James E. Franke

Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles

Diffraction from a periodic structure is sensitive to small changes in the shape of that structure. It is possible to exploit this behavior of the scatter data for accurate, precise, rapid, nondestructive, and in situ measurements of grating structures. We present the use of rigorous coupled-wave theory to generate diffraction profiles to train a partial least-squares (PLS) multivariate calibration routine. The resulting PLS calibration model was applied to experimental diffraction data from gratings in etched bulk silicon to predict etch depths. A single-detector scanning scatterometer was used to measure the scatter from 32-μm-pitch structures illuminated with a He–Ne laser beam. The scatterometer measured the diffraction patterns from grating structures at 14 die locations on each of a set of five wafers. The theoretically based PLS estimator was then used to predict etch depths from scatterometry data obtained from the 70 different grating structures. The etch depth predictions were in excellent agreement with those obtained with a scanning force microscope (i.e., 0.9-μm-deep structures were predicted with an average error of 0.007 μm). This is a significant step toward the solution of the parametric inverse grating diffraction problem: that of quantitative prediction of structure dimensions from the measurement of scatter data.

Characterization of pH variation in lysed blood by near-infrared spectroscopy

Near-infrared spectra (1300–2500 nm) collected from lysed blood solutions were shown to correlate with the pH of the solutions measured potentiometrically. Cross-validated partial least-squares (PLS) models were developed from these spectral data, which provided standard error of prediction (SEP) values below 0.05 pH units for a pH range of 1.0 (6.8–7.8). Experiments were designed to eliminate possible correlation between pH and other components in the blood in order to ensure that variations in the spectral data correlated to pH were due to hydrogen ion changes only. Further work was performed to discern the primary source of pH information in the lysed blood spectra by using spectra collected from plasma and histidine solutions. The blood, plasma, and histidine data sets were compared with the use of loading vectors from principal component analysis (PCA). These loading vectors show that variations in the spectra of the titrated amino acid histidine mimic those seen in lysed blood, but not those seen in plasma. These results suggest that histidine residues of hemoglobin are providing the spectral variation necessary for pH modeling in the lysed blood solutions. It is further shown that the observed pH-sensitive histidine bands do not arise from the exchangeable proton on the imidazole ring of histidine; rather they arise from the variation in the C–H bonds of the C2 and/or the C4 carbons of the imidazole ring as they are influenced by the titration of the nitrogen-bound proton of the imidazole ring.

Measurement of pH in Whole Blood by Near-Infrared Spectroscopy

Whole blood pH has been determined in vitro by using near-infrared spectroscopy over the wavelength range of 1500 to 1785 nm with multivariate calibration modeling of the spectral data obtained from two different sample sets. In the first sample set, the pH of whole blood was varied without controlling cell size and oxygen saturation (O2 Sat) variation. The result was that the red blood cell (RBC) size and O2 Sat correlated with pH. Although the partial least-squares (PLS) multivariate calibration of these data produced a good pH prediction cross-validation standard error of prediction (CVSEP) = 0.046, R2 = 0.982, the spectral data were dominated by scattering changes due to changing RBC size that correlated with the pH changes. A second experiment was carried out where the RBC size and O2 Sat were varied orthogonally to the pH variation. A PLS calibration of the spectral data obtained from these samples produced a pH prediction with an R2 of 0.954 and a cross-validated standard error of prediction of 0.064 pH units. The robustness of the PLS calibration models was tested by predicting the data obtained from the other sets. The predicted pH values obtained from both data sets yielded R2 values greater than 0.9 once the data were corrected for differences in hemoglobin concentration. For example, with the use of the calibration produced from the second sample set, the pH values from the first sample set were predicted with an R2 of 0.92 after the predictions were corrected for bias and slope. It is shown that spectral information specific to pH-induced chemical changes in the hemoglobin molecule is contained within the PLS loading vectors developed for both the first and second data sets. It is this pH specific information that allows the spectra dominated by pH-correlated scattering changes to provide robust pH predictive ability in the uncorrelated data, and visa versa.

Quantitative Analysis of Infrared Reflection Spectra from Phosphosilicate Glass Films

Infrared (IR) external reflection spectra of phosphosilicate glass (PSG) dielectric thin films deposited on undoped silicon wafer substrates were measured at an incident angle of 15 o . The IR reflection spectra of PSG thin films exhibited nonlinear or distorted spectral features arising from competing optical effects, including specular reflection and reflection-absorption. Quantitative analysis of the PSG IR reflection spectra was achieved by partial least squares (PLS) multivariate calibration techniques. The spectral regions used for the PLS analysis were selected to minimize the detrimental effects of competing optical effects in the IR reflection spectra. Phosphorus content and film thickness were determined with a cross-validated standard error of prediction (SEP) of 0.10 weight percent (w/o) and 60 A, respectively

Analyzing simulated and measured optical scatter for semiconductor process verification

We describe an experiment in which the etch depth of a diffraction grating is measured. A simulated experiment is used to develop and calibrate the measurement technique. A scatterometer was used to measure the diffraction patterns of a set of 5 wafers at 14 die locations. The estimator already developed is then used to find the etch depths at the 70 measured locations. Finally, a scanning force microscope is used as a reference method to validate the scatterometer measurements.

