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.
Analysis and design of monolithic resistors with a desired temperature coefficient using contacts
A technique for implementing monolithic resistors with a desired temperature coefficient (TC) over a wide temperature range is introduced. A typical monolithic resistor consists of a core resistive layer terminated with contact layers on each end. In a typical process, there are core resistive layers that have TCs with opposite sign of that of the contacts. The authors propose to take advantage of this property and distribute a certain number of contacts across the core resistor to achieve a desired overall TC for monolithic resistors. This TC can be negative, zero or positive. The methodologies for designing such resistors are presented. As a proof-of-concept, several resistor structures have been designed and implemented in a 0.13 μm complementary metal-oxide semiconductor technology. The simulation and measurement results over the temperature range of 25-200°C confirm the validity of the proposed technique.
Rubik's for cryptographers
Hard mathematical problems are at the core of security arguments in cryptography. In this paper, we study mathematical generalizations of the famous Rubik’s cube puzzle, namely the factorization, representation and balance problems in non-Abelian groups. These problems arise naturally when describing the security of Cayley hash functions, a class of cryptographic hash functions with very interesting properties. The factorization problem is also strongly related to a famous long-standing conjecture of Babai, at the intersection of group theory and graph theory. A constructive proof of Babai’s conjecture would make all Cayley hash functions insecure, but on the other hand it would have many positive applications in graph theory and computer science. In this paper, we classify existing attacks against Cayley hash functions and we review known results on Babai’s conjecture. Despite recent cryptanalytic progress on particular instances, we show that the factorization, representation and balance problems presumably remain good sources of cryptographic hard problems. Our study demonstrates that Cayley hash functions deserve further interest by the cryptography community.