Bincheng Li

Measurement accuracy analysis of photocarrier radiometric determination of electronic transport parameters of silicon wafers

Simulations are performed to investigate the accuracy of the simultaneous determination of the electronic transport properties (the carrier lifetime, the carrier diffusion coefficient, and the front and rear surface recombination velocities) of silicon wafers by means of the photocarrier radiometry (PCR) technique through fitting frequency-scan data to a rigorous model via a multi-parameter fitting process. The uncertainties of the fitted parameter values are analyzed by calculating the dependence of the square variance including both amplitude and phase variances on the electronic transport properties. Simulation results show that the ability of the PCR to accurately determine carrier lifetimes gradually decreases for lifetimes longer than roughly 100 microseconds. In case the carrier diffusion coefficient is previously known, the carrier lifetime and front surface recombination velocity can be determined with uncertainties approximately +/-20% or less. Experiments with an ion-implanted silicon wafer were performed and the carrier lifetime and front surface recombination velocity were determined with estimated uncertainties approximately +/-30% and +/-15%, respectively

Combined laser calorimetry and photothermal technique for absorption measurement of optical coatings

To the best of our knowledge, a combined sensitive technique employing both laser calorimetry and a surface thermal lens scheme for measuring absorption values of optical coatings is presented for the first time. Laser calorimetric and pulsed surface thermal lens signals are simultaneously obtained with a highly reflecting UV coating sample irradiated at 193 nm. The advantages and potential applications of the combined technique and the experimental factors limiting the measurement sensitivity are discussed.

Electronic transport characterization of silicon wafers by combination of modulated free carrier absorption and photocarrier radiometry

A combined modulated free carrier absorption (MFCA) and photocarrier radiometry (PCR) technique is developed to determine simultaneously the electronic transport properties (carrier diffusion coefficient, carrier lifetime, and front surface recombination velocity) of silicon wafers. Comparative computer simulations are carried out to investigate how the experimental measurement errors affect the simultaneous determination of the electronic transport parameters by introducing random or systematic errors into the simulated MFCA and PCR data and statistically analyzing the fitted results, by means of separate MFCA and PCR, as well as the combined MFCA and PCR through fitting the experimental dependences of signal amplitudes and phases to the corresponding theoretical models via a multiparameter fitting procedure, respectively. The simulation results show that with the combined MFCA and PCR the effect of experimental errors on the simultaneous determination of the transport parameters is significantly reduced...

Accuracy analysis for the determination of electronic transport properties of Si wafers using modulated free carrier absorption

Computer simulations are carried out to investigate the sensitivity of simultaneous determination of three electronic transport properties (carrier lifetime, carrier diffusivity, and front surface recombination velocity) of silicon wafers by modulated free carrier absorption (MFCA) via a multiparameter fitting procedure. The relative accuracy of the transport parameter determination by laterally resolved MFCA (LR-MFCA), in which the amplitude and phase are measured as functions of the pump-probe-beam separation at several modulation frequencies covering an appropriate range, and by conventional frequency-scan MFCA (FS-MFCA), in which only the modulation frequency dependences of the amplitude and phase are recorded, is theoretically analyzed and experimentally estimated by calculating the dependence of the mean square variance on individual transport parameter via a multiparameter estimation process. Simulated and experimental results show that the determination of the transport properties of silicon wafers by LR-MFCA are more accurate, compared with that by FS-MFCA. Comparative experiments are performed with a silicon wafer and the estimated uncertainties of the carrier diffusivity; lifetime and front surface recombination velocity are approximately +/- 3.7%, +/- 25%, and +/- 35% for LR-MFCA and +/- 7.5%, +/- 31%, and +/- 24% for FS-MFCA, respectively.

Optimization of thickness uniformity of optical coatings on a conical substrate in a planetary rotation system.

For a coating machine with a planetary rotation system and counterrotating shadowing mask configuration, a shadowing mask was designed using a numerical optimization algorithm to control the thickness uniformity of optical coatings formed on conical substrate. Single-layer magnesium fluoride (MgF(2)) and antireflective (AR) coating at 193 nm were fabricated on a convex conical substrate holder (with diameter 225 mm, apex angle 140 deg, and height 41 mm) by thermal evaporation. Thickness distribution determined from the transmittance spectra of single-layer MgF(2) thin films on BK7 slices showed that uniformities better than 99.3% were experimentally achieved with the designed counterrotating shadowing mask. From the reflectance spectra, uniform optical performance was also obtained for the 193 nm AR coating deposited on fused-silica substrates.

