Recent developments in modelling of liquid phase electroepitaxy under applied magnetic field

Abstract

Growth of single crystals under magnetic field is of interest for suppressing the adverse effect of natural convection and for better mixing in the liquid solution, which are the favorable conditions for prolonged growth and high quality crystals. In this short review article, recent developments in the modelling of electroepitaxy under magnetic field are presented. An application is given for the liquid phase electroepitaxial growth of GaAs bulk single crystals under a static magnetic field. Experimental results, that have shown that the growth rate under an applied static magnetic field is proportional to the applied magnetic field, and increases with the field intensity level, are predicted from the present model. The model also predicts growth interface shapes accurately.

A numerical simulation study for the effect of magnetic fields in liquid phase diffusion growth of SiGe single crystals

“…The interface still preserves its concave shape. One may therefore conclude that the application of a vertical magnetic field in the present LPD system is not so beneficial, contrary to what was observed in crystal growth by the traveling heater method (THM) [5,11,12,22], or by liquid phase electroepitaxy (LPEE) [8][9][10]13].…”

“…). Stationary magnetic fields are used to improve the quality of crystals by suppressing convection (natural and/or Marangoni) and controlling the directional solidification and segregation of species [1][2][3][4][5][6][7][8][9][10][11][12][13]. Rotating magnetic fields, on the other hand, have been used to obtain better mixing in the melt, better control for the heat and mass transport characteristics of the system and also for the shape of the growth interface [14][15][16][17][18][19][20][21][22][23].…”

Liquid phase electroepitaxy of semiconductors under static magnetic field

“…However, the extent to which liquid alloy supersaturation develops at the growth interface is limited and determined by convective mixing of the liquid alloy resulting from temperature and concentration fluctuations. As noted above, the increase in crystal growth rate with magnetic field strength (at constant electric current density), as given in Table 4, 26,61,63 can be attributed to dampening of convective mixing by magnetohydrodynamic forces. It can be assumed that the degree of suppression of convective mixing is directly proportional to the magnetic field strength.…”

“…One-dimensional and simple models are not sufficient for a full understanding of various aspects of the LPEE growth process. To gain a better understanding of the growth process of LPEE, over the past 10 years a number of numerical simulation modelling studies have been carried out by the author's research group (see for instance [34][35][36][39][40][41]46,[48][49][50][61][62][63][70][71][72][73].…”