On the accuracy of the quartz-crystal microbalance (QCM) in thin-film depositions

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ELSEVIER Sensor-, ;rod ,.\ctuattws A 63 ( 1007 ) 41 4~,

A

On the accuracy of the quartz-crystal microbalance (QCM) in thin-film depositions

Abdul Wajid t I,,'vhohl hlli,'on. "lifo "Fe~'iu~olo~v I'/a,','. I:~l.~t 5w'~:c~l~'. NY 13057. I :SA

Received 12 |:chruarv Iqt)6: rc~,i,,cd 13 Januur', It)07: accepted 14 January It)07

Abstract

"File quartz-crystal microbalancc ( QCM ) is traditionally ascd as at thin-lihn deposition monitor. The most commonly used monitor crystal is AT-cut quartz vibrating in it.', thickness .',hear mode. The mass of the deposited film on the quartz c6stal's surface is indicated by the change of its resonance frequency. With the introduction of the :-matchtX~ technique in the 1970s, the accuracy of the QCM dramatically improved. This technique takes into accounl the mismatch of acoustic impedance betv,een the quartz crystal and the deposited thin film. in recent years, new methodologies have bccn propo.xed to improve the accuracy of the QCM even further. For many years, we have carefully gathered a vast amount of data on the deposition of various metals, dielectrics and alloys on quartz crystals. In thi~ paper, we report results of the comparison of the recently proposed methods with the =-match technique, using the gravimetric mcuxurement of deposited mass on the quartz cu,'stals as the benchmark. We also report an extension formula, which bu,adens the validity of the --martin technique beyond a normalized frequency shift of 5()5~. ~O 1997 Elsevier Science S.A.

Keywonl.~: Quarlz-crysml nlicl'ohalancc~,: Thin l i lm~. Z-Iltalch techlliquc

I. Introduction

The quartz-crystal microhakmce ( QCN! ) h':s been widely ttsed tbr monitoring and control of thin-lilm growth in physical vapor deposition and sputtering processes. Ahhough in recent years, novel applications of tht: QCM in gaseous and liquid environments have been reported, controlling the rate of growlh of thin solid films still remains the pnncipai application of QCM instruments. In a typical application, a quartz crystal with appropriate elecirodes is placed in the deposititm chamber next to the substrate to be coated and is exposed to the deposition material's vapors through a suitably designed aperture. The materials that condense on the face of this monitor crystal decrease its resonance frequency. From the changes in the resonance frequency of the crystal, the amount of mass deposited on its surface is deduced. The exact meth- odology of interpreting this frequency change into deposited tilm thickness has, however, evolved ] I I over the last four decades,

The most widely used monitor crystal for the QCM is AT- cut quartz, which vibraies in its thickness shear mode. SuFe- rior temperature stability, excellent mass sensitivity and case of manufactttring makes this cut of quartz crystal a prime

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choice. Generally, one surface of the crystal is often rendered into a spherical shape ~ contoured ) to confine the vibrational energy to the central portion of the crystal, resulting in reduced coupling to unwanted modes [2] at the muunting ett ' . ,es w '

Sanerbrcy's 13 ] original formula, known as the frequency- measurement technique, relates the deposited mass to the concomitant rcs,mancc frequency change, written as

m,/m~ = (/"'~l-/"~ ) l E i ( I )

Here, mt and m,i represent areal mass d~nsities [ 3 ] or mass per unit area of the deposited film and quartz, respectively. The quantities Fq and/"~, represent the thickness shear mode resonance frequencies of the quartz crystal before and after coating, respectively. Thus, from the knowledge of the den- sities of quartz and the film material, its thickness is easily determined. The above formula is satisfactory for mass loads, m,/mq, of less than 2%.

