Numerical Model and System for Prediction and Reduction of Indoor COVID-19 Infection Risk

Airborne aerosol transmission is a significant route of SARS-CoV-2 and other viruses in indoor environments. The developed numerical model assesses the risk of a COVID-19 infection in a room based on the measurements of temperature, relative humidity, CO2 and particle concentration, as well as the number of people and occurrences of speech, coughing, and sneezing obtained through a dedicated low-cost sensor system [1]. As the model operates faster than real-time, it can dynamically feed this information back to the measurement system or building management system, and it can activate an air purifier with filtration and UV-C disinfection when the predicted infection risk is high. This solution enhances energy efficiency as (1) lower ventilation intensity is necessary in the cold season to reach the same safety level and (2) the purifier is activated only if the predicted infection risk is above a certain threshold.The model is integral and takes into account the average values of simulated variables. However, it considers the inhomogeneous vertical distribution of concentration of droplets and aerosol particles. The droplets expelled by a potentially infectious person at a certain height through breathing, speaking, coughing, and sneezing are characterized by the total amount of expelled liquid, droplet size distribution and virus particle concentration. The rate of droplet evaporation depends on the temperature and relative humidity. Droplets are redistributed within the room vertically through turbulent diffusion and gravitational force. If the final droplet diameter is less than 5 mm, these particles are considered airborne and can leave the room only by ventilation, filtration, or by sedimentation on surfaces through Brownian diffusion. As a person in the room inhales these droplets and aerosols, the risk of infection increases as the number of absorbed virions grows, with the probability of infection being 50% when 300 virions have been inhaled.The parameter studies using the model indicate that the coughing and sneezing events greatly increase the probability of infection in the room, therefore the identification of these events is crucial for the applied measurement system. A method for determining the unknown ventilation intensity by measuring the number of people and the CO2 concentration is proposed and tested

Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals

The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing

Modeling of melt flow influence on zone shape during the industrial floating zone crystal growth process

Darbā tiek modelēts silīcija monokristālu audzēšanas process ar peldošās zonas adatas acs metodi, izmantojot specializētu programmu fZone, kas ir verificēta liela diametra (4''-8'') kristālu audzēšanai ar ātrumiem līdz 4 mm/min. Atbilstoši Berlīnē veiktajai eksperimentu sērijai tiek veikti kausējuma zonas formas skaitliskie aprēķini relatīvi mazai 2'' sistēmai ar lieliem augšanas ātrumiem 5-8 mm/min gan neņemot, gan ņemot vērā kausējuma kustības ietekmi uz zonas formu. Analizējot HD ietekmi, tiek parādīts, ka konvektīvā siltuma pārnese kausējumā var būtiski ietekmēt temperatūras lauku un fāzu robežu formu. Aprēķinos iegūtie kristalizācijas frontes dziļumi tiek salīdzināti ar eksperimentālajiem mērījumiem, tiek parādīta divu skaitlisko atrisinājumu iespēja.In the current work the floating zone growth of silicon crystals with the needle-eye technique is modeled using a specialized program fZone. So far the program has been verified for crystals of large diameters (4''-8'') and growth rates up to 4 mm/min. In the present work numerical calculations of the shape of phase boundaries have been carried out for relatively small 2'' system for large growth rates (5-8 mm/min) according to the series of experiments in Berlin. The calculations were performed with and without taking into account the melt motion. It is shown that convective heat transfer in melt can noticeably affect the temperature field and the shape of the phase boundaries. The calculated deflections of crystallization interface are compared with the experimental measurements, and the possibility of two numerical solutions is shown

Modelins of the influence of gas flow on the zone shape and dopant transport in floating zone process

