330 Philips Tech. Rev. 43, No. 11/12,330-342, Dec. 1987

Behaviour of the oxide film in MOS devices

D. R. WoIters

The MOS transistor, which contains an insulating Si02 film between silicon and gate, is an im-portant component for the semiconductor industry. The oxide film is usually thinner than0.1 um, which means that the current in the silicon can be controlled effectively by the gatevoltage. The electric field-strength in the oxide film can be very high, a hundred times morethan would be possible in high-voltage cables. The charge leakage through the film must bevery small, of course and thefilm must not break down. With the continuing miniaturizationof semiconductor components, containing even thinner oxide films, it is becoming increasinglydifficult to meet these requirements. It is therefore important to have a detailed understandingof the processes that take place in the film when a voltage is applied to it and to recognize theconditions that lead to breakdown. In the article below the author describes an investigationthat he and other colleagues at Philips Research Laboratories have made into the behaviour ofthe oxide film in MOS devices.

Introduetion

Since the fifties the semiconductor industry hasmade enormous progress in the technology of manu-facturing electronic circuits. This owes much to theuse of silicon as the basic material. Silicon is a semi-conductor possessing a unique combination of prop-erties. It is particularly suitable for the manufactureof large pure single crystals that can be processed bysawing, grinding and polishing into 'slices' or'wafers'. Electrical conduction in the silicon is easilycontrolled and can be varied considerably by addingappropriate dopants.

In the sixties the discovery that it was useful tocover a silicon wafer with a thin film of silicon dioxide(Si02), e.g. by oxidation at about 1000 oe in an at-mosphere of oxygen or water vapour, lent consider-able impetus to the development of 'planar' technol-ogy. Films made in this way are dense and homogene-ous, and they adhere extremely well to the silicon sur-face. Because they are chemically resistant and imper-vious, they can be used as doping masks in the manu-facture of integrated circuits. Another useful propertyis that they are good electrical insulators, which is use-

Dr Ir D. R. Wolters is with Philips Research Laboratories, Eind-hoven.

ful for example in the stabilization of bipolar devices.Mastery of the technique of manufacturing very pureoxide films was particularly important in the devel-opment of MOS transistors (MOS = metal/oxide/semiconductor). In these field-effect transistors anSi02 layer acts as an insulator between doped siliconand the gate UI. Electrical conduction in the siliconbetween the source and drain is controlled by the volt-age on the gate. The properties of the Si02 films aresuch that films thinner than 50 nm can be used. Thismeans that the gate in such a device can be extremelyclose to the silicon to control the electrical conductionin the silicon effectively.The amount of charge that leaks through an Si02

film or is trapped when a voltage is applied must beextremely small, and there must be no premature elec-trical breakdown, which would make the device use-less. The miniaturization of MOS devices to sub-micron dimensions makes it increasingly difficult tomeet these requirements: thinner oxide films andstronger electric fields are the requirements of the day.For these and other reasons the manufacture of thefilms requires extremely accurate process control. It isalso necessary to know in detail what happens when a

Philips Tech. Rev. 43, No. 11/12 OXIDE FILM IN MOS DEVICES 331

voltage is applied to the film. At Philips ResearchLaboratories in Eindhoven extensive investigationshave been made in recent years into the processes thatplay a part in the manufacture of the films, in theirapplication in MOS devices and in electrical break-down [21.A study of the oxidation kinetics in the manufac-

ture of the film has shown that the mechanism of theoxidation is not the same as has until recently beenassumed [31. In particular, current ideas about thecatalytic action of the water vapour present were notreally satisfactory. The distribution of radioactivewater in the films showed us that water moleculesionize in pairs and that the resulting ions (H30+ andOH-) travel through the oxide film. The ion migrationtakes place close to the interface between the siliconand the growing Si02 film, while the migration ofoxygen molecules takes place closer to the surface [41.When a high electric field is applied to an Si02 film,

a certain amount of charge is always injected. Somecharge leakage is not in itself so serious, but some ofthe injected charge becomes trapped and may there-fore affect the control of current conduction in thesilicon. By accurately measuring the trapping rate and Qthe amount of trapped charge we have been able tomodel the mechanism of charge trapping and thenature of the trapping centres. We have accounted forthe fact that trapped charges have the effect of coun-teracting any further charge trapping in their imme-diate vicinity.

Charge leakage is an important factor affecting thelife of the Si02 film and hence the life of the device.The occurrence of electrical breakdown turns out infact to be determined by the amount of charge thathas leaked through the film. It seems as if the leakingcharge gradually 'wears out' the film. This suggests bthat the 'wear', i.e. a change in properties, starts longbefore the film breaks down. The understanding thusobtained now enables us to predict fairly accuratelywhen a device will start to deteriorate due to wear ofthe oxide film and when it will finally break down. Wecan therefore give better estimates of the usefullife ofMOS devices.

In this article we shall first consider charge trappingin an Si02 film. It will be shown that the repulsionbetween trapped and injected charges is an importantfactor. Next we shalliook at the phenomenon of elec-trical breakdown, examining defect-related break-down, intrinsic breakdown (i.e. breakdown not relat-ed to defects) and the effects of field-strength, currentand transferred charge. We shall also take a closerlook at the conditions under which intrinsic break-down occurs. Finally, the mechanism responsible forbreakdown will be indicated.

Charge trapping

As noted above, when an electric field is appliedacross an insulating Si02 film, some charge will beinjected. The current that flows through the film de-creases after some time because some of the injectedcharge is trapped. The space charge thus built up inthe film causes a distortion of the electric field at theinterface with the silicon. This has the effect of broad-ening the potential barrier for electrons at the inter-face between silicon and the Si02 film; see jig. 1. As a

e

M(+)

Ec----1

Ey----

Si(-)

E; ----....1I

t; -----1IIIII

Fig. 1. a) Energy diagram for the transition of electrons from siliconto Si02 in a MOS device in which the metallic layer M is at a posi-tive potential with respect to the silicon. E; upper edge of thevalence band. E; lower edge of the conduction band. An electron e:goes from the conduction band of silicon to the conduction band ofSi02. At the interface the electron tunnels through the potentialbarrier. b) In the presence of a negative space charge Ch, caused bythe trapping of electrons, the potential barrier becomes wider. Anelectron tunnelling through the barrier therefore has to cover agreater distance, which reduces the probability of electron injectioninto the Si02 film.

