Statistical properties of first-order bang-bang Pll with nonzero loop delay

A method to solve the stationary state probability is presented for the first-order bang-bang phase-locked loop (BBPLL) with nonzero loop delay. This is based on a delayed Markov chain model and a state How diagram for tracing the state history due to the loop delay. As a result, an eigenequation is obtained, and its closed form solutions are derived for some cases. After obtaining the state probability, statistical characteristics such as mean gain of the binary phase detector and timing error variance are calculated and demonstrated.

Computational study of the growth of copper thin films by atomic layer deposition

Copper is the main interconnect material in microelectronic devices, and a 2 nm-thick continuous Cu film seed layer needs to be deposited to produce microelectronic devices with the smallest features and more functionality. Atomic layer deposition (ALD) is the most suitable method to deposit such thin films. However, the reaction mechanism and the surface chemistry of copper ALD remain unclear, which is deterring the development of better precursors and design of new ALD processes. In this thesis, we study the surface chemistries during ALD of copper by means of density functional theory (DFT). To understand the effect of temperature and pressure on the composition of copper with substrates, we used ab initio atomistic thermodynamics to obtain phase diagram of the Cu(111)/SiO2(0001) interface. We found that the interfacial oxide Cu2O phases prefer high oxygen pressure and low temperature while the silicide phases are stable at low oxygen pressure and high temperature for Cu/SiO2 interface, which is in good agreement with experimental observations. Understanding the precursor adsorption on surfaces is important for understanding the surface chemistry and reaction mechanism of the Cu ALD process. Focusing on two common Cu ALD precursors, Cu(dmap)2 and Cu(acac)2, we studied the precursor adsorption on Cu surfaces by means of van der Waals (vdW) inclusive DFT methods. We found that the adsorption energies and adsorption geometries are dependent on the adsorption sites and on the method used to include vdW in the DFT calculation. Both precursor molecules are partially decomposed and the Cu cations are partially reduced in their chemisorbed structure. It is found that clean cleavage of the ligand−metal bond is one of the requirements for selecting precursors for ALD of metals. 2 Bonding between surface and an atom in the ligand which is not coordinated with the Cu may result in impurities in the thin film. To have insight into the reaction mechanism of a full ALD cycle of Cu ALD, we proposed reaction pathways based on activation energies and reaction energies for a range of surface reactions between Cu(dmap)2 and Et2Zn. The butane formation and desorption steps are found to be extremely exothermic, explaining the ALD reaction scheme of original experimental work. Endothermic ligand diffusion and re-ordering steps may result in residual dmap ligands blocking surface sites at the end of the Et2Zn pulse, and in residual Zn being reduced and incorporated as an impurity. This may lead to very slow growth rate, as was the case in the experimental work. By investigating the reduction of CuO to metallic Cu, we elucidated the role of the reducing agent in indirect ALD of Cu. We found that CuO bulk is protected from reduction during vacuum annealing by the CuO surface and that H2 is required in order to reduce that surface, which shows that the strength of reducing agent is important to obtain fully reduced metal thin films during indirect ALD processes. Overall, in this thesis, we studied the surface chemistries and reaction mechanisms of Cu ALD processes and the nucleation of Cu to form a thin film.