Theoretical design of shadowing masks for uniform coatings on spherical substrates in planetary rotation systems.

A straightforward theoretical routine is proposed to design shadowing masks which are used for preparing uniform coatings on flat as well as strongly curved spherical substrates with large diameters in planetary rotation system. By approximating a spherical substrate in planetary rotation to a corresponding flat substrate in simple rotation around the revolution axis, the initial shape of a shadowing mask is determined. The desired uniformity for the spherical substrate is further realized through expanding appropriately the arc length of the initial shadowing mask. Utilizing the shadowing masks designed with the theoretical routine, film uniformities better than 97% are experimentally achieved for large-diameter spherical substrates with ratios of clear aperture to radius of curvature range from approximately -1.0 to 1.3.

Self-eliminating instrumental frequency response from free carrier absorption signals for silicon wafer characterization

Accurate determination of electronic transport properties of semiconductor wafers with modulated free carrier absorption (MFCA) and multiparameter fitting requires the total elimination of instrumental response from the MFCA signals. In this paper, an approach to eliminate the effect of instrumental response on the frequency dependence of MFCA amplitude and phase is developed both theoretically and experimentally to simultaneously determine the transport properties (minority-carrier lifetime, carrier diffusion coefficient, and front surface recombination velocity) of silicon wafers. Experimental results showed that with the proposed method the instrumental frequency response was fully eliminated from the experimental MFCA data and had no impact on the multiparameter fitting, while with conventional methods the accuracy of the fitted transport parameters was influenced detrimentally by the errors of the measured instrumental frequency responses, in particular for the minority-carrier lifetime and the front surface recombination velocity.

Sensitivity analysis of laterally resolved free carrier absorption determination of electronic transport properties of silicon wafers

Simulations are performed to investigate the uniqueness of simultaneous determination of electronic transport properties (the carrier lifetime, the carrier diffusivity, and the front surface recombination velocity) of silicon wafers by laterally resolved modulated free carrier absorption (MFCA) and multiparameter fitting. The dependences of MFCA amplitude and phase on these transport properties at different pump-probe-beam separations and modulation frequencies are analyzed. The uncertainties of the fitted parameter values are analyzed by investigating the dependences of a mean square variance including both the amplitude error and phase error on corresponding electronic transport parameters. Simulation results show that the electronic transport parameters can be determined accurately through fitting experimental MFCA data carrying both frequency- and space-domain information of carrier diffusion to a rigorous MFCA model. Among the three transport parameters, the carrier diffusivity can be determined most precisely, with an uncertainty of less than +/- 5%, due to the highest sensitivity of the laterally resolved MFCA signal to the diffusivity. The highly accurate determination of the diffusivity further improves the precision of the carrier lifetime and the front surface recombination velocity values simultaneously determined via multiparameter fitting. Experiments were performed with a silicon wafer and the results were in good agreement with the theoretical simulations

Simultaneous determination of optical constants, thickness, and surface roughness of thin film from spectrophotometric measurements.

A model taking into consideration the refractive index inhomogeneity and surface roughness of a film was proposed for the simultaneous determination of the optical constants, thickness, and surface roughness of a single-layer thin film from spectrophotometric measurements. In the model, the rough surface was treated as an effective absorbing layer. The model was applied to determine simultaneously the parameters of single-layer MgF(2) thin films deposited on fused silica substrates by the oblique-angle deposition technique. The film thicknesses and rms surface roughnesses extracted from spectrophotometric measurements with the proposed model were in good agreement with the values measured by a spectroscopic ellipsometer and an atomic force microscope, respectively.

Photocarrier radiometric and ellipsometric characterization of ion-implanted silicon wafers

The photocarrier radiometry (PCR) responses of heavily implanted silicon wafers (As+ ion 1×1013–1×1016cm−2) were reported. The experimental dependence of the PCR amplitude on the implant dose was in good agreement with the theoretical prediction calculated with a three-layer PCR model, in which the implanted silicon wafer was assumed to be consisted of an amorphous, a polycrystalline, and a single-crystalline Si layer. The structural, optical, and transport properties of all layers used in the calculations were determined experimentally with spectroscopic ellipsometry (SE), spectrophotometry, and laterally resolved modulated free-carrier absorption to minimize the uncertainties of the theoretical calculations. The dose dependence of the PCR amplitude showed a nonmonotonicity at high dose implantation, as confirmed by the SE measurements.