Ti/Ni(80%)Cr(20%) Thin-Film Resistor With a Nearly Zero Temperature Coefficient of Resistance for Integration in a Standard CMOS Process
A thin-film resistor out of Ni(80%)Cr(20%) for integration in a standard complementary metal-oxide-semiconductor process with a temperature coefficient of resistance (TCR) below 10 ppm/K was realized by applying a thin Ti layer underneath. The Ti-layer thickness and the temperature and duration of furnace annealing after deposition were optimized in different experiments. The combination of 5-nm Ti + 10-nm NiCr and a 30-min heat treatment at 350degC in a forming gas ambient was found to yield a sheet resistance of about 140 Omega/sq and a TCR of below 10 ppm/K. The long-term drift of the sheet resistance after 1000 h at 200degC was about 0.3%. A transmission electron microscopy analysis was conducted to investigate the structure of the film and a possible change during annealing. An Auger analysis was conducted for film surface analysis.
Electron microscopic and AES studies on thin layers of NiCr
Abstract In order to understand the parameters affecting the properties of NiCr resistors prepared by various methods, the annealing properties of NiCr thin films were studied. TEM and electron diffraction were used to determine the structure of the films deposited onto SiOx coated microgrids, while electrical measurements and AES indepth profiling were carried out on the samples deposited under identical conditions onto silica substrates. The effect of a SiOx protective coating on the structural changes was investigated during high temperature annealing in vacuum. In the NiCr samples annealed without a protective layer the selective oxidation of chromium led to a rather metallic type of conduction, while in the protected samples the stabilization of the conduction was observed after the same annealing. By hindering oxidation and surface diffusion processes the protective layer resulted in the development of a more stable structure in the NiCr films.
How to do a p-descent on an elliptic curve
In this paper, we describe an algorithm that reduces the computation of the (full) p-Selmer group of an elliptic curve E over a number field to standard number field computations such as determining the (p-torsion of) the S-class group and a basis of the S-units modulo pth powers for a suitable set S of primes. In particular, we give a result reducing this set S of 'bad primes' to a very small set, which in many cases only contains the primes above p. As of today, this provides a feasible algorithm for performing a full 3-descent on an elliptic curve over Q, but the range of our algorithm will certainly be enlarged by future improvements in computational algebraic number theory. When the Galois module structure of E[p] is favorable, simplifications are possible and p-descents for larger p are accessible even today. To demonstrate how the method works, several worked examples are included.