Lecture 9. NMOS Field Effect Transistor (NMOSFET or NFET)
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1 ecture 9 MOS Field ffect Trasistor (MOSFT or FT) this lecture you will lear: The oeratio ad workig of the MOS trasistor A MOS aacitor with a hael otact ( Si) metal cotact Si Si GB B versio layer PSi substrate metal cotact 1
2 MOS aacitor: ffect of B ( GB > ) GB B GB B > versio charge decreases eletio regio exads gate versio layer charge: Q GB GB B eeds o B B < versio charge icreases eletio regio shriks GB B A MOS Trasistor Si Si y y y PSi Substrate (or Bulk) Basic dea: urret ca be made to flow i the iversio layer by alyig a voltage across it i the horizotal directio
3 A ote o oltage Symbols B = B = ( B ) = B = G S = G B B S = GB A MOS Trasistor i 3 Metal (tyically Silicide) cotacts Si PolySi gate Si PSi substrate 3
4 A MOS Trasistor: ircuit Symbols Bulk Bulk Bulk MOS Trasistor: The Gradual hael Arimatio The oeratio of the MOS trasistor is best uderstood uder the gradual chael arimatio which assumes that: lectrostatics of the MOS trasistor i the horizotal directio have othig to do with the electrostatics i the vertical directio This assumtio decoules the dimesioal comlicated roblem ito two 1dimesioal simler roblems oe for the vertical directio ad oe for the horizotal directio. The electrostatics i the vertical directio have alrea bee worked out by us i the cotext of the MOS caacitor this lecture we will work out the electrostatics i the horizotal directio ad calculate the curret flow 4
5 A MOS Trasistor: hael Potetials Si Si y y y PSi Substrate (or Bulk) s y B y s y B y B Potetial dro i the chael: s y s y MOS Trasistor: urret Flow urret i the iversio chael at the locatio y is: Q y v y y Q y versio layer charge (/cm ) v y y rift velocity of iversio layer charge (cm/s) rift velocity of electros is: v y y y y y Therefore: y Horizotal comoet of the electric field (/cm) Q y y y y y ote: ositive directio of curret is whe the curret flows from the drai to the source y y y y 5
6 MOS Trasistor: urret Flow et the otetial i the chael from the source to the drai ed be writte as: y s B y y At the source ed: B y At the drai ed: B B y s y y The the horizotal electric field i the chael is: y y y d s d B y Therefore: Q y db y y s y y MOS Trasistor: versio harge The iversio charge i the chael is: Q y For GB y y For y GB GB here the ositio deedet threshold voltage is: y FB B y q s a B y The chael otetial is y deedet, ad therefore the threshold voltage is also y deedet. osequetly, the iversio charge is also y deedet y y 6
7 MOS Trasistor: versio harge ad FT Threshold oltage So: Q y GB y use : GB FB B GB ad: y B y sqa B y y Q Q y y FB FB y y y sqa sqa y gore The MOS trasistor threshold voltage is defied as: FB q s a y y The iversio charge i the chael is: Q y MOS Trasistor: versio harge y ear the source ed: Q ad y y y y ear the drai ed: Q ad y y oclusios: versio layer charge is maximum ear the source ed ad miimum ear the drai ed (as show grahically i the figure) he <, the iversio layer disaears at the drai ed he <, the iversio layer disaears eve at the source ed 7
8 urret i the iversio chael at the locatio y is: Q Q y y y MOS Trasistor: urret Flow y d tegrate the above equatio from y= to y=: y y d B y y d y y Ad the result is: d Some iterretatio is required to uderstad the rage of validity of the above equatio. This we do ext.. MOS Trasistor: urret Flow First ote that: whe the There ca be o curret whe there is o bias ad o electric field i the chael to drive the curret y y Also ote that: The iversio layer charge is maximum at the source ed ad is give by: Q y y So whe there is o iversio charge aywhere i the chael ad therefore oclusio: oly whe : A 8
9 MOS Trasistor: urret Flow Suose ow: ad First lot the curve from the result:. 5 y y As is icreased the curret icreases but the it decreases!?? This decrease is uhysical! A mathematical artifact! ote that curret is maximum whe: Q MOS Trasistor: PichOff The iversio charge i the chael ear the drai ed is: y y he aroaches the iversio layer charge just ear the drai ed aroaches zero This coditio is called ichoff y y For > there is a small sectio of chael just ear the drai ed that is almost devoid of mobile carriers (i.e. electros). This is a highly resistive sectio. SiO The chael has bee iched off y 9
10 MOS Trasistor: PichOff ad urret Saturatio The chael has bee iched off For : y hael otetial: y hael otetial: SiO y Ay icrease i beyod comletely falls across this small resistive sectio For >, itegrate the curret equatio from y= to y=: d So for > the curret is what it was whe was equal to Thus for large value of (> ) the curret saturates! MOS Trasistor: urret Flow The curves for a MOS looks like as show i the figure iear or triode regio = The three curves are for differet values of 1. 5 = Pichoff oit For utoff Saturatio regio (utoff regio) For (iear or triode regio) For (Saturatio regio) 5 1
11 MOS Trasistor: urret Flow curves for a MOS are show i the figure The three curves are for differet values of iear regio Pichoff Poit = 1. For 6 (utoff regio) For (iear or triode regio) For (Saturatio regio) MOS Trasistor: Saturatio urret vs For > (i the saturatio regio) there is a small sectio of the chael just ear the drai ed that is almost devoid of mobile carriers (i.e. electros). SiO y hael otetial: y hael otetial: y saturatio, for >, itegrate the curret equatio from y= to y=: d
12 MOS Trasistor: Saturatio urret vs For > (i the saturatio regio) there is a small sectio of the chael just ear the drai ed that is almost devoid of mobile carriers (i.e. electros). SiO y hael otetial: y hael otetial: To a very good arimatio: So for (saturatio regio) : y 1 MOS Trasistor: Saturatio urret vs For ( saturatio regio): 1 iear or triode Saturatio creasig A better FT curret model is: 1 1 For (utoff regio) For (iear or triode regio) For (Saturatio regio) 1
13 MOS Trasistor: The Backgate ffect or the Bo ffect y y The MOS trasistor threshold voltage deeds o the alied source to bulk otetial differece: FB q s a sqa = Backgate effect arameter MOS Trasistor: The Backgate ffect or the Bo ffect To get rid of the bo effect, oe ca short the bulk (or the backgate) to the source such that = However, deedig o the techology used, this may ot always be ossible.. 13
14 MOS Trasistor: Breakdow arge fields ear the drai ed i saturatio ca lead to breakdow Breakdow limits the maximum value of SiO y hael otetial: hael otetial: y y Breakdow Potetial dro i this regio: Field i this regio: MOS Trasistor: elocity Saturatio The drift velocity vs field curve for almost all materials is ot liear ad therefore vd vd vd does ot really hold elocity saturates at high fields! vd sat A better arimatio is: vd 1 sat Silico: sat ~ /cm sat urret i the iversio chael at the locatio y is: d y Q y 1 d 1 1 sat sat y y 14
15 MOS Trasistor: elocity Saturatio urret i the iversio chael at the locatio y is: d y Q y 1 d 1 1 sat tegrate the above equatio from y= to y=: y 1 d 1 sat Aswer is (i liear regio): sat y y d 1 Aswer is (i saturatio regio): sat 1 sat sat sat elocity saturatio decreases the curret 15
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