Introduction to MOSFET operation

Transcription

1 Introduction to MOSFT operation Andrea Pacelli Department of lectrical and omputer nineerin SUNY at Stony Brook Second edition, Auust 2001 opyriht c 2001 Andrea Pacelli All Rihts Reserved 1 The nchannel MOSFT In these notes, the basic operation of the metaloxidesemiconductor fieldeffect transistor, or MOSFT for brevity, is presented. MOSFTs make up the vast majority of the devices employed in today s microelectronic industry. Bipolar junction transistors (BJTs) are nowadays employed only for limited applications, where their hiher current drivability allows a performance advantae. However, bipolar transistors have distinct disadvantaes in terms of interation density, power consumption, and fabrication cost. The MOSFT is today the active device of choice for most analo and diital desins. If havin to choose between studyin the MOSFT and the bipolar transistor, the wise student will study the MOSFT. MOSFTs come in two varieties, namely, nchannel and pchannel. They differ by the polarities of their currents and voltaes. In an nchannel MOSFT current is carried by electrons, which are neatively chared and attracted by a positive voltae. In a pchannel MOSFT current is carried by holes, which are positively chared and are attracted by a neative voltae. We introduce the nchannel MOSFT, or nmosft, first because it has better properties, and is slihtly simpler to describe. An nmosft is represented by one of the symbols in Fi. 1. The first notation is probably the most correct, since it represents all four terminals (source, drain, ate, and body, usually abbreviated as,,, ) and reveals the symmetric nature of the device. The second form is a shorthand for use in diital circuits with lare numbers of transistors. The third and fourth forms use a special notation to denote the source and the drain of the MOSFT. Unlike the vacuum tube and the bipolar transistor, the MOSFT is a symmetric device. The source and the drain are identically constructed. 1 The 1 In many cases, some deree of asymmetry is introduced by the MOSFT layout. For example, the drain area is usually made smaller than the source area, to minimize draintoround capacitance. However, such asymmetries only affect the A behavior of the transistor, while the D properties remain symmetric. 1

2 drain D D D ate body G G G source S S S Fiure 1: Four symbols for the nchannel MOSFT. drain of an nmosft is simply the one of the two terminals which is biased at the hihest voltae. That said, the arrownotation for the source may be useful in many analo applications where source and drain are fixed, to uide the eye in analyzin the circuit. 2 The four terminals The MOSFT has four terminals, called source, drain, ate and body (or substrate, or bulk). Under normal operation, current flows between the source and the drain only. The ate terminal is separated from the rest of the device by a thin insulatin layer and never conducts current, unless the insulator is physically damaed (e.., by overvoltae). The body is separated from the source and drain by reversebiased junctions. It may carry current durin brief transients without damae for the device, but this type of operation is not usually desired. The ate and body terminals are only control terminals, and are not expected to carry any D current. 2 Therefore, one always assumes. By Kirchhoff s current law, the drain and source terminals carry equal and opposite currents. It is therefore sufficient to deal with only one of them. Most people like to deal with the drain current. We note here that currents are conventionally defined as positive when they enter a device terminal. At dc, nmosft drain current is always positive, and source current is always neative. To avoid forward biasin of the source and draintobody junctions, the body of the n MOSFT is often connected to the lowest voltae reference available. We will introduce the operation of the nmosft assumin that the body is always rounded, as is the case in (almost) all diital circuits and most analo circuits. 2 The situation is different in A: Under sinusoidal operation and durin transients, substantial ate and substrate currents may flow, due to capacitive effects. 2

3 1 " % Fiure 2: An nmosft with its ate tied to the source. 3 The nmosft: cutoff reion The electrical function of a MOSFT is that of carryin a current between its source and drain terminals, dependin on the voltae applied on the ate. Aain, the source terminal is defined as the one at the lowest voltae, and the drain as the one at the hihest voltae. The condition for the nmosft to be in the cutoff reion, i.e., not to carry any current, is:! #" $ % & where is called the threshold voltae of the MOSFT. When, the n MOSFT is called enhancement type. When, it is called depletion type. Today depletiontype nmosfts are rare. Most threshold voltaes are in the rane to. When the MOSFT is in the cutoff reion the source and drain are electrically isolated with respect to each other. One can think of connectin them by a resistor with extremely hih value, which carries a neliible current. Since, by definition, the drain voltae is equal to or hiher than the source voltae, q. (1) above implies that in the cutoff reion, the followin relation also holds: + ) $*%+ ( When, we say that the source is turned or switched on. When, we say that the drain is turned on. Therefore, one can summarize as follows: The nmosft is in the cutoff condition when both source and drain terminals are switched off. 021 xample 1 onsider the circuit in Fi. 2. Assume that the voltae source is positive. Therefore the terminal connected to the voltae is the drain. Since., if (as is usually the case) the transistor is always in the cutoff reion, and does not carry any current. The case of 65 will be discussed in the next example., &341 3

