Higher-order rewrite systems (HRSs) and simply-typed term rewriting systems (STRSs) are computational models of functional programs. We recently proposed an extremely powerful method, the static dependency pair method, which is based on the notion of strong computability, in order to prove termination in STRSs. In this paper, we extend the method to HRSs. Since HRSs include λ-abstraction but STRSs do not, we restructure the static dependency pair method to allow λ-abstraction, and show that the static dependency pair method also works well on HRSs without new restrictions.

We have integrated a phase change random access memory (PRAM), completely based on 0.24 µm-CMOS technologies using nitrogen doped GeSbTe films. The Ge2Sb2Te5 (GST) thin films are well known to play a critical role in writing current of PRAM. Through device simulation, we found that high-resistive GST is indispensable to minimize the writing current of PRAM. For the first time, we found the resistivity of GST film can be controlled with nitrogen doping. Doping nitrogen to GST film successfully reduced writing current. A 0.24 µm PRAM using N-doped GST films were demonstrated with writing pulse of 0.8 mA-50 ns for RESET and 0.4 mA-100 ns for SET. Also, the cell endurance has been enhanced with grain growth suppression effect of dopant nitrogen. Endurance performance of fully integrated PRAM using N-doped GST shows no fail bit up to 2E9 cycles. Allowing 1% failures, extrapolation to 85 indicates retention time of 2 years. All the results show that PRAM is one of the most promising candidates in the market for the next generation memories.

A spherical-harmonics expansion method is used to find approximate numerical solutions of the Boltzmann Transport Equation in the homogeneous case. Acoustic and optical phonon scattering, ionized impurity scattering as well as an energy band structure fitting the silicon density of states up to 2.6 eV above the conduction-band edge are used in the model. Comparisons with Monte Carlo data show excellent agreement, and prove that detailed information on the high-energy tail of the distribution function can be obtained at very low cost using this methodology.