Mos Capacitor – Mosfet Transistor – Mos Inverters

MOS CAPACITOR – MOSFET TRANSISTOR – MOS INVERTERS

Prof. Philippe LORENZINI Polytech-Nice Sophia Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 2

Outline

• Metal Oxyde Semiconductor Structure • MOS Transistor • MOS Inverters • NMOS • CMOS Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 3

Metal Oxyde Semiconductor Structure Energy band diagram of the three components that make up MOS system

 MOS capacitor  E   g   SC SC 2e fi Pr. Ph.Lorenzini  From MOS Capacitor to CMOS inverter 4  Equilibrium of MOS structure

dV d 2V  (x) Vd  M  SC , E   , 2   dx dx  SC

Metal SC(n) Metal SC(n)

e SC eSC eVd e E M C e e M SC e E SC F EC EF E F EF E V EV dx Independant system Equilibrium state Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 5

Ox The five regimes : a function of work function

(a) Accumulation

(b) Flat band

(d) Weak inversion

(e) Strong inversion Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 6 Energy band diagram for ideal n and p type MOS capacitors under different bias conditions Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 7 Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 8

Field, potential and charges in Silicon

We suppose we deal with a p type semiconductor:

warning: in few books, e  E  E  0 absolute value is not Fi F Fi present!!!!

V (x  )  0, V (x  0) Vs, Vg Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 9

Field, potential and charges in Silicon

d2V  (x)  Poisson’s Equation: 2  dx SC

  (x)  ep(x)  n(x)  N D (x)  N A (x)Charge density

e   e Fi Fi p  n  N  N n  n exp( ) p0  ni exp( ) 0 0 A D 0 i kT kT eV(x) e(V (x)  ) n(x)  n exp( )  n exp( Fi ) 0 kT i kT

e(V (x)  ) p(x)  n exp( Fi ) i kT Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 10

Field, potential and charges in Silicon

eV ( x) eV ( x)    kT kT (x)  en0  p0  p0e  n0e   

2 eV (x) eV (x)     d V (x) e kT kT 2    p0 (e 1)  n0 (e 1) dx  SC  

d 2V (x) d  dV (x)  d  dV (x)  dV (x)       dx 2 dx  dx  dV  dx  dx

eV ( x) eV ( x)     dV (x)  dV (x)  e kT kT d     p0 (e 1)  n0 (e 1)dV (x) dx  dx   SC   Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 11

Field, potential and charges in Silicon •We compute the integral from bulk to a point x in SC

dV ( x ) MO S V(x=« bulk »)=0 et  0 Vg dx bulk

eV (x) eV (x) dV (x) V ( x)     dx dV (x)  dV (x)  e kT kT d    p0 (e 1)  n0 (e 1) dV (x) 0 0   dx  dx   SC   dV (x) As the Electric Field is given by: E(x)   dx

2 eV (x) eV (x) 2  dV (x)  2kTp0   eV (x)  n0  eV (x)  E (x)     e kT  1  e kT  1  dx   SC  kT  p0  kT  Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 12

Field, potential and charges in Silicon

2 2 eV (x) eV (x) 2  dV (x)   kT  2  kT eV (x)  n0  kT eV (x)  E (x)       2 e  1  e  1  dx   e  LD  kT  p0  kT 

 SC kT With the Debye length: LD  2 e po Q If we use the Gauss’s theorem: SC E(x  0)  ES    SC

1 eV e(V 2 ) 2  S S FI  kT   SC 2  kT eVS kT n0  eVS  QSC    e  1 e   1  Qmetal  e  LD  kT p0  kT  Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 13

Field, potential and charges in Silicon Allways negligible

1 eV e(V 2 ) 2  S S FI  kT   SC 2  kT eVS kT n0  eVS  QSC    e  1 e   1  Qmetal  e  LD  kT p0  kT 

For Vs (and so Vg) negative (accumulation)

For Vs (and Vg) positive but Less than 2fi (depletion – weak inversion)

For Vs (and Vg) > 2fi (strong inversion) Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 14

Weak / Strong Inversion 2kT  N   A  VS  2 Fi  ln  e  ni 

eFI

ns=p0=NA

This condition will define a very important parameter of the struture: the threshold voltage or the required gate voltage to be in strong inversion Pr. Ph.Lorenzini From MOS Capacitor to CMOS inverter 15