1970, No. 7/8/9 209

Operation and d.c. behaviour of MOS transistors

J. A. van Nielen

The MOS transistor (MOS = metal/oxide/semicon-ductor) is a type of field-effect transistor. It may beregarded as a resistor of semiconducting material whoseconductivity is determined by the potentialof a controlelectrode (the gate) situated outside the current path.The gate of a field-effect transistor is isolated from thecurrent path either by an insulating layer or by a reversebiased P-N junction. In the MOS transistor there is aninsulating layer.

MOS transistors are made on a relatively thick sub-strate of monocrystalline, lightly doped silicon by meansof the planar technique: a schematic cross-section canbe seen in the previous article (page 206). The in-sulator between semiconductor and gate is a layer ofSiO~, obtained by oxidation of the silicon. The sourceand drain electrodes are heavily doped zones of theopposite conduction type from that of the substrate.They are produced by diffusion, sometimes with the aidof a bombardment by fast ions (ion implantation).

There are two types of MOS transistor: those on anN-type substrate and those on a P-type substrate. Tnthe first type current conduction takes place by the flowof holes from the source to the drain, and the device iscalled a P-channel MOS transistor (fig. la). The othertype, in which the conduction is due to electrons, iscalled an N-channel MOS transistor (fig. Ib). We shallreturn to the current conduction in an MOS transistorin more detail later.

The relation, at constant gate voltage Vg, betweenthe current Id flowing through a MOS transistor andthe potential Vrt of the drain - we assume the poten-tial of the source to be zero - much resembles thela- Va characteristic of a pentode valve. Characteristicsof an N-channel MOS transistor are shown in jig. 2a.The lcl- Vg characteristic takes the form of a quadraticfunction (fig. 2b); in a MOS transistor lel is zero whenVg is less than a certain voltage Vth, called the thresholdvoltage. The transconductance of MOS transistors isusually between I and 10 mA /V. A special feature ofthe device is its exceptionally high input resistance, ofthe order of 1014 ohms.

In this article we shall first deal at somewhat greaterlength with the operation of a MOS transistor andconsider the factors that deterrnine the threshold volt-

Ir. J. A. van Nie/en is with Phi/ips Research Laboratories, Eind-hoven.

b

Fig. I. Schematic representation of the MOS transistor, aJ withP-channel, b) with N-channel. S source. G gate. D drain. Thediagram shows that the substrate is connected to the source;this connection is not always present.

10mA

g

5

o

1

Fig. 2. a) Some Id- Vd characteristics of a MOS transistor. Eachcharacteristic relates to a particular value of Vg and consists ofa curved region and an almost horizontal region (saturationregion).b) An Id- Vg characteristic relating to a value of Vd in the satura-tion region. The variation of the saturation value Id sat of thecurrent with Vg is a quadratic function and 1'1 is zero when Vgis lower than the threshold voltage VII,.

210 PJ;-IILlPS TECHNICAL REVIEW VOLUME 31

age Vth.We shall then derive some approximate equa-tions for the d.c.. voltage characteristics, and finallybriefly discuss the way in which the behaviour of aMOS transistor depends on the doping and potentialof the substrate.

Operation of an MOS transistor

Let us consider the case of a MOS transistoron a P-type substrate as illustrated in the previousarticle (page 206). The source S and the substrate forma diode and similarly the drain D and the substrateform a diode. When a voltage is applied between SandD, at Vg = 0, then one of these two diodes is biasedin the reverse direction and only an extremely weakcurrent flows through the transistor.

We shall now see what happens when Vg is graduallyincreased from zero, and we start with the simple casewhere no voltage has been applied. between Sand D(Vd = 0). The system constituted by gate; oxide layer. .andsilicon can.be regarded as a capacitor whose lowerplate is not a metal, but a P-type semiconductor. Aslong' as Vg = 0 the charge on both plates of the capac-itor is zero and the semiconductor is everywhereelectrically neutral. When Vg > 0, a positive chargeappears on Gand a negative charge of equal magnitudeappears on the semiconductor in a layer next to theoxide. At first this charge is carried solely by the (im-mobile) acceptor ions. Since their density is determinedby doping of the substrate, and is thus fixed, this layeris thicker the higher the positive charge, i.e. the greaterthe magnitude of Vg. Since the positive, mobile chargecarriers are driven out of this layer, it is referred to asa depletion layer.When Vg is further increased, the negative charge in

