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Validation of a Rapid Thermal Processing model in steady-state

Profile image of Pierre-Olivier LOGERAISPierre-Olivier LOGERAIS

2008, Microelectronic Engineering

https://doi.org/10.1016/J.MEE.2008.07.012
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8 pages

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Abstract

Rapid Thermal Processing (RTP) is widely used in advanced semiconductor manufacturing. The present work deals with the heat transfer from infrared lamps to the silicon wafer in a commercial RTP equipment. Both numerical and experimental approaches are considered. For numerical purposes, the RTP system is modelled in two (2D) and three dimensions (3D). Calculations are performed in steady-state. The computational fluid dynamics method (CFD) is used for solving the mass and heat conservation equations. The radiative heat transfer equation is solved with the Monte Carlo method. In order to validate these models, measurements of the wafer temperature are realized for five electric power values supplied to the infrared lamps. The experimental wafer temperature profiles are in good agreement with the numerically calculated ones. Moreover, a confrontation between the experimental temperature of the infrared lamp filaments evaluated from the Ohm law and the one used in the numerical calculations shows a good agreement with the 3D model. The slight difference observed with the 2D model is explained. So the numerical simulations are fully validated. Two relations are established in order to predict the power which has to be applied to infrared lamps to obtain the required wafer temperature.

FAQs

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What explains the differences in experimental and numerical temperature profiles in RTP?add

The study finds that discrepancies between experimental and calculated temperatures are less than 2% for both 2D and 3D cases, except for the 30% heating power case where differences reach up to 4.3%.

How does the steady-state temperature vary with lamp heating power?add

Experimental results show that the wafer reaches steady-state conditions after 900 seconds for all heating power values of 10%-30% maximum.

What impact do dimensional models have on temperature simulation outcomes?add

The 3D model provides more accurate temperature simulations than the 2D model, particularly because 2D does not realistically account for geometry, resulting in a 5-8% correction for filament temperatures.

How was the filament temperature determined during the experiments?add

Filament temperature is evaluated using Ohm's law based calculations from recorded values of current intensity and voltage during the heating process.

When do the experimental and numerical simulations achieve highest correlation?add

The highest correlation between experimental measurements and simulations occurs at the 20% heating power, where both models show very good agreement within ±0.4% accuracy.

Figures (12)
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.
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.
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.
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.

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