4 4 The nmosft: Saturation reion The most common mode of operation of the MOSFT is the saturation reion. In this reion, the MOSFT works as a current source. The condition for saturation is the followin: 7 : $8%9+ $8%9 The first equation simply says that the MOSFT is not in the cutoff reion. The two equations can be rewritten as follows: < Therefore, one can summarize as follows: $)%; ; The nmosft is in the saturation condition when the source is turned on and the drain is turned off. ++ In the saturation condition, the drain current is: = >@ A B"D GFH" In saturation, the drain current only depends on the ate and source terminal voltaes. Therefore the drain terminal behaves like a current source. 4 The quantity is sometimes called the ate overdrive. The overdrive measured by how much the ate is biased above threshold. q. (3) shows that the drain current depends only on the overdrive and not on the absolute ate voltae, or even the atetosource voltae. The ate overdrive plays a similar role to the junction voltae $I in a bipolar transistor. As in a BJT current flows when $I is in the rane , reardless of emitter voltae, so the drain current depends only on the overdrive. xample 2 One simple case in which an enhancementmode MOSFT is uaranteed to be in saturation is when the ate and drain are tied toether. This is called a diodeconnected MOSFT. Its schematic and J. curve are shown in Fi. 3. From the J. curve one can appreciate how a diodeconnected MOSFT really resembles a diode: It carries no current for an applied voltae below, and the current rapidly rises (albeit not as fast as with a real diode) for hiher voltaes. This pseudodiode can be used for rectification, peak detection, and all the circuits where a KL junction diode is commonly used. 4

5 U I I T Fiure 3: Diodeconnected nmosft: Schematic and MONQP curve. 5 The nmosft: Triode reion When the MOSFT is not in the cutoff reion, but is not in the saturation reion, we say that it is in the triode reion. oltaewise, this can be written as 7 : $8%9+ $89 ++ or in other terms, < $)%; %; We can summarize the above as The nmosft is in the triode reion when both source and drain terminals are switched on. The eneral expression for the current in this reion depends on all three voltaes, ate, source and drain: = >@SR This expression is awkward to use for both analysis and desin. The fact that the current depends on all three voltaes makes the MOSFT in the triode reion a complicated device to use. Desiners often try to bias the MOSFT either in the cutoff or the saturation reions. There is one particular subset of the triode reion, however, where the MOSFT performs a useful function. This is called the linear reion: T $SY $ T + A T " XW" AZ[" Under this assumption, the current becomes =\ >@ G $ +]"^A T " G_H" 5

6 3 3 R bias R bias R mos G Fiure 4: The nmosft as a switch: omplete schematic and simplified circuit for hih Pa`. Since the drain current is linearly proportional to the draintosource voltae, the device behaves like a resistor, whose resistance is inversely proportional to the overdrive: bdcfed >@ A This property is useful for both analysis and desin of circuits. If one knows or uesses that the draintosource voltae is small, and if the atetosource voltae is known, one can replace the MOSFT by a resistor with a known value. We summarize MOSFT operation as follows: $j%k + B" Y In circuit analysis and desin, the MOSFT can be replaced by a current source$if i + 9, and by a resistor if 2 <. It may be useful to try to understand a circuit usin only the saturation and linear reions, before delvin into the more complicated triodereion expressions. The use of the MOSFT as a resistor can be advantaeous in many cases. Resistors are not widely used in interated circuits, due to their lare area and poor quality. If ood resistors are needed, they can be fabricated at extra cost introducin additional processin steps. That is why most interated circuits use no or few resistors, compared to discrete circuits where resistors are widely employed. A MOSFT biased in the linear reion takes much less area than a resistor of the same value, and sometimes can replace a resistor with no deradation for the overall circuit performance. Moreover, while a resistor displays a fixed resistance, a MOSFT s resistance can be chaned at will by varyin the overdrive. This property, unique to fieldeffect transistors, makes the MOSFT a very useful element in analo circuits. xample 3 onsider the circuit of Fi. 4. When is low, e.., zero, the MOSFT is in the cutoff reion. Therefore no current flows throuh the resistor and the drain terminal is at alnmpo. When, the transistor turns on. Will it enter1 the saturation reion or the. The triode reion At the turnon point, condition for saturation reion is: alm o. 6, so that J + 91rq. and alnmpo Ah["