the semiconductor is then no longer carried by theacceptor ions alone, but also by electrons which nowappear in a very thin layer of the depletion region nextto the oxide. This layer, which may for example be10-2 fLÏn thick, forms a c.onductingconnection betweenthe source and drain and is therefore referred to as thechannel.In fig. 3 this picture is presented in the form of an

energy-band diagram. The bands are of course curvedin the depletion region. The curve for the Fermi energyEF, however, will.be a horizontal straight line, as thesemiconductor is everywhere in thermodynamic equi-librium. When Vg is sufficiently high, EF at the inter-face of the silicon and silicon dioxide may thereforecome to lie above El, the centre of the forbidden zone.This means that the silicon at that position has changedto the other conduction type. This change, which hasnothing to do with a change in doping, but is onlypresent when Vg is high enough, is called inversion.The inverted layer is the channel. Since Vg determines

the electron concentration in the channel, it also de-termines the conductivity of the channel and hence thecurrent flowing through the transistor when Vd =1= O.The minimum gate voltage needed at Vd = 0 to bringabout inversion is the threshold voltage Vth mentionedabove.When a gate voltage sufficient to give inversion is

applied the electron concentration in the channel veryquickly adjusts itself to the value appropriate to the.new situation, since most of the electrons required aresupplied from Sand D, where there are large numbersof electrons available. The new equilibrium thus comesabout much more quickly than if the electrons were tocome into the conduction band as a result of thermalexcitation alone.We now consider the situation that actually applies

in an operating MOS transistor: here Vd =1= O. Thepotential Vex) in the channel is then a function of thecoordinate x along the channel, and gradually increasesgoing from S to D. The extent of the inversion, or theconductivity of the channel, therefore gradually de-creases from S to D. The thickness of the depletionlayer, on the other hand, gradually increases, because

M o 5

- - - - - - - - - - - - - - -Ei------------EF

Q

M 0

N p

Fig. 3. a) Energy-band diagram ofthe metal/oxide/silicon system(M, 0 and S) when the silicon is P-type and there is no naturalband curvature near the interface of the semiconductor and theoxide. The Fermi energy EF in the silicon is lower than themiddle El of the forbidden zone (Ev is the upper edge of thevalence band, Ec the lower edge of the conduction band). Sincemetal and silicon are at the same potential, EF has the samevalue in both. .b) When the metal (the gate electrode) is raised to a potential Vg,the holes in the silicon are driven from the zone at the interface,giving rise there to a negative space charge, carried by ionizedacceptor ions. The corresponding band curvature may be so greatthat El at the interface comes below EF, so that an N-type layeris formed there (an inversion), the "channel",

1970, No. 7/8/9 OPERATION OF MOS TRANSISTORS 211

the voltage across the N-P junction formed by thechannel and the rest of the substrate rises from S to D(fig·4a).If we now gradually raise the potentialof D, at fixed

Vg, then the current Id also rises, but owing to thedecrease in the conductivity of the channel the increaseof Id gradually becomes less steep as Vd becomeshigher. At a particular value of Vd the effective gatevoltage Vg - Vd at the end of the channel, whereVex) = Vd, has decreased to Vth. At that position thecondition for inversion is no longer fulfilled; thechannel is said to be "pinched off" (fig.4b). Thisvalue of Vd, which is equal to Vg- Vth and is de-noted by Vd sat, is called the "pinch-off voltage". IfVd is increased further the point in the channel whereVex) = Vd sat. the pinch-off point, is shifted in thedirection of S. In the region of V'I values at which thechannel is pinched off, the current /'1 varies much lessstrongly with V,I (saturation region; see fig. 2a).

Later in this article. when we present an approximatetheory of the d.c. current behaviour of the MOS tran-sistor, we shall return to the current-saturation effect.First, however, we shall take a closer look at the thres-hold voltage Vth.

The threshold voltage V'h; four types of characteristic

In the simple case outlined above, where the energybands at the boundary surface were not curved in thesemiconductor at Vg = 0 and Vd = 0, the gate volt-age Vlh required to produce inversion could only bepositive. [n practice the situation is usually not assimple as that, because the structure of the MOS tran-sistor may already contain built-in charges. In MOStransistors on a P-type substrate VOl may be negative.Such transistors conduct even at Vg = O. For MOStransistors on an N-type substrate it is also possible inprinciple for Vth to be either positive or negative. Fourtypes of characteristic may therefore be encountered(fig. 5). The MOS transistors that conduct at Vg = 0- i.e. those in which a channel is naturally present -are called depletion-type MOS transistors, and theothers are said to be of the enhancement type. Thesenames come from the use of the MOS transistor asswitching devices in digital circuits. Devices of thedepletion type are normally open and require to beclosed by a gate voltage, which depletes the conductingchannel; those of the enhancement type are normallyclosed and require to be opened by a gate voltage.

