion, the charge grows sower since the votage is appied over a depetion region 18 University of Caifornia, Berkeey

19 MOS C Curve Prof. Rikky Muer Q G C C C Q ( ) N GB Q B,max ( ) GB GB FB Tn FB Tn Sma-signa capacitance is sope of Q- curve Capacitance is constant in accumuation and inversion Capacitance in the depetion region is smaest Capacitance is non-inear in depetion 19 University of Caifornia, Berkeey

20 C- Curve Equivaent Circuits Prof. Rikky Muer Accumuation Depetion Inversion C C C dep C 20 ε s CdepC C Cdep = C Ctot = = = xdep Cdep + C Cdep ε s t C ε x dep In accumuation mode the capacitance is just due to the votage drop across t In depetion region, the votage drop is across the ide and the depetion region In inversion the incrementa charge comes from the inversion ayer (depetion region stops growing). University of Caifornia, Berkeey

21 Numerica Exampe Prof. Rikky Muer MOS Capacitor with p-type substrate: 16 3 t = 20nm = 5 10 cm Cacuate fat-band: N a = ( φ φ ) = (550 ( 402)) = 0.95 FB n + Cacuate threshod votage: p 13 ε F/cm C = = -6 t 2 10 cm 1 Tn = FB 2φp + 2 qεs Na( 2 φp) C Tn =.95 2( 0.4) + = 0.52 C 21 University of Caifornia, Berkeey

22 Num Exampe: Eectric Fied in Oxide Prof. Rikky Muer Appy a gate-to-body votage: GB = 2.5 < FB Device is in accumuation The entire votage drop is across the ide: E GB + φ + φ n p ( 0.4) = = = = 8 10 t t cm The charge in the substrate (body) consist of hoes: 22 Q = C ( ) = C/cm B GB FB 7 2 University of Caifornia, Berkeey