7 1 s v ƒ { z s ƒ w s. s q q v v 3 We conclude that upon turnon, the transistor enters directly the saturation reion if $lmpo. As we increase the ate bias, the drain current increases, and the drain voltae decreases due to the voltae drop on the resistor: alm o.7s J However, in the saturation reion, the drain current does not depend on drain voltae, therefore the drain current is still iven by and the drain voltae is J rlmpo ut vxw x..7s ]y t v w x. ]y q At some point, the MOSFT will enter the triode reion. This occurs when or almpo.7s t v w. x. y. This is a secondorder equation that can be solved analytically. However the result is complicated and does not shed liht on the nature of the effect. Thins become more interestin when, for hiher values of, the MOSFT can be considered to be in the linear reion. In this case, the MOSFT is replaced by a resistor, and the simplified circuit on the riht of Fi. 4 can be employed. By inspection one therefore writes &{^1 1 Let us assume that s MOSFT resistance is then and the drain voltae is cfed o cfed alm cfedz 6{^1 1f~ + 1rq k}, A, 4ƒ {^1 1f~ B A v q q k} k} {^1 1 1rq #y k} 91rq { {ˆ q q, Let us verify that our uess was riht: The condition for the linear reion [q. (5)] is 1rq { {ˆ. 1rq ;Šaq k} q alnmpo 2ƒ. The which is certainly satisfied. ven when the condition (5) is not strictly true, still the linear approximation is more useful for desin than the cumbersome secondorder equation which the triodereion analysis forces us to solve. 7

8 Ž " Œ DD in out I bias Fiure 5: NMOS source follower. 6 Body effect So far we have considered cases where the source was connected to round, i.e., the source and body terminals were shortcircuited. The bodysource and bodydrain terminals in an nmosft are junctions, which are and should remain zero or reversebiased for correct operation. Therefore In an nmosft, one may only apply a neative voltae to the body with respect to the source and drain, or viceversa, one may only apply a positive voltae to the source and drain with respect to the body. Applyin a positive voltae to the source with respect to the body has the effect of increasin the threshold voltae, accordin to the followin law: da$ ++d " Œ Ž $ r r " G H" where is called (not surprisinly) the bodyeffect coefficient, and f is a maic number 3, of dimensions of voltae, of the order of to. xample 4 Since the body effect increases the threshold voltae and decreases the drain current, its usual effect is to derade the performance of nmos circuits where the source of the MOSFT is not biased at round. onsider the circuit of Fi. 5. The current source Jlmpo F Z makes the drain current of 3 A maic number is a physical quantity which depends on so many other quantities that its value has no obvious meanin. The bodyeffect coefficient is also a maic number. 8

9 w. v z q y. v q w y 5 4 Without body effect With body effect out [] in [] Fiure 6: NMOS source follower voltaetransfer characteristics. the nmosft constant. Let us assume that m 59 saturation. The followin equation holds: therefore J t v w m. ea š m ]. ea š +. By Jnlmpo t Jnlnmpo, so that the transistor is in This circuit is called a source follower because the output (the source) follows the input (the ate) with a voltae drop. 4 For the circuit to be functional, this voltae drop t i{^1 1f~ should be not too ;91rq lare, or else the4ƒ1f~ output will simply sit at zero voltae. If for example A,, Jnlm o A, then ea š {q q m ]. This result is shown in Fi. 6. In the above calculation we have nelected the body effect. Since the body now is biased at a lower voltae than the source, the threshold voltae will increase accordin to q. (8). The new inputoutput equation becomes ea š m. 1@y.x wdž ea š$z v Ÿ x. ž This is a secondorder equation and its solution is cumbersome. Qualitatively, oneea š sees immediately that the net effect is an additional voltae drop, which increases with, as shown by the dashed line in Fi. 6. v Ÿ Jnlnmpo t wœ {^1ay As the above example shows, the body effect may sometimes be inored durin an initial, firstorder analysis, but its effect cannot usually be nelected when accuracy is desired. 4 The syntax may be questionable, but the circuit works. 9