[IJ See the special issue on MOS transistors, Philips Tech. Rev.31,205-295, 1970.

[2J This investigation has been described in detail in the author'sdoctoral thesis, entitled: Growth, conduction, trapping andbreakdown of Si02 layers on silicon, Groningen 1985.

[3J A widely used model for the oxidation is described by B. E.Deal and A. S. Grove, General relationship for the thermaloxidation of silicon, J. Appl. Phys. 36, 3770-3778, 1965.

[4J D. R. Waiters, On the oxidation kinetics of silicon: the role ofwater, J. Electrochem. Soc. 127,2072-2082, 1980.

332 D. R. WOLTERS Philips Tech. Rev. 43, No. 11/12

consequence, there will be less chance of electrons'tunnelling' through the barrier, and fewer electronswill be injected into the film. The time-dependent in-jection and trapping of electrons can assume suchproportions that the film can no longer perform stablyand reproducibly in an electronic device. In MOStransistors, which often operate with a high field-strength (up to 3 X 106 V/cm), the space-charge effectslead to instabilities and drastic changes in the switch-ing or threshold voltage. It is therefore most impor-tant to be able to characterize and control theseeffects.

Charge trapping can usefully be studied in a MOScapacitor, in which the oxide film is situated betweenan aluminium (or polysilicon) gate and a silicon sub-strate. It is possible, for example, to measure the in-crease in voltage necessary to make a constant currentflow through the capacitor. From the measured volt-age the increase in the number of trapped charges canbe derived directly. Information about the number oftrapped charges can also be obtained by measuringthe capacitance as a function of the applied voltageduring interruptions of the injection.In the past a first-order approximation has gen-

erally been used to describe charge trapping as a func-tion of time [6]. It was assumed that the trapping ratewas equal to the product of the electron flux, theeffective cross-section a of the trapping centres andthe number of vacant trapping centres. The electronflux is Jvth/ av«, where J is the current density and qthe electronic charge, Vth is the mean velocity of hotelectrons (in all directions) and Vd the effective driftvelocity in the direction of the field gradient. Thenumber of vacant trapping centres is equal to the totalnumber of centres (N) less the number of centres al-ready occupied (n). The trapping rate dnldt can be ex-pressed as:

dn/dt = J(N - n)/Qo,

where Qo is qvelov«, Integration, for a constantvalue of J, gives:

n = N[1 - exp (- Jt/Qo)}.

If this relation applies, a plot of log(dn/dt) against tshould yield a straight line. In practice, however, thisis not always so; see for example fig. 2. In addition,eq. (2) indicates that n should rapidly saturate, sincethe exponential term rapidly goes to zero whenJt > Qo. As a rule, however, no such saturation isfound.To obtain better agreement between theory and

experiment the presence of centres of many differentkinds has been postulated in the literature [6] [7]. Itwill now be shown, however, that a good description

4r---------------~[og (dn/dt)

t 3\~o~2 ~~

1~--~---L--~--~o 2 4 6x103S

--+ t

Fig.2. Logarithm of the trapping rate dn/dt for charge carriers inSi02 as a function of the duration t of the applied voltage, for twothicknesses d of the oxide film. The data are derived from resultsreported by D. R. Young [61. The first-order approximation, whichpredicts the straight lines given by eq. (2), is clearly not applicablehere.

(1)

of charge trapping can be given without any suchassumption, provided sufficient account is taken ofthe repulsion experienced by injected charges fromcharges already trapped [8] [9].

Effects of Coulomb repulsion

Owing to the Coulomb repulsion between injectedcharges and charges already trapped, the trapping ofnew charges becomes less likely in the vicinity of cen-tres already occupied. The trapping probability willdecrease as the number of occupied centres increases.For a simple calculation of this diminished probabilityit may be assumed that ~n occupied centre makes aregion of volume h inactive for further trapping. Thevolume in which trapping can take place is then nolonger V, the total volume of the oxide film, butV-h. The trapping probability is thus reduced by afactor of (1 - hiV). If n charges have been trapped,the probability of further trapping is reduced by(1 - hlv)n. The trapping is reduced by this factor andnot by (1 - nhlV) because the various inactive regionscan overlap. Since h«: V, a good approximation is:

(2) (1 - h/V)n = exp (- nh/V). (3)

This exponential factor must be included in theexpression for the trapping rate (eq, (1», giving:

dn/dt = J(N - n) exp (- nh/V). (4)Qo

For n-e.N we have, after integration:

JNhtexp (nh/V) - 1 = --.

QoV(5)

Philips Tech. Rev. 43, No. 11/12 OXIDE FILM IN MOS DEVICES 333

100r---------------~n

t50

O~~------~------~3.0 3.5 4.0

~ /og{t+foJ

Fig.3. Number of trapped charge carriers (n) in arbitrary unitsplotted against log(t + to), see text, for different thicknesses d of theSi02 film. These data are also derived from Young's results [6]. Inall cases a straight line is found, as predicted by eq. (6).

This leads to

V t+ton= -ln--

h to'

where to = QoV/JNh. This indicates that the plot of nagainst ln(t + to) should be a straight line [8]. This isindeed found experimentally, as appears from jig. 3for oxide films of different thickness.

This model also gives a better description of thevariation in the current with the amount of trans-ferred charge. In general the current density J de-pends on the electrical field-strength Ei at the interfacewith the gate. To a good approximation the simpleexponential relation

J = Jo exp (Ei/Eo)

can be used, where Jo and Eo are constants. The valueof Ei is determined by the strength E of the appliedfield and by the field-strength induced by the trappedcharges:

Ei = E - nqx/e,where x is the mean distance of the trapped chargesfrom the electrode and e is the permittivity of the film.The number of trapped charges (n) should now be 'expressed in terms of the charge transferred per unitarea, defined as:

t

Q=j Jdt.o

For the first-order approximation we can write, byanalogy with eq. (2):

n=N[1 - exp(- Q/Qo)}. (10)

For Q::::;;Qo, a good approximation is:

n =Nln(go + 1).

