Infrared properties of chemical-vapor deposition ... - Semantic Scholar

Infrared properties of chemical-vapor deposition polycrystalline diamond windows Paolo Dore, Alessandro Nucara, Daniele Cannavo`, Gianluca De Marzi, Paolo Calvani, Augusto Marcelli, Ricardo S. Sussmann, Andrew J. Whitehead, Carlton N. Dodge, Astrid J. Krehan, and Hans J. Peters

Low-resolution transmittance and reflectance spectra of high-quality chemical-vapor deposition ~CVD! diamond windows were measured in the infrared in the 2.5–500-mm wavelength range ~20 – 4000 cm21!. High-resolution measurements on a window with nearly parallel surfaces show well defined interference fringes at low frequencies. By standard procedures the optical constants n and k of CVD diamond were determined, for the first time to the author’s knowledge, in the far-infrared region. It is shown that a window with a large wedge angle, close to 1°, does not produce appreciable interference fringes. Modeling of these results confirms that interference fringes can be avoided by use of properly wedged CVD diamond windows. This result is of considerable relevance to the use of CVD diamond windows in spectroscopic applications for which fringe suppression is a major requirement. © 1998 Optical Society of America OCIS codes: 160.0160, 160.4670, 160.4760, 300.6270, 260.3160, 120.2650.

1. Introduction

Strong covalent bonds confer on diamond a range of properties1 that make this material a key and unique component in optics and other fields of modern technology. In comparison with other known materials, diamond is the hardest and stiffest, has the highest room-temperature thermal conductivity combined with one of the lowest thermal expansion coefficients, and is chemically inert to acid and base chemical reagents. In the specific case of diamond as an optical material, its major advantages can be summarized as follows: ~i! diamond is transparent in a broad spectral range, from the ultraviolet to the mi-

P. Dore, A. Nucara, D. Cannavo`, G. De Marzi, and P. Calvani are with the Dipartimento di Fisica, Istituto Nazionale di Fisica della Materia, Universita` di Roma La Sapienza, Piazzale A. Moro 2, 00185 Rome, Italy. A. Marcelli is with the Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, C.P. 13, 0044 Frascati, Italy. R. S. Sussmann and A. J. Whitehead are with De Beers Industrial Diamond Division, Limited, Charters, Sunninghill, Ascot, Berkshire SL5 9PX, U.K. C. N. Dodge is with Diamanx Products, Ltd., Balasalla, Isle of Man, A. J. Krehan and H. J. Peters are with Drukker International B.V., Beversestraat 20, 5431 SH, Cuijk, The Netherlands. Received 24 November 1997; revised manuscript received 9 April 1998. 0003-6935y98y245731-06$15.00y0 © 1998 Optical Society of America

crowave regions, with the exception of the intrinsic multiphonon absorption bands in the 2.5– 6.7 mm range,2– 4 ~ii! it can be used in aggressive environments, and ~iii! it can be used to transmit high-power beams with minimum thermal distortion and minimum danger of thermal shock. Until now few of these properties have been extensively exploited because of the relative scarcity, limited size, and lack of controlled purity of natural single-crystal diamond windows. Recent progress in the new synthesis technology of chemical vapour deposition ~CVD! has made it possible to manufacture high-quality polycrystalline CVD diamond optical components of large dimensions as either flat plate windows or three-dimensional shapes such as domes.5–7 The ability to manufacture polycrystalline CVD diamond as a reliable and robust engineering material at an economical price is opening the way to the use of this material for technically demanding applications. Our first aim in the present study was to determine accurately the refractive indices n~n! and k~n! of highquality CVD diamond in the far-infrared region, for which data on these optical constants are still not available. Previous studies of the optical properties of CVD diamond reported transmission measurements only for frequencies above 400 cm21.4,6 From these measurements, values of refractive index n and 20 August 1998 y Vol. 37, No. 24 y APPLIED OPTICS