Apart from the relative positions of Ei and EF, i.e.the doping ofthe substrate, there are three other factorsthat determine the value of Vth found in a MOS tran-sistor. The first is that, during the oxidation of thesilicon, a quantity of positive charge qox enters theoxide, which has the effect of shifting Vth in the nega-

Q

b

Fig. 4. a) Schematic picture of the situation in a non-saturatedMOS transistor on a P-type substrate. Situated immediatelyunder the oxide is an extremely thin, inverted layer of the sub-strate, through which the current flows and whose conductivitygradually decreases from S to D. The latter is schematicallyrepresented by diminishing thickness. Under the channel, andalso under the drain, is a layer in which there are no mobilecarriers, the depletion layer (white); its thickness increases goingfrom S (x = 0) to D (x = /).b) The same for the case of current saturation. In the last partof the channel Vex) > Vg - V,h.

Depl Enh

Enh Depl

Fig. 5. In MOS transistors on either a P-type or an N-type sub-strare the threshold voltage V'h may in principle be either posi-tive or negative, so that there are four types of Ict- Vg characteristic.MOS transistors which conduct when Vg = 0 are "depletion-type" devices (Dep/) and the others "enhancement-type" de-vices (Enh).

tive direction. Because of this effect P-channel tran-sistors usually belong to the enhancement type andN-channel transistors to the depletion type.

In the second place Vth depends to some extent onthe metal from which the gate electrode is made. Thedifference between the work function of this metal andthat of the substrate, the contact potential <Pms, actsas a built-in contribution to the gate voltage (fig. 6a, b).Finally there may be effects from surface states whoseenergy levels lie in the forbidden band. These surface

, 212 PHILlPS TECHNICAL REVIEW

states may trap free charge carriers, which can thenmake no contribution to the conduction. The largerthe number of surfaces states, the higherthe gate voltageneeded to produce a particular concentration of freecharge carriers, in other words the threshold poten-tial IVthl is higher. Advances in recent years in thetechnology of manufacturing MOS transistors havemade it possible to keep the concentration of surfacestates so low that they no longer have any significanteffect [11. '

Ifwe include all these charges then the charge on thetwo plates of the capacitor formed by the MOS tran-sistor is:

where qg is the charge per unit area on the gate, qinv

M Vac s MOSeVc,xf --

E----F

- - - --E;

----·---EF~~g&:Ev

Q

VOLUME 31

Approximate theory of the d.c. current behaviour

Let us again consider the case of an MOS transistoron a substrate of P-type silicon, i.e. with a channel inwhich the conduction is by electrons. To calculate thecharacteristics we introduce two simplifications. In thefirst place we assume that everywhere in the layer of thesubstrate adjacent to the oxide - the lower face of thecapacitor - the charge per unit area'çix) is determinedby the difference between Vg and the potential Vex)at the position x in the channel, the relationship being:

q(x) =-Cox{Vg- Vex)}. (3)

(I)

(Expressed in the symbols used in equation (I),q(x) = qinv + qdepl + qss.) Let h be the thickness ofthe oxide layer and êox its relative 'dielectric constant,then Cox = êQêox/h.The minus sign in (3) indicates that

M o S

Fig. 6. a) Energy-band diagram of a metal ivf and a semiconductor S which are not in con-tact with each other and have a different work function (i.e. the work that must be performedin order to remove an electron with an energy Ev from the metal or the semiconductor intoa vacuum). The difference in work function is e(f)ms; ({)m5is the contact potential.b) If the metal and semiconductor in (a) are joined by an oxide layer to form an MOS struc-ture, then EF has the same value everywhere and the original difference eq)ms brings intoexistence a voltage Vox across the oxide and a band curvature e Vs in the semiconductor;Vox + Vs = (/>ms. Because of the band curvature, VII! has here a value different from thatin the case illustrated in fig. 3.e) As (b), but for the case where a gate voltage Vg is applied such that El - EF at the sur-face is exactly equal to -e(/>F.

the charge in the channel, qss that in the surface statesand qdepl that in the depletion layer. If we take theusual definition of the threshold voltage Vth as thevalue of Vg at which the energy difference Ei - E}, atthe interface between the silicon and the Si02 is equalto that in the bulk of the substrate but of oppositesign (fig. 6c), then:

Vth = <Pm +'2 (/JF- (qi~V + qss+ qox + qdepl)/Cox.(2)

Here Cox is the capacitance per unit area ofthe capac-itor. The term 2 (/JF is in this case the band curvaturecaused by Vg. The charge qinv is usually so much smal-ler than the other charges that it may be neglected inestablishing a value for the threshold potential.

the charge q(x) is negative if Vg- V(x) is positive.Equation (3) would apply exactly if the lines of force

in the dièlectric were perpendicular to the surface. Thissituation is approximated when Vex) in the channeldoes not vary too greatly with x, that is to say whend V(x)/dx and d2 V(x)/dx2 are small (this is Shockley'sgradual approximation [21); in practice this is the casein the greater part of the channel.

The second assumption is that the density qiJlv(X) ofthe negative charge carried by mobile electrons in thechannel is given by:

qinv(X) = -Cox{Vg' - Vex)}, (4)

where Vg' = Vg- Vth.

If this equation can also be used, the current, which

1970, No. 7/8/9 OPERATION OF MOS TRANSISTORS 213

is equal to the product of qinv(X), the width w of thechannel, the mobility f1 of the charge carriers and thefield strength -d V(x)jdx, is given by:

Id(X) = f1 Cox w{Vg' - V(x)}dV(x)jdx. (5)

We can now find an expression for the steady-state cur-rent by integrating equation (5) over the whole length Iof the channel. Since Id is independent of x in the steadystate, we may place Id in front of the integral sign:

I Vd

Id J dx = f1 Cox w J {Vg' - V(x)}d Vex).o o

From this we derive:

or

wherefJ = f1 Cox wjl.

The curve corresponding to equation (6) is a parabolawith the apex upwards.In these calculations we have tacitly made a third

assumption, which is that f1 depends on none of theother quantities. This is not entirely true, because ifVg is high, i.e. if there is a strong transverse field, f1 issomewhat smaller than when Vg is low [31.

In the special case where Vd = 0, we may deducefrom (6) the following expression for the conductivityGo of the channel:

Go = lim Iel Va = fJVg'.

Vd->-O

Within the limits of our approximation the conductivitythus varies linearly with Vg (fig. 7).

Let us now return for a moment to equations (4) and(5). The situation in the channel is that, going from Sto D, the charge density gradually decreases; the fieldstrength, on the other hand, increases, with the effectthat Id(X) has the same value everywhere in the channel.At the value of Vg where the right-hand side of (6)reaches its maximum - i.e. where Vg' = Vd, or whereVg = Vd + Vth - equation (4) shows that the chargedensity qinv(X) at the drain (x = l) is equal to zero,which means that the field strength there would beinfinitely high. The gradual approximation is thereforeno longer valid here; only the rising part of the para-bola represents a part of the Id- Vd characteristic. Themaximum current can readily be shown from (6) to beequal to tfJVg'2.

In the region Vd > Vg' we may expect as .a firstapproximation that the current will be independent ofVd and equal to this maximum value, on the followinggrounds. If we let the voltage Vd increase above Vg',then the potential Vex) in the channel reaches the

value Vg' at a point just before the end of the channel;the remainder of Vd appears across the part that liesbetween this point and the drain. Since the conductivityof this part is low, and yet the potential differenceVd - Vg' still causes a current flow there, the length ofthis part will be relatively small. The length of thehighly conducting part of the channel thus differs rela-tively little frc I, and the current will be approx-imately equa' the maximum current (the curre_ntatsaturation). Id sat denotes the saturation value ofthe current, we may thus write:

(6)

Id sat = tfJVg'2. •..... (9)

This equation shows that the current through a MOStransistor operating in the saturation region is a quad-ratic function of the gate voltage (see fig. 2b). The

(7)4mA/V

3

r(8) o~~~~~~~~--~-

o 1 t2 3 4 5 6V

l1h - Vg

Fig. 7. The conductivity Go of a MOS transistor with Vd = 0varies linearly with Vg over a wide range. The solid curve relatesto the results of measurements, the dashed line relates to equa-tion (8).

transconductance gm in this region is given by:

(10)

The transconductance is not constant but varies linearlywith Vg'. The calculation given here also shows thatgm is equal to Go (see equation 8).