10 { w { w y y " We conclude this section by notin that in most technoloies, the body of nchannel MOS FTs is always tied to round, as we have assumed in the above example. This is due to the fact that in an interated circuit, all transistors usually sit atop a heavilydoped layer that shorts all bodies to the backside of the wafer, which is rounded. The situation is different for pchannel MOSFTs, as explained in Section 9. 7 hannellenth modulation In the saturation reion we have assumed that the drain current is insensitive to drain voltae, i.e., that the MOSFT behaves as a perfect current source. In reality this is not true, due to a phenomenon known as channellenth modulation (LM). When reater accuracy in current calculationsbœ& is desired, A one $+"A must multiply the simple expressions of qs. (3) and (4) by the factor 9, where is a maic number stronly dependent on the channel lenth (see Section 10), and is usually in the rane of to +. The new expression for current in the saturation reion is and for the triode reion, ; ; >r A >@ G B"D where we have introduced the shorthand notation ª " Œ2 $O r hannellenth modulation is usually important only in the saturation reion, where it adds a finite output resistance in parallel with the drain. However, when accuracy is required, one should also account for it in the triode reion. Fiure 7 shows the effect of LM on the output characteristics. One can observe how the MOSFT no loner can be modeled as an ideal current source, but displays a finite output resistance. Also note how both triode and saturation reions are affected. xample 5 onsider the circuit of Fi. 8, where we assume transistors «and «to be identical. Both transistors share the same source and ate voltaes. Therefore, accordin to q. (3), they carry the same current. This circuit is called a current mirror because it reflects the reference current Ĵ œ on another branch of the circuit. If one accounts for channellenth modulation, however, the operation of the current mirror is not ideal. The drain current of the reference transistor «is while the drain current of transistor «J J t t w x. is w. 10 By y zt zt

11 J { { q Drain current [µa] Ideal With channellenth modulation Drain voltae [] Fiure 7: Output characteristic of an nmosft with and without channellenth modulation. I ref Iout M 1 M 2 Therefore the output current J Fiure 8: NMOS current mirror. ea š 1rq { Since the factor can be may be substantial if the voltae J ea š is J ± z² z² + or more, the error in the mirrorin of the reference current suffers a lare voltae swin. 8 nmosft characterization A typical characterization of MOSFT parameters is shown in Fi. 9. Two different curves are shown on the same plot. The first measurement is taken by biasin the MOS FT in the linear reion, with a small draintosource voltae (10 to 100 m), and sweepin the ate voltae. Linear extrapolation of the resultin vs curve allows the accurate + estimation of the threshold voltae from q. (6). Then, the ate is biased above (typically, close to the positive supply voltae ) and the drain voltae is swept. 11

12 F Z µ š o Drain current [µa] GS = 3, drain sweep DS = 10m, ate sweep oltae [] The resultin vs Fiure 9: Typical Nchannel MOSFT currentvoltae curves. curve is used to extract the values of and >@. In principle, one could use the first ) curve in the linear reion to obtain the value of >H from q. (6). However, due to nonideal behavior of the transistor, obtainin >H from hiher values of the ate and drain voltae ensures better accuracy in realistic applications, where voltaes of the order of are applied to the device and a substantial drain current flows. Note how much smaller the drain current in the linear reion (dashed line) is with respect to the saturation reion (solid line). In the example of Fi. 9, one immediately sees³ from the curve in the linear reion (dashed line) that the threshold voltae is about. The channellenth modulation is then obtained from the slope in the saturation reion (solid line). Note that the saturation condition starts at a drain voltae equal to One easily reconizes this point on the plot, as the voltae where the curve switches from a rounded shape to a straiht constant slope. Takin for example the points at ; and, we write the followin equation: 9 \ so that we obtain equation (11), in this case 9 The pchannel MOSFT j Œ2Zr AZa" Fr_rFOµ ŒFa GF[" F+ Zªµ A A +. The conduction parameter >a is finally obtained from r A. As mentioned above, in a pchannel MOSFT, or pmosft, current is carried by holes rather than electrons. Source and drain are also identically constructed, but this time 12