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of absorption coefficient a ~i.e., of refractive index k! were obtained.4,6 We report on reflection and transmission measurements of high-quality CVD diamond windows in the frequency range 20 – 4000 cm21. From the lowresolution interference-free transmittance and reflectance spectra of a window with nearly parallel surfaces, the frequency dependence of the refractive indices n~n! and k~n! is determined,8 for the first time to our knowledge, in the far-infrared region. Highresolution measurements clearly show interference fringes and, from their spacing, the accuracy of the n~n! values is greatly improved. We observed that the amplitude of the interference fringes decreases with increasing frequency. This effect can be described by a model9 that takes into account small deviations from perfect parallellism between the window faces ~i.e., a small wedge angle f > 0.1°!. We show that the same model can describe the far-infrared transmittance spectrum of a wedged window ~f > 1°!, which does not produce appreciable interference fringes in high-resolution measurements. This result confirms that properly wedged CVD diamond windows can be used in spectroscopic applications in which a nearly flat transmission in the far-infrared region is required. 2. Experiment

CVD diamond plates of high optical quality as large as 100 mm in diameter and more than 2 mm thick are now produced under the brand name Diafilm.10 These plates can be cut and processed to precise optical tolerances. Both faces can be polished to an optical finish, and the parallelism of the faces can be controlled so that either parallel or wedge samples ~with wedge angles of ~f . 1°! can be produced. The general properties of Diafilm material were described previously.5–7 We performed detailed optical measurements of two CVD diamond windows. Sample A was 8 mm in diameter and 482 mm thick. The faces were not intentionally wedged but revealed a small wedge angle, f 5 ~0.10 6 0.03!°. One side of the sample was slightly saddle shaped, and the other showed an irregular distortion. The total distortion over the diameter of the sample is estimated at no more than 0.5 mm ~fewer than two or three fringes at 630 nm!. Currently, samples can be produced with a surface flatness of better than one fringe over that diameter. Sample B was 15 mm in diameter and intentionally wedged with a wedge angle f 5 ~0.90 6 0.03!°. The minimum and maximum thicknesses were dmin 5 250 mm and dmax 5 490 mm, respectively. Transmission and reflection measurements were performed in the far-infrared ~FIR! region from 20 to 600 cm21 with a chopped Michelson interferometer. A Bomem DA3 rapid-scanning interferometer was used in the mid-infrared region from 500 to 4000 cm21. Different sources, beam splitters, and detectors were used to investigate different spectral regions. Details of the experimental setups employed for transmission and reflection measurements are 5732

APPLIED OPTICS y Vol. 37, No. 24 y 20 August 1998

Fig. 1. Low-resolution transmittance and reflectance spectra of sample A.

given elsewhere.11 In reflection measurements, the incidence angle ui was 8° in both the FIR and the MIR regions. Figure 1 shows the low-resolution, interferencefree transmittance @TLR~n!# and reflectance @RLR~n!# spectra of sample A. By using a spectral resolution of 10 cm21 ~frequency step Dn 5 5 cm21! we avoid interference fringes. The reproducibility of the results and the good match between spectra obtained with different optical configurations attest to the accuracy of the measured spectral shapes. For the T~n! and R~n! spectra the estimated errors are 1% and 2%, respectively. These errors affect not the spectral shapes but only the absolute intensity of the measured spectra. In the MIR region the TLR~n! spectrum is qualitatively in agreement with previous data.4,6 The two-phonon effects in the 1500 –2700cm21 band as well as the three-phonon effects in the 2700 – 4000-cm21 band4 are well resolved in the transmittance spectra. To observe interference fringes, we performed measurements with a spectral resolution of 1 cm21 ~Dn 5 0.5 cm21! in the regions 20 –300 and 800 –900 cm21. For convenience, Fig. 2 shows the high-resolution THR~n! and RHR~n! spectra of sample A in the selected spectral regions 20 –70, 180 –230, and 810 – 860 cm21. In these high-resolution spectra, interference fringes are well defined and the accuracy of the data is good.

Fig. 2. High-resolution transmittance ~—F—F—! and reflectance ~—■—■—! spectra of sample A in three selected frequency ranges.

