Eddy current technique for testing large-area, high Tc superconducting films with high spatial resolution

Ctyyqenics 3.5 (1995) 155-160 0 1995 Else&r Science Limited Printed in Great Bntain. AI1 rights reserved 001 l-2275/95/$10.00

Eddy current technique for testing large-area, high TCsuperconducting with high spatial resolution

films

K. Wegendt, R.P. Huebener, R. Gross, Th. Trtiuble, W. Geweke*, W. Patzwaldt”, W. Prusseit+ and H. Kinder+ Physikalisches Institut, Lehrstuhl Experimentalphysik II, Universitat Tiibingen, Morgenstelle 14, D-72076 TObingen, Germany “Institut Dr. FGrster GmbH, In Laisen 10, D-72766 Reutlingen, Germany +Physik Department E 10, Technische UniversiMt MOnchen, James-Franck-Strasse D-85747 Garching, Germany Received 29 July 1994; revised 19 October

1,

1994

An eddy current technique has been developed which allows non-destructive quality testing of high temperature superconducting thin films with a spatial resolution of -50 pm. This technique allows inexpensive and fast diagnosis of large-area superconducting films on substrates with a diameter up to 6 in. The eddy current probe is scanned over the surface of the superconducting film without the need for extra electrical or mechanical attachments. Reports are given on experiments with both well defined test geometries and large-area epitaxial YBa,Cu,O,., films prepared on 4 in silicon wafers. Keywords: high T, films; non-destructive

To date the fabrication of large-area epitaxial high T, superconducting films on substrates with a diameter up to 10 cm has been achieved’ and extension of this work up to a wafer diameter of 15 cm (6 in) can be expected in the near future. Such large-diameter wafers covered with high T, superconducting films will serve as the starting material for the subsequent fabrication of superconducting microelectronic devices. However, this goal of device fabrication can only be accomplished if adequate diagnosis is incorporated into this process. Here the primary task will consist of quality control of the superconducting films representing the starting material. The goals of such a diagnosis are clear: namely, the detection of deviations from spatial homogeneity of the electric conductance of the superconducting films due to inhomogeneities in film composition and thickness, microcracks, irregularities of substrate surface, etc. In addition, a meaningful diagnostic tool must also satisfy the following requirements: it must be rapid, yield high spatial resolution and provide just sufficient information, but not more, in the interests of speed. Furthermore, the diagnosis must be economical, i.e. inexpensive and simple. All these requirements call for a local probe, rapidly scanned over the surface of the superconducting films, without the need for extra electrical or mechanical attachments (contacts) to the individual wafer under test. A promising approach to the diagnostic goal outlined above is provided by eddy current techniques having a long

testing;

eddy current technique

and successful tradition in non-destructive testing2. In this paper we describe such a technique based on a specific, well established technology for non-destructive testing of electrically conducting and/or magnetic materials. In the course of our work dealing with large-area high T, superconducting films, a new design of the coil geometry for generating and detecting the eddy current signal has emerged, increasing the spatial resolution to -50 pm (reference 3). We report on experiments performed with both well defined test geometries and with large-area YBa,CU~O,_~ films prepared by a technique suitable for covering substrates with a diameter of 10 cm or larger.

Principle

of the eddy current method

For non-destructive testing a variety of eddy current probes has been developed, and the most suitable configuration is selected according to the specific objective of the test?‘. In our case, for large-area high T, superconducting films, detection of the reflected eddy current signal appears most convenient, allowing simple and rapid scanning of the sample surface. Using this reflection geometry either the absolute signal or the difference signal can be recorded, the latter case operating with a gradiometer coil configuration. We describe the probe coil in terms of a superposition of individual conductor loops (delta-function coils) with

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derived from Maxwell’s equations. With a sinusoidal driving current density, the vector potential is likewise a sinusoidal function of time, x(?,t) = zp)e-‘wr. Then, the complex vector potential inside the superconducting sample is described by the differential equation5

