Measuring the thickness profiles of wafers to subnanometer resolution using Fabry-Perot interferometry

The resolution of an angle-scanning technique for measuring transparent optical wafers is analyzed, and it is shown both theoretically and experimentally that subnanometer resolution can be readily achieved. Data are acquired simultaneously over the whole area of the wafer, producing two-dimensional thickness variation maps in as little as 10 s. Repeatabilities of 0.07 nm have been demonstrated, and wafers of up to 100 mm diameter have been measured, with 1 mm or better spatial resolution. A technique for compensating wafer and system aberrations is incorporated and analyzed.     

Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry

We describe a low-coherence interferometric technique for simultaneous measurement of geometric thickness and group refractive index of highly dispersive samples. The technique is immune to the dispersion-induced asymmetry of the interferograms, thus overcoming limitations associated with some other low-coherence approaches to this simultaneous measurement. We use the experimental configuration of a tandem interferometer, with the samples to be characterized placed in an air gap in one arm of the measurement interferometer. Unambiguous, dispersion-insensitive measurements of critical group-delay imbalances in the measurement interferometer are determined from the optical frequency dependence of interferogram phases, by means of dispersive Fourier transform spectrometry. Sample thickness and group refractive index are calculated from these group delays. A thickness measurement precision of 0.2 mum and group index measurement accuracy of 5 parts in 10(5) across a wavelength range of 150 nm have been achieved for BK7 and fused-silica glass samples in the thickness range 2000 to 6000 mum.     

Measurement of the physical thickness and refractive index of thin epitaxial garnet films

A technique for the measurement of refractive index and physical film thickness of epitaxial garnet films is described which utilizes variable wavelength measurements. Experimental results are presented for gadolinium gallium garnet substrates and two different bubble domain film compositions. From these results, it is concluded that the technique is not applicable to wafers with films on both sides due to the differences in film thickness of the two films. For single sided wafers, the refractive index can be determined with an accuracy of ±0.3 percent.     

测量薄膜折射率的光栅衍射干涉方法

根据光的干涉理论,讨论了条纹周期数对测量薄膜折射率不确定性的影响,推导出干涉条纹错位量与薄膜折射率和厚度的关系式。由此提出采用光栅衍射干涉测量薄膜折射率的方法和实验方案。实验表明:该方法的干涉条纹测量精度达λ/10~λ/20,薄膜折射率测量精度可达 0.01 以上。     

IR spectroscopic determination of the refractive index and thickness of hydrogenated silicon layers

IR spectroscopic techniques widely used to determine the thickness and refractive index of layers and thin films of various materials are adapted for determining those of hydrogenated silicon layers. Based on a literature analysis, three formulas are chosen which enable the refractive index and thickness of such layers to be determined from reflection and transmission spectra. The formulas are applicable, with some restrictions, to other samples in the form of relatively transparent layers (films) on transparent substrates. Experimental data are presented that illustrate the use of the formulas.     

Precise thickness and refractive index determination of polyimide films using attenuated total reflection

Surface plasmons generated at a silver-polyimide interface and the guided modes coupled into planar films cause dips in the reflectivity curve of a transparent dielectric-silver-polyimide-air structure. These minima in the reflectivity curve were used to measure the polyimide thickness as well as the real and imaginary parts of the polymer refractive index (extinction). Precision within 1% of the polymer coat thickness was achieved through the use of this technique over the range 0.5-10 μm. In some cases, this technique is capable of yielding a precision of ~ 10% on the imaginary part of the polymer refractive index and provides a useful method for determining the performance of a low-loss polymer waveguide. Techniques in fitting the experimental reflectivity data to obtain the optical constants are also described.     

Simultaneous determination of thickness and refractive index based on time-of-flight measurements of terahertz pulse

We present a simple technique for simultaneous determination of thickness and refractive index of plane-parallel samples in the terahertz radiation domain. The technique uses time-of-flight measurements of the terahertz pulse. It has been employed on nine different polymers and semiconductor materials, which are transparent for terahertz frequencies. Our results of thickness measurement are in good agreement with micrometer reading. The accuracy in the determination of refractive index is on the order of two decimal points.     

