APPLIED PHYSICS LETTERS VOLUME 78, NUMBER 11 12 MARCH 2001

High-frequency eddy-current technique for thickness measurementof micron-thick conducting layers

F. Sakran, M. Golosovsky,a) H. Goldberger, and D. DavidovThe Racah Institute of Physics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel

A. FrenkelMSI Engineering Software Ltd., 6 Asherman Street, 61251 Tel-Aviv, Israel

~Received 23 October 2000; accepted for publication 18 January 2001!

We demonstrate a reflection-mode eddy-current technique operating in the 100 MHz to 5 GHzrange. It allows contactless measurement of the thickness of conducting layers~Ag, Al, Cu, W, etc.!0.1–1mm thick with the spatial resolution of 1–2 mm. ©2001 American Institute of Physics.@DOI: 10.1063/1.1355298#

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An important task facing semiconductor industry is cotactless measurement of uniformity of metallic layers of;1mm thickness on silicon and GaAs wafers with a spatial relution better than 1 mm. Available methods, including x-rabsorption, fluorescence, and laser ultrasonics are expeand cumbersome. In analogy to transparent layers whthickness is easily measured by interferometry of optiwaves, the thickness of conducting layers may be measusing low-frequency electromagnetic waves which papenetrate into conductor. This task is not easy since techlogical limitations allow only reflection measurement. Morover, the spatial resolution of;1 mm excludes free-spacpropagation and leaves only near-field electromagnprobes. Such probes have recently been developed formicrowave range and allow resistance mapping with a stial resolution of 1–10mm.1–4 For a material with knownconductivity, the thickness is inferred from the resistandata. Sensitivity of microwave probes limits their applicatito conducting layers with the sheet resistance~resistance persquare! above 1–10V. In the context of Al, Cu, and Ag thiscorresponds to layer thickness below 0.1mm. Much morethicker conducting layers~above 50mm! can be characterized by an eddy-current technique,5–11 which operates alower frequencies~1 kHz–10 MHz! and achieves spatiaresolution down to 50mm.10 Hence, there is no satisfactorelectromagnetic technique to probe highly conducting melic layers with the thickness between 50 and 0.1mm. In thiswork we demonstrate a microwave eddy-current techniwhich can probe highly conducting layers in the most imptant thickness range of 0.1–1mm. This technique extendcapabilities of existing high-frequency inductive probes,cluding superconducting quantum interference device12 andsingle loop probe.4,13

A surface-scanning eddy-current probe consists of amounted above the conducting sample. The sample affecimpedance of the coil due to eddy-currents excited therethe time-varying magnetic field of the coil. The impedanchange depends on the frequencyv, on the parameters of thcoil, on the coil-to-sample distanceh, and on the thicknessdand conductivitys of the sample. The latter parameters a

a!Electronic mail: golos@vms.huji.ac.il

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determined from the impedance change using known consion procedure,14 although it reduces to simple analytical fomulas only in a few limiting cases.15 We consider one ofthese cases, namely, a thin nonmagnetic conducting lwith the thicknessd much smaller than the skin depth,d!d5(2/m0sv)1/2. We assume a single layer coil with thradiusr whose axis perpendicular to the sample surface. Timpedance change imposed by the sample is characteby dimensionless parameterd2/dr52Rsh/m0vr , whereRsh

is the sample sheet resistance

Rsh5~sd!21. ~1!

Strong screening limit, d2/dr!1, corresponds to a thinsample with high conductivity. The impedance change is15

D Im~Z!>X0 ;D Re~Z!5RshX0

m0vh, ~2!

whereX05kXL is the reactance change for an ideally coducting sample,XL is the probe inductance, andk,1 is thedimensionless coefficient.

Weak screening limit, d2/dr@1, corresponds to a thinsample with low conductivity. The impedance change is

D Im~Z!>0;D Re~Z!>m0vrX0

2Rsh. ~3!

In both regimes the dissipative part of the impedance chayieldsRsh. Then, Eq.~1! allows to find thickness for knownconductivity. Note, that in two limiting cases@Eqs. ~2! and~3!# the impedance change depends onRsh in the oppositesense. Frequency dependence ofD Re(Z) is also different inthese two cases. This means that for a given loop radiusgiven conductivity, the maximum sensitivity to the thicknevariation is achieved at some intermediate frequency wd2/dr;1.6

Spatial resolution of thickness mapping is determinedthe coil sizer which should be as small as possible. Redution of the coil size decreases the reactanceXL5vm0rN2

and the sensitivity. To compensate for decrease in sensitthe number of turnsN should be increased. Since the restance of the coil also increases (}N for a multilayer coil and}N2 for a single layer coil! the increase ofN can provideonly partial solution for the sensitivity problem. The on

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1635Appl. Phys. Lett., Vol. 78, No. 11, 12 March 2001 Sakran et al.

possibility left is to increase the frequency, although this ahas limitations. Indeed, since the electromagnetic fieldcays exponentially in the conductor, the layer thickneshould not considerably exceed the skin depth. For a gifilm thickness this sets an upper frequency limit,f max

;(m0s/pd2)21. In particular, for a 1-mm-thick layer, f max

;7.3 GHz for Al and f max;4.4 GHz for Cu. On the othehand, the frequency should not be too low, otherwiseelectromagnetic wave penetrates too deep and senseonly the required layer, but the substrate and all underlymaterial as well. The tradeoff between fine spatial resolutand high sensitivity sets the optimal frequency. In particufor a 1 mm size coil and for;1-mm-thick Cu layer theoptimal frequency range is between 100 MHz and 4 Gwhich is beyond the scope of known eddy-current teniques. To check feasibility of operation of the eddy-curretechnique at such high frequencies we use a new probe

It is based on a recently developed planar thick fiinductor chip ~Fig. 1!16 with the size of 1.532 mm2, L515 nH, f res 1.5 GHz,Q546 ~at 0.8 GHz!, N'3 ~Fig. 1!.To make a well-controlled transition from the coaxial cabto the inductor we designed and fabricated a 50V-microstripline using a 0.36-mm-thick mylar substrate The microstripvery thin, so the radiation losses constitute only 2%–3%total losses. The ground plane faces the sample. The mictripline also serves as a flexible cantilever which allowsput the probe into a gentle mechanical contact withsample, if needed.