Substituting eq. (8) and eq. (11) in eq. (7) shows thatthe curve of lnJ against lnQ is horizontal at first forsmall Q. Then lnJ decreases linearly with a slope thatis proportional to N. Beyond a saturation value (Qsat)the curve should again be horizontal: saturationoccurs because n has become equal to N and no morenew charges can be trapped. The value of Qsat can bederived from eq. (11) by putting n = N. This givesQsat= Qo(e - 1) "'" 1.7 Qo. The curve of lnJ as afunction of lnQ is shown schematically in jig. 4a.When the Coulomb repulsion is taken into account,

analogy with eq. (6) gives the following expressionfor n:

(11)

n = V ln( 2_ + 1)h Ql '

(12)

(6)

InJ

tt t t

Q,t

---+ triû

g

(7)Fig.4. Schematic curve of 1nl as a function of lnQ as given by thefirst-order approximation (a) and after taking into account theCoulomb repulsion between injected electrons and electrons al-ready trapped (b); see text. The main difference is that the slopingsection in (a) is much steeper and the saturation point (Qsat) isreached much earlier than in (b).

(8)

[5] The applicability of this approximation to earlier experimentsis to some extent demonstrated in:E. H. Nicollian, A. Goetzberger and C. N. Berglund, Avalancheinjection currents and charging phenomena in thermal Si02,Appl. Phys. Lett. 15, 174-177, 1969;E. H. Nicollian, C. N. Berglund, P. F. Schmidt and J. M.Andrews, Electrochemical charging of thermal Si02 films byinjected electron currents, J. Appl. Phys. 42, 5654-5664, 1971.

[6] D. R. Young, Electron trapping in Si02, Inst. Phys. Conf.Ser. 50, 28-39, 1980.

[7] See also: T. H. Ning and H. N. Yu, Optically induced injectionof hot electrons into Si02, J. Appl. Phys. 45, 5373-5378, 1974;R. A. Gdula, The effects of processing on hot electron trappingin SiOz, J. Electrochem. Soc. 123, 42-47, 1976;D. R. Young, E. A. Irene, D. J. Di Maria, R. F. De Keers-maecker and H. Z. Massoud, Electron trapping in Si02 at 295and 77 oK, J. Appl. Phys. 50, 6366-6372, 1979.

[S] D. R. Wolters and J. F. Verwey, Trapping characteristics inSiÛ2, in: Insulating Films on Semiconductors, M. Schulz andG. Pensl (eds), Series in Electrophysics, Vol. 7, Springer, Ber-lin 1981, pp. 111-117.

[9] D. R. Wolters and J. J. van der Schoot, Kinetics of chargetrapping in dielectrics, J. Appl. Phys, 58, 831-837, 1985.

(9)

334 D. R. WOLTERS Philips Tech. Rev. 43, No. 11/12

where Q1 = VqVd/ hNavth. At first sight this expres-sion resembles eq. (11). If, after substituting eqs (8)and (12) in eq. (7), we plot the value of 1nl against thevalue of lnQ, we again obtain a curve with two hor-izontal sections, linked by a sloping section; see fig. 4b.

However, two important differences should benoted. The first concerns the slope of the sloping sec-tion: this is now much smaller because it is not pro-portional to N but to the much smaller value of V/h.The second difference concerns the saturation pointQsat. In the model with the Coulomb repulsion, sat-uration does not occur until the number of trappedcharges is equal to the maximum number of spheresof volume h that can be accommodated in the totalvolume V. If the spheres do not overlap, this numberis V/h. If the spheres overlap to the maximum possibleextent, this number becomes 8V/h, which is equal to

J

i

~,~~{Y-s.!(:} 5~43nm 5i02 <,p=Sii«) " -,

--QFig.5. Log-log plot of the current density I measured in a MOSdevice as a function of the charge transferred per unit area (Q) fordifferent field-strengths E. As eq. (13) indicates curves with twoasymptotes (dashed lines) are obtained: 1nl is constant at low Q anddecreases linearly with lnQ at high Q.

poly=Sii «)43nm 5i02p=Sil»}

___ 00_0_0

5 6 7-E

8 X 106 V/cm

Fig.6. Effective cross-section CTeff for electron trapping in the Si02film of the MOS device in fig. 5, and the effective density Nar of thetrapping centres, as a function of the applied field-strength E.Whereas Ne« is independent of E, the value of (Jeff first decreaseswith E until a virtually constant value is reached at high E.

the number for the maximum close-packing (with nooverlapping) of spheres of half the radius. Fromeq. (12) this means that In {(Qsat/Q1) + IJ = 8, so thatQsat = (e8 - 1)Q1 = 2980 Q1. The value of Qsat isthus more than three orders of magnitude larger thanthe characteristic value Q1, whereas in the first-orderapproximation Qsat is not much larger than the char-acteristic value Qo for that case. Such a high value ofQsat cannot be reached experimentally because othereffects (e.g. breakdown) can occur beforehand. Whenthe Coulomb repulsion is taken into account it cantherefore be seen why no saturation is found in therange in which measurements can be made.

Results of measurements of I as a function of Q fordifferent applied field-strengths are shown in fig.5.The measured curves agree well with the expressionthat can be derived from equations (7), (8) and (12):

E Vqx (Q )In (l/lo) = - - -- In - + 1 .Eo heEo QI

(13)

The curves have two asymptotes. At a low value of Q,I is constant; from the values of 1/10 and the externalfield-strength E we can then derive E«. At a high valueof Q, 1nl decreases linearly with lnQ.

