Thermal modelling of RTP and RTCVD processes

Iterative identification of temperature dynamics in single wafer rapid thermal processing

“…Here, a lumped model as in Huang et al [7] and Kersch and Schafbauer [9] is used. (1) where i the index of the radial cell on the wafer with volume V i , mass density ρ, heat capacity c P , and temperature T i .…”

“…These radiative exchange factors depend on the geometry of the RTP chamber and the optical properties of the wafer surface. They need complicated computations such as Monte Carlo simulations [9]. Schaper et al [8] showed that the off-diagonal terms in Γ ij are small and can be ignored for the purpose of control system…”

“…Then we have (8) Applying the above test procedure, we obtain the multivariable steady state gain matrix, , between and . A refined (k+1)-th gain matrix of RTP becomes (9) When the process is not ill-conditioned, two or three iterations are sufficient. Fig.…”

“…To design these control systems, accurate models for RTP are required. Models based on the first principles are available [6,[8][9][10]. They have been shown to be approximated by diagonal nonlinear first order dynamics with multivariable static gains [5,7,11].…”

Modelling of an infrared halogen lamp in a rapid thermal system

“…Kersch and Schafbauer modelled a rapid thermal system in which measured values for the lamp power are entered in the studied RTP system model [9].…”