In the spectral range near 3000 cm21 no appreciable fringes were observed. Figure 2 clearly shows that the intensity of the interference fringes decreases with increasing frequency and that, as expected, the THR~n! and RHR~n! spectra have opposite phases at low frequencies, whereas at high frequencies they are nearly in phase. 3. Refractive Indices n and k

For an optical material, knowledge of the frequency dependence of the complex refractive index n˜~n! 5 n~n! 1 ik~n! permits computation of the transmittance and reflectance spectra of a sample of known thickness d. When the specimen has perfect parallel faces, different procedures8,12,13 result in equivalent high-resolution spectra in which interference fringes ~with spacing 1y2nd! are well defined in regions of high transmission. According to the standard procedure of Ref. 12 ~procedure a!, we can obtain the transmittance T~a! of the system vacuum~1!– crystal~2!–vacuum~3! at a given wavelength l ~l 5 1yn! by superposing P transmitted waves:

U

U

P

T~a! 5 t12t23

(

2

@r21r23 exp~id!#m ;

m50

(1a)

d, i.e., the phase difference that corresponds to a double traverse of the sample, is given by d 5 ~4pyl!n˜d cos q2,

(1b)

where q2 is the refraction angle at the 1–2 interface and tlm and rlm are the Fresnel coefficients for the transmitted and reflected electrical fields, respectively, at the lm interface. As P 3 `, i.e., in the limit of infinite internal reflections, one obtains T~a! 5

U

U

2

t12t23 . 1 2 r21r23 exp~id!

(2)

Procedure a also provides an exact expression for the reflectance spectrum R~a!.12 Note that the absorption of the sample can be accounted for by use of complex quantities. For an ideal layer with parallel surfaces, exact expressions are available to compute low-resolution, interference-free spectra ~at normal or near-normal incidence!, which exactly account for multiple internal reflections.8,14 According to this procedure ~procedure b!, at each frequency the low-resolution spectra are given by T~b! 5 R0 5

~1 2 R0!2D , 1 2 R02D2 ~1 2 n!2 1 k2 , ~1 1 n!2 1 k2

R~b! 5 R0@1 1 T~b!D#, D 5 exp~2ad!,

(3)

where a 5 4pkn is the absorption coefficient. Obviously, one can obtain the interference-free spectrum T~b! @R~b!# by averaging T~a! @R~a!#. In a first approximation, sample A is considered an ideal sample with parallel surfaces ~we neglect its

Fig. 3. ~a! Refractive index n and ~b! absorption coefficient a. Dotted curves, the limits between which n and a can be varied.

small wedge angle!. The TLR~n! and RLR~n! spectra can then be described by use of procedure b, which is valid in the case of an experimental setup ~such as the one that we employ11!, in which the incident beam probes the system vacuum– crystal–vacuum in both transmittance and reflectance measurements. The n and k values can then be determined at any frequency by inversion of Eqs. ~3! because the experimental RLR and TLR values are both available. The n~n! and k~n! obtained from this inversion procedure8,15 can be regarded as experimental refractive indices because they are directly obtained from measured spectra without the need to resort to any modeling or fitting procedure. Figure 3a shows the resulting n~n!. In Fig. 3b the absorption coefficient a~n!, rather than k~n!, is shown, to allow for a better comparison with published results.4 A smoothing procedure was performed to remove features associated with noise in the experimental data. When we take into account the percentage error ~see Section 2! that affects the TLR~n! and RLR~n! spectra @with the constraint that TLR~n! 1 RLR~n! , 1#, the shapes of the n~n! and a~n! spectra shown in Fig. 3 do not change, whereas their absolute intensities can vary significantly. From the inversion procedure, the values of n are affected by a percentage error of the order of 2%, but their accuracy can be further improved if the highresolution measurements are taken into account. Indeed, if interference fringes are evident, their spacing is given simply by 1y2nd. The percentage error in n is thus reduced to 0.2%, as shown by the dotted curves in Fig. 3a. At 1000 cm21 the resulting n value is 2.377 6 0.005, which compares well with the most accurate value previously reported ~2.375 6 0.014! for CVD diamond.6 Figure 3b shows that a large percentage error ~of the order of 50% near 200 cm21, 25% near 1000 cm21, and 5% ~near 2100 cm21! affects the a values. Ow20 August 1998 y Vol. 37, No. 24 y APPLIED OPTICS

