MOSFET device models and conventions

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Nicholas Phelps
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1 MOFET device odels ad coveios ybols: V hreshold volae; V T kt/q, W µ OX. W W W, L L L L µ elecro obiliy i he MOFET chael (ca be uch lower ha he obiliy i bulk silico). 1. RA URRET ro versio: V -V >>4V T ( V ) ( + λv ) 1 (sauraio reio: V > V -V ) (1) V V V (riode reio: V < V -V ) () The hreshold volae depeds o he body-source volae (V B ) accordi o he law: ( φ V φ ) 0 + γ B (body ec). (3) where aa (γ) is he body ec coicie. Paraeer labda (λ) deeries he sall sial oupu resisace o he MOFET accordi o: 1 1 λ rd (4) λ oe ha he r d expressio is siilar o he r o expressio or BJTs, ideiyi λ -1 wih he BJT early volae (V A ). Labda depeds o he MOFET diesios ad also o he operai poi (V, V, V B ). Tradiioal PE odels (Level 1,,3) do o provide a precise represeaio o l, ad, cosequely, o he MOFET oupu resisace. More rece odels (EKV, BM3, Philps 9) produce accurae represeaios o he vs V depedece, resuli i ore precise siulaios o he ecive MOFET oupu resisace i os operai codiios. For had calculaios ad desi purposes, i is possible o elec he labda depedece o he operai poi (provided ha he MOFET is i sauraio reio) ad cosider oly he depedece o he chael leh. A sipliied liear depedece o λ -1 o he chael leh ca be used oly or irs order esiaios o oupu resisaces: λ 1 k λ L (5) where k λ is a cosa. i is ipora o poi ou ha expressio (5) ca be used oly o have a rouh idea o he ipac o chai he device lehs o he circui dc perorace. For exaple, i suess o he desier ha he oupu resisace o a curre irror ca be approxiaely doubled by doubli he oupu MOFET leh. The acual ai i circui perorace should be adaorily checked usi a accurae elecrical siulaor. Equaio (5) ca be used oly or MOFET i sro iversio ad whe L is uch larer ha he iiu chael leh.

2 Weak iversio: V -V <<4V T V V ς M e 1 e (6) where: V hreshold volae, V T kt/q ad: ς qε i A 1 + M µ OX φ i VB L W (7) Expressio (6) icludes a depedece o boh V ad V. The depedece o V vaishes whe V >> V T. pracice, due o he expoeial depedece, is suicie ha V > 4V T o elec he depedece o V. This codiio is siilar o sauraio reio or sro iversio. As or sro iversio, he depedece o V is o copleely cacelled, bu a residual sesiiviy o he curre o V is prese. This pheoeo ca be odeled wih he paraeer labda. Thereore: M e V ς ( 1 + λv ) or V > 100 V (weak iversio + sauraio reio) (8) hor chael ecs, such as drai iduced barrier loweri (BL), coribue o he ecive labda value.. TRAOUTAE Tracoducace ( ) is he os ipora sall sial paraeer o elecroic devices. Usi he square law drai curre orulas (sro iversio) i is possible o derive he ollowi equivale expressios: ( V V ) (-MOFET, sauraio +sro iversio) (9) (-MOFET, sauraio +sro iversio) (10) ( V V ) (-MOFET, sauraio +sro iversio) (11) weak iversio, cosideri equaio (8) he becoes: (-MOFET, weak iversio+sauraio) (11) ς The depedece o he MOFET curre i weak iversio is he siilar o ha o bipolar rasisors, or which: (BJT, acive reio) (1) is possible o use a sile orula, represeaive o MOFETs i sro ad weak iversio ad BJTs:

3 wih VEQ ( V ) / MOFET i sro iversio V ς MOFET i weak iversio EQ (13) BJT 3. TEMPERATURE EFFET Teperaure aecs os o he physical paraeers ha deerie he MOFET behavior. Thereore i is diicul o represe i a siple way he ecs o eperaure. eerally, oial paraeers values are ive or a reerece eperaure T 0 (TOM i PE). For sall eperaure variaios wih respec o T 0, i is possible o approxiae he behavior o paraeers ad V usi he ollowi expressios: 3 T ( T ) ( T0 ) (14) T0 V T ) V ( T ) + α( T ) (15) ( 0 T0 A ypical value or a is 1 V/K. 4. OE oise is odeled cosideri a ideal (oiseless) MOFET wih a oise curre source coeced across drai ad source, as i he iure. epedi o he proble, i ca be coveie o odel he oise wih a oise volae source coeced i series wih he ae. The wo represeaios are perecly equivale. real device drai reerred curre oise ae reerred volae oise deal (oiseless) device Fi. 1 dicai wih V ad he power specral desiies o he volae oise source ad o he equivale curre oise source, hese quaiies are ied by he ollowi relaioship: ( ) (16) V For very hih requecies (RF applicaios) i is ecessary o add a curre source across he ae ad source (ipu oise curre source). ice he ai o his docue is MOFET odeli or basebad applicaios, he ae-source curre source will be eleced.

4 oise curre specral desiy (MOFETs i sauraio reio) Theral oise: 8 T ( ) kt ( 1+ ) (17) 3 where b / ad b is he body ec rascoducace: B VB Flicker oise: 1 F ( ) (18) W L where is a process depede paraeer ( or -MO ad p or PMO). oise volae specral desiy (MOFETs i sauraio reio) Applyi (16) o (17) ad (18) i is possible o derive he power specral desiy o he equivale, ae reerred volae source: Theral oise: 8 1 ( ) kt 1 3 ( ) + Flicker oise VF ( ) W L 1 5. PARAMETER MATH σ ; σ V V 6. PARAT APATAE Meyer MOFET capaciace odel: c d c bd s d bs 3 do bd ox W L W j c s c bs

5 Exaple o MOFET paraeers or a 0.5 µ MO process. Paraero -MO p-mo µ ox, µ p ox A/V A/V V,V p 0.43 V V γ (eo body) 0.44 V 1/ 0.59 V 1/ k λ 50 V/µ 50 V/µ α (co. erico della V) -1 V / º 1 V / º, p (aore ruore licker) V µ V µ V (achi V) 8.5 V µ 8.5 V µ (achi bea) 0.03 µ 0.03 µ OX 6. F/ µ 6. F/ µ L (luhezza iia /) 1. µ 1. µ J 1.8 F/µ 1.8 F/µ do 0.6 F/µ 0.6 F/µ ox

ES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017)

ES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017) Pae1 Nae Soluios ES 330 Elecroics II Hoework 03 (Fall 017 ue Wedesday, Sepeber 0, 017 Proble 1 You are ive a NMOS aplifier wih drai load resisor R = 0 k. The volae (R appeari across resisor R = 1.5 vols