Zhaohua Feng

Stress-based prediction of dislocation generation in GaN during lateral epitaxial overgrowth

Finite element models were developed to simulate the stress history during an entire gallium nitride lateral epitaxial overgrowth process, from seed layer deposition on a substrate to GaN overgrowth above an SiO2 mask at 1100 °C and then cooldown to 20 °C. Lattice and thermal expansion mismatches between GaN and sapphire were considered simultaneously. Shearing stresses on a series of crystal planes were transiently analyzed. Based on the computational results, it is possible to predict the locations of high-density dislocations and when they develop, as well as Burgers vectors, dislocation types and their directions.

EUV Mask Stress Mapping by an Experimental and Hybrid Finite Element Technique

Image fidelity is one of the fundamental requirements in lithography and it is becoming more important as feature sizes shrink below 90 nm. Image distortion depends on the mask deformation caused by the intrinsic stress in the film-substrate system. To develop an understanding of stress generation and to control film quality, measuring film stress is essential. In recent years, research laboratories and industry have increasingly adopted indirect methods for determining film stress. All of these methods are based on the measurement of substrate deformation, and the film stress is calculated from the substrate curvature by the local application of Stoney’s equation. When the two principal stresses at each point in the film plane are not equal to each other and their distribution is not uniform, the local application of Stoney’s equation is invalid. Even though the accuracy of the measurement may be high, the stress determined may not be. An alternative technique based on numerical analysis has been developed. The limitations of using Stoney’s equation and the new stress measurement technique are discussed in this paper.

Modeling thermal reflow of resist contact hole arrays

Accurate contact-hole imaging depends on the relative size of the contact hole to be patterned and the resolution of the stepper. The hardbake process includes desirable thermal reflow of the resist contact-hole arrays; this effect is driven by the temperature dependence of the polymer-based resist that is densified on the silicon substrate. Thermal reflow is completely independent of current and near-term lithographic printing tools. Resist reflow is a thermomechanical phenomenon dominated by the polymer after development, during which thermal reactions of the polymer produce permanent mechanical deformations of the contact holes. Resist behavior can effectively be classified into solid and viscous, below and above the characteristic glass transition temperature, respectively. The basic states are characterized by changes in the stress states and the phases depending on the thermal behavior of the resist material. The thermal transitions of the resist in the process are strongly influenced by the temperature-dependent mechanical properties, i.e., the modulus, the yield stress, and the coefficient of thermal expansion. Other influences include the surface tension and the bake cycle parameters. This analysis assumes conventionally generated contact holes in the resist, followed by thermal cycling until the thermal reflow produces reduced size contact holes of the desired dimensions. Finite element models were utilized to identify the principal physical parameters influencing resist thermal reflow.

Film Stress Characterization Using Substrate Shape Data and Numerical Techniques

Intrinsic stress in a film-substrate system can have deleterious effects. To facilitate an understanding of stress generation and control film quality, measuring film stress is essential. In recent years research laboratories and industry have increasingly adopted indirect methods, which are usually based on the measurement of substrate deformation. The film stress is calculated by equations relating the stress to the deformation, such as the well-known Stoneys equation. However, when the two principal stresses at each point in the film plane are not equal and their distribution is nonuniform, the local application of Stoneys equation does not provide correct stress results. A numerical technique is presented, which overcomes these limitations and makes accurate stress determination possible.

Simulating the effects of bake process parameters on resist thermal reflow

Producing smaller feature sizes by extending current and near-term lithographic printing tools is a cost-effective strategy for high-volume production of integrated circuits. The hardbake process, as an annealing step to strengthen resist structures, includes a desirable thermal reflow that can facilitate this objective. Thermal reflow of polymer-based resists is a phase-dependent phenomenon in which a polymeric material with recyclable/reversible thermal characteristics experiences dimensional changes through relaxation during thermal cycling at hardbake. Unlike polymer melts, resist reflow is accompanied by a continuous change in the physical state of the resist over a specific temperature range, so it can be described on the basis of the relaxation modulus-temperature relation. Resist behavior during thermal transitions (e.g., glassy, leathery, rubbery plateau, etc.) can effectively be classified into either solid or viscous, depending on whether the resist material is below or above the characteristic glass transition temperature. In general, resist contact hole size can be significantly reduced by optimizing the principal factors driving resist reflow, i.e., temperature-dependent material properties, bake cycle parameters, contact-hole dimensions, and the type of contact array. Recognizable size reduction of the contact hole appears as the resist passes through the leathery state, and its maximum permanent deformation after thermal cycling completely depends on the resist material used. This research focuses on a bake profile of the resist described by the parameters in typical three-stage proximity contact wafer processing. Simulation programs were developed to characterize the primary thermal properties and process parameters affecting the bake profile, and to identify their relative effects on the resist contact-hole response.

Simulation of Stress Generation during GaN Lateral Epitaxial Overgrowth

To facilitate an understanding of defect production in gallium nitride during lateral epitaxial overgrowth, computer models have been developed to simulate the complete mechanical stress and strain fields. The virtual process included the deposition of a GaN seed layer on a sapphire substrate followed by a silicon dioxide stencil mask through which, and over which, the GaN product layer evolved and then cooled down to room temperature. Lattice mismatch and thermal strain were continuously assessed. Shear stresses on different crystallographic planes were analyzed to predict dislocation generation.

Transient thermal distortions of x-ray mask membranes during exposure scanning

During x-ray lithography exposure scanning, intensive x-ray energy deposition in the mask membrane and absorbers causes thermal stresses and mask distortions. Transient heat transfer and thermal distortion models of the masks are presented in this paper. The x-ray beam, which has a Gaussian distribution in the vertical direction and is uniform in the horizontal direction, intermittently scans the pattern area in the vertical direction. The models were used to analyze the ARPA-NIST National x-ray Mask Standard with a 50 mm X 50 mm field size. Effects of exposure parameters are discussed.

Effects of Surface Constraints on Stresses in Heteroepitaxial Films Grown on Compliant Substrates

As films heteroepitaxially grow on substrates, lattice mismatch strain at the interfaces causes stresses in the films and substrates. These stresses can have deleterious effects on film quality. To facilitate an understanding of defect production and control during growth of films on compliant substrates, transient finite element models were developed to simulate the complete mechanical stress and strain fields. Effects of constraints between the template and handle wafer on the film stresses were examined. The investigation showed that different types of constraints caused stress variations over a large range. Other factors affecting the stresses, such as lattice mismatch strain, wafer radius, film and template thickness, were also assessed.