The Effect of Quartz Window on Bistability of the Silicon Wafer in Lamp-Based Reactor

The effect of a quartz plate (window) on the silicon wafer temperature is stu-died in the conditions of the combined thermal transfer in a lamp-based chamber for the rapid thermal treatment (RTP) set up. The chamber for RTP is simulated by a radiative-closed thermal system including the influence of quartz window as a spectral filter of lamp emission and a source of emitted thermal radiation. Energy equations for thermal fluxes involved in the heat input and output from the working wafer and quartz window are solved in spectral approximation. The transfer characteristics that are defined by the temperature dependencies of the silicon wafer and the quartz window on the temperature of the heater are accounted. It is shown that temperature bistability in the silicon wafer initiates an induced bistability into the quartz window that does not reveal bistable behavior because of the linear temperature dependence of its total optical characteristics. A possibility for simulation of the quartz window by spectral restriction of the heater radiation is confirmed. The availability of the weak bistable effect in the mode of zero effective heat exchange coefficient of a non-radiative component of the thermal flux removed from the working wafer has been obtained.


Introduction
The processes of thermal treatment are an integral part of the micro-and nanoelectronics technology. A lamp-based chamber is one of the main units of the rapid treatment equipment that is widely used at present time for thermal processes including a post-implantation annealing [1] [2], diffuse doping [3] [4], crystallization of amorphous films [5] [6], contact annealing [7] [8], oxidation [9] [10] and etc. Thermal treatment processes differ in duration and radiation power from parts per million of second and peak power until 100 MW on flesh-annealing [3] [4] to tens of seconds and radiation power ~0.1 kW on low-temperature annealing [11]. On thermal treatment of a semiconductor wafer by high-powered radiation a temperature gradient along the depth of the wafer reaches very high values [2] and the wafer is exposed by powerful incoherent radiation fluxes transmitted through it. As a result, the wafer is far from the thermal equilibrium and together with non-linear optical properties of semiconductors these result in complicated thermal behavior of the wafer. The investigation of the silicon wafer behavior during its thermal process carried out in non-isothermal conditions for a lamp-based chamber makes it possible to predict theoretically and detect experimentally the hypothesis about the bistable behavior of the wafer [12]. The bistable behavior of the wafer proposes that in its thermal treatment process there is an interval of a controlling parameter (a heater temperature, as a rule) in which the wafer temperature takes different values according to whether the controlling parameter increases or decreases. A manifestation of the temperature and optical bistability phenomenon in a silicon wafer is caused by the non-linear temperature dependencies of its total emissivity and transmissivity. A stepwise increase of the optical characteristics is observed in the temperature interval from 600 to 800 K (see [12], for instance). As a consequence, the theoretical transfer characteristic of the working wafer (i.e., its temperature dependence on the temperature of the heater) has an S-like shape and is experimentally observed as a hysteresis loop [12]. Parameters of the hysteresis loop are determined by the optical properties of the thermal reactor elements, and the correspondence of theoretical and experimental transfer characteristics depends on the model of the reactor used in simulation. The thermal reactor in the system for the temperature-gradient heat treatment of semiconductor wafers is used for the experimental detection of the temperature bistability in the silicon wafer [12]. The detailed description of its construction has been presented in [12] [13]. The reactor includes a heating block and a working chamber. The working chamber is separated from the heating block by a quartz glass plate which is further referred to as "a quartz window". The chamber is filled by gas, as a rule, by argon or nitrogen. A water-cooled pedestal is located inside the working chamber. The silicon wafer is mounted on the special pins positioned on the water-cooled pedestal. The distance between the working wafer and the pedestal can be controlled by varying the height of the pins, then by controlling removal conductive flux from the wafer through a gas-filled gap to absorber. The model of the thermal chamber usually used in thermal simulation includes three plates: a heater plate, a working plate (wafer) and the absorber plate [14]. The quartz window influence, as a rule, is considered by restriction of the spectral interval for the heater emission in the spectral range from 0.4 to 4.0 µm [1] [15]. However, functions of the quartz window in the thermal system V. P. Prigara et al. Journal of Materials Science and Chemical Engineering which models the lamp-based chamber extend further. The quartz plate is involved in the compound thermal exchange process. On the one hand, it is a semitransparent shield taking part in the exchange of thermal radiation between the heater and the working wafer, and on the other it is involved in convective energy transfer with the flow of air cooling the lamp block. Then, being part of the thermal system, the quartz influences the working wafer temperature. It absorbs, reflects, and reemits a radiative flux incident both to its face surface from the heater side and to its back from the working wafer side.
The object of the present investigation is analysis and comparison of different ways of simulating the lamp-based chamber and their impact on the shape of transfer characteristics that describe silicon wafer temperature dependence on the temperature of the heater modeling a lamp block of the thermal chamber. Particular attention has been given to the quartz window as a filter of radiation incident from the heater to the silicon wafer and as a source of emitted radiation.

The Thermal Model of the Lamp-Based Chamber
The thermal model of the non-isothermal lamp-based chamber includes four infinite-sized parallel-plane plates (Figure 1(a)). An upper plate (1) that is referred to as "the heater" models the block of tungsten-halogen lamps. The bottom plate (2) that is referred to as "the absorber" is meant for the simulation of walls and the bottom of the working chamber. Two semitransparent plates are located between the plates of the heater and the absorber. They are the protective shield, which is the quartz glass plate (q), and the working wafer made from material possessing non-linear optical characteristics (silicon) (f). The semitransparent plates have subscripted indexes q and f, and their surfaces are marked by the second subscripted index. The surface turned to the heater and to the absorber are specified by the subscripts "1" and "2", respectively.
The gray surfaces approximation used in [16] is crude enough to describe thermal radiation heat transfer in the lamp-based chamber with regard to quartz glass window influence. The restriction of the upper bound of the heater radiation is exclusively spectral effect. So, we refine the gray approximation [16] by the spectral one: Here, where d A B q − is radiation flux between A and B plates in the spectral range of dλ ; is the hemispherical spectral emissive power for a surface of blackbody at temperature T [17];

Heat Transfer Simulation of the Thermal System
Including the Quartz Window

The Transfer Characteristics of the Silicon Wafer
The spectral optical data are used for quartz plate of QI type and 5 mm thick [18] [19] [20] in Figure 1    are varied as in Figure 2(a). Figure 2(b) shows the high-temperature fragments of the transfer characteristics in the heater temperature range more than 1000 K because the portions of the transfer characteristics of the quartz plate increase near-linearly in the range from 300 to 1000 K and ones are not of special interest. Figure 2

Discussion
Analysis of Figure 2(a) and Figure 2 (Figure 2(a)). Because the quartz plate transmits in the spectral range from 0 to 4 µm while it is practically opaque in the remainder part of the interesting for us spectrum range from 0 to 20 µm (for exception of the peak near 9 µm), it behaves as an opaque shield with the spectral window in the range 0 to 4 µm. The shield can be considered as a composed heater with relation to working wafer: it emits as an ABB heater at the heater temperature 1 T in the spectral range from 0 to 4 µm, and one does as the source of emitted radiation at quartz plate temperature q T in the spectral range from 4 to 20 µm.

Comparison between the Silicon Wafer Transfer Curves Simulated by Different Models of the Quartz Window
To understand the quartz window influence on the transfer curves of the ther- As a result, the wafer is step-wise switched to the high-temperature state.

Conclusion
Thus