Analysis of Temperature Distribution and slip in Rapid Thermal Processing

급속 열처리시 실리콘 웨이퍼의 온도분포와 슬립 현상의 해석

A numerical solution of temperature and thermally induced stress in a wafer during rapid thermal processing (R.T.P) is obtained, and an analysis of onset and propagation of slip is performed and compared with experiment. In order to calculate temperature distribution of a wafer in R.T.P system, heat conduction equation that incorporated with radiative and convective heat transfer model is solved, and the solution of the equation is calculated numerically using alternating direction implicit (A.D.I) method. In dealing with radiative heat transfer, a partially transparent body that absorbs the radiation energy is assumed and this transparent body undergoes multiple internal reflections and absorptions. Two dimensional (assuming plane stress) thermoelastic constitutive equation is used to calculate thermal stress induced in a wafer and finite element method is employed to solve the equation numerically. The stress resolved in the slip directions on the slip planes of silicon is compared with the yield stress of silicon in order to predict the slip. The result of the analysis shows that the wafer temperature at which slip occurs is affected by the heating rate of the R.T.P system. It is observed that once slip occurs in the wafer, the slip grows.

본 연구에서는 텅스텐 할로겐 램프를 이용한 급속 열처리 장치로 웨이퍼를 가 열할 때 시간에 따라 변하는 웨이퍼의 2차원 온도 분포와 온도 구배에 의해 발생하는 열응력을 실리콘 웨이퍼의 결정방향에 따라 다른 값을 갖는 탄성계수를 고려하여 계산 하고, 슬립의 발생 시기, 웨이퍼의 가열속도와 슬립량의 관계, 그리고 웨이퍼에 발생 한 슬립의 진전 특성에 대하여 살펴보고 실험결과와 비교하였다.