Weiqi Li

High-Performance Polymer Tandem Solar Cells Employing a New n-Type Conjugated Polymer as an Interconnecting Layer.

UNLABELLED A new n-type polymer, PF3N-2TNDI, with high electron mobility, is developed as efficient cathode interfacial material and interconnecting layer (ICL) for constructing high-performance tandem organic solar cells. Tandem cells employing the ICL with structure of PF3N-2TNDI/Ag/ PEDOT PSS achieve a high power conversion efficiency (PCE) of 11.35%. Moreover, flexible tandem cells with PCE over 10% are also demonstrated.

Depolarization artifacts in dual rotating-compensator Mueller matrix ellipsometry

Noticeable depolarization effects are observed in the measurement of the air using an in-house developed dual rotating-compensator Mueller matrix ellipsometer. We demonstrate that these depolarization effects are essentially artifacts and mainly induced when the compensator with wavelength-dependent optical properties is integrated with the finite bandwidth detector. We define a general formula to represent the actual Mueller matrix of the compensator by taking into account the depolarization artifacts. After incorporating this formula into the system model, a correction method is further proposed, and consequently, improved accuracy can be achieved in the Mueller matrix measurement.

Accurate alignment of optical axes of a biplate using a spectroscopic Mueller matrix ellipsometer

The biplate that consists of two single wave plates made from birefringent materials with their fast axes oriented perpendicular to each other is one of the most commonly used retarders in many optical systems. The internal alignment of the optical axes of the two single wave plates is a key procedure in the fabrication and application of a biplate to reduce the spurious artifacts of oscillations in polarization properties due to the misalignment error and to improve the accuracy and precision of the systems using such biplates. In this paper, we propose a method to accurately align the axes of an arbitrary biplate by minimizing the oscillations in the characteristic parameter spectra of the biplate detected by a spectroscopic Mueller matrix ellipsometer (MME). We derived analytical relations between the characteristic parameters and the misalignment error in the biplate, which helps us to analyze the sensitivity of the characteristic parameters to the misalignment error and to evaluate the alignment accuracy quantitatively. Experimental results performed on a house-developed MME demonstrate that the alignment accuracy of the proposed method is better than 0.01° in aligning the optical axes of a quartz biplate.

Characterization of curved surface layer by Mueller matrix ellipsometry

The authors apply Mueller matrix ellipsometry to characterize the curved surface layers, by utilizing the noticeable anisotropy observed from the measured data. The authors demonstrate that this anisotropy is introduced by the curved surface shape as well as the misalignment between the illumination spot and the surface vertex. An optical model is proposed to expound the anisotropy, and is applied to evaluate the curved thin thermal oxide layer on a silicon sphere crown. After incorporating the proposed optical model in the parameter extraction, the experimental results show that not only will the accuracy of the oxide layer thickness measurement at an arbitrary location on the surface be improved, the curvature radius as well as the position of detection can also be determined directly.

Measurement errors induced by axis tilt of biplates in dual-rotating compensator Mueller matrix ellipsometers

Dual-rotating compensator Mueller matrix ellipsometer (DRC-MME) has been designed and applied as a powerful tool for the characterization of thin films and nanostructures. The compensators are indispensable optical components and their performances affect the precision and accuracy of DRC-MME significantly. Biplates made of birefringent crystals are commonly used compensators in the DRC-MME, and their optical axes invariably have tilt errors due to imperfect fabrication and improper installation in practice. The axis tilt error between the rotation axis and the light beam will lead to a continuous vibration in the retardance of the rotating biplate, which further results in significant measurement errors in the Mueller matrix. In this paper, we propose a simple but valid formula for the retardance calculation under arbitrary tilt angle and azimuth angle to analyze the axis tilt errors in biplates. We further study the relations between the measurement errors in the Mueller matrix and the biplate axis tilt through simulations and experiments. We find that the axis tilt errors mainly affect the cross-talk from linear polarization to circular polarization and vice versa. In addition, the measurement errors in Mueller matrix increase acceleratively with the axis tilt errors in biplates, and the optimal retardance for reducing these errors is about 80°. This work can be expected to provide some guidences for the selection, installation and commissioning of the biplate compensator in DRC-MME design.

Correction of depolarization effect in Mueller matrix ellipsometry with polar decomposition method

Mueller matrix ellipsometry has been demonstrated as a powerful tool for nanostructure metrology in high-volume manufacturing. Many factors may induce depolarization effect in the Mueller matrix measurement, and consequently, may lead to accuracy loss in the nanostructure metrology. In this paper, we propose to apply a Mueller matrix decomposition method for the Mueller matrix measurement to separate the depolarization effect caused by the MME system. The method is based on the polar decomposition by decomposing the measured depolarizing Mueller matrix into a sequence of three matrices corresponding to a diattenuator followed by a retarder and a depolarizer. Since the depolarization effects will be only reflected in the depolarizer matrix, the other two matrices are used to extract the structure parameters of the measured sample. Experiments performed on a one-dimensional silicon grating structure with an in-house developed MME layout have demonstrated that the proposed method achieves a higher accuracy in the nanostructure metrology.

Mueller matrix polarimeter with imperfect compensators: calibration and correction

We propose a method to calibrate the depolarization parameters of the imperfect compensators in dual-rotating compensator Mueller matrix polarimeters, and deduce a set of correction equations for the Mueller matrix calculation.

Depolarization effect of bandwidth in Mueller matrix imaging polarimetry

Obvious depolarization effect of bandwidth is observed in Mueller matrix imaging polarimetry (MMIP) with a dual-rotating compensator configuration. A method is proposed to correct the effect and to improve the measurement accuracy.

Correction on the effect of numerical aperture in optical scatterometry

Optical scatterometry, also referred to as optical critical dimension (OCD) metrology, has been introduced for critical dimension (CD) monitoring and overlay metrology with great success in recent years. Forward modeling to calculate the optical signature from the measured diffractive structure is one of the most important issues in OCD metrology. To simplify the forward modeling approach, such as rigorous coupled-wave analysis (RCWA), the incidence and azimuthal angles are usually assumed to be constant. However, since some focusing elements, such as focusing lens or parabolic mirrors with finite numerical aperture (NA), are always used to gain a sufficient small spot size onto the sample, this assumption is not true in the whole exit pupil of the focusing elements, leading to a modeling error in forward modeling, and finally leading to a fitting error in OCD metrology. In this paper, we propose a correction method with consideration of the effect of NA to decrease the modeling error in the forward modeling. The correction method is an average integral method based on Gaussian quadrature in two dimensions inside a circle, and is performed on forward modeling with varied incidence and azimuthal angles over the exit pupil. Experiments performed on silicon gratings with a Mueller matrix polarimeter have demonstrated that the proposed correction method achieves a higher accuracy in OCD metrology.

Reduction of measurement errors with two-channel configuration in the Mueller matrix ellipsometer

The random noise and the systematic errors caused by azimuthal errors of the optical elements, i.e., the polarizer, the analyzer, or the compensator, would lead to measurement errors in the Mueller matrix ellipsometer (MME). In this paper, we develop the two-channel MME of the optical configuration PCr1SCr2Wp by replacing the analyzer with a Wollaston prism. In the two-channel MME, two intensity spectra would be acquired simultaneously due to the separation and orthogonal polarization of two light beams by the Wollaston prism and are combined to deduce the Mueller matrix. Two figures of merit are derived to evaluate the effects of random noise and systematic errors on the Mueller matrix measurement, and numerical simulations demonstrate that the two-channel MME can give access to higher accuracy by reducing measurement errors due to random noise and systematic errors.