(2) where: b, is the vacuum permeability; A the skin depth; hL the London penetration depth; and Jo the current density of the probe coil. Equation (2) is based on the two-fluid model of a superconductor, where the total induced eddy current density 2 is the sum of the supercurrent density Is and the normal current density yqqp 7 = 1, -I-sqp

0.060

0.040 0.020 Re(Z) / Z(air)

0.000

7, satisfies the London equation

Figure 1 Complex impedance of coil of radius r, = 60 km and length I= 1.6 mm calculated for a semi-infinite normal and superconducting sample for different values of distance h (B,, h = 10 pm; B,, C,, h = 100 pm; B,, h = 500 pm) between the coil tip and sample surface as a function of the normal state skin depth A, (lines B) and the London penetration depth AL (line C,), respectively. The broken lines represent lift-off curves (variation of h) for constant values of A,

radius r,, located at a distance z = h above the superconducting film. The loops carry the sinusoidal current density Jo( r,t) = Z,,e’“’. 6(r - r,,) . 6(z - h)

(1)

Here, 6 is the Dirac delta function, and w and I,, are the angular frequency and the amplitude of the driving current, respectively. The z-direction is assumed to extend perpendicular to the film surface with the film surface at z = 0. The differential equation for the vector potential can be

I

I

I

I

b hl cl 10 0 A

(3)

50 100

(4)

/-& whereas we have jqp = a”

(5)

with (T = (T/r,)4a, for the normal current density. Here, on is the normal state electric conductivity and E the electric field. As an example, for an epitaxial YBazCu~O,.s film at T= 100 K the electrical resistivity fn = l/a, is typically 100 ~0 cm, corresponding to a normal state skin depth A, = 500 pm at 0/2rr = 1 MHz. On the other hand, except for the region close to T,, the London penetration depth is = 150 nm, independent of frequency in the range relevant for the eddy current technique (fS 100 MHz). The differential equation (2) has to be solved for the particular conductor configuration of the experiment to obtain the vector potential A(F,t). By superimposing a number of delta-coils any desired shape of coil can be modelled. Once the vector potential is determined one can calculate any physically observable electromagnetic quantity, such as the induced eddy currents @,t)

= &(F,t)

= -iwoi(?,t)

(6)

or the voltage in the driving coil

V(t) =

iw

;i(?,t)dT

Here, the integration path is along the windings of the coil. Finally, from the self-induced voltage the coil impedance is obtained 0.00

0.02

0.04

0.06

0.08

0.10

Re(Z) / Z(air)

(8)

Figure 2 Complex impedance of coil of radius r, = 60 pm and length I = 1.6 mm calculated for normal conducting thin films of different thickness d as a function of the normal state skin depth A,. For comparison, the result of the semi-infinite sample is also shown. The distance h between the coil tip and sample surface is 10km. The symbols mark the impedance values obtained at different film thicknesses for constant A,

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The impedance is usually normalized by dividing it by the magnitude of the air impedance. The complex impedance Z depends on the distance h between the coil tip and the sample surface, the skin depth and the London penetration depth. In order to analyse the operation of the eddy current

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1

z

x4---+

y;”