As could be seen from fig. 2a, the current in thesaturation region is in reality not entirely independent

[IJ See the article by J. A. Appels, H. Kalter and E. Kooi inthis issue, page 225, and also H. C. de Graaft' and J. A. vanNielen, Electronics Letters 3, 195, 1967. .

[2J W. Shockley, A unipolar "field-effect" transistor, Proc. LR.E.40, 1365-1376, 1952.C. T. Sah, Characteristics of the metal-oxide-semiconductortransistors, IEEE Trans. ED-H, 324-345, 1964. ' .

[3J See the article by N. St. J. Murphy, F. Berz and L Flinn inthis issue, page 237.

214 PHILIPS TECHNICAL REVIEW VOLUME 31

of Vd. One of the reasons for this is that near the drainthe lines of force from the gate are no longer perpen-dicular to the interface between oxide and channel,which is the assumption made in the gradual approxi-mation. On increasing Vd the distribution of the linesof force in insulator and substrate around the pinch-offpoint of the channel varies in such a way that the pinch-off shifts slightly towards the source, making thechannel shorter. This increases the transconductanceof the device (see equations 10 and 7) and also, sincethere is no change in the gate voltage, it increases the

I current as well.

Transconductance and gain

The characteristics and relations arrived at in ourtheoretical treatment are of significanee in the practicalapplication of the MOS transistor. Very often a maxi-mum voltage gain is required from the MOS transistor.The voltage gain ILl Vd/LI Vgl in the amplifier circuit offig. 8 is approximately equal to the product ofthe trans-conductance gm and the load resistance RI. Now gm inthe MOS transistor increases with the d.c. current Id;equations (9) and (10) show that the relation is:

This means that to obtain a high voltage gain the userwill be inclined to bias the transistor to a high current.At a given supply voltage Vdd a limit is set to this,however, by the maximum permissible voltage dropacross RI, i.e. IdRI. Therefore not gm, but the quan-tity gm/Id is a measure of the available voltagegain in .any given circuit [4]. As a rule the transcon-ductance of MOS transistors is smaller than that ofbipolar transistors, and a higher load resistance istherefore needed to obtain an equally high voltagegain.

The purely second-order characteristic of the MOStransistor (see equation 9) is an advantage for applica-tions in receiver input stages. If the valve or transistorin this stage has a non-linear characteristic, strongsignals outside the passband of the receiver can intro-duce spurious signals (intermodulation products) byinteraction with the desired signal. With a selectivereceiver, most of these intermodulation products donot appear within the pass band of the following stagesand introduce no interference. If however the expres-sion for the characteristic of the valve or transistorcontains higher terms in odd powers of the inputvoltage, the intermodulation products will include asignal at the carrier frequency of the desired station,but with its amplitude determined by the modulationof the interfering station. The programme from theinterfering station appears to be modulating the carrierfrom the desired station: this effect is called "cross-

modulation". A MOS transistor, whose characteristicdoes not contain such higher odd terms, does not intro-duce cross-modulation [5].

The substrate

To conclude this article we shall examine how thebehaviour of a MOS transistor is affected by thedoping of the substrate and by a substrate potential Vbdiffering from zero [6]. We again consider a transistoron a P-type substrate and again start with the casewhere Vd = 0 and a gate voltage Vg is applied to pro-duce an inversion layer. We have already seen that thislayer is extremely thin, and that the depletion layer isrelatively thick (e.g. I (Lm) because the charge densityin it cannot be greater than the density N of the accep-tor ions present in the silicon. The charge density in thedepletion layer is therefore constant over a large part

(11) I~Fig. 8. Circuit for voltage amplification with a MOS transistor.RI load resistance. Vdd supply voltage.

of the thickness, and there is a fairly sharp boundarybetween this layer and the rest of the substrate.

To calculate the space charge in the depletion layerwe may regard the channel and depletion layer togetheras an abrupt Nl--P junction and apply the appropriateequations. If a particular Vg produces a voltage Vsacross the Nv-P junction - the band curvature is then-eVs (fig. 6b) - then the thickness d of the depletionlayer is:

( 12)

and the depletion charge per unit area qdepl is:

qdepl = -(2 eoeeN)t vst = a Vst. (13)

In the approximate theory leading to equations (4) and(6), qdepl is taken to be zero or regarded as constant,i.e. independent of Vg and x. In calculating the effectof Vg on qdepl this is a very good approximation, be-cause provided the inversion is not unduly small - i.e.provided the charge density in the channel is greaterthan that in the depletion layer - a variation of Vginfluences the electron concentration in the channelvery much more than the depletion charge [7]: thefirst varies exponentially with Vs, whereas qdepl only