Eq. (13) shows that the slope of the asymptote athigh Q is Vqx/heEo. Since q, e and Eo are known to afirst approximation and x can be equated to half thethickness of the oxide film, the slope will give thevalue of V/h, which can be seen as the effective densityNat of the trapping centres. It has been found thatNet does not depend on the applied field; see fig. 6.The experimental curves of 1nl versus lnQ can also beused for determining Q1. The value of the effectivetrapping cross-section aeff can then be derived fromQ1:

(leff = q/QI. (14)

Fig. 6 shows that with increasing field-strength, thevalue of a eff decreases by more than an order of mag-nitude. At high field-strengths, aeff is virtually con-stant.We believe that the results described here will con-

tribute to a much better understanding of chargetrapping. The knowledge gained can help us to sup-press the undesired effects resulting from charge trap-ping in the silicon, or to control them better. The re-sults have also put us on the track of the mechanismthat plays a major part in the breakdown of the film.We shall now look at some aspects of electrical break-down.

[101 D. R. Welters and J. J. van der Schoot, Dielectric breakdownin MOS devices, Part I: Defect-related and intrinsic break-down, Philips J. Res. 40,115-136,1985.

Philips Tech. Rev. 43, No. 11/12 OXIDE FILM IN MOS DEVICES 335

Electrical breakdown

When the voltage across the oxide film in a MOScapacitor is increased, a value is eventually reached atwhich the field-strength in the film becomes so greatthat it breaks down [lol. The breakdown takes theform of a sudden current surge accompanied by de-struction of the film. This effect is also found at a lowerconstant voltage if the voltage is applied for longenough. Fig. 7a gives the current density as a functionof time measured at various field-strengths for a MOScapacitor with a polysilicon gate. The current densityat first gradually decreases, then after a time suddenlyincreases, indicating that the oxide film has brokendown. The breakdown is very rapid; it is complete inless than 100 ns.The effect of breakdown on the device on a micro-

scopic scale is shown in fig. 7b. At the place where the

0.0.1

I E = 9.9 x IOsV/cm2 ID.33 10..84 11.0

ooty=Sil-}125nmS/02p-Si(+)

J

t 0.1

G.1 10. 10.0. 10.0.0.5-- t

1

bFig. 7. a) Current density J as a function of time t in a MOS capac-itor for four field-strengths E. After a slow decrease, J suddenlyrises sharply and the film breaks down. The time to breakdowndecreases as the field-strength is increased. b) Scanning electron mi-crograph (each dash represents 1 urn) of a failed MOS capacitorconsisting of n-doped silicon, a 40-nm thick Si02 film and a poly-silicon gate. The gate voltage was negative and the area of thecapacitor was 0.2 mm". At breakdown a crater was formed thatpenetrated right through into the silicon. After the first breakdowna voltage was applied to the capacitor again until it broke downonce more, and a second crater was formed.

film broke down the polysilicon has melted and a cra-ter has formed with a diameter of 4 to 5 urn. The outerring of the crater consists of molten polysilicon, andthe hole in the centre extends into the silicon sub-strate. The polysilicon often draws back from the cen-tre of the crater, probably because of the surface ten-sion of the molten gate material. When this happens,the oxide film continues to act as an insulator and avoltage can again be applied to the device until there isa second breakdown. Then a second crater forms,which resembles the first one (fig. 7b). The occurrenceof holes in the silicon substrate with a diameter of1.5 urn indicates that the energy density at breakdownis very high.

The effect of breakdown at constant current isshown in fig. 8 for four very different current values.The dimensions of the craters appear to be virtuallyindependent of the current. It can also been seen thatthe craters generally form at the corners and edges ofthe device. This is not so surprising, since these are theplaces where the highest field-strength would be ex-pected.

Defect-related and intrinsic breakdown

The breakdown of a MOS capacitor often takesplace at a weak spot, a defect, in the oxide film. Thedefect may have been caused during manufacture bythe incorporation of impurities or by the formation ofhair-line cracks, asperities or pinholes. Defects mayalso be introduced when the gate is deposited. Break-down at a defect will occur at a lower field-strengththan intrinsic breakdown, i.e. breakdown for a filmwith no defects. If there are many defects, the break-down will occur at the weakest spot. In general, there-fore, the breakdown field-stength will decrease as thenumber of defects in the film increases.Defect-related breakdown can clearly be distin-

guished from intrinsic breakdown in a statistical anal-ysis of the results of tests on a large number of ca-pacitors nor This analysis uses the same sort of prob-ability calculation as would be used for the breakingof chains at the weakest link. A test capacitor, consid-ered as an imaginary row of capacitors connected inparallel, will fail when the weakest capacitor in therow breaks down. The percentage of failed capacitors(F) is plotted on probability paper. This means thatln{ln(l - F)-I) instead of Fis plotted as a function ofa variable parameter, such as the field-strength E. Theadvantage of this is that it is easier to make a distinc-tion between defect-related breakdown and intrinsicbreakdown. It also offers advantages for predictingthe behaviour of electronic devices from the results ofmeasurements on smaller or less complicated devices.For example, if we have a large number of capacitors

336 D. R. WOLTERS Philips Tech. Rev. 43, No. 11/12

a b

d

Fig. 8. Scanning electron micrographs (scale division I urn) of craters formed during breakdownof MOS capacitors for different current values: a) 10 nA. b) lOO nA. c) 1 ~A. d) 10 ~A. Thedimensions of the craters are virtually independent of the current. The craters usually form at cor-ners and edges of the device.

containing defects and connected in parallel, then to agood approximation [11]:

where A is the area of the individual capacitors, andCl and C2 depend on the distribution of the defectsand the number of observations.Fig.9 gives a plot of In {ln(l - F)-I] as a function

of the field-strength E for 12000 capacitors, each withan area of 0.02 mm". On increasing the field-strengtha gradual rise is first observed, followed by a verysteep increase atE"'" 9x 106 V/cm, where Fbecomesalmost 100070.From the variation of F with E it maybe deduced that in about 7070of cases the breakdownis defect-related. The other 93070fail at practically thesame field-strength, and we can therefore assume thatthese breakdowns are intrinsic.If we now consider the capacitors in groups of say

400, we find that breakdown in a group occurs as soon

as the weakest capacitor fails. The probability ofbreakdown will increase to the same extent as it wouldif the area were increased by a factor of 400. The re-sults for the breakdown distribution are also given infig.9. As eq. (15) predicts, a straight line is obtained,shifted in the vertical direction by In 400 with respectto the curve for the single capacitors.The defect density D can be derived from the point

where there is a sudden increase in the slope of thecurve for the single capacitors. When this point hasbeen reached all the capacitors with defect-relatedbreakdown have been detected. If the defects are ran-domly distributed over the surface, a Poisson distri-bution may be assumed. The probability Fk that oneor more defects will be present in an area A is thengiven by:

I (AD)m exp( - AD)rn!

