A Thermal Model for Silicon-on-Insulator Multilayer Structure in Silicon Recrystallization Using Tungsten Lamp

텅스텐 램프를 이용한 실리콘 재결정시의 SOI 다층구조에 대한 열적모델

A onetimensional distribution of the temperature and the heat source in the SOI (silicon-on-insulator) multi-layer structure illuminated by tungsten lamps from both sides was obtained by solving the heat equation in steady state on a finite difference grid using successive over-relaxation method. The heat source distribution was obtained by considering such features as spectral components of the light source, multiple reflection at the internal interfaces, temperature and frequency dependence of the light absorption coefficient, etc. The front and back surface temperatures, which are boundary conditions for the heat equation, were derived from a requirement that they satisfy the radiation conditions. The radiation flux as well as the conduction flux was considered in modelling the thermal behaviour at the internal interfaces. Since the temperature and the heat source profiles are strongly dependent upon each other, the calculation of each profile was iterated using the updated profile of the other until they are consistent with each other. The experimental temperature at the front surface of the wafer as measured by Pyrometer was about 1200$^{\circ}$K, while the simulated temperature was 1120$^{\circ}$K.

양면에서 텅스텐 램프를 조사하는 실리콘 재결정시의 SOI(silicon-on-insulator) 다층구조에 대한 1차원적 온도 및 열원(열원)의 분포를 SOR(successive over-relaxation)방법을 이용하여 정상상태의 열방정식의 해로부터 구하였다. 열원의 분포는 광원의 스펙트럼, SOI sample 내부 계면에서의 다중반사, 광흡수 계수의 온도, 주파수 의존성 등을 고려하여 구하였으며, 열 방정식의 경계조건이 되는 wafer의 전면과 후면의 온도는 혹체복사 조건으로부터 구하였다. 내부계면에서는 전도열속(conduction heat flux)과 복사열속(radiation heat flux)에 의한 연속조건을 만족하도록 하였다. 본 문제에서의 온도분포와 열원의 분포는 상호간에 큰 영향을 주게 되므로, 두가지 변수가 일치되는 값을 보일 때까지 iteration을 계속하였다. Pyrometer을 이용하여 측정한 wafer 전면의 온도는 약1200°K이었고 이때의 simulation 결과는 1120°K 정도로 나타났다.