Hanyou Chu

Fundamental solutions for real-time optical CD metrology

We have developed fast numerical solutions to the diffraction of light from periodic array structures that allow real-time regression fitting to optical data. In contrast to previous publications, the solutions we have developed are easily applied to focused beams with arbitrary angles of incidence on periodic structures with complex shapes and multiple layers both within and below the structure. The adaptive nature of the shape definition makes it relatively easy to characterize typical microelectronic patterning effects, including undercut, rounding, footing and encroachment in a robust manner on poly-gate, STI, Damascene and resist structures. This real-time approach is not limited by a priori knowledge or assumptions about the range of variation of the CD parameters, and is therefore able to deal with large excursions in process parameters. It is also not limited by parameter discretization effects. The program itself is easily configured for any type of optical measurement (ellipsometry, reflectometry, etc). Data will be presented for several categories of microelectronic CD structures that have been measured with this approach.

Efficient finite-element, Green's function approach for critical-dimension metrology of three-dimensional gratings on multilayer films.

We present an efficient method for calculating the reflectivity of three-dimensional gratings on multilayer films based on a finite-element, Greens function approach. Our method scales as NlogN, where N is the number of plane waves used in the expansion. Therefore, it is much more efficient than the commonly adopted rigorous-coupled-wave analysis (RCWA), which scales as N3. We demonstrate the effectiveness of this method by applying it to a two-dimensional periodic array of contact holes on a multilayer film. We find that our Greens function approach is about one order of magnitude faster than the RCWA approach when applied to typical contact holes considered in industry. For most cases, this method is efficient enough for application as a realtime, critical-dimension metrology tool.

Time ordering theorem and calculational recipes for thermo field dynamics

Abstract We show that in thermo field dynamics (TFD), with a particular choice of the parameters, internal times cannot be larger than the largest external time for a Feynman diagram with any number of external points. We present a simple recipe which finally makes Feynman diagram calculations in TFD feasible. In fact, frequency integration becomes trivial compared to the Matsubara approach when the time property is utilized.

Contact hole inspection by real-time optical CD metrology

We have developed fast numerical solutions to the diffraction of light from a periodic array of contact holes (CH) in microelectronic structures. We present results for contact holes in oxide and in 193 nm and 248 nm photoresists. We also show detectability limits of the CH and observed variations across wafers processed with state-of-the-art lithography.

Detection and analysis of depolarization artifacts in rotating-compensator polarimeters

Absolute constraints, namely, the Schwarz inequality and a complementary expression derived by us, are used to obtain corresponding absolute constraints on the Fourier coefficients of the intensity transmitted through rotating-compensator polarimeters and ellipsometers. These expressions allow the investigation of artifacts that result in mixed or apparently mixed polarization states over the cross section of the beam, the averaging time of the detector, or the frequency passband of the dispersing element. Examples include multiple internal reflections or inhomogeneous strain within an element, scattered light, and other types of system and component defects that cannot be accessed by means of polarization-state data alone. We apply these results to our polarizer-sample-compensator-analyzer (PSCA) ellipsometer to illustrate capabilities. A simple analytic model is shown to give a quantitative description of depolarization in systems for which the resolution is finite and the retardation varies with wavelength.

Saddle-point excitons in GaAs/GaAlAs superlattices - magneto-optical effects

Abstract We have studied the luminescence excitation properties of a series of GaAs GaAlAs superlattices in a magnetic field. The periods of the samples are such that the miniband widths for electrons range between 0 and 20 meV. New structures are observed at zero magnetic field, which we attribute to excitons based on their magnetic field dependence. Comparing experimental spectra and theoretical calculations, we discuss the possibility that these structures are saddle point excitons.

Phonons in semiconductor superlattices

Abstract We present theoretical studies of phonon modes in semiconductor superlattices in a rigid-ion model. We examine the dispersion curves for phonons propagating in any directions, taking into account the long-range Coulomb interaction. We introduce an alternative approach which avoids direct computation of the Coulomb interaction in superlattices. Our calculations indicate that several superlattice optical phonon branches can have different frequencies when → k approaches zero from different directions. Such anisotropic splitting was observed experimentally and was interpreted in a macroscopic model involving layers of different dielectric constants. The predictions of our microscopic model are in qualitative agreement with those of the macroscopic model.

Optical Properties of Semiconductor Superlattices

Semiconductor quantum wells and superlattices1 have received growing interest in recent years. Optical measurements including photoabsorption, photoluminescence, and Raman scattering are widely adopted for probing the electronic states of these heterostructures. Using a simple quantum mechanical model which contains essentially a particle in a one-dimensional square-well potential (particle-in-a-box model)2, one can obtain a fairly accurate description of the energy levels in a GaAs-AlxGa1−xAs quantum well with well size between 50 A and 300 A. This model predicts a selection rule for the inter-band optical transitions which requires the difference in principal quantum numbers of the initial hole state and the final electron state in a quantum well to be zero, i.e. Δn = 0. Indeed, most experimental data indicate that Δn = 0 transitions are at least an order of magnitude stronger than the other transitions which violate this selection rule.

Some peculiar features of layered superconductors

Abstract In this brief communication, the effect of fluctuations on the superconducting order parameters in a layered superconductor is studied. It is found that, within a certain parameter range, the fluctuations induce a first order phase transition. We also study the specific heat anomaly in such systems.

Phonon dispersion curves of GaAsAlAs superlattices

Abstract The phonon properties of (GaAs)m(AlAs)n superlattices are studied with an eleven-parameter rigid-ion model. Short-range interactions up to the second neighbours are included, and the long-range Coulomb interaction is calculated exactly. Modes propagating both normal (k// = 0) oblique (k// ≡ 0) to the interfaces are studied. Anisotropy of zone center optical phonons is examined. The theoretical results are compared with the existing experimental data with favorable agreement.