MOS Field-Effect Transistors (MOSFETs) Review

Transcription

1 MOS Feld-Effect Transstors (MOSFETs Revew 4.1 evce Structure and Physcal Operaton Fgure 4.1 shows the physcal structure of the n-channel enhancement-type MOSFET. Fgure 4.1 Physcal structure of the enhancement-type NMOS transstor: (a perspectve vew; (b cross-secton. Typcally L = 0.1 to 3 mm, W = 0. to 100 mm, and the thckness of the oxde layer (tox s n the range of to 50 nm. The transstor s fabrcated on a p-type substrate. The notaton n + ndcates heavenly doped n-type regons. A thn layer of slcon doxde (SO of thckness tox (typcally -50nm whch s an excellent nsulator s grown on the surface substrate, coverng the area between source and dran. Next metal s deposted to from a 4 termnal devce: Termnals are labeled Source (S, Gate (G, ran ( and Body (B. Note that ths confguraton forms back to back dodes. Wth no bas voltage appled to the gate, the back to back dodes prevent current conducton from dran to source when a voltage VS s appled. Next consder the stuaton shown n Fgure 4. Fgure 4. The enhancement-type NMOS transstor wth a postve voltage appled to the gate. An n channel s nduced at the top of the substrate beneath the gate.

2 Postve voltage appled at vgs causes the free holes (postve charge to be repelled from the regon of the substrate under the gate. These holes are push downward nto the substrate, creatng a carrer depleton regon (depleton regon s populated by negatve charge due to the neutralzng holes that have been pushed down. In addton, the postve gate voltage attracts electrons from the n + wells, creatng an n regon (channel connectng the source and dran. Thus current can flow through ths nduced regon. The MOSFET of fgure 4. s referred to as a n-channel MOSFET (Note ann-channel MOSFET s formed n a p-type substrate. The value of vgs at whch a suffcent number of moble electrons accumulate n the channel regon to form a conductng channel s called the threshold voltage and s denoted as (Vt. Vt ranges between 0.5 to 1.0V. Havng nduced a channel and applyng a postve voltage vs, between the dran and source (Fgure 4.3 causes a current to flow through the nduced channel. Fgure 4.3 An NMOS transstor wth vgs > Vt and wth a small vs appled. The devce acts as a resstance whose value s determned by vgs. Specfcally, the channel conductance s proportonal to vgs Vt and thus s proportonal to (vgs Vt vs. Note that the depleton regon s not shown (for smplcty. Current s carred by free electrons from source to dran, thus by conventon current flow s from dran to source. The magntude of depends on the densty of electrons n the channel, whch depends on vgs>vt. As vgs exceeds Vt, the channel ncreases and the resstance across the channel s reduced (or conductance ncreases. In fact, the conductance of the channel s proporton to the excess gate voltage (vgs-vt, also known as the effectve voltage or overdrven voltage. Thus the current ncreases and s proportonal to (vgs-vt and vs (Fgure 4.4.

3 Fgure 4.4 The vs characterstcs of the MOSFET n Fg. 4.3 when the voltage appled between dran and source, vs, s kept small. The devce operates as a lnear resstor whose value s controlled by vgs. From Fgure 4.4 t s seen that the resstance s nfnte when vgs<vt and ts value decreases as vgs exceeds Vt. Increasng vgs above Vt enhances the channel, hence the name enhancementmode operaton and enhancement-type MOSFET. Fgure 4.5 llustrates the operaton of the NMOS transstor as vs s ncreased. For ths purpose vgs let be held constant. Fgure 4.5 Operaton of the enhancement NMOS transstor as vs s ncreased. The nduced channel acqures a tapered shape, and ts resstance ncreases as vs s ncreased. Here, vgs s kept constant at a value > Vt. As we travel along the channel from source to dran, the voltage ncreases from 0 to vs. The voltage between the gate and source s vgs, whle the voltage between the gate and dran s vgs-vs. The channel depth depends on ths voltage, thus the channel s no longer of unform depth. As vs s ncreased the channel becomes more tapered and ts resstance ncreases correspondngly.

4 Thus the - vs curve does not contnue as a straght lne but bends as shown n Fgure 4.6 Fgure 4.6 The dran current versus the dran-to-source voltage vs for an enhancement-type NMOS transstor operated wth vgs > Vt. When vg=vt or vgs - vs = Vt or vs= vgs Vt: the channel depth at the dran end decreases to almost zero, and the channel s sad to be pnched off. Increasng vs beyond ths pont has lttle effect (theoretcally on the channel shape and the current remans constant. The transstor s turned off when vgs < Vt (cutoff regon. When vgs > Vt, the transstor s on. The transstor s sad to be n the trode regon when vs< vgs Vt. The transstor s sad to be n the saturaton regon when vs>= vgs Vt. (Note: Saturaton n BJT means somethng completely dfferent from that n a MOSFET. The saturaton mode of BJT s analogous to the trode regon of the MOSFET. The saturaton regon of the MOSFET corresponds to the actve mode of BJT Relatonshp between -vs. The relatonshp between -vs based on the frst order approxmaton s: W 1 ncox ( vgs Vt vs vs L (Trode regon 1 W nc ox ( vgs Vt L (Saturaton regon or 1 K ( vgs Vt vs vs (Trode regon (Eq1 1 K ( vgs Vt (Saturaton regon (Eq

5 W where K s a constant K n Cox. L C ox s capactance per unt gate defned as C ox ox / tox, where ox s the permttvty of the slcon oxde and t ox s the oxde thckness determned by the process technology. n s the moblty of the electrons n the channel called surface moblty. It s a physcal parameter that depends on the process technology. L s the channel length and W s the channel wdth. The rato of W/L s know as the aspect rato of the MOSFET. The L and the W are selected by the crcut desgner to obtan desred v characterstc. Note when vs s small (Eq1 becomes K( v V v GS t S. Ths lnear relatonshp was dscussed n Fgure 4.4 and represents the operaton of the MOS transstor as a lnear resstance as vs 1 r ( ( 1 S K VGS Vt K VOV where V OV V GS t V, and VOV s referred to as the gate-to-source overdrve voltage Crcut Symbol The crcut symbols for an NMOS transstor are shown n Fgure Fgure 4.10 (a Crcut symbol for the n-channel enhancement-type MOSFET. (b Modfed crcut symbol wth an arrowhead on the source termnal to dstngush t from the dran and to ndcate devce polarty (.e., n channel. (c Smplfed crcut symbol to be used when the source s connected to the body or when the effect of the body on devce operaton s unmportant. The polarty of the transstor s determned by the arrow. Crcut symbol a: Arrow at the body (B ndcates a p-type substrate (body, thus NMOS transstor. Crcut symbol b: Although a MOSFET s symmetrcal devce, t s often useful n crcut desgn to desgnate one termnal as the source and the other as the dran. To acheve ths crcut symbol b s used. The arrow s placed on the source termnal and ndcates an NMOS transstor. Crcut symbol c: The source s connected to the body.

6 4.. The -vs Characterstc. Fgure 4.11 shows an n-channel enhancement-type MOSFET wth voltages vgs and vs appled. Fgure 4.11b shows 3 dstnct regons of operatons: The transstor s turned off when vgs < Vt. (cutoff regon. When vgs > Vt, the transstor s on. The transstor s sad to be n the trode regon when vs< vgs Vt. The transstor s sad to be n the saturaton regon when vs>= vgs Vt. Fgure 4.11 (a An n-channel enhancement-type MOSFET wth vgs and vs appled and wth the normal drectons of current flow ndcated. (b The vs characterstcs for a devce wth k n (W/L = 1.0 ma/v. The saturaton regon of the FET s used to operate as an amplfer. For operaton as a swtch, the cutoff and trode regons are utlzed. In saturaton mode, the MOSFET provdes a dran current whose value s ndependent of the dran voltage vs and s determned by the gate voltage vgs accordng to the square law relatonshp (.e. K / ( v V. A sketch s shown n Fgure 4.1. ( GS t Fgure 4.1 The vgs characterstc for an enhancement-type NMOS transstor n saturaton (Vt = 1 V, k n W/L = 1.0 ma/v.

7 The large sgnal crcut equvalent model based on ( K / ( vgs Vt s shown n Fgure Fgure 4.13 Large-sgnal equvalent-crcut model of an n-channel MOSFET operatng n the saturaton regon Fnte Output Resstance n Saturaton The large sgnal model of Fgure 4.13 ndcates that n saturaton s ndependent of vs. Ths mples that the resstance lookng nto the dran s nfnte. However, ths s based on the premse that once the channel s pnched off at the draned end and further ncreases n vs have no effect on the channel s shape. However ncreasng vs n saturaton mode, the channel pnch-off pont s moved slghtly away from the dran toward the source (Fgure The channel length s n effect reduced from L to L-L, a phenomenon known as channel-length modulaton. Fgure 4.15 Increasng vs beyond vssat causes the channel pnch-off pont to move slghtly away from the dran, thus reducng the effectve channel length (by L. Snce s nversely proportonal to the channel length, ncreases wth vs. 1 W nc ox ( vgs Vt L To account for the dependence of on vs 1 W ( nc ox vgs Vt (1 vs L where s a process-technology parameter wth dmensons V -1.