(16)m=l

Philips Tech. Rev. 43, No. 11/12 OXIDE FILM IN MOS DEVICES 337

The probability of finding capacitors without any de-fects is then:

(AD)O exp( ~ AD)I~Fk= =exp(~AD). (17)

Ol

Taking Fç = 711/0and A = 0.02 mm", it follows fromthis that D = 3.7 X 102 cm-2•It is also possible to demonstrate indirectly that the

failures to the left of the sharp increase in the slope ofthe curve are due entirely to defects. To demonstratethis, capacitors were made with a much lower defectdensity than the value given above. Fig. 10 shows thatin this case all 16000 capacitors tested failed at vir-

3in (In (1-Fr) /' I 99%

t 08mm~ t 63 F

/ ) 20 tVol' (nWO

-32 VO 5

1002mm <I'd

/ Alr-)-6 00 40nm 5i02 0.25

oJ p=Si !«)

Is' 0 0.055

0 4 8 12x 106 V/cm-E

Fig. 9. Lower curve: Breakdown distribution of 12000 MOS capac-itors of area 0.02 mm". The value of ln] In(J - F)-I} is plotted as afunction of the field-strength E; F is the percentage of failed capac-itors. There is a sharp increase in the curve at about 9 x 106 V/cm,where F is about 70/0. Above this value there is a very steep increasein F and hence in 1n{ln(1 - F)-I}. Upper curve: Breakdown distri-bution for groups of 400 capacitors, with a combined area of8 mm", As eq. (15) predicts, the points lie on a straight line shiftedby In 400 with respect to the lower curve.

3In {In (1-Ft) Alr-) 00

99%

154nm 5iOz F

t 0 p-5i t+) 631 20 t0

-3 5

1

0.25

0.055

12x 106V/cm

-6

o 8-E

Fig.IO. Breakdown distribution for 16000 capacitors, each with anarea of 0.02 mm". The capacitors contain so few defects that theyonly give intrinsic breakdown, and all of them fail at virtually thesame field-strength.

tually the same field-strength. This points to intrinsicbreakdown as the sole reason for failure. It can be de-duced from the absence of defect-related breakdownthat the defect density here must be less than 0.3 cm".

Field-dependent and time-dependent breakdown

Instead of testing with increasing field-strength, wecan also test the capacitors by applying a constantfield and then measuring the time to the moment ofbreakdown, as shown in fig.7a. This was done forfour groups of 900 capacitors on a slice on which16000 capacitors had first been tested with a varyingelectric field. These had a high defect density becauseof the incorporation of large amounts of impurities.Fig. 11a shows the breakdown distribution with in-creasing field-strength. The transition to intrinsicbreakdown is found at 13x 106 V/cm, where abouthalf of the capacitors fail. On the basis of this distri-

3~----------------~In (In(1-F)~

t a

-6

5

AI(-)99%11rim Siû»

p-Si(+)

0.,........-/0 114 J

/

11.1 ,

o E=10.8Xl06v/cmjl 0.250.055

12x 1dV/cm

63 F

t20.

-3

a 8-E

3r-----------------~(

') A/{-) ~ 32 1In In(1-FI n omsto, I I! ;t a p-Si(+) I o°:l~)

~<p~o~oo~~o 00

-3 00

0.25

0..055

99%

6320.5

F

t1 E = 10.8 x 10

6V/cm

2 11.13 11.44 11.6

-6

0.01 0.1 10 1005-tb

Fig. 11. a) Breakdown distribution for MOS capacitors with a highdefect density. The arrows indicate the values of the field E at whichtime-dependent tests were carried out. b) Breakdown distribution intime-dependent tests on capacitors of (a) for four different field-strengths E. The sudden increases in the curves occur at about thesame value of F.

[u] E. J. Gumbel, Statistics of extremes, Columbia Univ. Press,New York 1958.

338 D. R. WOLTERS Philips Tech. Rev. 43, No. 11/12

bution four groups of 'virgin' capacitors were testedat constant field, for four values of E that were signifi-cantly lower than the value for intrinsic breakdown.Fig. 11b shows the result in breakdown distributionsas a function of time. The curves are not only very sim-ilar but they also resemble the distribution in fig. IIa.The defect densities that can be calculated from the

various changes in the slope of the curves are almostidentical. A similar correspondence between defectdensities determined from field-dependent and time-dependent tests is also found for slices with fewer de-fects. These results indicate that capacitors that failbecause of defect-related breakdown at a relativelyweak field will also fail in a constant field after a rela-tively short time (and vice versa).Other methods for applying the field to the capac-

itor can be compared in the same way. Fig. 12 givesthe distribution for constant field and for constantcurrent. For convenience the breakdown distributionis shown in both cases as a function of the integratedcharge transfer per unit area (Qbd). The curves are vir-tually coincident above a particular value of Qbd, be-fore the change in slope. In short, the way in whichthe field is applied for breakdown tests on MOScapacitors is not important.

2r-----------------------~In {In (1-FJ')

i 0

-2

po/y-Si(-)

llnm SiOzp- Si !+)

-4

10-· 10-2 1Cl cm'-Qbd

Fig. 12. Breakdown distribution for MOS capacitors as a functionof the integrated charge transferred per unit area (Qbd) at a constantcurrent of 40 u A (curve a) and at a constant voltage of 12.9 V(curve b). Beyond Qbd values greater than 0.01 C/cm2 the curvesare virtually coincident.

Principal parameter for intrinsic breakdown

The tests on MOS capacitors indicate that the cir-cumstances that lead to intrinsic breakdown do notdepend essentially on the method of application of thefield. This can be seen if we consider the time thatelapses before breakdown [12]. The measured pointsin fig. Ila related to measurements in which the field-

strength was increased by 2 x 107 V lcm per second.An increase in the field-strength from 11 X 106 V Icmto 13x106V/cm thus takes about O.Is. If thecurves in fig. 11b are extrapolated to a curve for13X 106 Vlcm, the time obtained has about this value.The simplest method of testing is to use a constant

current, as in curve a of fig. 12. In this method thefield-strength and the time are measured, and thecharge transfer at breakdown is proportional to time.We used this method to test a large number of capac-itors in which there where differences in gate material,the thickness of the oxide film (between 10 and 50 nm)and the manufacturing process. The current densitywas varied and only the intrinsic breakdown was stud-ied. Fig. 13 gives a plot of the measured time to break-down (tbd) as a function of current density]. For nottoo high values of J, logzsa is given to a good approxi-mation by:

log tbd = - log] + c, (18)

where the constant c is determined by the characteris-tics of the capacitor. The total charge transferred perunit area (Qbd) is given by:

(19)

Equations (18) and (19) indicate that Qbd is deter-mined entirely by the capacitor and does not dependon the conditions in which the breakdown is produced.This indicates that Qbd is the quantity that mostaffects intrinsic breakdown. In other words: a capac-itor fails as soon as a critical amount of charge has

10·5 .-------------------------------~

tbd

i102

1

1-)

Fig. 13. Log-log plot of the time to breakdown (tbd) against currentdensity J, for MOS capacitors with differences in the gate (alumin-ium or polysilicon), in the thickness of the Si02 film (between 10and 50 nm) and in the manufacturing process. If the current den-sities are not too high, straight lines with a slope of about - I areobtained.

Philips Tech. Rev. 43, No. ll/12 OXIDE FILM IN MOS DEVICES 339

been transferred through the film, however this trans-fer was produced.

The value of Qbd varies little in a wide range of cur-rent densities. At very high current densities, above acritical value J«, there is often a sharp decrease in thevalue of Qbd; this decrease also depends on the direc-tion of the field; see jig. l4a. If the gate voltage is neg-ative, Jer is much lower (by a factor of ten) and the de-crease in Qbd is steeper than with a positive gate volt-age. The fall in Qbd beyond Jer is closely connectedwith the change in the gate voltage (Vbd) necessary tokeep the current constant; see fig. 14b. At moderatecurrent densities, Vbd increases linearly with 10gJ.Beyond J«, however, there is either a steep rise in Vbd(at a negative gate voltage) or a steep fall (at a positivegate voltage). These effects are attributed to the accu-mulation of space charge in the film, which is depen-dent on the direction of the field. This will be dis-cussed later.

1C/cm2~-----------------------------,

o.:t 10-2

-J

24

28 V AI23nm 5;02s-s.

b

Fig.14. a) Amount of charge transferred per unit area beforebreakdown (Qbd) as a function of current density J for MOS capac-itors with a positive or a negative voltage on the aluminium gate.Below a critical value Jcr the current density has little effect on Qbd,but above it there is a decrease that depends strongly on the direc-tion of the field. b) Breakdown voltage Vbd as a function of currentdensity J for these two cases. Beyond J = Jcr the value of Vbdincreases sharply when the gate voltage is negative and decreasessharply when the gate voltage is positive.

108 S2«: -0

i 107

106

10510-4

Al (-)-0--........ 23nm 5;02" p-Si(+)0\

L\0_0_

-- JFig. IS. Resistance of a MOS capacitor after breakdown (Rbd) as afunction of current density J at breakdown. Beyond J = Jcr thevalue of Rbd decreases sharply with J.

Another result that is closely related to the decreaseof Qbd at high current densities concerns the resist-ance of the capacitor after breakdown (Rbd). Fig.15shows Rbd as a function of the current density atbreakdown. Beyond Jer the value of Rbd falls by twoorders of magnitude. Clearly, a breakdown at J> Jer

causes a different kind of damage from that at J < Jer.From the results in figs 14 and 15 we can conclude

that different mechanisms enter into the breakdownon opposited sides of J = Jer. A model will now bepresented that gives a good explanation of the behav-iour at both low and high current densities.

Mechanism for wear and intrinsic breakdown

The breakdown of a MOS capacitor with no defectsmay be regarded as a two-stage process. The leakageof charge first causes structural changes in the filmthat ultimately result in the formation of a low-resist-ance path between the electrodes. The capacitor candischarge along this path. The energy released causespermanent damage to the oxide film, as can be seen infigs 7band 8. The leaking charge wears out the film,so that it gradually degenerates and finally breaksdown.

This model explains the test results described abovefairly well, especially the behaviour at moderate cur-rent densities. The greater the leakage in the oxidefilm, the sooner it will fail. How the leakage arises isimmaterial. The capacitor fails as soon as a particularamount of charge has been transferred. We shall nowbriefly consider why this is so.

Breakdown at constant Qi«

From the observation that Qbd does not vary muchat moderate currents and fields it may be deduced that

[12J D. R. Wolters and J. J. van der Schoot, Dielectric breakdownin MOS devices, Part II: Conditions for the intrinsic break-down, Philips J. Res. 40,137-163, 1985.

340 D. R. WOLTERS Philips Tech. Rev. 43, No.ll/12

collision ionization [13) and ion migration (14) playlittle part in the breakdown. Mechanisms based on thekinetic energy of the charge carriers predict that Qbdwill be closely dependent on the injection rate and thefield-strength. The dependence on the previous historyof the device excludes mechanisms with an avalanchetype of breakdown.

So how can we explain the constancy of Qbd whileaccepting that the total of dissipated energy is propor-tional to the applied voltage? This question can onlybe answered if the kinetic energy does not contributeto the breakdown. To understand this, we have toconsider the energy of electrons injected into the Si02film; see fig. 16. Electrons that tunnel through the po-

Ec--~E; ----,

IIIIIIIt\.1evI EFII

Si(-) M(+)

Fig. 16. Energy diagram for electron transfer in a MOS capacitor.E; upper edge of the valence band. E; lower edge of the conductionband. Ep Fermi level of the metal. The energy gain for an electronis much greater in the transition to the metal M than in migration inthe conduction band of Si02.

tential barrier from the silicon into the Si02 film havea high potential energy in the conduction band. Pro-vided the values of the electric field-strength are nottoo high, the kinetic energy of the electrons in theconduction band will be low because of interactionswith the vibrating lattice atoms (phonon interactions)in the film. Since the interaction length is no morethan 2 to 4 nm, the energy gain in a field of 5 x 106V/cmwill be no greater than 1 to 2 eV. The number of elec-trons with this gain in energy will also be very small.As the minimum energy required to break a silicon-oxygen bond is about 4 eV, it follows that the kineticenergy of the electrons in the conduction band isinsufficient to cause any significant damage.

The energy dissipated by the electrons becomesconsiderable, however, if they are emitted into thegate from the Si02 conduction band or if they aretrapped in centres in the Si02 film. The high energy,the sum of the potential energy in the conductionband and the acquired kinetic energy, is dissipated ina distance that is short compared with the thickness ofthe film. Consequently the density of the energy dissi-

pation is much higher than that of the kinetic energydissipation in the conduction band, which is distrib-uted throughout the entire volume. Since all the in-jected electrons have a high potential energy that theymust dissipate on leaving the Si02 conduction band,the dissipation that ultimately leads to breakdown isentirely determined by the number of injected elec-trons. The damage produced is permanent, so that theeffect is cumulative.

Behaviour at high current densities

As the field-strength or the current density increasesthe injected electrons acquire more and more kineticenergy, while the potential energy remains virtuallyconstant. A field-strength could then be reached forwhich Qbd was field-dependent. This might explainthe decrease in Qbd at J> Jer (fig. 14a), except that ata positive gate voltage the injection voltage at break-down (Vbd) decreases instead of increasing with J(fig. 14b).

A better explanation can be obtained if we assumethat the trapping centres in the film are regularly filledand emptied while a field is applied to the film. At lowcurrent densities (J<Jer) most of the centres will noton average be occupied. Space-charge effects will thenbe negligible, and the injection of electrons will behomogeneous over the entire area of the electrode. Athigh current densities (J> Jer) the mean occupancyof the trapping centres can be more than 50% [12), sothat space-charge effects will be significant. This canbe seen in the effect that the direction of the field hason the injection voltage at breakdown (fig. 14b). Ifthere are trapping centres close to an aluminium gate,then at a negative gate voltage the injection of elec-trons will be opposed by the formation of a negativespace charge. This means that Vbd becomes higher. At apositive gate voltage a positive space charge is formed.This stimulates the injection of electrons from the sili-con, so that Vbd becomes lower.

For both directions of the field the injection will beinhomogeneous at high current densities. When thegate voltage is negative the injection will take placemainly in regions of low space-charge density. Thecurrent density will then be very high .locally, so thatat such places Qbd will be reached while the amount ofinjected charge is still relatively small. When the gatevoltage is positive, the injection will take place mainlyin regions where the space-charge density is high. Butthis also means that J will be higher locally and thatthe value of Qbd will be reached earlier.

Confirmation of the model outlined here is foundfrom measurements of Qbd for capacitors with dif-ferent gates and different thicknesses of the oxidefilm; see fig. 17. In the vicinity of an aluminium gate

Philips Tech. Rev. 43, No.ll/12 OXIDE FILM IN MOS DEVICES 341

102Clcm' -"_o __ o

o.,Î --0--°-Z__o

10-20~-----2~0~-----4~0-n-m~

-d

Fig.17. Amount of charge transferred per unit area up to break-down ({?J,d) plotted as a function of the thickness d of the oxide filmfor MOS capacitors with a polysilicon and an aluminium gate. Inpolysilicon, Qbd is a hundred times higher. In both cases, log Qbd

decreases linearly with d.

more centres will be formed than in the vicinity of apolysilicon gate. This means that the space-chargeeffects will be more pronounced with aluminium, andthe film will therefore break down at a lower valueof Q. In general, Qbd decreases exponentially withfilm thickness. In thicker films the trapping probabil-ity is higher, so that the space-charge effects will bemore marked.

Wear before breakdown

There are now sufficient indications that chargeleakage causes wear. For a given amount of trans-ferred charge, for example, breakdown will occurirrespective of the number of current interruptions.Cumulative damage of this nature can be consideredto be the result of the formation of a discharge pat-tern due to the injection of electrons [151 [161. Thispattern has a tree structure, as illustrated infig. 18. Asthe damage increases, the structure spreads, and thetree acquires more and thicker branches. It appearsthat the injected electrons by preference lose their po-tential energy at places that have been damagedbefore. The growth of the discharge pattern continuesuntil it forms a low-resistance path between the twoelectrodes, and the capacitor discharges along thispath.

This picture is rather like the pattern produced byrivers eroding a landscape. The mechanism for theformation of a discharge pattern can be comparedwith the erosion caused by the flowing water. Thaterosion is also cumulative: the wear is not related tothe rate of flow but to the total volume of the flowingwater. Just as small streams eventually form a broadriver and leave deep traces in the landscape, so theleaking charge wears away the insulating film andfinally destroys it.

Both the damage and the breakdown require a cer-tain amount of energy. A simple representation of the

energy content of a charged capacitor is given infig. 19 in the form of a plot of the applied voltage Vasa function of the charge supplied Q. The area underthe curve is proportional to the amount of energy sup-plied. As long as no charge leaks through the dielec-tric, the stored charge is proportional to V. The pro-portionality factor is the capacitance C, and thestored energy is !CV2

• Above a particular voltage (VI)the curve departs from a straight line as a result ofcharge leaking through the Si02 film. At a voltage V2the stored energy is given by !CV~; the remainder ofthe area under the curve up to Q = Q2 gives the energythat has been dissipated in the dielectric and has been

Fig.18. Tree-shaped discharge pattern after injection of 3-MeVelectrons into an insulator that was then earthed at a centralpoint [16].

