(443d) Temperature Sensing and Control in a Rapid Thermal Processing Reactor to Produce CuInGaSe2 Absorber Layers

Copper indium gallium diselenide (CIGS) has been identified as a strong candidate for the absorber layer in thin film solar cells and CIGS-based photovoltaics have achieved high efficiency at both the cell (20.4%) and module (15.5%) levels.  The most common method for synthesizing CIGS in industry is the selenization reaction, where a Cu-In-Ga precursor is deposited on Mo-coated glass and reacted with gas-phase H₂Se and H₂S to produce CIGS.  However, long reaction times limit the throughput of the selenization method.  Recently, there has been growing interest in selenization by Rapid Thermal Processing (RTP), which because it is characterized by a fast temperature ramp rate and high temperature reaction, improves throughput substantially.  We have designed, constructed, and implemented a pilot-scale RTP selenization reactor that is capable of heating our sample to reaction temperature in less than 2 minutes.  The reactor consists of a 2-inch diameter quartz tube with a 1-inch sample held by a graphite susceptor.  The samples are pieces of soda-lime glass where the top surface is coated by Mo and a thin (<2 µm) Cu-In-Ga precursor.  H₂Se and H₂S gases diluted in Ar flow across the sample and react with the metal precursor, and the effluent passes through a waste treatment system.  A 1000 W quartz-halogen lamp mounted above the reactor tube heats the samples.  Due to the presence of corrosive hydride gases, we cannot measure temperature inside the reactor with a thermocouple or other measurement device and instead we use a short-wavelength pyrometer mounted below the tube to measure the bottom surface temperature of the graphite susceptor.  Our aim was to design a control system to track rapid, linear set point ramps and high temperature holds in the top surface (the reacting film) temperature.  We accomplished our aim in two steps: (1) design of a controller to track a ramped temperature set point, and (2) design of an observer to obtain online estimates of the sample surface temperature.  For both steps, we developed temperature models based on first-principles and we fitted model parameters to experimental data.  To design the controller, we obtained a nonlinear ODE temperature model accounting for heat input from the lamp and heat losses by convection and radiation.  We fit temperature data to the ODE in the least-squared sense, using order of magnitude parameter estimates as starting points.  To eliminate steady-state offset during both ramps and holds, we used a proportional-integral-double integral (PII²) controller.  To tune the controller, we linearized the temperature model at several points, and chose our tuning parameters to ensure stability (by the Routh stability criterion) and monotonicity (by confirming poles of the closed-loop transfer function are real numbers) over the entire temperature range.  Our observer design is based on a 1-dimensional unsteady PDE model of the temperature distribution through the sample with convection, radiation, and heat flux from the lamp appearing as boundary conditions.  Our observer is a PDE that takes the same form as the temperature model, with the addition of observer gains and error measurements in the bulk and at the boundary with the sensor.  These observer gains were derived using the method of Smyshlyaev and Krstic.  The observer was implemented by discretizing the PDE with the method of finite differences, which gives a system of coupled ODEs at several points that can be solved online.  For our purposes, we are interested in the ODE that corresponds to the sample surface in order to obtain an estimate of surface temperature.  We are able to track rapid temperature ramps and holds using the PII² controller in conjunction with the surface temperature observer.  Our system will now be used to study the kinetics and transport phenomena that govern the production of CIGS absorbers by RTP, as well as to study CIGS microstructure and electronic properties.  We anticipate that our controller design procedure can find application in many processes of interest to the solar energy and semiconductor communities.