This dissertation studies load balancing algorithms for many-server systems (with N servers) and focuses on the steady-state performance of load balancing algorithms in the heavy traffic regime. The framework of Stein’s method and (iterative) state-space collapse (SSC) are used to analyze three load balancing systems: 1) load balancing in the Sub-Halfin-Whitt regime with exponential service time; 2) load balancing in the Beyond-Halfin-Whitt regime with exponential service time; 3) load balancing in the Sub-Halfin-Whitt regime with Coxian-2 service time.

When in the Sub-Halfin-Whitt regime, the sufficient conditions are established such that any load balancing algorithm that satisfies the conditions have both asymptotic zero waiting time and zero waiting probability. Furthermore, the number of servers with more than one jobs is o(1), in other words, the system collapses to a one-dimensional space. The result is proven using Stein’s method and state space collapse (SSC), which are powerful mathematical tools for steady-state analysis of load balancing algorithms. The second system is in even “heavier” traffic regime, and an iterative refined procedure is proposed to obtain the steady-state metrics. Again, asymptotic zero delay and waiting are established for a set of load balancing algorithms. Different from the first system, the system collapses to a two-dimensional state-space instead of one-dimensional state-space. The third system is more challenging because of “non-monotonicity” with Coxian-2 service time, and an iterative state space collapse is proposed to tackle the “non-monotonicity” challenge. For these three systems, a set of load balancing algorithms is established, respectively, under which the probability that an incoming job is routed to an idle server is one asymptotically at steady-state. The set of load balancing algorithms includes join-the-shortest-queue (JSQ), idle-one-first(I1F), join-the-idle-queue (JIQ), and power-of-d-choices (Pod) with a carefully-chosen d.

This study investigates three issues that are relevant for the development of multinational investment banks in China. The first is about the domestic market conditions that are necessary for a country to develop multinational investment banks. The second issue is about the degree to which China has met these conditions. The last issue focuses on the potential strategies Chinese investment banks can undertake to become multinational corporations.

To address the first issue, I draw an important distinction between international investment banks and multinational investment banks. For an international investment bank to be regarded as a multinational, I propose that it must have a strong presence (i.e., holding at least one percent of the market share) in at least two of the seven major capital markets in the world. Using this criterion, I identify 25 multinational investment banks. I then analyze their home countries’ domestic market conditions and propose that the following six factors are important to the development of multinational investment banks: the size of the home country’s gross domestic product (GDP), the total capitalization of its domestic security market, the number of its Global 500 firms, the volume of its foreign direct investment (FDI), the internationalization of its currency, and the openness of its capital market to foreign investors.

By comparisons, I find that China’s domestic market conditions are comparable to the home countries of multinational investment banks with respect to the size of GDP, total market capitalization, the number of Global 500 firms, and the volume of FDI. What China lags behind are the internationalization of currency and the openness of capital market to foreign investors. Given the current trends of development, it is very likely that China will be able to catch up on the latter within ten years, thus meeting all the conditions necessary for the development of multinational investment banks.

Based on the above findings, I suggest that Chinese investment banks seize this historical opportunity, speed up the internationalization of their businesses, and learn from the experiences of global industry leaders to become truly multinational corporations.

In this dissertation, remote plasma interactions with the surfaces of low-k interlayer dielectric (ILD), Cu and Cu adhesion layers are investigated. The first part of the study focuses on the simultaneous plasma treatment of ILD and chemical mechanical polishing (CMP) Cu surfaces using N2/H2 plasma processes. H atoms and radicals in the plasma react with the carbon groups leading to carbon removal for the ILD films. Results indicate that an N2 plasma forms an amide-like layer on the surface which apparently leads to reduced carbon abstraction from an H2 plasma process. In addition, FTIR spectra indicate the formation of hydroxyl (Si-OH) groups following the plasma exposure. Increased temperature (380 °C) processing leads to a reduction of the hydroxyl group formation compared to ambient temperature processes, resulting in reduced changes of the dielectric constant. For CMP Cu surfaces, the carbonate contamination was removed by an H2 plasma process at elevated temperature while the C-C and C-H contamination was removed by an N2 plasma process at elevated temperature. The second part of this study examined oxide stability and cleaning of Ru surfaces as well as consequent Cu film thermal stability with the Ru layers. The ~2 monolayer native Ru oxide was reduced after H-plasma processing. The thermal stability or islanding of the Cu film on the Ru substrate was characterized by in-situ XPS. After plasma cleaning of the Ru adhesion layer, the deposited Cu exhibited full coverage. In contrast, for Cu deposition on the Ru native oxide substrate, Cu islanding was detected and was described in terms of grain boundary grooving and surface and interface energies. The thermal stability of 7 nm Ti, Pt and Ru ii interfacial adhesion layers between a Cu film (10 nm) and a Ta barrier layer (4 nm) have been investigated in the third part. The barrier properties and interfacial stability have been evaluated by Rutherford backscattering spectrometry (RBS). Atomic force microscopy (AFM) was used to measure the surfaces before and after annealing, and all the surfaces are relatively smooth excluding islanding or de-wetting phenomena as a cause of the instability. The RBS showed no discernible diffusion across the adhesion layer/Ta and Ta/Si interfaces which provides a stable underlying layer. For a Ti interfacial layer RBS indicates that during 400 °C annealing Ti interdiffuses through the Cu film and accumulates at the surface. For the Pt/Cu system Pt interdiffuion is detected which is less evident than Ti. Among the three adhesion layer candidates, Ru shows negligible diffusion into the Cu film indicating thermal stability at 400 °C.