13 ¹ ¹ ¹ G S S S S G B G G D D D D Fiure 10: Four symbols for the pchannel MOSFT Drain current [µa] Drain voltae [] Fiure 11: Pchannel MOSFT currentvoltae curves, as presented in the technical literature. the source is the terminal biased at the most positive voltae. Schematic symbols for p MOSFTs are shown in Fi. 10. Note how the source is drawn at the top of the symbol rather than at the bottom. In the popular imaination, positive voltaes lie above neative voltaes, and current flows from top to bottom. The pchannel MOSFT is described by exactly the same equations as the nchannel MOSFT, if one reverses the sins of all the currents. This can be confusin to say the least. In many technical publications the drain current, atesource voltae, and drainsource voltae are all taken to be neative, so that a typical 2 curve, for T6 and varyin values of, looks like Fi. 11. In practice, one may et rid of the neative quantities, by reversin the sins of all the voltaes in the equations: ¹ >À A$ 7 >À A$ ¹»++¼½¹ $ %º¹»++¼½¹ %º¹»++¼½¹ ¹»++¼½¹³" ¾ Œ $ 7 " $ Œ $ Á Source turnon Drain turnon Saturation reion Triode reion Note that usin the above equations, one obtains positive currents, which makes sense in 13

14 out in Fiure 12: Pchannel source follower. practice, but may upset purists who insist that outoin terminal currents must be neative. That is why we have written expressions for the absolute value of the drain currents. ¹»Â¼½¹ Also, note ¼ that we have added an absolute value around the threshold voltae ( instead of ) since also the enhancementtype pmosft threshold is often assumed to be neative. When dealin with the pchannel MOSFT, all quantities are usually positive if reversed with respect to the nmosft. The turnon condition for the source ¹»¼ ¹ (drain) is that the sourcetoate (draintoate) voltae must exceed. Also, in all biasin conditions the current flows from source to drain rather than drain to source as in the nmosft. Apart from this reversal, the same equations hold as for the nchannel device. One peculiarity of the pchannel MOSFT is that its body can be independently biased. In fact, pchannel transistors are built on ntype reions which are not automatically shorted to round, but may be connected to other voltae nodes. This property makes it possible to implement precision source followers which do not suffer from body effect (Fi. 12). 10 The physical transistor So far we have not even mentioned what the MOSFT physically looks like. Most of the time the physical structure of the device can be inored, and the circuit desiner can focus on their main job, which is that of arranin abstract models of devices to make a workin circuit. Sometimes, however, this convenient illusion breaks down, and one is brouht back from the dreamlike quality of circuit schematics to the rim reality of silicon and aluminum. In this section we will learn how the physical structure affects 14

15 Ž Ž aluminum plu W polysilicon ate t ox L L eff heavilydoped source and drain L D silicon wafer ¼ Fiure 13: Physical structure of a MOSFT. the electrical MOSFT parameters:, >@,, (and the correspondin pchannel parameters, >À,, ). For simplicity, in the followin we will omit the subscripts and, since the same equations apply to both n and pchannel MOSFTs. A detailed treatment of MOSFT structure and principles of operation can be found in most introductory electronics textbooks, so we will be brief here. A simplified, but realistic crosssection of a MOSFT is shown in Fi. 13. The device consists of a reion exä of a silicon wafer (the body), a thin layer of insulatin oxide of thickness Ã, and a ate electrode made of polysilicon. Polysilicon is just like sinlecrystal silicon, only it is richer in structural defects and has a lower conductivity. The ate has dimensions uæç, where and Ç are the lenth and width. The source and drain are heavilydoped diffusions, connected to the rest of the circuit by plus made of some metal alloy. The wires connectin different devices are made of aluminum. All devices and wires are embedded in amorphous lass which provides electrical insulation. The structure shown in Fi. 13 is almost entirely determined by the fabrication process. For example, the thicknesses of the ate oxide and of the polysilicon, the spacin from the poly to the plus, the depth of the sourcedrain diffusions, are optimized by process enineers and cannot be chaned easily. The only two variables which the circuit desiner can chane are the transistor width Ç and lenth. ven then, there are min 15

