The catalyzation of TaN/SiO 2 /Si substrates was carried out by immersion in SnCl 2 /HCl and PdCl 2 /HCl solutions for electroless Cu deposition. The sizes and morphologies of the catalytic sites on the TaN layers were found to be a function of catalyzation conditions, including solution temperature, immersion time, and the surface oxides. The appropriate formula for catalyzation was obtained by considering both the quality and efficiency. The catalytic sites were composed of Sn and Pd, and the ratio of Sn/Pd was about 1.3. During electroless Cu deposition on the catalyzed TaN/SiO 2 /Si substrates, Cu nuclei first formed at the catalytic sites in the early stage, gradually agglomerated into dense islands, and finally merged to continuous deposition films. The Cu films were uniformly and smoothly deposited with a surface roughness of 6.2 nm under a film thickness of 210 nm. The lowest electrical resistivity of the Cu films was 2.5 ⍀ cm, and the residual resistivity contributed to the participation of Sn-Pd catalyst and internal defects. Good gap-filling capability of electroless Cu deposition on Sn/Pd catalyzed, patterned substrates exhibited its high potential to act as a seed layer for Cu electrodeposition and even to completely fill submicrometer gaps in ultralarge-scale integrated metallization.Metallization is a critical issue in the production of ultralargescale integrated ͑ULSI͒ circuits. As the size of the devices scales down and chip density highly increases, copper ͑Cu͒ has been proposed as the most reliable interconnect material to replace aluminum because of its significant advantages of low electrical resistivity, low power dissipation, and high resistance to electromigration. 1,2 Recently, Cu deposition by electrochemical methods has received great attention, since high-quality Cu films can be easily obtained at a low deposition temperature and by low tool cost. 3,4 Electroless copper deposition has excellent step-coverage capability for high-aspectratio ͑A.R.͒ gaps and can be used either to produce the seed layer for copper electrodeposition or to fill the fine gaps directly. 5-7 Besides, due to the high selectivity, the low processing temperatures, the low cost of raw materials and equipment, and the feasibility, 8 it becomes attractive and is under continuous investigation.However, some problems associated with Cu metallization must be solved, especially, the easy diffusion of Cu into SiO 2 and Si and its poor adhesion to dielectric layers. Therefore, for the successful integration of Cu metallization with integrated circuit ͑IC͒ processes, proper diffusion barrier layers of refractory metals and their nitrides are required to be placed between Cu and either the dielectric layers or the Si substrate to prevent the diffusion of Cu and to improve interfacial adhesion. Tantalum nitride ͑TaN͒, recognized as one of the most promising diffusion barriers for Cu, not only provides high thermal stability, but also has characteristics such as acceptable conductivity and the chemical inactivity with Cu. 9,10...

We give an operator algebraic formulation of the stabilizer formalism for error correction in quantum computing. The approach relies on an analysis of commutant structures, and gives a natural extension of the classic stabilizer formalism to the general case of arbitrary (not necessarily abelian) Pauli subgroups and subsystem codes. We show how to identify the largest stabilizer subsystem for every Pauli subgroup and discuss examples.