1970, No. 7/8/9 OPERATION OF MOS TRANSISTORS 215

varies with Vst, as we have seen. This means that whenthe gate voltage Vg is made high enough, the depletioncharge remains practically constant, whereas the mobilecharge increases linearly with Vg.When Vd =1= 0, the potential Vex) in the channel goes

from 0 to Vd, and similarly the reverse voltage acrossthe induced N+-P junction also goes from 0 to Vd.This reverse voltage can be further increased by givingthe substrate an additional reverse bias Vb with respectto the source. The total depletion charge per unit areais then a{Vs + Vex) + Vb}t and is thus dependenton x. The increase in the depletion charge due to thecontributions from Vex) and Vb takes place at theexpense of the mobile charge qinv(X), since the totalcharge is still that given by equation (3). The directconsequence of this is that the current reaches satura-tion at a drain voltage lower than Vg- Vth and thesaturation value Id sat is also smaller than that givenby equation (9). The transconductance is now alsolower and no longer equal to Go.The effect of applying h is thus to change the

amount of mobile charge, and with it the current. Thesubstrate contact may therefore be regarded as a secondgate electrode. If the doping N of the substrate is1016 per cm3 the transconductance can in fact be justas high when the device is driven via the substrate aswhen it is driven via the insulated gate electrode G.We should also note that when Vb =1= 0 the value ofthe threshold potential is of course different:

Vth(Vb) = Vth(O) + {(Vb + 2q>F)t - (2q>F)t}a/Cox.

As can be seen from (I3),qdepl is proportional to Nt.

(4] G. Klein and H. Koelmans, Active thin film devices, Fest-körperprobleme 7, 183-199, 1967.

(5] R. J. Nienhuis, A MOS tetrode for the UHF band with achannel 1.5 ILm long; this issue, page 259.

(G] J. A. van Nielen and O. W. Memelink, The influence of thesubstrate upon the DC characteristics of silicon MOS tran-sistors, Philips Res. Repts. 22, 55-71, 1967.

(7] A. S. Grove, B. E. Deal, E. H. Snow and C. T. Sah, Solid-State Electronics 8, 145, 1965, and T. I. Kamins and R. S.Muller, Solid-State Electronics 10, 423, 1967.

(S] See the article by R. D. Josephy in this issue, page 251.

Equations (6), (9) and (10) for Id, Id sat and the trans-conductance gm, respectively, will thus become moreaccurate as N decreases, i.e. as the doping is reduced;the deviation is already very small for N = 1014/çm3.

In spite of the deviations from these equations whenthe substrate is more strongly doped, it is still fairlyaccurate to take the variation in transconductance withVg as linear and the variation of the saturation cur-rent Id sat with Vg as a quadratic function.

Punch-through

We should note here an unwanted effect that mayoccur in the substrate when the drain voltage is toohigh, particularly when the substrate is weakly doped.The higher the voltage of the drain with respect to thesubstrate, the wider becomes the depletion zone aroundthe drain. In MOS transistors with a short channel thiszone may become so wide that it touches the source.The electric field in the depletion region then actsdirectlyon the charge carriers in the source diffusion,causing the carriers to move outside the channel to thedrain. This effect is known as punch-through. It sets alimit to the improvement in the high-frequency char-acteristics of a MOS transistor that can be achievedby making it with a shorter channel; it also limits themaximum drain voltage in high-frequency power tran-sistors [81.

Summary. A MOS transistor is a field-effect transistor in whichthe gate is insulated from the semiconductor (silicon) by a layerof Si02. If the semiconductor is P-type the source and drain arestrongly doped zones of N-type silicon. The current flows througha thin layer at the surface of the oxide, called the channel, inwhich the silicon is changed by the field of the gate from P-typeto N-type. The input resistance is very high (about 1014 l.1). Thecurrent-voltage characteristic (when the gate voltage is constant)shows saturation, just as in the case of a pentode valve. Thetransconductance varies linearly with the gate voltage and is ofabout the same magnitude as in thermionic valves. If the gatevoltage has a magnitude lower than a certain threshold voltage,no current flows. This threshold voltage in both an N-type andP-type transistor may be either positive or negative. The dopingof the silicon substrate makes the behaviour of the MOS tran-sistor deviate from the theoretical description given in the article;with a doping level of N = 1014/cm3 or less, however, the devia-tions are small and can be neglected.