Behrndt 141 extended the range of mass loads to alxmt loft-, by introducing a modification in the form

m , l m, I = ( V'q - !"~ ) I F , ( 2 )

This is known as the period-measurement technique and Ii:.ts been satisfactory for many applications. Miller and Bolef l 51 and, subsequently, Lu and Lewis 161 trea:ed the problem

42 A. W+aiid l Sensr, r,v and Actuatnrs A 63 f lOO7j 41+46

of lilm deposition on t! quartz crystal as that of a one-dimensional composite mechanical resonator, taking into account the multiple reflections occurring tit the quartz-tilm interface dtie to mismatch in the elastic properties. The result is expressed as

Z<~tan ( rd:< t k,~ ) + Z, tan( -rrF<.l t.] ) = 0 < 3 )

Here+ Zq and Zf. respectively, represent the specilic acoustic impedance of the quartz and the film material. The quantity k~ = Vt/211~ denotes the resonance frequency o1' the deposited film. had it been vibrating alone. Here+ V, and h~ denote the speed of sound in the film and the thickness of the deposited film. respectively. Likewise, the resonance frequency of the uncoated quartz. I.] r is also related to the speed of sound in quartz. V,,, ~md Ihe thickness of the quartz crystal. It,, by F,~ = V,/2hq. Delining two dimensionless quantities, reduced mass. m = m,/mq = (prh~) / (pqhq) and acoustic impedance ratio or :-ratio.: = Zq/Z, = ( pq V,,) 1(prV,), we can rewrite Eq < 3) to obtain

m = -/:<,/( +'r :/+'< )arctan[ : tan( tr/.~ / Fq) ] ( 4 )

Then. by using the aforementioned relations, we can cal- culate the deposited film's thickness, h , as

h I = mZ, i/( 2pfF, l) ( 5 )

Eqs. (4) and (5) define the so-called ;,-match [7[ technique, which drastically improved the accuracy of thickness prediction. This new lechnique quickly became the state-of- the-art in commercial quartz-crystal thickness monitoring and control instrumenls. The accuracy of the z-match technique has been empirically verified and well substantiated [8] by many users over many years ofuse in a variety of applications.

2. Attempts at improvement

The great success of the :-match technique appears a bit puzzlintz, considering the severe simplifying assumptions inherent in its basic formulation 1 I I. However, when exam- ined in depth, it is found to be adequate for explaining the mass-~;ensing properties of quartz crystals, as has been etaborated elsewhere 19]. One of the objectit;ns to the mechanical mode[ of the z-match technique is that it completely ignores the implications of piezoelectric loading on the resonance frequencies. Attempts have been made to incor- porate the effects of piezoelectric loading on the composite resonator 18,10] model. Bones I lO], in particuhtr, utilized the transmission network analog ofa vibratintz quartz crystal to derive a ntodified :-match theory, which can be written as

K( ~l"</l:,~)Zqtan< ~/:<.1F,+) + Zttan( rd:<tF, I =(t (6)

The scaling [actor K(,I) is expressed as

Kl .~ )= l l - (2k ' l .~ ) tan l .~ t2 i l l l l - ¢k " l . tW, in(.~l] (7i

The electromechanical coupling constant k-' is about 0.007 for AT-cut quartz, Clearly, if k 2 is ignored. Eq. (6) reduces to the Lu-Lewis equation, Eq. ( 3 ).

Recently, Mecea [ 11 I proposed tin energy-transfer model of the vibrating quartz crystal. He considered the deposited film as an inert load tin the top of the quartz crystal. Thus, unlike the :-match technique, it ignores the implications of the elastic properties of the deposited film. In summary, the mass load in Mecca's model is independent of the ~-ratio and is expressed as

m = [ (Fq/F<)'-- 11/2 (8~

In Fig. I, we have plotted the reduced mass. m. as a func- lion of the normalized frequency shift, (i.', I -b'~ )/F< r using Eqs. ( t ), ( 2 ). ( 4 ), (6) anti ( 8 ). The traces A, B, and E tire independent of ~:-ratio. The ;.-ratio is assumed to be O. I for the traces CI, DI and 2.5 for the traces C2, D2. As can be seen from the Figure. the curves corresponding to C and D are nearly indistinguishable for tiny given z-ratio value. This is not surprising, because the electromechanieal coupliwg constant in AT-cut quartz is very small and therefore, the scaling hlctor in Eq. ( 7 ) is close to unity, rendering Eq. (6) nearly identical to Eq. ( 3 ). Thus, the difference between the inodified and the conventional ~-match techniques is negligible.

