Crucible-free Pulling of Germanium Crystals

Commonly, germanium crystals are grown after the Czochralski (CZ) method. The crucible-free pedestal and floating zone (FZ) methods, which are widely used for silicon growth, are hardly known to be investigated for germanium. The germanium melt is more than twice as dense as liquid silicon, which could destabilize a floating zone. Additionally, the lower melting point and the related lower radiative heat loss is shown to reduce the stability especially of the FZ process with the consequence of a screw-like crystal growth. We found that the lower heat radiation of Ge can be compensated by the increased convective cooling of a helium atmosphere instead of the argon ambient. Under these conditions, the screw-like growth could be avoided. Unfortunately, the helium cooling deteriorates the melting behavior of the feed rod. Spikes appear along the open melt front, which touch on the induction coil. In order to improve the melting behavior, we used a lamp as a second energy source as well as a mixture of Ar and He. With this, we found a final solution for growing stable crystals from germanium by using both gases in different parts of the furnace. The experimental work is accompanied by the simulation of the stationary temperature field. The commercially available software FEMAG-FZ is used for axisymmetric calculations. Another tool for process development is the lateral photo-voltage scanning (LPS), which can determine the shape of the solid-liquid phase boundary by analyzing the growth striations in a lateral cut of a grown crystal. In addition to improvements of the process, these measurements can be compared with the calculated results and, hence, conduce to validate the calculation.Comment: 4 pages, 10 figures, ICCG-1

Performance boost of time-delay reservoir computing by non-resonant clock cycle

The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered to be equal. Here we show that the case of equal or resonant time-delay and clock cycle could be actively detrimental and leads to an increase of the approximation error of the reservoir. In particular, we can show that non-resonant ratios of these time scales have maximal memory capacities. We achieve this by translating the periodically driven delay-dynamical system into an equivalent network. Networks that originate from a system with resonant delay-times and clock cycles fail to utilize all of their degrees of freedom, which causes the degradation of their performance

Connecting reservoir computing with statistical forecasting and deep neural networks

Among the existing machine learning frameworks, reservoir computing demonstrates fast and low-cost training, and its suitability for implementation in various physical systems. This Comment reports on how aspects of reservoir computing can be applied to classical forecasting methods to accelerate the learning process, and highlights a new approach that makes the hardware implementation of traditional machine learning algorithms practicable in electronic and photonic systems

Growth Angle and Melt Meniscus of the RF-heated Floating Zone in Silicon Crystal Growth

This article presents a direct measurement of the growth angle during the growth of a cylindrical 2" silicon crystal using a radio-frequency heated floating zone process. From the high-resolution pictures taken during the process, this growth angle was evaluated to be 11{\deg}{\pm}2{\deg}. Furthermore, the free surface of the melt was modeled using the Laplace-Young equation. This model has to include the electromagnetic pressure calculated by the surface ring currents approximation. The results were compared to the experimental free surface derived from video frames. It could be shown that the calculated free surface will only fit the experimentally determined one if the right growth angle is considered