Extrinsic fiber-optic Fabry-Perot interferometer sensor for refractive index measurement of optical glass

A simple fiber-optic sensor based on Fabry-Perot interference for refractive index measurement of optical glass is investigated both theoretically and experimentally. A broadband light source is coupled into an extrinsic fiber Fabry-Perot cavity formed by the surfaces of a sensing fiber end and the measured sample. The interference signals from the cavity are reflected back into the same fiber. The refractive index of the sample can be obtained by measuring the contrast of the interference fringes. The experimental data meet with the theoretical values very well. The proposed technique is a new method for glass refractive index measurement with a simple, solid, and compact structure.     

Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness

We have developed a low-coherence interferometer system used for the simultaneous measurement of refractive index n and thickness t of transparent plates. Both the phase index n(p) and group index n(g) can be determined automatically in a wide thickness range of from 10 microm to a few millimeters. Two unique techniques are presented to measure n(p), n(g), and t simultaneously. One allows us to determine n(p), n(g), and t accurately by using a special sample holder, in which the measurement accuracy is 0.3% for the thickness t above 0.1 mm. In the other technique the chromatic dispersion delta n of index is approximately expressed as a function of (n(p) - 1) on the basis of measured values of n(p) and n(g) for a variety of materials, and then the simultaneous measurement is performed with a normal sample holder. In addition, a measurement accuracy of less than 1% is achieved even when the sample is as thin as 20 microm. The measurement time is also 3 min or more.     

Transmission interference spectrometric determination of the thickness and refractive index of barrier films formed anodically on aluminum

Aluminum oxide films were formed anodically under carefully controlled conditions and prepared for transmission by dissolving part of the base metal in a solution containing iodine.A spectrophotometric technique to determine the refractive index of the anodic oxide is presented. This technique, based on the transmission interference spectra of two films with slightly different thicknesses, yielded precise results and enabled problems derived from the relatively low refractive index of alumina to be overcome. The film thickness was also calculated from the data, and the results indicated that the refractive index did not depend on the film thickness, at least for the range under study.The anodic alumina showed normal dispersion over the UV, visible and near- IR regions and its refractive index varied from 1.88 at 200 nm to 1.65 at 1300 nm.     

Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates

We advance a method to determine the diameter D and the complex refractive index (n + n'i) of marine particles from flow cytometric measurements of forward scattering, side scattering, and chlorophyll fluorescence combined with Mie theory. To understand better the application of Mie theory with its assumptions to flow cytometry (FCM) measurements of phytoplankton cells, we evaluate our flow cytometric-Mie (FCM-Mie) method by comparing results from a variety of phytoplankton cultures with independent estimates of cell D and with estimates of n and n' from the inversion of bulk measurements. Cell D initially estimated from the FCM-Mie method is lower than independent estimates, and n and n' are generally higher than bulk estimates. These differences reflect lower forward scattering and higher side scattering for single-cell measurements than predicted by Mie theory. The application of empirical scattering corrections improves FCM-Mie estimates of cell size, n, and n'; notably size is determined accurately for cells grown in both high- and low-light conditions, and n' is correlated with intracellular chlorophyll concentration. A comparison of results for phytoplankton and mineral particles suggests that differences in n between these particle types can be determined from FCM measurements. In application to natural mixtures of particles, eukaryotic pico/nanophytoplankton and Synechococcus have minimum mean values of n' in surface waters, and nonphytoplankton particles have higher values of n than phytoplankton at all depths.     

The syncang method for simultaneous measurement of film refractive index and thickness

The synchronous angle method (SYNCANG) for the simultaneous determination of the refractive index and film thickness of thin dielectric films is especially useful for researchers involved in integrated optics.The method involves the measurement of the synchronous angles θ_5E and θ_5M (see Fig. 1) required to couple transverse electric (TE) and transverse magnetic (TM) modes into light guides, and the solution of the resulting pair of simultaneous transcendental eigenvalue equations yields n₁ and W.The sensitivity of the method has been studied, and it is shown that n₁ may easily be resolved within 0.002 per minute of arc, considering θ_5E and θ_5M as having equal errors. W may be resolved within 0.02 μ (200 Å) per minute of arc, depending primarily on the proximity of the synchronous guide angle θ₁ to 90°. The method does not require a step in the film, and may be easily reduced to measuring n₁ knowing either the TE or the TM synchronous angle and W.     

