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Polymerizates of imidazole and epichlorohydrin (Imep) serve as one of the benchmarks for today's chemistry development of leveler additives in context of the industrial copper Damascene process. We therefore studied the synergistic and antagonistic interplay of the Imep polymer with other additives, commonly present in copper plating baths used for the state-of-the-art IC manufacturing. Characteristic oscillations in the applied electrode potential appear in galvanostatic copper electrodeposition when Imep is used in combination with SPS (bis­(sodium sulfopropyl) disulfide). We identified the reversible Cu­(I) coordination chemistry of the Imep polymer as a second prospective driving force beyond interfacial anion/cation pairing toward the formation of such suppressor/leveler ensembles at the interface. OH groups of the pristine Imep polymer coordinate with H2O-Cu­(I)-MPS units (primary effect) that appear as side products of the copper electrodeposition in the presence of SPS. The latter transforms during copper deposition into monomeric MPS (mercaptopropanesulfonic acid/sulfonate) as result of the adsorptive SPS dissociation on the copper surface. Electrostatic coupling between the anionic sulfonate of the MPS and the cationic imidazolium group in the formed linear, bidentate Imep-Cu­(I)-MPS complex results into a neutral, hydrophobic species that finally precipitates (secondary effect). The presence of diamagnetic Cu­(I) species in those precipitates is proven by elementary analysis in combination with magnetic SQUID measurements. The observed potential oscillations under galvanostatic conditions are discussed in terms of an alternating precipitation and dissolution of the Imep-Cu­(I)-MPS suppressor ensemble at the copper/electrolyte interface. Linear sweep experiments prove a partially hidden, N-shaped negative differential resistance (HN-NDR) as physical origin for the observed instabilities under galvanostatic conditions. SIMS (secondary ion mass spectroscopy) depth profiling of copper films deposited under such oscillatory conditions reveals periodic modulations in the contamination level parallel to the surface normal. Cross-sectional FIB analysis of the grown copper deposit reveals periodically repeating lines of grain boundaries in the copper deposit.

We study the generalized transfer operator £f p f{z) = £ x n = i\z + nj /(1/(Z + H)) of the Gauss map Tx = (l/x)modi on the unit interval. This operator, which for β = 1 is the familiar Perron-Frobenius operator of T, can be defined for Re β > \ as a nuclear operator either on the Banach space AJJ)) of holomorphic functions over a certain disc D or on the Hubert spacê Reβ(H-1/2 ) of functions belonging to some Hardy class of functions over the half plane #_i /2 The spectra of <£ β on the two spaces are identical. On the space ^Reβ(H-ι/2) &β is isomorphic to an integral operator X β with kernel the Bessel function % 2 β-i(2y/st) and hence to some generalized Hankel transform. This shows that S£ β has real spectrum for real β > \. On the space A^D) the operator $£ } β can be analytically continued to the entire β-plane with simple poles at β = β k = (1 -fc)/2, k = 0,1,2,... and residue the rank 1 operator jfWf = i(l/fc!)/ (fc) (0). From this similar analyticity properties for the Fredholm determinant det (1 -if β ) of if β and hence also for Ruelle's zeta function follow. 00 Another application is to the function ζ M (β) = Σ [ή]β , where [n] denotes theextends to a meromorphic function in the β-plane with the only poles at β = ± 1 both with residue 1.