Elektroniskā versija nesatur pielikumusDarbā tiek veikta silīcija monokristālu audzēšanas ar peldošās zonas metodi matemātiskā modelēšana. Izveidotais matemātiskais modelis ļauj aprēķināt gāzes plūsmu un tās radīto papildus dzesēšanu uz silīcija virsmām. Tāpat ir izveidots vienots modelis piemaisījumu pārnesei gāzē un kausējumā, kas apraksta piemaisījumu ievadīšanu no atmosfēras. Jaunizveidotie modeļi tika sajūgti ar esošo modeļu sistēmu. Modeļu kopums realizēts datorprogrammu veidā, galvenokārt uz atvērtā koda bibliotēkas OpenFOAM bāzes. Tika veikti peldošās zonas procesa skaitliskie aprēķini, kuros pētīta gāzes un kausējuma plūsma un to ietekme uz silīcija fāzu robežvirsmām, kā arī piemaisījumu pārnese gāzē un kausējumā.In the present work mathematical modeling of floating zone silicon single crystal growth is carried out. The developed mathematical model allows to calculate the gas flow and additional cooling at silicon surfaces caused by it. Additionally, a unified model of the dopant transport in the gas and melt is developed, which describes doping from the atmosphere. The developed models have been coupled with the existing system of models. The set of models is implemented in computer programs, mainly based on the open source library OpenFOAM. Numerical calculations of the floating zone process have been carried out in which gas and melt flow and their influence on the silicon phase boundaries as well as dopant transport in the gas and melt was investigated

Modelins of the influence of gas flow on the zone shape and dopant transport in floating zone process

Elektroniskā versija nesatur pielikumusDarbā tiek veikta silīcija monokristālu audzēšanas ar peldošās zonas metodi matemātiskā modelēšana. Izveidotais matemātiskais modelis ļauj aprēķināt gāzes plūsmu un tās radīto papildus dzesēšanu uz silīcija virsmām. Tāpat ir izveidots vienots modelis piemaisījumu pārnesei gāzē un kausējumā, kas apraksta piemaisījumu ievadīšanu no atmosfēras. Jaunizveidotie modeļi tika sajūgti ar esošo modeļu sistēmu. Modeļu kopums realizēts datorprogrammu veidā, galvenokārt uz atvērtā koda bibliotēkas OpenFOAM bāzes. Tika veikti peldošās zonas procesa skaitliskie aprēķini, kuros pētīta gāzes un kausējuma plūsma un to ietekme uz silīcija fāzu robežvirsmām, kā arī piemaisījumu pārnese gāzē un kausējumā.In the present work mathematical modeling of floating zone silicon single crystal growth is carried out. The developed mathematical model allows to calculate the gas flow and additional cooling at silicon surfaces caused by it. Additionally, a unified model of the dopant transport in the gas and melt is developed, which describes doping from the atmosphere. The developed models have been coupled with the existing system of models. The set of models is implemented in computer programs, mainly based on the open source library OpenFOAM. Numerical calculations of the floating zone process have been carried out in which gas and melt flow and their influence on the silicon phase boundaries as well as dopant transport in the gas and melt was investigated

Application of the Alexander–Haasen Model for Thermally Stimulated Dislocation Generation in FZ Silicon Crystals

Numerical simulations of the transient temperature field and dislocation density distribution for a recently published silicon crystal heating experiment were carried out. Low- and high-frequency modelling approaches for heat induction were introduced and shown to yield similar results. The calculated temperature field was in very good agreement with the experiment. To better explain the experimentally observed dislocation distribution, the Alexander–Haasen model was extended with a critical stress threshold below which no dislocation multiplication occurs. The results are compared with the experiment, and some remaining shortcomings in the model are discussed

Evaluation of the Performance of Published Point Defect Parameter Sets in Cone and Body Phase of a 300 mm Czochralski Silicon Crystal

Prediction and adjustment of point defect (vacancies and self-interstitials) distribution in silicon crystals is of utmost importance for microelectronic applications. The simulation of growth processes is widely applied for process development and quite a few different sets of point defect parameters have been proposed. In this paper the transient temperature, thermal stress and point defect distributions are simulated for 300 mm Czochralski growth of the whole crystal including cone and cylindrical growth phases. Simulations with 12 different published point defect parameter sets are compared to the experimentally measured interstitial–vacancy boundary. The results are evaluated for standard and adjusted parameter sets and generally the best agreement in the whole crystal is found for models considering the effect of thermal stress on the equilibrium point defect concentration

Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals

The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing