Anal. Chern. 1990, 62, 1135-1138
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Phase-Measurement Interferometric Microscopy of Microlithographically Fabricated Platinum Electrodes Christopher P. Smith, Heidi L. Kennedy, Harlan J. Kragt, and Henry S. White* Department of Chemical Engineering and Material Science, University of Minnesota, Minneapolis, Minnesota 55455
J. F. Biegen ZYGO Corporation, Middlefield, Connecticut 06455
Phasemeasurement Werferometrk mlcroscopy ( W I M ) was used to measure the topography of Pt microelectrodes faklcated on slllcon wafers. Disk (10 pm radlus) and band (10 pm X 1000 pm) electrodes were prepared by deposnlon and llthographlc patternlng of a 0.2 pm thkk SK), layer on a 0.05 pm thick Pt film. Quantltatlve topographical Images of the resulting electrodes are obtained from PMIM by accounting for the complex refractive Index of Pt and for multiple reHectbns of kghl which occur within the transparent SO, layer. I n sltu, quantltatlve measurement of microelectrode topography In water is also demonstrated.
INTRODUCTION Microelectrodes fabricated by using lithographic techniques (1-8) show particular promise in chemical analysis, in device fabrication, and in the measurement of fundamental physical parameters associated with electron-transfer reactions. It is possible to design diverse electrode geometries, including several dissimilar electrodes grouped as an array. Because of the small electrode size, complete electrochemical cells (9, 10) may be fabricated on silicon wafers or other sufficiently smooth surfaces. In this report, we describe an optical interferometric microscopy used in measuring the three-dimensional topography of platinum microelectrodes. In general, lithographic fabrication requires multilayer deposition of metal and insulating films, followed by chemical etching to expose the desired electrode geometry. This procedure yields a stepped surface with the electrode slightly raised or recessed relative to an insulating plane. In mathematical analyses of current-voltage behavior, the microelectrode is usually assumed to be flush with the insulating plane. This assumption is generally acceptable for single electrodes when the step height is small compared to the width (bands) or radius (disks) of the electrodes. In other situations, a more careful analysis of the electrode/substrate topography is required. For example, measurements of diffusion constants in polymer redox films coated a c r w the surface of an array of band electrodes require at least a qualitative consideration of the electrode height relative to the polymer thickness (8, 11). In our own laboratories, recent measurements of the current and potential distribution surrounding microelectrodes and arrays of microelectrodes using refractive-index mapping (12)necessitate quantitative knowledge of the true electrode geometry. In previous reports, we have described applications of phase-measurement interferometric microscopy (PMIM) to measure the topography of a number of electrode substrates (13,14). PMIM is a nondestructive optical microscopy that images substrate topography with a vertical resolution of 0.6
* Author to whom correspondence should be addressed. 0003-2700/90/0362-1135$02.50/0
nm and a horizontal resolution of -0.25 pm. In the preceding article, we have also shown that it is possible to obtain high-resolution images of electrode surfaces submerged under relatively thick (1-4 mm) layers of aqueous electrolytes (14). PMIM imaging of surface topography is based upon the interferometric measurement of the phase, 4, of light reflected from a test surface relative to light reflected from an optical reference surface (15-17). The difference in phase between light reflected from two positions on the surface, A+, is a complex function of the topography of the electrode, the refractive index of the intervening media, and the reflection coefficients of the test surface (vide infra). In our previous work, measurements have been restricted to electrodes constructed from a single material for which the phase change of light occurring upon reflection is constant over the entire surface. Under this condition the optical image may be considered a direct image of the physical surface. The imaging of microelectrode topography is considerably more involved, however, since the surface comprises materials with dissimilar refractive indices and optically transparent overlayers. Accurate topographical information may be obtained from these optical images only after correcting for the difference in reflective phase changes for the dissimilar materials and accounting for the multiple reflections which occur within the transparent layer and modify the phase of the reflecting beam. The purpose of this paper is to demonstrate that topographical images of devices constructed from metallic and dielectric materials can be quantitatively analyzed, in air and in liquids, by inclusion of complex reflection coefficients and multiple reflections in the analysis.
EXPERIMENTAL SECTION Fabrication of Microelectrodes. Microelectrodes were fabricated at the Center of Microelectronics and Information Science at the University of Minnesota by coating a Pt-covered silicon wafer with SiOzand then selectively removing the Si02to expose the Pt in the desired electrode geometry. Approximately 50 nm of platinum was radio frequency (rf) sputter deposited onto a 3-in. Si wafer after a brief Ar etch to remove any surface impurities. The Pt was deposited at a rate of 0.5 nm/min at a base pressure of Torr. The Pt-coated wafer was then heated at 450 "C for 15 min to increase the adherence between the metal f i i and the substrate. After cooling, a uniform Si02 layer was electron-beam evaporated (0.5 nm/s) onto the Pt surface at a base pressure of 4 X 10" Torr. An approximate value of 200 nm for the SiOz film thickness was obtained by viewing a fractured sample edge-on using a JEOL 840 scanning electron microscope. Microlithographic techniques were used to selectively remove the SiOzfilm, exposing the underlying Pt surface in geometrical patterns that defined the microelectrode shape. The Si/Pt/Si02 substrates were vacuum baked for 30 rnin at 150 "C. After cooling for 30 min, a 450 nm thick layer of positive photoresist (Shipley 1300-17) was deposited on the substrate by spin-coating and soft-baked at 110 "C for 1 min. The photoresist was exposed through a photolithographic mask to a Hg arc lamp (320 nm) for 10 s using a Karl Suss MJB3 Exposure System. The exposed 0 1990 American Chemical Society
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ANALYTICAL CHEMISTRY. VOL. 62. NO.
11. JUNE 1. 1990 Air
I Fbure 1. Schematic diagram showing the cross section of a PI
microeiechode
I
'"1"
t "m
I pm-
~
33.7 urn
-40.7
pm-
Flgwa 3. PMIM Image of a 10 pm wide band e(eCtr0de taken at 40X magnhtion rnIhe suface covered wkh a t (len) and 3 mm ot wala (right)
t
36.1 lun
Flgure 2. PMlM image of 10 pm wide band (top) and 20 am disk (bonom) electrode at a magnification of IOOX. photoresist was developed with an 8 1 ratio of H,O-Shipley AZ for 80 s, followed by rinsing with deionized HzO for 5 min. The SiO, film below the developed photoresist was removed by etching in a %I NH,F/HF solution for 10 s. Following a IO-min rinse in deionized H,O, the remaining photoresist was stripped by soaking the wafer for 5 min in PRS-loo0 Baker Resist Stripper. The wafer was rinsed again in deionized H,O and dried in a N, stream. The ohotolitbomaohic masks were eenerated with HP 9835 compuier using a&&m card prom& and printed with a &ex Pattern Generator. The pattern size was reduced using a D.W. Mann step-and.repeat camera and printed on emulsion plates. The electrode geometries reported in this work m a 10 pm X loo0 urn band and a disk with a IO om radius. The nominal geometry of the cross section is shown in Figure 1. A single die containing a lOrm x IOOOrm band electrode was uniformly coated with 40 nm of Ag so a PMlM measurement of the electrode geometry could be made without the complications resulting from the transparent SiO, overlayer (vide infra). The Ag was thermally evaporated onto the SiO, side of the die at a rate of 0.2 nm, s at a base pressure of 2.4 x IO* Torr. Phase.Measurement Interferometric Microscope. A ZYGO (Middlefield. CT) Maxim 3D loser intcrferometric mi. croscope, hereafter referred to as a phase-measurement interferometric microscope (PMIM). was used to image the PI microelectrodes. Topographical features of the test surface are measured by the microscope using optical phase-measurement interferometry. PMlM meawres the phase. @, of monochromatic. coherent light with wavelenpth A ( 4 3 2 . 8 nm) reflected from the test substrate relative to light reflected from an optical reference surface. Differenres in phase. 30,between two locations I n the surface are proportional t o the optical height, h . between these two Incations. 351 developer
A4 = 4 r h / A (1) An optical image of the surface can thus be constructed by measuring the phase as a function of x and y. For surfaces with uniform optical properties. the optical image obtained in air is equivalent to the substrate topography. A detailed description
-26.9
p m -
Flgure 4. PMlM image of sibersoBted 10 am wlde band taken at IOOX magnificalbn. of the m i m p e and measurement theory is given elsewhere ( I s ) .
RESULTS Representative PMIM images of band and disk Pt microelectrodes obtained in air are shown in Figure 2. The most obvious difference between the nominal geometry (Figure 1) and the imaged geometry is an apparent inversion of the step between the SiO, and Pt surface (i.e., the Pt surface appears to be raised above the SiO, surface). The second difference is that the magnitude of the SiO,/Pt step is approximately half of the physical height indicated by SEM. However, this apparent height is a n optical height calculated on the basis of phase differences measured interferometrically across the surface. This optical height, h, is a function of the substrate optical properties as well as the optical properties of the medium surrounding the substrate. For example, Figure 3 shows how the optical height of a band electrode is reduced when the electrode is immersed under 2 mm of H20. In air the optical height of the SiO,/Pt step is -105 nm, while in water it appears to be -29 nm. T o correlate the optical and physical heights, one must consider all contributions to phase differences between p i n t a on the surface as measured by PMIM. These considerations are greatly simplified when measurements are made on a surface with uniform optical properties. In that case the optical image is a direct measurement of the physical topography. This is exemplified in Figure 4, which shows the PMIM image in air of a hand electrode which had been
ANALYTICAL CHEMISTRY. VOL. 62. NO. 11. JUNE 1. 1990
6 I= a,,
1137
Table 1. Individual and Net Reflected Amplitude and Phasea ray
Flgun 5. Schematic diagram of the Ag-coated electrode (see text).
1
n.im
2
0.728
3
0.101 0.014 0.002
4
5 a 2 =4 1 n,dlA + ba,,m
individual amplitude phase (4'
6 a
net amplitude phase ( 4
I....n 1.462 0.924 0.386 1.849 1.311
O.Oo0 O.Oo0
0.1e-i . ~.~
1.0
0.772 0.790 0.776 0.776 0.777 0.777
i.3, 1.346 1.345 1.346 1.346 1.346'
Flgure 6. Multiple-beam reflections within a transparent overlayer.
'Assuming a 250 nm thick SiOp layer on Pt; illumination at nm, and optical constants of (corresponding to the notation indicated in Figure 6): n, = 1; n, = 1.45; and rl, = 2.3 + i4.1. 'The phase is referenced to the SiO,/air interface (see Figure 6). The individual amplitudes and phases were calculated as the individual terms of the Airy summation carried out for a transparent film on an absorbing substrate. (The infinite value was calculated according to eq 2 in the test.
previously coated with a uniform 40 nm thick layer of Ag. The direction and magnitude (-248 nm) of the Ag coated Si02/Pt step are consistent with the actual electrode geometry.
fact that the overlayer is t r a v e 4 twice. rI2is the reflection coefficient for a transverse electric wave incident on medium 2 from medium 1
632.8
n3
I
I
DISCUSSION The correlation between actual physical height, d, and optical height, h, is straightforward when the optical properties of a surface are uniform, as is the case for the Ag coated microelectrode. The schematic in Figure 5 shows two rays reflected from the Ag coating which, though much thinner than the SO,, behaves as an infinitely thick medium due to the absorption of light in the Ag. Ray 1 reflects from the Ag over the SiO, with a phase change of Ray 2, in addition to undergoing a phase change a t the air/Ag interface, also travels an additional phase of 4wnld/X as it doubly traverses a distance d through air with refractive index, nl (=l).Since the phase change upon reflection from the Ag overlayer is the same for both rays, the net difference in phase (A@= @I - @2) is attributed only to the additional phase traveled by ray 2; Le., A@ = 4nnld/X. Assuming normal incidence of the light, the change in optical height is thus calculated to be h = XAm/4w = nld, which may be solved directly for the physical thickness: d = h/nl = 250 nm (Figure 3). If the reflected phase changes across the surface were not the m e . e.g. if both metals and dielectrics were present, the height would have to be corrected for the difference in the reflective phase angles. The correlation between optical and physical height is more involved when there is no Ag overlayer present. Figure 6 shows a ray incident on the S O 2 layer which is split into a reflected and transmitted beam a t the outer interface (air/SiO, or water/Si02). The transmitted beam undergoes multiple reflections between the top and bottom interfaces of the SiOz film giving rise to an infinite series of reflected (and transmitted) beams of diminishing amplitude. T o calculate the net phase of the reflected light, one may either compute the amplitude and phase of the individual rays and sum them or approach the problem by solving Maxwell's equations with the appropriate boundary conditions (18-20). Both approaches yield the identical expression, eq 2, for the phase change of the light (@I) as measured at the interface between the first and second media
Here, 6 is the phase involved with traversing the optical thickness of the Si02 overlayer, i.e., the product of the overlayer refractive index, n,, and the overlayer thickness, d, multiplied by 2n/X. The factor of 2 before 0accounts for the
(3) while p , and &., are the amplitude and phase of the reflection coefficient for the interface between media 2 and 3 n2 - 5, ra=-pZ3eih (4) n2 ii,
+ -
In eq 4, ti, is the complex refractive index (=n, + ik,) of the Pt film. Solving eq 4 for the real and imaginary parts of rB yields
(n, - n#
+ k,2
= (n, + n,)'
+ k,2
and @23
= tan-'
[
-2k3n2
nZ2- n,2 - k,2
(5)
]
(6)
where either is calculated as a four-quadrant angle and the positive value of p B is used or p , is given a sign of fl for n2 and 6 , is calculated as a two-quadrant angle. These conventions must be followed to give the correct value of @., The well-known limit of eq 6 is fork, = 0. This gives a value of 0 or w for @a depending on the magnitudes of n2 and n3. (In this limit one may drop &., from eq 2 and replace p B with r,. which may be calculated with eq 3 by replacing subscripts 1and 2 with 2 and 3.) Table I shows the amplitude and phase for the individual reflected beams and the net amplitude and phase that are to be detected by the microscope The second ray in Figure 6 is incident on the Pt electrode and has a phase (m2) that is the sum of the phase from traversing the distance d twice. 4unld/X, and the phase in reflecting from the air/Pt interface, m & / ~ @Z
= 4nn1d/X
+h/pt
(7)
The phase @&,i./pt is calculated according to eq 6 by replacing n2 with n,. The theoretical optical height of the Si02/Pt step, h. is obtained by solving eqs 2 and 7 for the phases O1 and 4, and substituting these values into eq 1, Le., h = (01- QZ)X/4w. Values of h (for air and in H20) are plotted in Figure 7 as a function of SiO, thicknesa assuming literature values (21) for the refractive indices of the SiO, (n, = 1.45) and Pt (6= 2.3
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 11, JUNE 1, 1990
below the resolution of the microscope.
120 140
1
4- air
ACKNOWLEDGMENT We thank the 3M Co. (St. Paul, MN) for the deposition of the Pt films used in this study.
/A .
40 + . . . 100
3 . . . . , . . . . , . . . . , . . . . , . . . . / 200 300 400
60
20 0
d (nm)
Flgure 7. Theoretical curves of optical thickness (h) vs physical thickness ( d )calculated according to eqs. 1, 2, and 7 (dashdot line). The soli lines indicate the optical thickness neglecting multiple reflections.