One genuine inconvenience of the z-match technique is that the z-ratio of the deposition m~tterial must be known. Often the :-ratio of the deposited thin lilm is different from that of the bulk material, because it is sensitive to process parameters. For many exotic materials and customized alloys, the :-ratio is not even known+ Bones I I01 proposed using the fundamental and the third quasi-harmonic mode frequencies

10+ : A - Frequency measurement [ ' B - Period measurement C1 i

C1, C2 - Z-match . i 0.8 D1, D2. Modified z-match, ~Benes D1

E- Energy Transfer, Mecca

J

0.2 . . . . . . . ~2 m

0.0 + <: + . . . . . . 0.00 005 0.10 0.15 0.20 0.25 0.30 0,35

(Fq-Fc)/Fq j : i~ ~ ~ ~ ` ~ : ~ ` ( ~ 1 ~ v . ~ i ~ : ` ~ h ~ d ~ ~.(~ C~M~l~1~ ~Ct~uCcd ~n;~.~`q~ = /ni /

m,+. I'Ioul the Imrm,dizcd frequency q l i l t , ( I,,~ I . )/I.~r Fhe trace A is b:lsed L~ll the Ireqtl'.:h .'.-mqa:,llrcll|¢rlt l¢~_'hnlq,.,'. ~:(, ~, 1~ ti~lk'¢ |:~ on Ih¢ Period-

inc-:..,.i:-91ni.'nl te+.llniqu,c, l+i,l . ( +' ): l rau 'cs C I, ( . '2 on the .-l l lalC]l tcchniq t l i : ,

!)'t' I4 ); Ira:c,, 1)], D " 4+11 Hones" nlodi l icd I IOI :+match teclmique+ Eqs.

( 6 ) al|d 17 )'. trauc 1- is b;Jscd o1| M¢cca'n ener~,,~-tral|st'¢r I I I I modal, l k I.

( 8 ), For If:Ice,, ('1 il l l l j D I . the :+ratio i'~ ;lshUlllcd ILl b+ n. I . For trac¢s L'2 and I)2. it is 2.5. Th,: Ir:lees correspondin B Io (" and D are nearly idt 'ntk'al Ior a gix en ~ alu¢ o1 : nltio, bccam, c el + the ,.soak ¢lcctrom¢chanic'at c~. piing t;t)llslanl ill A'I+-cul quart,, ( W' = O J)07 )+

E

mmO.6: E :

~ 0 . 4

n¢

A. I,V@d / Senst,rs and A ,mator.~ A 63 ( 1997j 4 I--46 43

of a quartz crystal to determine the z-ratio and the reduced mass simultaneously. An alternative patented method [121 utilizes the small difference in the mass sensitivity between the fundamental and the first anharmonic modes of a contoured AT-cut quartz crystal. The frequency shifts of these two modes are utilized m detect changes in the effective shear modulus of the quartT-tilm composite resonator, thereby yielding the effective z-ratio of the deposited film material in real time. For many metals, alloys and sequential layers of dissimilar materials, this method resu'!s in significant improvement 191 in rate and thickness predictions. However. this is not an attempt to replace the one-dimensional mode! of the z-match technique. Rather, this is an enhancement to make the z-match technique more accurate and useful.

Mecca I I I I also points out an apparent mathematical inconsistency in the z-match technique. When the frequency shift reaches or exceeds 50% of the uncoated crystal's frequency. Eq. (4) yields a negative value for the reduced mass or fails altogether. This would imply that the :.-match technique could not be used lbr F,_./Fq <_ 0.5. In reality, this is not a problem at all. The monitor quartz crystal's frequency rarely shifts by 50%, because acoustic attenuation in the deposited material often terminates its useful life long before that. For a 6.0 MHz crystal, 1.0-1.5 MHz frequency shift i~t,m the deposition of metals is typical. Crystals u::ed for monitoring dielectric coatings I 13 ] last much less time. Besides, a slight misapplication of mathematics is also responsible tor this apparent shortcoming.

