Effect of high frequency vibrations on PV silicon purification

Abstract

Silicon purification for photovoltaic applications is a crucial challenge to improve the energy production performance of solar panels. In the present work, we focus on the metallurgical grade silicon purification process through a directional solidification technique, namely the horizontal Bridgman technique. By means of numerical simulations, it is shown that high frequency vibrations applied to the crucible can be used to enhance the convective level in the molten silicon (thermal-vibrational effect) and improve the purification of the final silicon ingot. The direction of the vibration, however, has to be carefully chosen, as it strongly influences the flow intensity and structure in the melt and can lead to multi-rolls and even reverse flows, with a direct effect on the induced purification.

Three-dimensional effect of high frequency vibration on convection in silicon melt

“…The maximum velocity will be obtained for a value of α xz close to 45 • . This result is in agreement with the numerical and theoretical results obtained in the two-dimensional studies [18,19]. The velocity amplification achieved by vibrations is important: for example, for α xz = 45 • , it leads to u max = 12.85 (255% increase, Fig.…”

“…To go further, we will compare the situations at α yz = 90 • −α and 90 • + α. When α yz is changed from 90 • −α to 90 • + α, W z is not changed and W y is changed to its opposite in agreement with the properties of the sine and cosine functions in (18) and (19), respectively. The vibrational forces for 90 • −α and 90 • + α are found to be equal.…”

“…By using the averaging method proposed by Gershuni and Lyubimov [7] in the case of highfrequency harmonic vibrations and using H, H 2 /ν, ν/H, T /A x = (T h − T c )/A x , and ρν 2 /H 2 as scales for length, time, velocity, temperature, and pressure [the temperature is (T − T 0 )A x / T , where T 0 = (T h + T c )/2 is the mean temperature] as in our previous works [18,19], the dimensionless governing equations for a Newtonian and incompressible buoyant flow under the effect of HF vibrations are…”

“…Their derivatives in the plane of vibration are expected to be small and their main variations are expected to be along x, as expressed in (18) and (19).…”

“…The effect of high frequency vibrations has been extensively studied in two-dimensional cavities. An overview of the literature on this topic can be found in [10][11][12][13][14][15][16][17][18][19]. It is however crucial to investigate these effects when the problem cannot be modeled through a two-dimensional approach.…”