+ i4.1). Figure 7 is used to convert the experimentally measured optical heights of the SiOz/Pt steps to a physical thickness. In air, we have obtained an average step height of 105 f 3 nm from measurements of several electrodes which corresponds, using Figure 7, to a physical height of 258 f 10 nm. In HzO, the measured value of h = 28.6 f 2.7 nm corresponds to a physical height of 263 f 10 nm. Both values are within error of the step height measured on the silvercoated electrode (Figure 4). The positive value of h indicates that the phase over the SiOz is greater than that over the bare Pt; the light reflecting from the Si02-covered Pt appears to have traveled farther than light reflecting from the air-covered Pt. This is consistent with the inversion of the images shown in Figures 2 and 3, which show the Pt electrode "closer" to the microscope objective. It is interesting to note that the optical thickness of the Si02/Pt step over certain regions may be very insensitive to the physical thickness due to the nonlinear relationship between the two, Figure 7. For instance, if the SiOz thickness varied from 180 to 220 nm along some region of the electorde, the optical thickness would vary less than 0.4 nm, which is
LITERATURE CITED White. H. S.; Kttleson, G. P.; Wrighton, M. S. J. Am. Chem. SOC. 1984. 106, 5375. Klttleson, G. P.; White, H. S.;Wriclhton. M. S. J. Am. Chem. Soc. 1984, 106, 7389. Paul, E. W.; Ricco, A. J.; Wrighton, M. S. J. Phys. Chem. 1985, 89. 1441. Thackery, J. W.; White, H. S.; Wrighton, M. S. J. phys. Chem. 1985, 89, 5133. Bard, A. J.; Crayston, J. A.; Kittleson, G. P.; Shea, T. V.; Wrighton, M. S. Anal. Chem. 1988. 5 8 , 2321. Crooks, R . M.; Chyan, M. R.; Wrighton, M. S. Chem. Meter. 1989, 1 , 2. Wohitjen, H. Anal. Chem. 1984, 56. 87A. ChMsey, C. E.; Fledman, B. J.; Lundgren, C.; Murray, R. W. Anal. Chem. 1986, 58, 601. Chao. S; Wrighton. M. S. J. Am. Chem. Soc. 1987. 109, 2197. Chao. S.; Wrighton. M. S. J. Am. Chem. Soc. 1987, 109. 6627. Kttleson, G.; White, H. S.; Wrighton, M. S. J. Am. Chem. SOC. 1985, 107, 7373. Kragt, H. J.; Smith, C. P.; White, H. S. J. flectroanal. Chem. Interfacialfktcfrochem. 1990, 278, 403. Kragt, H. J.; Earl, D. J.; Norton, J. D.; White, H. S . J. Electrochem. Soc. 1989, 136, 1752. White, H. S.; Earl, D. J.; Norton, J. D.; Kragt, H. J.; Mason, F. Anal. Chem., preceding paper in this issue. Bbgen, J. F.; Smythe, R. A. Roc. SPIE 1988, 897, 207. Perry. D. M.; Robinson, G. M.; Peterson, R. W. I € € . Trans Magn. 1983, 19, 1656. Perry, D. M.; Morgan, P. J.: Robinson, G. M. J. Inst. Nectr. Rad. 1985, 55, 145. Born, M.; Wolf, E. Princ/ples of Optics, 2nd ed.; Pergamon Press: New York, 1964; sectlons 1.6 and 7.6. Heavens, 0. S. Optical Ropeft&s of Thin Solid Films; Academic Press: New York, 1955. Tolansky, S. An Introduction to Interferometw , 2nd ed.: Lonamans: London -1973. CRC Handbook of Chemlstry and Physics, 70th ed.;West, R. C., Ed.; CRC Press: Boca Raton, FL, 1989..
RECEIVED for review December 7,1989. Accepted March 2, 1990. The phase-measuring interference microscope was purchased through an NSF Instrumentation Grant (CBT8807676).