Eqs. (3) and (4) have been derived by applying appropriate boundary conditions to the solutions of the acoustic wave equation in the quartz-fihn composite resonato:'. The principal surlaces of the composite resonator are stress free, and stress and particle displacement arc continuous at the quartz-film interface [ I I. For an uncoated quartz crystal, the node for particle displacement is half way along the thickness direction. When a foreign film is deposited on the crystal, this node gradually moves closer !o the qtmrlz-film interface, eventually reaching it when F~ = I",/2. In this situation, the particle displacement is not only continuous, but also zero at the interface. This is precisely the reason why the tangent fimctions in Eq. (4) misbehave, It is easy to show that one of the admissible solutions implies F~ =/',1, or equivalently mz= I. With additional material deposited, the resonance frequency is further reduced, and the displacement node moves deeper into the film. This requires the muhiple-valued arctan function to be taken beyond its principal value. In summary,

, :-- ,~/( rrz,./"~)arctan[ z tan(7r~:.//:,,) I (ga)

for FJF,, >I).5

m = I / : for FJ[~,=O.5 (gb)

E 8 g / m~ z--.O.2 (

6

~ 4 21 /z=to

IX

2 ~ .......... / -- "" ~3"0

0.00 0.25 0.50 0.75 1.00 (Fq-Fc)/Fq

Fig. 2. Conventional z-match. Eq. (4). i~ ~,'alid for frequencies F,/F,.,>0.5. The extended :.-match technique. Eq. ~9). is plotted over a range of normalized lrequcncy shifts. I F,, - I i )/F.,. beyond 0.5. The traces are drawn fi~r .'.-ratios of 0.2 ( open square ). 0.5 ( open triangle). 1.0 (oper~ circle ) arid Y0 t tilled triangle). The, tlick line is according" to Mecca's ertergy-transfer I III model, Eq. (8). wh "h is independent of z-ratio.

furnish the complete solution, though only the first part is of any practical significance. It can be seen from Eq. (3) that, if FJFq < 0.5, it is necessary that ~F,:/F, have a value in the second or the fourth quadrant. In particular, as FclFq approaches 0.5 from the low side, F,JFr must approach 0.5, 1.5, etc., from the high side. Thus, as the film gradually grows from zero thickness, the quantity Fr correspondingly reduces in magnitude from infinity. Hence, at FJF,+=0.5, the first admissible solution is F~IF,=0.5. This corresponds to m = I/z. as given in Eq. (9) . Fig. 2 shows the reduced mass, m, computed on the basis of Eq. (9), plotted as a function of normalized frequency shift, ( Fq- F,:.)/Fq, for different values of z-ratios. Although Eq. (9) is defined piece wise, the plotted curves a~e smooth and continuous, attesting to the correctness of the above equation. Thus, the mathematical limitations of the conventional z-match technique are circum- vented. For comparison, Eq. (8) of Mecea's theory is also plotted in the same Figure.

3. Experimental

It is clear from Fig. I that the larger the frequency shift, the wider is the disagreement among different methods of mass calculation. Thus, if material is deposited on the quartz crystal in sufficiently thick layers, then the mass predictions by different methods could be directly compared with the gravimetricaUy measured mass of each layer.

The experimental procedure was quite straighttbrward. A monitor crystal was weighed before any coating had been applied and its fundamental mode frequency measured using a network/impedance analyzer (HP model 4194-A). The accuracy and resolution of this instrument was adequate. A digital microbalance (Sartorius model 2405), capable of I Isg resolution, was used for weighing the quartz crystals. After each layer of coating was applied, the crystal was carefully taken out from the deposition chamber, weighed and its

44 A. w~tjid / Sensors and Actuators A 63 (I Y97) 41~46

frequencies measured in the same manner. The process was repeated for each layer of material deposited. Since the crystal was exposed to the material through a circular aperture in the holder, the film's thickness could be easily calculated from the knowledge of the incremental mass. the exposed area and the material's bulk density.

The mass of a typical layer ranged from a few hundred to a few thousand micrograms. The apertures of crystal covers ranged from 8.25 to 11.75 mm in diameter, whereas the back- dectrode diameter on the quartz crystal was less than 7 ram. Thus. the active area of the crystal was fully covered by deposited material in all cases. A toolmaker's traveling microscope wa~ used to determine the radius of the aperture. The overall uncertainty in the gravimetrically measured thickness is about 1%.