Control

,Q

L---i3

Scanning

r

Probe

r Defectoscope

L Figure 3

Experimental

AF

set-up of eddy current technique

probe one usually discusses the complex impedance plane shown schematically in Figurrs I and 2“-‘. In these figures we show the calculated complex coil impedance Z normalized to the impedance in air both for normal and superconducting samples of different thickness d. The horizontal and vertical axes represent the real (resistive) and imaginary (reactive) part, respectively. We first discuss the impedance plane for a semi-infinite normal conducting sample. The impedance has been calculated for a coil of radius r,, = 60 pm and length I= 1.6 mm with one end of the coil located at a distance h above the sample surface’. The impedance is plotted for three different values of h (curve B,: h = 10 pm, BZ: h = 100 pm, B,: h = 500 pm) as a function of the normal state skin depth A,, = (2/p,,wa,,)“‘. For A, - SC, i.e. for w - 0 or cr, 0, the eddy currents become vanishingly small and the impedance of the coil is equal to the air impedance. With decreasing A,, the point on the impedance plane is moving along one of the lines B away from the Im(Z)-axis. The induced eddy currents result in a reduction of the reactive component and a finite resistive component of Z. Finally, for very small A,, i.e. for very high o or a,, dissipative eddy currents again become negligibly small, resulting in a purely reactive component. The magnitude of Im(Z) for A,, - 0 depends on the distance h and the coil dimensions. It is evident that Im(Z) decreases with decreasing h and saturates for h < r,,. For fixed A,, i.e. for constant w and 200pm

Y line scan t X

0.27-

x(mm) Figure4 Eddy current signal recorded at J= 77 K for a single line scan along the test geometry. The test geometry shown in the top part was patterned into a 300 nm thick epitaxial YBa,Cu,O,~, film deposited on (100) SrTiO,

a,, the complex impedance moves along the lift-off curves (broken lines) on varying h. The lift-off curves shown in Figure I have been calculated for different values of A, ranging between 10 pm and 50 mm. In order to be able to discriminate between changes of Z caused by variations of h and cr, the operation frequency is chosen such that the lift-off curve is cutting the lines B almost perpendicularly. If the conductivity of the sample varies due to spatial inhomogeneities, the complex impedance moves along one of the lines B. In contrast, variations of h cause a movement perpendicular to line B. For l/u” = 100 ~0 cm a suitable measuring frequency is ~1 MHz. We also note that for h < r, the calculated impedance plane is almost independent of h, i.e. in this case variations of h during the scanning process do not strongly influence the eddy current signal. We next consider a semi-infinite superconducting sample. For high temperature superconductors A, is in the 100 nm and pn = l/cr, in the 100 ~0 cm regime, i.e. we have All G A, up to frequencies in the GHz regime. Therefore, for the typical measuring frequencies used in eddy current techniques (< 100 MHz), on the right-hand side (rhs) of Equation (2) the imaginary term i2/Az can be neglected. Hence, the sample response is purely inductive, resulting in a purely reactive component of Z. The magnitude of Im(Z)/Z(air) is determined by the distance h between the coil and the sample surface, and is equal to the value obtained for the normal sample in the limit A,, - 0. In general, close to T, or due to sample imperfections, the London penetration depth can become large and the imaginary term on the rhs of Equation (2) can no longer be neglected. Then, with increasing &, the normal eddy currents result in a finite resistive and an increased reactive component. The impedance moves along line C2 and merges with line B? for A, = A,,. In Figure 1 we have plotted only the line Cz corresponding to h = 100 pm. For thin film samples the situation is different. In order to clarify the influence of the film thickness we have plotted the impedance plane for normal conducting films of different thickness d in Figure 2. The curves were calculated again for a coil of radius r,, = 60 pm and length I= 1.6 mm located at a distance h = 10 pm above the film surface. For comparison, we also show the result of the semi-infinite sample (d = m). It is evident that for A, % d the coil impedance is almost unaffected by the presence of the film. Hence, the impedance is purely reactive and about equal to

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10

20

30

40

x(mm)

