Rapid Thermal Processor Modeling, Control, and Design for Temperature Uniformity

Abstract

With the ability to perform heat cycles on a wafer quickly and within low thermal budgets, Rapid Thermal Processor (RTP) systems offer potential advantages over conventional furnaces. However, RTP' have an inherent problem with wafer temperature uniformity which can cause process nonuniformity and wafer stress.In this work, a thermodynamic model of a wafer is used to form an understanding of the wafer heating problem. This model shows that an idealized heating flux density profile can maintain thermal uniformity at steady-state temperatures. This profile uniformly heats the wafer while counteracting the additional cooling at the wafer edge. However, this profile induces temperature nonuniformities during wafer temperature transients, such as overheating of the edge during temperature rises. Therefore, a dynamic flux-density profile is needed during temperature transients to ensure continuous temperature uniformity. The model is used to predict the steady-state and dynamic profiles required to process a wafer with complete temperature uniformity. The predicted profiles can be used to adapt an RTP chamber and control system to approach production of uniform wafers and also for the design of new systems. This paper will explain the theory of wafer heating, describe the dynamic profiles required for continuous uniformity, review the wafer model, show the result of an idealized profile for steady state and transients processing, and present a new control methodology to achieve uniform temperatures.

Thermal uniformity of 12-in silicon wafer during rapid thermal processing by inverse heat transfer method

“…For simplicity, the emissivity in all surfaces is assumed to be the same and only temperature dependence as [19] (7) Thus, (3) and (6) may be rewritten, respectively, as (8) and at (9) The numerical solution techniques used here are from the finite-difference method. A central-difference representation of the space derivative and an implicit backward-difference representation of the time derivative are adopted.…”

“…Zöllner et al [8] compensated for radial temperature decreases using an adjustable lamp arrangement with optimized power settings calculated from wafer heat losses. Riley and Gyurcsik [9] determined the amount of lateral heating needed to counteract edge cooling during RTP. Cho et al [10] optimized the incident heat flux profile over a wafer by determining the heat loss profiles using Lord's thermal model [3], which simulates radial temperature gradients by assuming uniform temperature through the wafer thickness.…”

“…Cho et al [10] optimized the incident heat flux profile over a wafer by determining the heat loss profiles using Lord's thermal model [3], which simulates radial temperature gradients by assuming uniform temperature through the wafer thickness. Following the work of Riley and Gyurcsik [9], Perkins et al [2] used their special wafer-edge node analysis to show that idealized intensity profiles can maintain thermal uniformity at steady-state temperatures, and that dynamic continuously changing profiles are required to maintain temperature uniformity during thermal transients. The works mentioned above describe quantifying incident heat flux over a wafer to achieve the necessary thermal uniformity requirement during RTP.…”

Thermal uniformity of 12-in silicon wafer in linearly ramped-temperature transient rapid thermal processing

“…Sorrel et al [6] applied power-law (first-, second-, and seventh-degree) irradiation profiles to study the increases required in perimeter radiation to maintain a wafer at an approximately uniform temperature. Riley and Gyurcsik [7] presented a wafer-edge nodal analysis to determine the amount of lateral heating needed to counteract edge cooling. Cho et al [8] presented a method for optimizing incident-heat-flux profiles by studying wafer heat-loss profiles.…”

“…Cho et al [8] presented a method for optimizing incident-heat-flux profiles by studying wafer heat-loss profiles. Following the work of Riley and Gyurcsik [7], Perkins et al [9] used wafer-edge node analysis to determine the idealized intensity profiles required for maintaining thermal uniformity both during transient and steady states. The works mentioned above describe quantifying incident heat fluxes over wafers to achieve the necessary thermal uniformity requirements during RTP.…”