We used electron-beam deposition, d,c. sputtering, r.f. sputtering and resistive source evaporation to deposit a wide variety 191 of materials, including pure metals, metal alloys, dielectric oxides and fluorides, sequential layers of dissimilar metals, alloys formed by co-deposition of metals and reac- tively formed oxides and nitrides. We used primarily 6 and 4 MHz piano-convex crystals. The vast amount of data were gathered over many years primarily to verify the z-match and the automatic z-ratio techniques.

4. Results

The reduced mass. m, of a layer of deposited film was calculated from the measured resonance frequencies using the z-match technique, Eq. (4~. Similar calculations were made using Benes" modified z-match technique, Eq. (6), and Mecea's theory, Eq. (8). The relationship in Eq. (5) we, s used to convert reduced mass into corresponding film thickness, using Zq= 8.765 × I06 MKS units. The values for Fq are 6.045 and 4.045 MHz for the nominal 6 and 4 MHz monitor crystals, respectively. Then, the predicted thickness was compared with the thickness computed from the gravimetrically determined mass. The frequency measurement technique, Eq. ( 1 ), and the period measurement technique, Eq. (2), are not included in this comparison, as they have been previously proven to be of limited use, We also avoided comparison with the automatic z-ratio technique, as it has been discussed elsewhere [ 91.

It is noticed from Fig. I that, according to Eqs. (4) and (6), the impact of z-ratio on thickness progressively grows as a substantial amount of material accumulates on the crystal. in other words, the importance of using the correct z-ratio is more critical in a heavily loaded crystal than in a lightly loaded crystal. On the other hand, Eq. (8) is independent of z-ratio. As a result, if a comparison is made on the basis of per layer of deposited material, then any discrepancy among the aforementioned three methods will dramatically increase in the later stages of crystal life. The method that best represents the true nature of mass deposition on a quartz crystal

will have the least error when compared with the gravimetric method.

Fig, 3(a)-(d) shows a few of our representative results, where calculated layer errors are plotted in the 1brm of bar graphs. The cross-hatched, hatched and open bar graphs, respectively, correspond to the layer errors computed according to the z-match technique, Eq. (4), modified z-match technique. Eq. (6), and Mecca's energy-transfer model, Eq, (8). Fig. 3(a) shows the results of electron-beam deposition of copper on a 6 MHz AT-cut quartz crystal. The assumed z- ratio value is 0.437, and the bulk density of copper is 8.93 g cm - 3. Fig. 3(b) represents the results of electron-beam deposition of molybdenum on a 6 M Hz crystal. The bulk density and the z-ratio of molybdenum are 10.2 gcm ~ ~ and 0,257, respectively. The results of aluminum deposition on a 4 MHz crystal by d.c. magnetron sputtering are shown in Fig. 3(c). The assJmed z-ratio is 1.08, and the bulk density is 2.7 g cm- 3. Fig. 3(d) shows results of r,f. sputtered quartz on a 4 MHz crystal. The z-ratio of quartz is assumed to be 1.07, and its density 2.65 gcm ',

The tbur parts of Fig. 3 have some common features, even though the materials are different and deposition techniques were varied. It is very clear that Bones' modified z-match technique yields results very similar to those of the conventional z-match technique. This is quite expected, and has been explained above. The results of Mecca's energy-transfer model are totally disappointing and unacceptable. The ,,rrors grow progressively as more material accumulates. The mean absolute errors are an order of magnitude worse in Mecca's model than in either the ;,-match technique or Benes' modilied z-match technique. This clearly shows that the underlying assumptions of Mecea's theory are faulty, The deposited film cannot be treated as an inert mass vibrating synchronously with the quartz surface. On the other hand, the one-dimensional mechanical composite resonator model of the z-match technique is still a reasonably correct description of deposition on quartz crystals, even over a wide range frequency shills.