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Fig. 4. The high-resolution transmittance and reflectance spectra of sample A: ■, experimental data; dotted curves, T~a! and R~a!; solid curves, T~c! and R~c!.

ing to the inversion procedure used in this study, large errors in the a values are indeed expected15 when the absorption is very low @i.e., when TLR~n! 1 RLR~n! is close to unity#. The shape of the a~n! spectrum shown in Fig. 3b is qualitatively in agreement with those derived for n . 600 cm21 from transmission measurements of CVD samples.4 The a~n! values are consistent with previous ones4 in the range 1800 –2600 cm21 ~i.e., when the intrinsic diamond absorption is high!, whereas they are much higher than the previous data outside this range. At 1000 cm21, for example, a is of the order of 1 cm21 ~see Fig. 3b!, whereas previous values, derived from transmission measurements, are in the range 0.1– 0.3 cm21.4,6 More accurate measurements of the absorption coefficient were performed by calorimetry in samples of similar quality to the ones used in this study, indicating that considerably lower values, in the range 0.029 – 0.07 cm21, are typical of this quality of CVD diamond.16 The large discrepancy in the values of absorption obtained from the measurements in this study is due to ~i! surface and bulk scattering,17 ~ii! nonuniformity of window thickness, or both. These effects, which have been ignored in this analysis, can reduce the average transmission or reflection intensities or both, thus providing overestimated a values when the inversion procedure is used. When the intrinsic absorption is high, such as near 2000 cm21, these effects are negligible. On the contrary, when the intrinsic absorption is low, these effects can become predominant and the a values provided by the inversion procedure can be significantly overestimated. 4. Wedge Effects

Using the assumption that sample A is a window with perfect parallel faces, we used the n~n! and k~n! values derived above to evaluate high-resolution spectra through procedure a @see Eqs. 1#. From Fig. 4 ~where only selected spectral regions are shown for convenience! it is evident that only at low frequencies do the computed transmittance T~a!~n! and reflectance R~a!~n! spectra provide a good description of the measured THR~n! and RHR~n!. The amplitude of the fringes slowly decreases in T~a!~n! and R~a!~n!, owing to the increase of k~n! with increasing frequency. 5734


Therefore the strong decrease in the fringe amplitude observed in THR~n! and RHR~n! is not due to the increase of k~n!. In a real specimen, besides effects ~i! and ~ii! ~Section 3!, also divergence of the incident beam ~iii! and nonparallelism between specimen surfaces ~iv! can cause a decrease in the fringe amplitude. Using simple analytical models, we verified that effects ~i!– ~iii! cannot describe the observed frequency dependence of the fringe amplitude. In case ~ii!, for example, a variable window thickness d can be introduced if we consider a Gaussian distribution of width s for the d values, centered at d0 5 482 mm. The window transmission, as computed through numerical integration, can correctly describe the far-infrared THR~n! only if a s value of ;5 mm is used. This result is not in agreement with direct profile measurements, which provide a s value of the order of 0.5 mm ~see Section 2!. Furthermore, if s > 5 mm, interference fringes would be completely absent in the computed spectra above 800 cm21, whereas they are still evident in the experimental data ~Fig. 4!. To account for effect ~iv! we use a procedure reported in the literature9 ~procedure c! in which a wedge angle f between the window surfaces is assumed. Considering a clear aperture of diameter D, the window thickness d varies between d1 and d2 5 d1 1 D tan f. For a monochromatic wave incident at a given d, the phase difference between the directly transmitted wave and the qth transmitted wave is given by9 d~q! 5 dq 5

4p sin~q 2 1!f n˜d @cos~q2 1 qf!#. l tanf

(5)

If the first M transmitted waves are superposed, the transmittance associated with the monochromatic wave incident at d is then given by

U

T~M, d! 5 t12t23

M

(

m51

U

2

~r21r23!m21exp~idm! .

