Constitutional Supercooling in Czochralski Growth οf Heavily Doped Silicon Crystals

Abstract

This study analyses the phenomenon of constitutional supercooling, which is one of the major problems in industrial growth of heavily doped (> 10 20 atoms/cm 3 ) silicon crystals by the Czochralski technique. The systematic study is based on theoretical models and experimental data considering the eect of three important dopants (B, P, and As) in dependence of the relevant growth parameters for the Czochralski process. Based on these results, conclusions will be drawn for the stability limits of the Czochralski growth of dislocation-free heavily doped silicon crystals in dependence of the doping species and their concentration.

The Heat Treatment Influence on the Microstructure and Hardness of TC4 Titanium Alloy Manufactured via Selective Laser Melting

“…However, the macroscopic structures of the side view consist of columnar grains that grow epitaxially through multiple cladding layers with an average width of 120 μm, as shown in Figure 2b. According to the theory of constitutional supercooling by Chalmers [30], in order to use the alloy orientation to obtain planar crystals, following criteria that is supported to be satisfied, $\frac{G_L}{R}\ge \frac{m_0{c}_{0}false(k_0-1false)}{k_0{D}_L}=\frac{\mathrm{sans-serif\Delta }{T}_0}{D_L}.$…”

A review on single crystal and thin film Si–Ge alloy: growth and applications

“…53 Freidrich et al illustrated that probability of existence of ''structure loss'', i.e., presence of dislocations and grain boundaries increases the manifold by CZ growers thanks to the high concentration of doping; therefore, the phenomenon is often termed as ''constitutional supercooling''. 54 The phenomenological description of constitutional supercooling can be described by Fig. 4(b).…”

“…Reproduced with permission from ref. 54. continuously discharge the solute atoms into the molten zone where they bring together and are propelled toward the intense end of the bar, i.e., within the similar direction of the zone movement.…”

Erlangen—An Important Center of Crystal Growth and Epitaxy: Major Scientific Results and Technological Solutions of the Last Four Decades

“…CGL has analyzed these special features of growing heavily n‐doped silicon in collaboration with Siltronic since 2012. In the frame of his Ph.D. thesis, Ludwig Stockmeier found that the structure loss occurs regularily, although the well‐known criteria for constitutional supercooling are not yet fulfilled . By using different analytical methods, like defect selective etching or X‐ray topography (XRT) he revealed that the origin of the structure loss can be attributed to instabilities of the growth process which are caused by temperature fluctuations in the melt.…”