llealizatiuii of Optiiiiuin Coiitrul Fuiictiun
1. I n Crod uct,iuii
'l'lie topic of this paper is the fortilation of defined doping profilcs in silicon epitaxial layers grown hy chetiiical vapour deposition. For t.his purpose we treat,ed the epitaxial reactor as a linear cont,rol systeni, using u ( t ) = Ig p:'),t(t) as the input and y ( t ) = Ig N ( t ) as the output.
and N ( t ) represent the input partial pressure of t,hc dopant 4ource and the concentration of incorporated iiiipiirity at.oiiis, respectively.)
A procedure for the forriiat,iori of defined doping profiles was developed, which consists of the following steps: 1. 1)eterniination of the transition properties (described by the transition function h ( t ) of the system, using an approach siniilar to REIF et al. (1978, l979), 2. C!alculation of t h e optirnal c:ontrol funvtion relating t o any certain defined doping profile, using linear-quadratic* control theory (BKYSON, Yu-Crrl Ho ; CSAKI), 3 . Experitiiental realization of such optiiiial control funct'iori using a conventional CVD reactor. St>cps 1 and 2 of t h i s proccdure arc presentcd in t'he first two parts of this serics, using SiH, and PH, as Silicon and dopant source, respectively ( KGSZA et al. ; V A L K ~ ct a].). I n Part 11 optiinal control functions for a desired ahrupt high-low transition