(6)

Procedure c also provides expressions for the reflectance spectrum R~M, d!. The transmittance ~reflectance! spectrum T~c! @R~c!# that results from procedure c can then be obtained, in the limit M 3 `, by numerical averaging of N contributions T~d! @R~d!# that correspond to the d values d 5 d1 1 m~d2 2 d1!yN ~m 5 0, N!. Figure 4 shows the T~c! and R~c! spectra obtained with f 5 0.12° and D 5 3 mm, which is the spot size employed in the high-resolution measurements. It is clear that the computed spectra satisfactorily describe the experimental data. In particular, it can be seen that only through procedure c is it possible to explain the nearly in-phase fringes observed in transmittance and reflectance data above 800 cm21. Figure 5 shows the transmittance spectra measured on the wedged sample ~sample B! at low frequencies. Low-resolution transmittance is nearly flat, and the high-resolution data do not show, within experimental accuracy, clear interference effects ~i.e.,

Fig. 5. Low-resolution ~F! and high-resolution ~1! transmittance spectra of sample B. Solid curve, computed T~c! spectrum.

well-defined fringes!. Figure 5 also shows transmittance T~c! computed through procedure c, with f 5 0.9° and D 5 8 mm, corresponding to the spot size employed in the transmission measurements on sample B. For frequencies higher than 20 cm21, the calculated transmittance exhibits small interference effects, with a maximum intensity of the order of the spread of the high-resolution data ~;3%!. Only at low frequencies, where experimental data are not available, are interference fringes clearly seen in the computed T~c!. 5. Conclusions

Transmittance and reflectance spectra of CVD diamond windows between 20 and 4000 cm21 have been measured in two high-quality samples. From the spectra of sample A ~which has nearly parallel surfaces with a wedge angle of 0.1°! the frequency dependence of n~n! and a~n! was obtained. The highly accurate values of n~n! are in agreement with previously reported results.6 The a~n! values are consistent with those reported in the literature4 for the range 1800 –2500 cm21 ~i.e., when the intrinsic absorption of diamond is high!, whereas they are considerably higher than those reported4,6,16 outside this range when the intrinsic absorption is low. This discrepancy is attributed to the inversion procedure that we employed to derive a~n!. In this procedure the sample is indeed considered an ideal sample with parallel surfaces. Other effects are thus ignored, which can provide significantly overestimated a values when the intrinsic absorption of diamond is low. In spite of the above discrepancy, the n~n! and a~n! of CVD diamond, reported for the first time to the author’s knowledge in the FIR region, indicate that high-quality CVD diamond does not exhibit any significant absorption feature in the FIR part of the spectrum. These values of dielectric constants can be used for the modeling of the FIR properties of high-quality CVD diamond windows in applications in which power absorption is not an issue. The high-resolution spectra of sample A show well-

defined interference fringes. At very low frequencies ~20 –50 cm21! the fringes correspond to an ideal window with parallel surfaces. The fringe amplitude is ;30% of that of the low-resolution interference-free transmittance. With increasing frequency, the fringe amplitude decreases. Such an effect can have different origins in a real window. However, we show that the experimental data can be satisfactorily described only by use of procedure c,9 in which a wedge angle f between the window surfaces is assumed. High-resolution transmittance measurements of sample B ~wedge angle f > 1°! do not show appreciable interference effects within experimental accuracy. This is certainly the case in the specific range from 20 to 50 cm21. This means that, if interference effects are present, their amplitude is 3% lower than the low-resolution, interference-free transmittance. The computed T~c! spectrum does predict small interference effects, with a maximum intensity of the order of the spread of the high-resolution data. Only below 20 cm21, for which experimental data are not available, are relevant interference fringes predicted. In conclusion, it has been shown that a properly wedged diamond window can strongly reduce the amplitude of the interference fringes that are present ~especially in the FIR! in windows with parallel ~or nearly parallel! surfaces. This result can be of particular importance for the use of diamond windows in the realization of infrared synchrotron beam lines,18 to ensure a high-brillance source with a nearly flat FIR spectrum.

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