489 Journal of Crystal Growth 92 (1988) 489—497 North-Holland, Amsterdam CALCULATION OF THE THERMAL AND STRESS FIELDS IN LEC GALLIUM ARSENIDE AFTER SEPARATION FROM THE MELT C.E. SCHVEZOV “, IV. SAMARASEKERA and F. WEINBERG Department of Metals and Materials Engineering, The University of British Columbia, Vancouver, BC, Canada V6T / W5 Received 4 June 1987; manuscript received in final form 22 July 1988 Stress fields in LEC GaAs after removal from the melt, during transient cooling, have been calculated. The results show that the stresses developed near the bottom of the crystal can be two to four times larger than the stresses developed in the crystal during growth. If growth is terminated by tapering, the stress levels in the crystal remain below the growth stresses. 1. Introduction 2. Model formulation In the LEC growth of gallium arsenide crystals In the models developed for computing the thermal gradients develop which produce local thermal and stress fields in growing LEC GaAs stresses. These stresses can lead to dislocation crystals [1,2] the thermal field was considered to generation if the resolved shear stress is suffi- be at quasi-steady state. When the crystal is re- ciently great. A mathematical model has been moved from the melt, the temperature field is time used to calculate the thermal fields during growth dependent. Accordingly, an analytical procedure [1], and the resolved shear stresses [2]. With the has been used to determine the thermal fields in model the effect of the growth variables on the this case. The corresponding stress distribution resolved stress field and dislocation density has was determined from the thermal field using a been determined [3]. In this report the thermal finite-element stress model [2]. The following as- and stress fields developed at the end of solidifi- sumptions were made in the model. cation will be considered. Solidification may be (1) The temperature field is time dependent and terminated by rapidly removing the crystal from axi symmetric. the melt and allowing it to cool slowly in the inert (2) The crystal is a finite cylinder with constant gas or boron oxide in the growing chamber. This cross-section. could result in rapid changes in the thermal field (3) The crystal is immersed in a medium (gas or at the end of the crystal, producing higher disloca- liquid) at a constant temperature. tion densities. Alternatively, solidification may be (4) Newton’s Law of Cooling applies at the crystal completed by slowly reducing the crystal diame- surface. The heat transfer coefficient at the surface ter, tapering the end of the crystal. Both cases will is constant and its value is determined by the be considered, temperature and nature of the surrounding medium. (5) The initial temperature of the crystal is axially * On leave from Universidad Nacional de Misiones (Argen- dependent (radial temperature gradients during tina). growth are small). The initial temperature is given 0022-0248/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)