8 A typcal set of -vs characterstcs showng the effect of channel-length modulaton s shown n Fgure Fgure 4.16 Effect of vs on n the saturaton regon. The MOSFET parameter VA depends on the process technology and, for a gven process, s proportonal to the channel length L. To account for the dependence of on vs the large sgnal model ncludes an output resstance ro, as shown n Fgure Fgure 4.17 Large-sgnal equvalent crcut model of the n-channel MOSFET n saturaton, ncorporatng the output resstance ro. The output resstance models the lnear dependence of on vs and s gven by Eq. (4.. The output resstance s defned as where I r 0 W ( V L 1 I V I 1 nc ox GS Vt A V A 1

9 4.1.7 The p-channel MOSFET. A p-channel enhancement-type MOSFET (PMOS, operates n the same manner as the n-channel devce except that vgs and vs are negatve and the threshold voltage Vt s negatve. Also, the current enters the source termnal and leaves through the dran termnal. For PMOS transstor The transstor s turned off when vgs > Vt (cutoff regon. The transstor s on when vgs < Vt. The transstor s sad to be n the trode regon when vs> vgs Vt. The transstor s sad to be n the saturaton regon when vs<= vgs Vt. The relatonshp between -vs for the PMOS transstor s the same as the NMOS transstor: where K 1 K ( vgs Vt vs vs 1 K( vgs Vt 1 GS Vt K ( v p C ox W L (1 v S (Trode regon (Saturaton regon. For PMOS vgs, Vt, and vs are all negatve. (Saturaton regon [channel length modulaton] The crcut symbols for a PMOS transstor are shown n Fgure Fgure 4.18 (a Crcut symbol for the p-channel enhancement-type MOSFET. (b Modfed symbol wth an arrowhead on the source lead. (c Smplfed crcut symbol for the case where the source s connected to the body. (d The MOSFET wth voltages appled and the drectons of current flow ndcated. Note that vgs and vs are negatve and flows out of the dran termnal.

10 4..5 The Role of the Substrate Body Effect In many applcatons the source termnal S s connected to the substrate (or body termnal B. In such a case the substrate does not play any role n crcut operaton. If there s voltage dfference between the source and the body VSB then ths changes the threshold voltage Vt. Specfcally, t has been shown that ncreasng the reverse substrate bas voltage VSB results n an ncrease n Vt as V V V t to ( f SB f where Vto s the threshold voltage for VSB=0 f s a physcal parameter (typcally f =0.6V s known as the body-effect parameter and s a fabrcaton-process parameter Ths phenomenon s known as body effect. The Juncton Feld Effect Transstor (JFET As wth other FET types, the JFET s avalable n polartes: n-channel and p-channel. The basc structure of a n channel JFET s shown n Fgure 5.. The p-channel can be fabrcated smply by reversng all the semconductor types. The n regon s the channel and the p-type regons are electrcally connected together the gate. Thus the JFET s a 3 termnal devce. When vgs=0v, the applcaton of vs causes current to flow from the dran to the source. When a negatve vgs s appled, the depleton regon of the gate-channel juncton wdens and the channel becomes correspondngly narrower; thus the channel resstance ncreases and the current decreases for a gven vs. One way to thnk of a JFET s as a resstance whose value s controlled by vgs. If vgs s ncreased n the negatve drecton, eventually a value s reached at whch the depleton regon occupes the entre channel. The channel has n effect dsappeared (.e. the channel s pnched, as shown n Fgure 5.7.

11 The JFET characterstcs are dsplayed n Fgure 5.10 and Fgure 5.14, for threshold voltage Vt=Vp=-4V, ISS=8mA. Although Fgure 5.10, shows to be ndependent of vs n the saturaton regon, ths s an deal stuaton. In fact JFETs also suffer from channel-length modulaton. For JFETs the threshold voltage s usually called the pnch-off voltage and s denoted by Vp, thus Vp=Vt. For n-channel JFET Vp s negatve.

12 The JFET characterstcs can be descrbed by the same equatons used for MOSFETs. The n-channel transstor s turned off (cutoff regon when vgs <= Vp. When 0 >= vgs > Vp, and vs s postve the transstor s on. The transstor s sad to be n the trode regon when vs< vgs Vp. The transstor s sad to be n the saturaton regon (pnch-off when vs>= vgs Vp The equatons relatng and the appled voltages are 1 K ( vgs VP vs vs (Trode regon 1 K ( vgs VP (Saturaton regon 1 GS VP K ( v (1 vs (Saturaton regon [channel length modulaton] where K I SS / V. The current ISS s the dran current when vgs=0v. P

13 4.3 MOSFET Crcuts at C To keep the C analyss smple the followng assumptons Neglect channel-length modulaton, (assume =0 Example 4.5 etermne the voltages at all nodes and currents through all branches. Let Vt=1V and ma/v. Assume =0 W K n Cox =1 L Fgure 4.3 (a Crcut for Example 4.5. (b The crcut wth some of the analyss detals shown. Example 4.6 esgn the crcut so that the transstor operates n saturaton wth I = 0.5mA and V=3V. What s the largest value that R can have whle mantanng saturaton regon. Assume =0 Fgure 4.4 Crcut for Example 4.6.