QUANTITATIVE ANALYSIS OF BOROPHOSPHOSILICATE GLASS FILMS ON SILICON USING INFRARED EXTERNAL REFLECTION-ABSORPTION SPECTROSCOPY

Borophosphosilicate glass (BPSG) dielectric thin films deposited on both bare and oxide‐coated undoped silicon wafers have been analyzed using infrared external reflection–absorption spectroscopy (IRRAS). The partial least‐squares (PLS1) algorithm was used to simultaneously determine boron content, phosphorous content, and film thickness, with standard errors of prediction of 0.08 wt %, 0.11 wt %, and 24 A, respectively, in the BPSG films on oxide‐coated wafers (similar results were obtained with the bare wafer BPSG sample set). These results were statistically equivalent to the precisions of the reference methods used to determine each BPSG property, indicating that the precisions of the PLS1 models were limited by the precisions of the reference methods. IRRAS reproducibility and repeatability results verified that the method can be more precise than the reference methods. The reproducibility results were derived from the standard deviation of ten PLS1 predictions of ten IRRAS spectra that were obtained...

Quantitative determination of borophosphosilicate glass thin-film properties using infrared emission spectroscopy

We have completed an experimental study to investigate the use of infrared emission spectroscopy (IRES) for the quantitative analysis of borophosphosilicate glass (BPSG) thin films on silicon monitor wafers. Experimental parameters investigated included temperatures within the range used in the microelectronics industry to produce these films so that the potential for using the IRES technique for real-time monitoring of the film deposition process could be evaluated. The film properties that were investigated included boron content, phosphorus content, film thickness, and film temperature. The studies were conducted over two temperature ranges, 125 to 225 °C and 300 to 400 °C. The latter temperature range includes realistic processing temperatures for the chemical vapor deposition (CVD) of the BPSG films. Partial least-squares (PLS) multivariate calibration methods were applied to spectral and film property calibration data. The cross-validated standard errors of prediction (CVSEP) from the PLS analysis of the IRES spectra of 21 calibration samples each measured at six temperatures in the 300 to 400 °C range were found to be 0.09 wt % for B, 0.08 wt % for P, 3.6 nm for film thickness, and 1.9 °C for temperature. Upon lowering the spectral resolution from 4 to 32 cm−1 and decreasing the number of spectral scans from 128 to 1, we were able to determine that all the film properties could be measured in less than one second to the precision required for the manufacture and quality control of integrated circuits. Thus, real-time in situ monitoring of BPSG thin films formed by CVD deposition on Si monitor wafers is possible with the methods reported here.

Optimized external IR reflection spectroscopy for quantitative determination of borophosphosilicate glass parameters

Infrared (IR) external reflection spectroscopy has been optimized for the quantitative determination of composition and film thickness of borophosphosilicate glass (BPSG) deposited on silicon wafer substrates. The precision of the partial least-squares calibrations for boron and phosphorus contents and thin-film thickness were measured as the cross-validated standard error of prediction statistic. The results showed that BPSG IR reflection spectra collected over a wide range of incident IR radiation angles (15°, 25°, 45°, and 60°) can be used for the simultaneous quantification of these three BPSG parameters. When high angles of incidence were employed, the measurement was found to be more sensitive to small errors in the angle of incidence. The polarization state of the incident IR radiation did not noticeably affect the prediction of the three calibrated BPSG parameters. The results achieved in this study provide guidelines for at-line process monitoring and quality control of BPSG thin films used in the fabrication of microelectronic devices. Index Headings: IR reflection; Multivariate calibration; Partial least-squares

Near-infrared spectroscopy of lysed blood: pH effects

Recent investigations by our group have demonstrated that near-infrared spectra collected from lysed blood solutions can be used to create clinically useful partial least squares (PLS) models for pH with standard errors of prediction below 0.05 pH units for a pH range of 1 (6.8 to 7.8). Further work was performed in order to discern the primary source of pH information in the spectra. Results from these experiments are presented using spectral data acquired over the spectral range of 1300 nm to 2500 nm from plasma, lysed blood and amino acids solutions. Data were analyzed by principal component analysis (PCA) and loading vectors were compared. Experiments were designed to eliminate possible correlation between pH and other components in the system in order to ensure variations in the spectral data were due to hydrogen ion changes only. Results indicate that variations in the spectral characteristics of histidine mimic those seen in lysed blood, but not those seen in plasma, suggesting that histidine residues from hemoglobin are providing the necessary variation for pH modeling in the lysed blood solutions.

Hemoglobin Correction for Near-Infrared pH Determination in Lysed Blood Solutions

The near-infrared (NIR) measurement of blood pH relies on the spectral signature of histidine residing on the hemoglobin molecule. If the amount of hemoglobin in solution varies, the size of the histidine signal can vary depending on changes in either the pH or hemoglobin concentration. Multivariate calibration models developed using the NIR spectra collected from blood at a single hemoglobin concentration are shown to predict data from different hemoglobin levels with a bias and slope. A simple, scalar path length correction of the spectral data does not correct this problem. However, global partial least-square (PLS) models built with data encompassing a range of hemoglobin concentration have a cross-validated standard error of prediction (CVSEP) similar to the CVSEP of data obtained from a single hemoglobin level. It will be shown that the prediction of pH of an unknown sample using a global PLS model requires that the unknown have a hemoglobin concentration falling within the range encompassed by the global model. An alternative method for correcting the predicted pH for hemoglobin levels is also presented. The alternative method updates the single-hemoglobin-level models with slope and intercept estimates from the pH predictions of data collected at alternate hemoglobin levels. The slope and intercept correction method gave SEP values averaging to 0.034 pH units. Since both methods require some knowledge of the hemoglobin concentration in order for a pH prediction to be made, a model for hemoglobin concentration is developed using spectral data and is used for pH correction.