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Comparison between the experimental filament temperatures and the ones in the 2D model remains an acceptable agreement. So the validity of the model is checked on a larger domain. It should be added that for most of the thermocouples, the difference is within the +0.4% accuracy interval of the measured temperature.

Table 2 Comparison between the experimental filament temperatures and the ones in the 2D model remains an acceptable agreement. So the validity of the model is checked on a larger domain. It should be added that for most of the thermocouples, the difference is within the +0.4% accuracy interval of the measured temperature.

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Fig. 2. Thermocouple positions on the backside of the wafer. Concerning the lamps, the aim was to obtain the tungsten fila- ment temperature. The methodology to obtain it is as follows. Both the intensity I.xp and the voltage Ucxp were taken for each lamp
Fig. 2. Thermocouple positions on the backside of the wafer. Concerning the lamps, the aim was to obtain the tungsten fila- ment temperature. The methodology to obtain it is as follows. Both the intensity I.xp and the voltage Ucxp were taken for each lamp
Fig. 1. Schematic diagram of the RTP AS-One 150 reactor, respectively, the 2D and 3D model.
Fig. 1. Schematic diagram of the RTP AS-One 150 reactor, respectively, the 2D and 3D model.
Fig. 4. Evolution of the experimental wafer temperature for the five lamp heating power considered. The steady-state numerical calculations are performed using the finite volume method which consists in integrating the conser- vation equations over each domain cell of the geometry system [13,14]. The conservation equations govern the conservation of mass (continuity equation), momentum (Navier-Stokes equation) and energy. Most of the equations can be expressed in the form of a generalized transport equation given by the below expression (8). The latter is composed of four terms that are respectively the transient term, the convective term, the diffusion term and the The radiative heat transfer equation is solved by using the Monte Carlo method [16]. It is well known that the Monte Carlo method is precise for solving thermal radiative problems like the ones involved in RTP processes [17,18]. The scheme of the method is explained in [19]. It can be summed up as follows. The principle is to trace bundles of rays and to account for the various events
Fig. 4. Evolution of the experimental wafer temperature for the five lamp heating power considered. The steady-state numerical calculations are performed using the finite volume method which consists in integrating the conser- vation equations over each domain cell of the geometry system [13,14]. The conservation equations govern the conservation of mass (continuity equation), momentum (Navier-Stokes equation) and energy. Most of the equations can be expressed in the form of a generalized transport equation given by the below expression (8). The latter is composed of four terms that are respectively the transient term, the convective term, the diffusion term and the The radiative heat transfer equation is solved by using the Monte Carlo method [16]. It is well known that the Monte Carlo method is precise for solving thermal radiative problems like the ones involved in RTP processes [17,18]. The scheme of the method is explained in [19]. It can be summed up as follows. The principle is to trace bundles of rays and to account for the various events
Fig. 3. Tungsten resistivity versus temperature (from [12]). can be seen as well on Fig. 1. The modelling of the infrared lamp was realized as follows. Since the filament is composed of a huge number of whorls, it was represented by a cylinder in a 3D model. The influence of the rings which support the filament is considered negligible on the filament temperature. As the 2D model is a cut in the (Oxy) plane (Fig. 1), the filament representation corresponds to a circle. source term. Concerning the variables, ¢ corresponds to the gen- eral flow variable, p to the density, t to the time, V to the velocity and I to the diffusion coefficient.
Fig. 3. Tungsten resistivity versus temperature (from [12]). can be seen as well on Fig. 1. The modelling of the infrared lamp was realized as follows. Since the filament is composed of a huge number of whorls, it was represented by a cylinder in a 3D model. The influence of the rings which support the filament is considered negligible on the filament temperature. As the 2D model is a cut in the (Oxy) plane (Fig. 1), the filament representation corresponds to a circle. source term. Concerning the variables, ¢ corresponds to the gen- eral flow variable, p to the density, t to the time, V to the velocity and I to the diffusion coefficient.
Fig. 5. Evolution of the experimental lamp filament temperature for the five lamp heating power considered
Fig. 5. Evolution of the experimental lamp filament temperature for the five lamp heating power considered
Fig. 6. Variation of the experimental wafer temperature for the five lamp heating power considered.