3.29 2.74 2.19

1.64 1.09 0.54 -0.01

16 Figure5 Two-dimensional images of the eddy current signal of an 80 nm thick YBa,Cu,O,., film on a Si wafer. In (a) the contour lines of the voltage signal are shown. In lb) the voltage signal of the upper left part of (a) is shown in a quasi-three-dimensional representation. The ring shaped structures in (a) mark regions with increased electrical conductivity

the air impedance [Im(Z)/Z(air) = 11. With decreasing A,, i.e. with increasing frequency or conductivity, the real or resistive component increases and reaches a maximum, if A, and d are of the same order of magnitude. On further decreasing A, the real component decreases again. Finally, for A, 4 d one has about the same result as for the semiinfinite sample. Discussing the situation for a superconducting film we note that the typical film thickness used in superconducting microelectronics applications is less than 1 pm. With the normal state conductivity a, = 1 x lo4 (a cm)-’ of high T, superconductors we obtain A, = 500 pm at a typical measuring frequency of 1 MHz. That is, we usually have A, % d 2 AL. According to the above discussion again we can neglect the imaginary part on the rhs of Equation (2) and hence obtain a purely reactive coil impedance. For d > A,_ the magnitude of Im(Z)/Z(air) is the same as that obtained for the semi-infinite superconducting sample and again only depends on the dimensions of the coil and its distance from the sample surface. For d < AL the coil

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impedance is still purely reactive. However, Im(Z)/Z(air) increases with decreasing d, approaching 1 ford -=% AL. That is, the impedance is moving vertically on the Im(Z) axis on decreasing d/AL, since the effect of the normal eddy currents is negligibly small. From our discussion we can conclude that in a superconducting film with d = AL, spatial variations of AL result in considerable variations of Im(Z)/Z(air). Such variations can be caused, for example, by variations of the critical temperature or the presence of weak links.

Experimental

set-up and results

Our experimental set-up is shown in Figure 3. The wafer covered at the top by the superconducting film is placed in a flat, thermally insulating container (made from Styropor) filled with liquid nitrogen (boiling at 77 K). The eddy current probe is mounted on the moving arm of an x-y-z scanning table and is scanned over the sample surface. We

NDT eddy current

0

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10

x(mm)

3.91

9

2.98

5

2.05

& z

1.11 0.18 -0.75 -1.69

Figure 6 Two-dimensional images of the eddy current signal of a 70 nm thick YBaJu,O,., film on a Si wafer. In (a) the contour lines of the voltage signal are shown. In (b) the voltage signal of part of (a) is shown in a quasi-three-dimensional representation. The structures in (a) are probably caused by scratches in the substrate or microcracks in the thin film

emphasize that the sample is completely covered with liquid nitrogen and that the probe coil dips into the liquid nitrogen. The eddy current signal is detected using the Defektoskop AF lo. The Defektoskop AF allows the phase sensitive detection of the detection coil voltage signal. Our operation frequency was typically 1 MHz. The distance between the probe coil tip and sample surface was = 10 pm. Control of the x-y-z scanning and further handling of the eddy current signal were performed by a computer. We have studied wafers up to a diameter of 10 cm. Figure 4 shows the eddy current signal of a single line scan obtained at 77 K for the test geometry of an epitaxial superconducting YBa,Cu,O,.p film (thickness 300 nm; substrate SrTiO,) indicated at the top. The four stripes of 50 Frn width are clearly resolved. By taking many such line scans slightly displaced along the y-direction, a twodimensional image of the sample in a quasi three-dimensional plot of the recorded signal is obtained. Whereas Figure 4 refers to an artificial test structure, we next turn to large-area epitaxial YBazCu,0,.8 films pre-

pared on 10 cm diameter Si wafers covered with an YSZ/Y,O, buffer layer of 46 nm thickness. The films were deposited by means of a co-evaporation technique with a rotating substrate’. In Figure 5 we present results found for an YBa2Cu30,.s film of 80 nm thickness, showing an eddy current signal with a distinct ring structure. In the signal plotted in Figure 5 a constant offset signal has been subtracted. From the amplitude and phase of the signal we can conclude that the peaks correspond to sample regions yielding a reduced value of Im(Z)/Z(air), i.e. a reduced value of the reactive component of the coil impedance. According to the discussion given above this corresponds to an enhanced value of d/AL. The ring-shaped signal peaks appear at radii of 6.0, 12.2, 14.7 and 15.6 mm. They result from substrate rotation during the deposition process and indicate an inhomogeneous distribution of the film thickness or effective penetration depth. These structures could not be detected using a scanning electron microscope and an optical microscope. A second example is shown in Figure 6, referring to an