16 > > Ç Æ µ µ > Æ Ç Z Æ Z imum values for Ç and which the technoloy dictates. The minimum Zªµ value of is usually identical to the feature size of the process. ZOµ For example, in a m technoloy, the smallest object that can be defined is m wide. The minimum value for Ç is usually a little larer than for Zªµ ³FaZªµ (about 50% more). So for a m technoloy, the minimum width may be about m or so. ven thouh other eometrical parameters cannot be chaned, they influence the electrical parameters, and must be accounted for. An example is the lateral diffusion lenth. This is the fraction of the channel lenth which is eaten into by the source and drain contacts. The real, or effective channel lenth is not, but rather ±È0 Process enineers do their best to make sure that as the minimum is reduced, ZOµ also shrinks, to avoid the risk of a shortcircuit ZOµ between source and drain. In a m tech m. Therefore the transistor with a minimum noloy, a reasonable value for is will have an Zªµ Zªµ ±È of mq m É parameter > for a MOSFT is computed as >HË Ê Zªµ ±È m. Given œè and Ç, the conductance where > Ë is a maic number which depends on the oxide thickness, oxide dielectric constant, channel dopin concentration, oxide defectivity, temperature, ate bias voltae, and many other physical parameters. Mercifully, the circuit desiner does not have to deal with such details. Process and device enineers determine from measurements a typical value Zªµ of > Ë for a iven technoloy, which the desiner can use. So, for example, in a m technoloy with > Ë FrZ Zªµ r A, m MOSFT will have a conductance parameter >HË r A ³FaZ j FrF@µ A Like >, the channellenth modulation parameter depends on the channel lenth. Unlike >, it does not depend on the channel width. Generally speakin, to a lon channel corresponds a small. The physical reason for channellenth modulation is that when the drain voltae increases, the depletion reion around the drain widens, eatin into the channel lenth. The channel appears to be shorter, and the current increases. A lon channel can withstand such erosion better than a short channel, and its LM parameter is smaller. In numbers, one can write where a lare Ì. \ÍÌ7Î is a maic number which is empirically obtained from measurements. To obtain, one can increase, as lon as one can withstand the correspondin decrease of 16

17 Ç µ Ì µ Ž Ž Ž Ž The remainin electrical parameters, namely, and, are entirely determined by the fabrication process, and the circuit desiner has no power over them. In reality, there is a small dependence of and on and Ç $. Typically, both and increase for increasin and decreasin Ç. In other words, a wideandshort MOSFT with hih ratio tends to have lower and lower than a narrowandlon MOSFT with low Ç. However, such chanes are quite small and unpredictable, and are better not relied upon. One last word. In this brief introduction we have not shown proofs for any numerical expressions. We have never even mentioned under which conditions the equations hold. The truth is, most of these equations were derived in the 1960s, around the time the first practical MOSFTs were fabricated. These ancient equations are valid under very restrictive assumptions, which are not satisfied by modern devices. For example, q. (3) is valid for channel lenths of several micrometers, and an oxide thickness of at least ten nanometers, while a modern MOSFT has a channel lenth of the order of m and an oxide of 3 nm! Rarely, thouh, has anyone thouht of usin different equations. Stateoftheart analo and diital circuits are bein desined today, usin models developed for archaic devices. How is that possible The answer is that models can be tweaked. The parameter > Ë, for example, is iven exä exä in textbooks as, where is the mobility and is the oxide capacitance. That expression was correct for devices fabricated in 1965, Ì maybe in 1985, certainly not today. However, expression (3) for the drain current remains approximately valid, if > Ë is treated as a fittin parameter, which is adjusted to ive the correct result under typical operatin conditions. From the point of view of the circuit desiner, the loss of mathematical rior, and some minor accuracy deradation, are more than compensated by the intuitive approach to desin which is only allowed by the simplicity of the archaic equations. $ Ê Zªµ 17