Mecca [ 111 cites his copper deposition data on a BT-cut quartz crystal in support of his theory. The difference between the errors due to the z-match technique and his model is small, but his model appears to yield better results. However, Mecca does not indicate the eslimate of experimental uncertainty in his gravimetric measurements. It is well known 1141 that evaporated (electron-beam or resistive source) copper gen- erates tensile stress on a quartz crystal, unless the deposition is carried out at very low rate, Such stress, in turn, can affect the resonance frequency. The rate of deposition can also affect the density and elastic shear modulus of the deposited tilm, making its z-ratio different from that of the bulk copper material. Any of these effects might be responsible for the seemingly better results of his method, But one piece of favorable data cannot establish the universality of a new physical theory.

A. W~qid l Sensor,i and Actuator.~ A 63 f 1997141-46 45

4

2

0 A ~-2

-10

-12

-14

(a)

Z-match !!~!i Benes I ...... Mecca

6,5 12,7 18,3 22.3 26.0 Thickness of copper (micrometer)

2 0 . . . . . . .

Z-match l;~i] Benes liiil Ivteeea

15 ..,,,.

"ZIO

® r o

.,J , i

0 "~*" . . . .

-5

i

i

i l

33.1

:L d! =,.,

. . . . . + . . . . . . . . . . . . . . . . . 3.9 12.4 22.1 31.7 39.9 44.2 50.0 60.0

(c) Thickness of aluminum (micrometer)

6

5

i ~4 ! i 3 i i

i : ; i

! ^ 8 1

=4 "J 2

1

O -

(b)

12 . . . . . . . . . . . . . . . . . . . . .

10 ! ~ Z - m a t c h ~ B e n e s L _ ] ~ ,l !i i!

:i ii ! ~

] ! ;

0.9 2.2 3.8 6.1 7.3 Thickness of ~ (micrometer)

IL

:! !J

~ 2 EL~

-2 . . . . . . . . . . . . . . . . . . . . . ~ .............. 2.9 8.8 12.5 16.1 20.2 24.7 29.0 32.0 38.2

(d) Thickness of quartz (micrometer)

Fig. 3. Thickness error per layer of deposited material when compared to the gm~imetrically determined thickness, shown as bar graphs against accumulated thicknesses, The cross-hatciJcd bar graphs and the halched hat graphs correspond Io the ,:-mulch, Eq. t4), and Benes" modified [lOi z-match technique, respectively, The open bar graphs are based on Mecca's energy-transfer I I I I model, Eq. q 8 I_ (a) Electron-beam evaporated copper ( ,z-ratio, 0.437; density. 8.93 gcm t) on a 6 MHz crystal, inducing a frequency shift from 5.969 to 4.494 MHz. Mean absolute deviation from gravimetric measurements: z-match, 0.40eM Benes, 1.26%: Mecea, 5.69f;~, {b) Electron-beam deposited molybdenum (,:-ratio, n.257: density. 10.2 g c m ~) on a 6 MHz crystal. The frequency shift was from 5.983 to 5,439 M Hz. Mean absolute deviation from gravimelric measurements: z-match, 1.58c,~: Benes, 0.76%; Mecca, 4.~'},L (c) D.c. sputtered aluntinum (:,ratio. 1.08: density. 2.7 gcm ' ) on a 4 MHz cryxtal. The net frequency shift was from 3.974 to 3.2tR) MHz. Mean absolute deviation from gravimetric measuremems: :.-nlatch, 0.97'}i ; Bone,,,, tl.97~i; Mecca. 14.19(}i, ( d t R.f. sputtered quartz I z-ratio, I.O7; density, 2.65 gcm ~ i on a 4 MHz crystal, Total frequency shift was from 3.979 to 3.595 MHz. Mean absolute deviation from gravtmetric measurements: :...retch, 0.73'~; Benes, n,6351-; Mecca, 7.73%.

5. C o . c l u s i o n s References

We have demonstrated that the frequency-shift-related lim. itation of the z-maich technique is only superficial. An extension formula, defined by Eq. (9), easily overcomes this limitation, We have compared the z-match techmque with

two alternative theories, Benes" modilied z-match model

I I01, and Mecea 's energy-transfer model [111. We used

gravimetrically determined mass 11% maximum uncer-

tainty) as the standard lbr comparison. On the basis of exper-

imental data, it appears that Benes' model provides little

improvement over the z-match technique, because of the

weak electromechanical coupling in AT-cut quartz. It is clear

that Mecca 's model is completely untenable in the light of

overwhelming experimental data, Thus, considering its accu-

racy and ease of implementation, the z-match technique still

remains the best method for quartz-crystal microbalance

applications in thin-film depositions, In cases where the z-

ratio is not known, or layers of dissimilar materials are to be

deposited, the automatic :-rat io determination method pro-

vides a superior alternative 19,12 I.