Reflectometry measuring refractive index and thickness of polymer samples simultaneously

It is proposed and demonstrated that a novel reflectometry based on the Michelson interference measures simultaneously group refractive index and thickness of polymer samples. Such a reflectometry is a contactless measurement technique, and no damage occurs to the sample measured. Moreover, the measurement error of refractive index decreases linearly with the increasing measured sample's thickness. The ingenious planar polymer sample fabricated acts as not only the measured sample but also the fixed mirror that is necessary in other Michelson interference systems, which simplify the measurement configuration. Our reflectometry exhibits some advantages, such as simple measurement configuration, straightforward principle, easy operation, contactless measurement and high measurement precision.     

Dual-capillary backscatter interferometry for high-sensitivity nanoliter-volume refractive index detection with density gradient compensation

A simple, stable, ultrasensitive dual-capillary dual-bicell (DCDB) microinterferometic backscattering detection (MIBD) system was developed. In DCDB MIBD, a He-Ne laser beam passes through a half-wave plate onto the cross section of two capillaries, one for reference and another for sensing analyte. The position of the backscattered fringe from each capillary, which are in proximity or essentially identical thermal environments, was detected with matched bicell photodetectors. The configuration was found to effectively compensate for thermal drift, which is normally the major source of noise in refractive index (RI) detection systems. It is shown that passive environmental compensation leads to greatly enhanced signal in nanoscale refractometry preformed by MIBD. An order of magnitude improvement in detection limits over single channel configurations is possible. Performance reaches the 10(-9) RIU level for like solvents in the presence in extremely large thermally induced RI gradients. At this level of detectability, DCDB MIBD could facilitate nanoliter-volume, femtomole-level universal detection in applications ranging from mu-HPLC and on-chip CE to scanning microcalorimetry.     

Errors in determination of the refractive index for axially symmetric inhomogeneity

We estimate the error of a multichannel laser refractometer in the investigation of an axially symmetric structure. We consider the effect of photon noise and determine the contribution of the intrinsic noise of the photodetector. We take into account the error due to fluctuation of the refractive index along the path of the light rays, and also consider the interpolation error. Translated from Izmeritel'naya Tekhnika, No. 5, pp. 28–30, May, 1995.     

3-D mapping with ellipsometrically determined physical thickness/refractive index of spin coated sol-gel silica layer

Precursor sol for sol-gel silica layer was prepared from the starting material, tetraethylorthosilicate (TEOS). The sol was deposited onto borosilicate crown (BSC) glass by the spinning technique (rpm 2500). The gel layer thus formed transformed to oxide layer on heating to 450°C for ∼ 30 min. The physical thickness and the refractive index of the layer were measured ellipsometrically (Rudolph Auto EL II) at 632.8 nm. About 10 × 10 mm surface area of the silica layer was chosen for evaluation of thickness and refractive index values at different points (121 nos.) with 1 mm gap between two points. Those data were utilized in the Autolisp programme for 3-D mapping. Radial distribution of the evaluated values was also displayed.     

Determination of thickness, refractive index, and thickness irregularity for semiconductor thin films from transmission spectra

A simplified theoretical model has been proposed to predict optical parameters such as thickness, thickness irregularity, refractive index, and extinction coefficient from transmission spectra. The proposed formula has been solved for thickness and thickness irregularity in the transparent region, and then the refractive index is calculated for the entire spectral region by use of the interference fringes order. The extinction coefficient is then calculated with the exact formula in the transparent region, and an appropriate model for the refractive index is used to solve for the extinction coefficient in the absorption region (where the interference fringes disappear). The proposed model is tested with the theoretical predicted data as well as experimental data. The calculation shows that the approximations used for solving a multiparameter nonlinear equation result in no significant errors.