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YBa,Cu,O,.B film of 70 nm thickness. Similar to Figure 5, a constant offset signal has been subtracted. In this figure the phase of the eddy current signal is opposite to that of Figure 5. That is, the peaks in the eddy current signal correspond to regions with an enhanced reactive component of the coil impedance or, equivalently, a reduced value of d/h,. The distinct structures displayed by the eddy current imaging technique are probably due to scratches in the substrate affecting the film epitaxy or due to microcracks in the film. These defects are expected to result in a larger value of the effective penetration depth. Again the structures could not be detected by an optical microscope or a mechanical microprobe (o-step).

Discussion The results presented in the last section clearly demonstrate that spatial inhomogeneities in high T, superconducting films can be detected with a resolution of 50 pm using a state-of-the-art eddy current coil configuration scanned over the sample surface. Whereas we have investigated various test structures and also studied large-area epitaxial YBa,Cu,O,, films, a detailed evaluation of the sensitivity of this method for detecting local variations in the critical temperature T, or the critical current density J, still needs to be done. Accurate information on the local values of T, or J, can be obtained by varying the sample temperature”~” or the amplitude of the current passing through the eddy current probe 13,14 . However, for a rapid quality test of the output of a large-area wafer production line, the technique described in this paper appears highly promising. An important aspect in the evaluation of the potential of this method in the field is the possible speed at which this quality testing can be performed. The experience we have obtained during the course of this work yields the following estimate. We assume a wafer diameter of 150 mm (6 in), a distance of 100 pm between the data points during the scanning process and a sampling rate of lo4 s-l. This sampling rate allows real time data handling using a standard PC and data display in terms of a 1500 x 1500 array. The scanning velocity then amounts to lo4 s-’ x 100 pm = 1 m s-l. Such

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a high value of scanning velocity is compatible only with a continuous scanning process (without intermittent stopping and accelerating of the probe). Complete coverage of the two-dimensional wafer surface can be achieved in two ways: by a rotating relative motion of the probe around the wafer axis combined with (1) movement in the radial direction or (2) a second rotary motion. In the first case we obtain a spiral scanning trace and in the second case a trace in the form of an evolute. Case ( 1) leads to changes in velocity. Case (2) means oversampling and a more complicated spatial pattern reconstruction, while the velocity remains constant. The wafer area of 180 cm* and the lo4 cm* area per data point yields 1.8 x 10” for the total number of data points. With the sampling rate of lo4 s-’ the time for scanning the whole wafer is 180 s or 3.0 min. Due to possible oversampling, this time may increase by about a factor of 2.

Acknowledgement Encouragement acknowledged.

and support by M. Junger

are gratefully

References

6 I 8 9 IO II

Berberich, P., Utz, B., Prusseit, W. and Kinder, H. Physica C ( 1994) 219 497 McMaster, A. Nondestructive Testing Handbook Vol 2, Ronald Press, New York, USA (1959) German Patent application for eddy current probe P 44/0987.3 (March 1994) Ptister, H. and Junger, M. Eine Hilfe fiir die Praxis: Materialpriifung (1992) 34 I83 Jackson, J.D. Classical Electrodynamics John Wiley & Sons, New York, USA (1975) Fiirster, F. 2 Metal/k (1952) 43 163 Fihster, F. and Stampke, K. 2 Metal/k ( 1954) 45 166 Fiirster, F. 2 Metallk ( 1954) 45 I97 Dodd, C.V. and Deeds, W.E. J Appl Phys ( 1968) 39, 2829 Defektoskop AF, Institut Dr FGrster GmbH, Reutlingen, Germany Huebener, R.P., Gross, R. and Bosch, J. Z Phys B: Cond Matter

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