[ I I C. La a,d A.W. C,(a[ideiL|l ,I, ApplA'ati<ms +~1 Pi,'zaelc,'tric Quart:. Crystal Mic'rvb, hi,we,~. Elsevier, New York, 1983. Ch. 2.

[ 2 ] D. Salt. Hy-Q H,mdb,,ok ,~ Quart:. Crystal De|'ice.~, Van Nostrand, UK, 1987, p. 59.

I .~ I G.Z. Sauerbrcy, The use of quartz oscillators for weighing thin layers and micro~eighing, Z. Phy.i,, 155 ! 1959) 206 (in Gcrman),

141 K.H. Behrndt, Long-term operation of crystal oscillators in thin-film dcposition,l Vuc. Sci. f i ' chno l . . 8(1971) 622.

15 [ J.G Millet and D.I. BoteL Acoustic wave analysis of the operation of quartvcry'stal film-thickness monitors, J. AppL Phys.,39(1968) 58t5.

161 C. Lu and O. Lewis, Investigation of lilm-thickness determination by oscillating quar.z resonators with large mass load, J. Appl. Phys.. 43 t It)72 ) 4385.

171 Z-ntatch v'~ is a legisiered trademark of Leybold Inficon. 181 C,E Reed, K.K. Kana#awa and JH, Kaufc~an, Physical description of

a viscoelastically loaded AT-cut quartz resonator, J. Appl. Phys., 68 l Iq l l ) 1993.

I~)! ,-\, Wajid, Improving the accuracy of a quartz crystal micmbalance with aulomatic determination of acoustic impedance ratio, Rev. Sci. hlstrum,, 62 ( 199 ! ) 24)26.

I lnl E. Bones. Improved quartz crystal microbalance technique, J. Appl. Phys.. 56 ( 19841 00~.

46 A. Wtqid / St,n.wr~ aml Act!raors A 63 ~1997) 41.-46

1 I ] V.M Mecca, Loaded vibrating quartz sensors, Sensors atul,4ctttalors .4, 40 (1904) I.

12] A. Wajid, Measuring and controlling deposition on a piezoelectric monilor crystal. US Patent No. 5 112 642. Auto --ratio technique is implemented in l.,:ybold Inticon's IC4/Plus and IC5 I~arnily t)[ thin- hhn deposition controllers,

i3l A. Wajid, Long-tili~ quartz crystals lor dielectric coatings, Surl.ce Coating~ Technol.. 62 11993~ 691,

141 M. Schmid, M(~glichk¢iten und Grcnzcn dcr Schwtngquartz- Schichtdicken messung, Doctoral Di.~.~ertutwn I E. Benes, supervisor), Technischen Univcrsil/it Wien. 11989 ), pp, 53-54,

Biography

Abdul Wajidreceived his Ph.D+ degree in condensed matter physics from the University of Rochester in 1983. Fie studied

acoustic attenuation in silicon single crystals at low temper- atnres, focusing in particular on the contributions of boron and phosphorus point defects to the internal friction. After a brief academic career at the SUN Y College at Bmckporl, he joined Leybold Inticon. where he is currently employed as senior research engineer, tie. has published a number of papers and holds live patents in the areas of quartz-crystal microbalances (QCMs) in thinqilm depositions and acoustic sensors for the identification of the purity o( various refrig- erants, He is a recipient of the R&D 100 award in 1091 fl)r

an innovation m 0CM. He is currently engaged in the devel- opment of a low-pressure acoustic sensor for the monitoring of precursor gases in metallo-organic chemical vapor deposition (MOCVD) reactors.

Documents

On the accuracy of the quartz-crystal microbalance (QCM) in thin-film depositions