Fig. 6. Variation of the experimental wafer temperature for the five lamp heating power considered.
Fig. 7. Experimental lamp filament temperature variation for the five lamp heating power considered.
Fig. 7. Experimental lamp filament temperature variation for the five lamp heating power considered.
Fig. 8. Relative difference between the experimental wafer temperature profiles and the calculated ones.
Fig. 8. Relative difference between the experimental wafer temperature profiles and the calculated ones.
Filament temperatures for all the cases Table 1 Table 2 stabilisation, it occurs after 10 s of electrical power supplying since the variation becomes inferior to 10 K s~'. It can be noticed that after 10s of supplying, the filament temperature fluctuates in a small interval of +10 K which represents about +0.5% of the fila- ment temperature.
Filament temperatures for all the cases Table 1 Table 2 stabilisation, it occurs after 10 s of electrical power supplying since the variation becomes inferior to 10 K s~'. It can be noticed that after 10s of supplying, the filament temperature fluctuates in a small interval of +10 K which represents about +0.5% of the fila- ment temperature.
Fig. 9. Comparison between the experimental filament temperatures and the ones introduced in the calculations. We can notice on Fig. 8 graphs that the calculated profiles are in good agreement with the experimental data. The difference be- tween the calculated temperatures and the measured ones is infe- rior to 2% in both the 3D and the 2D case for all of the thermocouples. For the 20% heating power, the good agreement is observed as well for experimental and calculated temperatures obtained when the thermocouple position is rotated by 180°. The only exception is for the 2D case at the high lamp power of 30% in which the difference is slightly superior for the thermocouples close to the wafer edge. The latter is between 2% and 4.3% which For the 2D case, the filament temperatures in the simulations are all inferior to the experimental results. For the heating of 20% and 25%, the values remain in the uncertainty domain whereas in the three other cases they don’t. In order to have a better eval- uation, the difference to the experimental filament temperature is given in percentage by Table 2. For all the lamp power, the dif- ferences are between 4.8% and 8.6% below the experimental value, which stay inferior to 10%. An acceptable agreement is then ob- tained but the difference should be borne in mind when 2D calcu- lations are performed. The difference is due to the two dimensional representation. The 2D equipment geometry corresponds to a cut in the (Oxy) plane as shown in Fig. 1. This representation implies that the lamp and the wafer have an infinite length if we imagine
Fig. 9. Comparison between the experimental filament temperatures and the ones introduced in the calculations. We can notice on Fig. 8 graphs that the calculated profiles are in good agreement with the experimental data. The difference be- tween the calculated temperatures and the measured ones is infe- rior to 2% in both the 3D and the 2D case for all of the thermocouples. For the 20% heating power, the good agreement is observed as well for experimental and calculated temperatures obtained when the thermocouple position is rotated by 180°. The only exception is for the 2D case at the high lamp power of 30% in which the difference is slightly superior for the thermocouples close to the wafer edge. The latter is between 2% and 4.3% which For the 2D case, the filament temperatures in the simulations are all inferior to the experimental results. For the heating of 20% and 25%, the values remain in the uncertainty domain whereas in the three other cases they don’t. In order to have a better eval- uation, the difference to the experimental filament temperature is given in percentage by Table 2. For all the lamp power, the dif- ferences are between 4.8% and 8.6% below the experimental value, which stay inferior to 10%. An acceptable agreement is then ob- tained but the difference should be borne in mind when 2D calcu- lations are performed. The difference is due to the two dimensional representation. The 2D equipment geometry corresponds to a cut in the (Oxy) plane as shown in Fig. 1. This representation implies that the lamp and the wafer have an infinite length if we imagine
Fig. 10. Relation between the lamp applied power and the wafer temperature.
Fig. 10. Relation between the lamp applied power and the wafer temperature.
Related topics:
Semiconductor ManufacturingComputation Fluid DynamicsRadiative Heat TransferSilicon WaferElectrical and Electronic EngineeringNumerical Calculation
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