14 Example 4.7 The NMOS and PMOS transstors are matched K n C ox W L p C ox W L =1 ma/v. Vtn=-Vtp=1V. Assume =0 for both devces. Fnd the dran currents N and P as well as the voltage vo for vi = 0V, -.5V and.5v. Fgure 4.5 Crcuts for Example 4.7. Example 4.9 esgn a crcut to establsh I=0.5mA. Vt=1V, supply 15V. K n C ox W L =1 ma/v. Assume =0. Use power Fgure 4.31 Crcut for Example 4.9.

15 4.6 Small Sgnal Operaton and Models Consder the crcut n Fgure 4.34 Fgure 4.34 Conceptual crcut utlzed to study the operaton of the MOSFET as a small-sgnal amplfer. The C current I s found by settng vgs=0. Thus 1 K( vgs Vt Here, we have neglected the channel-length modulaton (.e. =0. The C voltage V s V V R I To ensure the saturaton regon V VGS Vt In addton, the total voltage at the dran wll have an AC sgnal supermposed on V. Thus V has to be suffcently greater than V V to allow for the requred sgnal swng. ( GS t Next consder the stuaton wth the nput sgnal vgs appled. v V v GS The total current becomes K( VGS vgs Vt K( VGS Vt K( VGS Vt vgs K( vgs The frst term on the RHS can be recognzed as the C bas current I. The second term s a current component that s drectly proportonal to the nput sgnal vg. The thrd term s a current component that s proportonal to the square of the nput sgnal vg. Assume that vgs s kept small such that the second term s much greater that the thrd term. 1 K( VGS Vt vgs K ( vgs resultng v ( V V gs GS gs GS t If ths small-sgnal condton s satsfed, we can neglect the thrd term and can be expressed as

16 where and the MOSFET transconductance gm s Substtutng K for g I /( VGS Vt n m d I GS d K( V V v m v gs g yelds K t gs ( VGS t V I g m K ( VGS Vt VGS Vt Fgure 4.35 presents a graphcal nterpretaton of the small-sgnal operaton The total voltage at v s Thus V V v R V I v d V v R d ( I d R d g m v gs R The small sgnal voltage gan s vd Av v gs g A graphcal llustraton of the voltages s shown n Fgure m R Fgure 4.35 Small-sgnal operaton of the enhancement MOSFET amplfer.

17 Fgure 4.36 Total nstantaneous voltages vgs and v for the crcut n Fg Small Sgnal Equvalent Models From the above analyss, small sgnal models for the FET transstor are shown n Fgure Fgure 4.37 Small-sgnal models for the MOSFET: (a neglectng the dependence of on vs n saturaton (the channel-length modulaton effect; and (b ncludng the effect of channel-length modulaton, modeled by output resstance ro = VA /I.

18 Fgure 4.37b ncludes the effect of the channel-length modulaton whch s modeled by the output resstance ro. 1 V A r0 I I The T Equvalent Model. The development of the T equvalent model s shown n Fgure Fgure 4.39b adds a second current source n seres (ths does not change the termnal currents and s equvalent to Fgure 4.39a. Then node X s joned to the gate termnal G n Fgure 4.39c (ths connecton also does not change the termnal currents and s equvalent to Fgure 4.39a. Next the controlled source between node X and S can be replaced by a resstance 1/gm as shown n Fgure 4.39d. Fgure 4.39d s referred to as the T model. Fgure 4.40 shows varous T models whch nclude the effect of the channel-length modulaton. Fgure 4.39 evelopment of the T equvalent-crcut model for the MOSFET. For smplcty, ro has been omtted but can be added between and S n the T model of (d.

19 Fgure 4.40 (a The T model of the MOSFET augmented wth the dran-to-source resstance ro. (b An alternatve representaton of the T model Modelng the Body Effect The body effect occurs n a MOSFET when the source s not ted to the substrate. Thus the sgnal voltage between the body (B and source (S vbs gves rse to a dran current component whch can be modeled as gmvbs, where the body transconductance s defned as g mb g m where f V SB The small sgnal model ncludng the body effect s shown n Fgure 4.41 Fgure 4.41 Small-sgnal equvalent-crcut model of a MOSFET n whch the source s not connected to the body.