How to obtain thermostatted ring polymer molecular dynamics from exact quantum dynamics and when to use it

We obtain thermostatted ring polymer molecular dynamics (TRPMD) from exact quantum dynamics via Matsubara dynamics, a recently-derived form of linearization which conserves the quantum Boltzmann distribution. Performing a contour integral in the complex quantum Boltzmann distribution of Matsubara dynamics, replacement of the imaginary Liouvillian which results with a Fokker-Planck term gives TRPMD. We thereby provide error terms between TRPMD and quantum dynamics and predict the systems in which they are likely to be small. Using a harmonic analysis we show that careful addition of friction causes the correct oscillation frequency of the higher ring-polymer normal modes in a harmonic well, which we illustrate with calculation of the position-squared autocorrelation function. However, no physical friction parameter will produce the correct fluctuation dynamics for a parabolic barrier. The results in this paper are consistent with previous numerical studies and advise the use of TRPMD for the computation of spectra.Comment: 12 pages, 2 figures. Submitted to Molecular Physic

Derivation of a true (t->0+) quantum transition-state theory. II. Recovery of the exact quantum rate in the absence of recrossing

In Part I [J. Chem. Phys. 138, 084108 (2013)] we derived a quantum transition-state theory by taking the t->0+ (short-time) limit of a new form of quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t->0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that quantum TST (i.e. RPMD-TST) is exact if there is no recrossing (by the real-time quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the long-time limit of the ring-polymer flux-side time-correlation function with that of a hybrid flux-side time-correlation function (containing a ring-polymer flux operator and a Miller-Schwarz-Tromp side function), and by representing the resulting ring-polymer momentum integrals as hypercubes. Together with Part I, the results of this article validate a large number of RPMD calculations of reaction rates.Comment: 14 pages, 4 figures. Argument and wording clarified, typographical errors corrected and references adde

On the uniqueness of t->0+ quantum transition-state theory

It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t->0+ limit of a (new form of) quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here we provide evidence which suggests very strongly that this QTST (= RPMD-TST) is unique, in the sense that the t->0+ limit of any other flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a generalized flux-side time-correlation function which includes all other (known) flux-side time-correlation functions as special limiting cases. We find that the only non-zero t->0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST.Comment: 10 pages, 1 figure. Typographical errors corrected, references updated and adde

Formation kinetics of copper-related light-induced degradation in crystalline silicon

Light-induced degradation (LID) is a deleterious effect in crystalline silicon, which is considered to originate from recombination-active boron-oxygen complexes and/or copper-related defects. Although LID in both cases appears as a fast initial decay followed by a second slower degradation, we show that the time constant of copper-related degradation increases with increasing boron concentration in contrast to boron-oxygen LID. Temperature-dependent analysis reveals that the defect formation is limited by copper diffusion. Finally, interface defect density measurements confirm that copper-related LID is dominated by recombination in the wafer bulk.Peer reviewe

Controlling iron and copper precipitation in silicon wafers

This thesis studies the two most common transition metals in silicon – copper and iron. The purpose of the experiments and theoretical calculations presented in this thesis is to increase the current knowledge of the precipitation behavior of these metals under different processing conditions. The study also includes the development of recombination lifetime methods for impurity characterization in silicon. A method to measure trace copper contamination in silicon using the microwave photoconductivity decay is proposed. The method is based on the observation that copper precipitates can be created using light activation. It is shown that external charge on wafer surfaces can reduce the copper out-diffusion, which extends the applicability of the method. Moreover, oxide precipitates are found to increase the sensitivity of the method. An analytical solution to the current continuity equation for excess carriers in an epitaxial structure under time dependent optical excitation is derived. In addition, some analytical approximations are developed and numerical calculations are made to check their accuracy. The built-in potential between the epitaxial layer and the substrate is taken into account and also the light induced barrier lowering is included in the model. The barrier lowering is found to be noticeable and can affect the effective lifetime by up to two orders of magnitude. Several annealing profiles and contamination levels are used to study the iron gettering behavior at varying supersaturation levels. It was found that the gettering efficiency depends strongly on the initial iron concentration and considerably high supersaturation is needed to initiate the gettering. The results are discussed from the perspective of thermodynamics. The thermal stability of internally gettered iron is studied experimentally by deep level transient spectroscopy. The experiments reveal that the dissolution is a reaction limited process. The simulations of iron re-dissolution show that instead of simulating only the final cooling, it is important to simulate the whole thermal cycle. This is important since low thermal budgets are becoming more and more common in the IC technology.reviewe

Meeting Global Cooling Demand with Photovoltaics during the 21st Century

Space conditioning, and cooling in particular, is a key factor in human productivity and well-being across the globe. During the 21st century, global cooling demand is expected to grow significantly due to the increase in wealth and population in sunny nations across the globe and the advance of global warming. The same locations that see high demand for cooling are also ideal for electricity generation via photovoltaics (PV). Despite the apparent synergy between cooling demand and PV generation, the potential of the cooling sector to sustain PV generation has not been assessed on a global scale. Here, we perform a global assessment of increased PV electricity adoption enabled by the residential cooling sector during the 21st century. Already today, utilizing PV production for cooling could facilitate an additional installed PV capacity of approximately 540 GW, more than the global PV capacity of today. Using established scenarios of population and income growth, as well as accounting for future global warming, we further project that the global residential cooling sector could sustain an added PV capacity between 20-200 GW each year for most of the 21st century, on par with the current global manufacturing capacity of 100 GW. Furthermore, we find that without storage, PV could directly power approximately 50% of cooling demand, and that this fraction is set to increase from 49% to 56% during the 21st century, as cooling demand grows in locations where PV and cooling have a higher synergy. With this geographic shift in demand, the potential of distributed storage also grows. We simulate that with a 1 m$^3$ water-based latent thermal storage per household, the fraction of cooling demand met with PV would increase from 55% to 70% during the century. These results show that the synergy between cooling and PV is notable and could significantly accelerate the growth of the global PV industry

Meeting Global Cooling Demand with Photovoltaics during the 21st Century

Space conditioning, and cooling in particular, is a key factor in human productivity and well-being across the globe. During the 21st century, global cooling demand is expected to grow significantly due to the increase in wealth and population in sunny nations across the globe and the advance of global warming. The same locations that see high demand for cooling are also ideal for electricity generation via photovoltaics (PV). Despite the apparent synergy between cooling demand and PV generation, the potential of the cooling sector to sustain PV generation has not been assessed on a global scale. Here, we perform a global assessment of increased PV electricity adoption enabled by the residential cooling sector during the 21st century. Already today, utilizing PV production for cooling could facilitate an additional installed PV capacity of approximately 540 GW, more than the global PV capacity of today. Using established scenarios of population and income growth, as well as accounting for future global warming, we further project that the global residential cooling sector could sustain an added PV capacity between 20-200 GW each year for most of the 21st century, on par with the current global manufacturing capacity of 100 GW. Furthermore, we find that without storage, PV could directly power approximately 50% of cooling demand, and that this fraction is set to increase from 49% to 56% during the 21st century, as cooling demand grows in locations where PV and cooling have a higher synergy. With this geographic shift in demand, the potential of distributed storage also grows. We simulate that with a 1 m$^3$ water-based latent thermal storage per household, the fraction of cooling demand met with PV would increase from 55% to 70% during the century. These results show that the synergy between cooling and PV is notable and could significantly accelerate the growth of the global PV industry