FIG. 1. Probe design.

FIG. 2. Measurement system.

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A microstripline with the probe is connected to the H8510C microwave network analyzer~Fig. 2!. The reflectedsignal comes from a small sample area, of the order ofprobe size~1.5 mm!, and depends on sample resistivity athickness. By moving the sample under the probe~at con-stant probe-sample separation! and measuring reflectivitywe map sample resistance with the spatial resolution comrable to the probe size.

To extract quantitative information we measure the coplex impedance of the probe-sample assembly. While thiroutinely done in low-frequency eddy-current testing, higfrequency operation imposes complications such as stanwaves and phase shift in the feeding structure. To accofor it, we find reflectivity

G load5Z2Z0

Z1Z0exp~22 j b l !, ~4!

whereZ is the impedance of the coil above the sample,Z0

550V is the characteristic impedance of the coaxial feedline, l is the length of the microstrip, andb is the propagationconstant. In general,b is complex since it includes radiationThe microstrip is matched, hence, its effect reduces tsimple exponential factor which is found through reflectivmeasurement without sample and without probe~‘‘open’’boundary condition,Z5`). Equation~4! yields then

Gopen5exp~22 j b l !. ~5!

Dividing Eq. ~4! by Eq.~5! excludes the effect of the microstrip and yields impedance of the probe-sample assemThis allows to find electrical characteristics of the sampAnalytical procedure for doing this in the case of simple cgeometry had been developed by Dodd and Deeds.14 Sinceour coil ~Fig. 1! is very different from that described in Re14, extraction of electrical characteristics of the samplequires sophisticated three-dimensional numerical simula~to be discussed elsewhere!. Here we restrict ourselves to thmeasurement of probe impedance above the sampleanalysis in terms of the simple model@Eqs.~2! and ~3!#.

We operated our probe below and above its resonafrequency. Although the sensitivity to resistance variationsthe resonance is higher, this region is much more sensitivthe variations in the probe-sample distance. Therefore,concentrate here on the frequencies below resonance wdistance dependence is weaker. Figure 3 shows probe retivity for a linear scan over a Cu layer with varying thickness. The sample was fabricated by consequent evaporof Cu onto the 5-mm-thick glass substrate through approate masks. Reflectivity is sensitive to thickness variatioand shows a series of plateaus with sharp transitions cosponding to the steps in the thickness profile. Spatial restion, determined from the steepness of the transition~;2mm!, corresponds to the lateral size of the probe, aspected. The spatial resolution may be further increasedthe deconvolution techniques. Similar results have beentained using different conductors~Ag, Ti!, frequencies, andcoils.

Figure 4 shows a real part of the coil-sample impedanRe(Z). Clearly, Re(Z) decreases upon increasing layer thicness, as expected. Figure 5 shows the same data versusresistance of the layer@estimated through Eq.~1! and assum-

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1636 Appl. Phys. Lett., Vol. 78, No. 11, 12 March 2001 Sakran et al.

ing bulk conductivity#. The results at two different frequencies exhibit linear dependence with the same slope. Thispendence may be qualitatively explained as follows. Whthe sample thickness is much smaller than the skin de~;4 mm!, the conductivity is so high that all samples arethe strong screening limit@Eq. ~2!# where impedance changis linearly proportional to the sheet resistance,D Re(Z)}Rsh. Equation~2! yields the slope of this linear dependen

D Re~Z!

DRsh'kN2

r

h, ~6!

since X0'kvm0rN2. In our experiment we havek'0.11,r;0.75 mm, andh50.16 mm. This yields a frequencyindependent slope of;4.2 which reasonably agrees with thexperimentally found value of 6. In order to increase tvalue Eq.~6! suggests that the number of turnsN should be

FIG. 3. A linear scan over conducting layer with varying thickness~rawdata!. The lines are a guide to the eye.

FIG. 4. Probe-sample impedance vs sample thickness. Coil-sample setion is 160mm.

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as big as possible. The practical limitation here is the retance of the coil which also increases withN.

In summary, we demonstrate that the operation ofeddy-current technique at microwave frequencies is possand may solve a very important problem of thickness msurement of;1 mm-thick Cu or Ag films. We achieve spatial resolution of 1–2 mm using a probe based on commcial planar thick-film inductors. Higher spatial resolutiomay be achieved by using dedicated planar inductors.

This work was supported by the Israeli Ministry of Scence and Arts. The authors are grateful to D. Shainer forintroduction to the field of thickness measurement.

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Israel Ltd., Har Hozvim P.O.B. 450080, 91450 Jerusalem, Israel.ra-

FIG. 5. Probe-sample impedance vs sample sheet resistance. Opeclosed symbols correspond to experiments at different frequencies usinsame probe and samples.

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