[13] See the book by E. H. Nicollian and J. R. Brews, MOS (MetalOxide Semiconductor) physics and technology, Wiley, NewYork 1982, and the articles by N. Klein:Electrical breakdown in thin dielectric films, J. Electrochem.Soc. 116, 963-972, 1969;Switching and breakdown in films, Thin Solid Films 7, 149-177, 1971;Electrical breakdown of insulators by one-carrier impact ion-ization, J. Appl. Phys. 53, 5828-5839, 1982.

[14] See C. M. Osburn and D. W. Ormond, Dielectric breakdownin silicon dioxide films on silicon, J. Electrochem. Soc. 119,591-603, 1972;H. J. de Wit, C. Wijenberg and C. Crevecoeur, The dielectricbreakdown of anodic aluminium oxide, J. Electrochem. Soc.123, 1479-1486, 1976.

[Ió] D. R. Waiters and J. J. van der Schoot, Dielectric breakdownin MOS devices, Part Ill: The damage leading to breakdown,Philips J. Res. 40, 164-192, 1985.

[16] J. G. Trump and K. A. Wright, Injection of megavolt elec-trons into solid dielectrics, Mater. Res. Bull. 6, 1075-1084,1971.

342 OXIDE FILM IN MOS DEVICES Philips Tech. Rev. 43, No. 11(12

vt

---QFig.19. Schematic representation of the energy content of a chargedcapacitor. The voltage V is plotted as a function of the charge sup-plied Q. The area of a shaded region corresponds to the conser-vatively stored energy and is equal to !CV2, where C is the ca-pacitance of the device. Below V = VI the value of V increaseslinearly with Q: all the energy supplied is conservatively stored.Above V= VI there is a less marked increase with Q because ofcharge leakage. At V= V2 the stored energy is !CV~; the remainderof the area under the curve up to Q = Q2 gives the energy dissipatedby the capacitor. At V= Vbd, where Q= Qbd, the energy dissipa-tion is so great that the film breaks down. The stored energy (!CV~d)is then released and causes permanent damage to the capacitor.

lost, most of it as heat. If the voltage is increased stillfurther, then at Vbd the total dissipated energy willdamage the capacitor to such an extent that break-down occurs. The stored energy is then released andcauses the damage observed after breakdown (see forexample figs 7band 8). The variation in the crater di-mensions with the area of the capacitors confirms thatthe damage is entirely due to the release of the storedenergy (~CV~d).

Analogy with mechanical wear

The behaviour of the oxide film in an operatingMOS capacitor can be compared with the behaviourof solid materials under mechanical stress. In bothcases there is a force or a field that causes a displace-ment of material in the mechanical system or a dis-placement of charge in the capacitor. The energy sup-plied is to some extent stored conservatively, and tosome extent lost as heat. In the conservative storageof energy the mechanical energy is proportional to the

extension (elastic behaviour). If mechanical energy islost as heat, then the energy is no longer proportionalto the extension (plastic behaviour). Something sim-ilar takes place in a capacitor: the stored energy isproportional to the charge, until the film starts to leakand energy is converted into heat. Beyond a certainextension a material will often start to oppose furtherextension ('stress hardening'). The analogy here isthat charged centres oppose further injection ofcharge because of the Coulomb repulsion.

The collapse or fracture of material follows theapplication of a short-term high stress or a lowerstress applied over a longer period (fracture due tocreep or fatigue). A dielectric film with a high voltageacross it breaks down in a very short time. At a lowervoltage it takes longer for breakdown to occur. Andjust as cracks and dislocations accelerate mechanicalwear, so dielectric wear is accelerated by the presenceof defects and charges.

Finally, there is also an analogy with the behaviourof materials subject to rapidly changing stress. A solidmaterial that gives considerable extension when sub-jected to a slowly varying stress may break withoutany significant extension if the rate at which the stressis applied exceeds a critical value. Below this value thematerial is considered to be ductile, above it brittle.The deformation after brittle fracture is relativelygreat. Something similar is found in the electricalbehaviour of an oxide film. Above a certain injectionrate there is a marked decrease in Qbd (fig. 14a) andthe structure of the film is altered to such an extentthat the resistance also decreases markedly after thebreakdown (fig. IS).

Summary. Charge trapping by the oxide film in a MOS capacitorand the current flowing through it are greatly affected by the inter-action between injected electrons and trapped electrons. If an elec-tric field is applied to the film it eventually breaks down. This canhappen very quickly i f the field-strength is high, if a large amountof charge has leaked through the film or if there are many defects.An important factor in breakdown is the amount of charge trans-ferred. The mechanism for wear and breakdown is reminiscent ofthe erosion of a landscape by rivers, and there is an analogy withthe occurrence of mechanical wear followed by fracture.

Philips Tech. Rev. 43, No.llfI2, Dec. 1987 343

ND NOW 198'1937 THEN

High-voltage rectifiers

The term 'solid-state' probably first makes us think of integrated circuitsfor low-voltage applications like digital memories or microprocessors. Butthere are other fields in which solid-state devices have been responsible forradical changes.

The figure [*1 at the right shows the single-phase rectifier DCG5/30 11 of1937, for a current of 6 A and a voltage of 6 kV. This 'rectifying valve' had anincandescent cathode and a mercury-vapour filling. The overall length wasapproximately 56 cm. A mica cone at the top trapped the rising hot air toprevent condensation of mercury in the top bulb. The ignition voltage of this'relay valve' could be controlled by varying the voltage on the metal ring justbelow the upper sphere.

In 1987 high-voltage rectifiers look rather different. The figure below showsa modern solid-state rectifier of the type OSS9115-4A, also suitable for a volt-age of 6 kV and a current of 6A (with oil cooling) or 3.5 A (with air cooling).The rectifier consists of a series circuit of four specially mounted diodes('diode cells'), whose operation is based on the avalanche effect. A separatediode cell and a separate diode are also shown in the photograph. Up to 36diode cells can be connected in series, giving rectifiers that will work up to54 kV. The diode cells are mounted on a non-flammable triangular plastic core.The core is assembled as desired from modules about 4 cm long, which can

each contain up to three diodecells. These basic units arealso convenient for use inslightly different diode con-figurations such as voltagedoublers or full-wave recti-fiers.

[*] From Philips Technical Review,April 1937.