Chapter 3 Numerical methods
3.6 Boundary conditions
A uniform, downward airflow of 0.3 m/s was assigned as one of the inlets at the top boundary of the domain. The rest of 5 boundaries of the simulation domain were assigned as pressure boundaries. Moreover, 14 inlets were imposed separately at the opening of each
distribution tube. In this study, SF6 released from the gas distribution tubes was solved as a scalar species.
3.7 Rotating reference frames
To simulate the wiping of the chamber wall during preventive maintenance, rotating reference frames method was applied to the chamber with a cover. The rotating reference frames enables one to model the cases where entire mesh is rotating at a constant angular velocity. Modeling strategy was that the mesh of fluid inside the chamber was assigned to the rotating frame to make the fluid rotating, and local coordinate systems was defined from Cartesian to Cylindrical at the center of the chamber bottom. Entire fluid inside the chamber was made to rotate at an angular velocity of 5 rpm about a prescribed axis.
3.8 Control efficiency
By Fick’s law, the total one-dimension diffusion flux, J, can be defined as
1 where A is the area across which diffusion occurs, D is the diffusion coefficient, c is the concentration, x is the distance, ? is the air density, air Y is the mass fraction of species, and the subscript i is the grid. In data reduction, D is the diffusion coefficient of SF6 in air and is calculated to be 9.64 10× −6 m/s by Champman-Enskog theoretical equation (Cussler, 1997).
The complete description of the mass transfer requires separating the contribution of convection and diffusion. The usual way of effecting this separation is to assume that these two effects are additive：
(Total masstransport)=(Masstransported by convection) (+ Masstransported by diffusion)
out out 100%
out out out air out out out air
m Y Q ? Y V A ?
are the mass flow of inlet and the mass flow rate of outlet by convection, respectively. Q and in Qoutare the inlet flow rate and the outlet flow rate, respectively.
[ ]
Yin kg m/ 3 is the mass concentration of species at the inlet in kg/m3. V and outA are the velocity at outlet cross section and the area at outlet cross section, respectively. out
The subscript out is outlet which represents the side window in this study.
Table 3.1. Information of mass sink
Table 3.2. Size of calculation domains and grids used for simulation
Calculation domain
(X * Y * Z) Grids CPU time
(min)
2m * 2m *3m 393,000 130
4m * 4m *5m 799,000 280
Table 3.3. Inlet flows at the opening of each gas distribution tube
Flow rate (m3/min) Diameter of opening (m) Inlet velocity (m/s)
0.001 0.002 0.3789
0.005 0.002 1.8947
0.008 0.002 3.0315
0.01 0.002 3.7894
Fig. 3.1. Sink region at the side window
(a)
(b)
(c)
Fig. 3.2. Mesh scheme of the chamber (a) mesh scheme (b) in edge plot (c) in total view.
(a)
(b)
Fig. 3.3. Mesh scheme of the chamber with a designed cover (a) mesh scheme (b) in edge
Chapter 4 Results and discussions
4.1 Simulated airflow field and concentration field (case 1)
In the study, the flow and concentration fields were simulated for both case 1 (without the enclosed hood, the chamber is open at the top), and case 2 (with the enclosed hood). Different SF6 release flow rates (1, 5, 8 and 10 L/min) and side venting flow rates (0, 31.3, 93.9, 156.5, 313, 1565, 3130 and 4695 L/min) were simulated. Only the flow and concentration fields of the maximum SF6 flow rate are shown here. Small velocity vectors are difficult to display clearly in the figures, so the following airflow fields are presented using a fixed velocity scale.
Fig. 4.1 shows the airflow field when SF6 is released at the flow rate of 10 L/min, and the side venting flow rate is at the maximum of 3130 L/min, at two different cross-section planes of the domain 2x2x3m. Upward injected SF6 flow at the opening of the gas distribution tubes can be observed vividly at the bottom of the chamber. Both airflows inside the chamber and near the chamber top are seen to be sucked into the side window completely. There is no outward SF6 flow at the top of the chamber. The concentration fields of SF6 at the SF6 release flow rate of 10 L/min, and the side venting flow rate of 3130 L/min (100%) is shown in Fig.
4.2. It is observed that with large venting flow rate of 3130 L/min, the SF6 concentration near the top of the chamber is about zero, meaning there is no observable SF6 outflow from the chamber. The results are consistent with the flow fields seen in Fig. 4.1.
4.2 Comparison between experimental data and simulation results (case 1)
To validate the simulation model, the experimental data are compared with the numerical results. Good agreement is obtained. Table 4.1 is the summary of the experimental data for case 1 and case 2, when the side venting flow rate is 3130 L/min. As listed in Table 4.1, the
98.0% for the SF6 release flow rate of 1, 5, 8, and 10 L/min, respectively. The agreement between experimental data and simulation results is greatly affected by the reliability of the boundary conditions used in the calculations. In the simulation, a uniform downward airflow of 0.3 m/s is assigned as one of the inlets at the top boundary of the domain. Table 4.2 shows the simulated control efficiency when the side venting flow rate is 3130 L/min for case 1.
Convection is mainly responsible for the control efficiency at different SF6 release flow rates.
In smaller domain, the simulated control efficiency are 98.8%, 95.6%, 95.5% and 95.5% at the inlet flow rate of 1, 5, 8, and 10 L/min, respectively. In larger domain, the simulated control efficiency are 99.5%, 96%, 95.4% and 95.7% at the inlet flow rate of 1, 5, 8, and 10 L/min, respectively. The contribution to the control efficiency by diffusion is weak, which is about 0.1%. As shown in Fig. 4.3, the simulation results compare well with the experimental data. Hence, the modeling method and the setting of boundary conditions should be reliable in this study.
It is necessary to look into the personnel exposure at the breathing zone after utilizing the side venting method for fully open chamber (case 1). As shown in Fig 4.4, there is no
observable SF6 concentration at the breathing zone at different planes when SF6 is released at the flow rate of 10 L/min, and the venting flow rate is at a maximum of 3130 L/min. In Table 4.1, the experimental results of case 1 show that SF6 concentration at the breathing zone is lower than FTIR detection limit of 5 ppb at different SF6 release flow rates. Simulated SF6
concentration at the breathing zone is also lower than FTIR detection limit at different SF6
release flow rates when the side venting flow rate is 3130 L/min, as listed in Table 4.3.
4.3 Simulated airflow field and concentration field (case 2)
In order to simplify the geometrical configuration in the simulation, a cover was designed
simulate the wiping of the chamber wall during preventive maintenance, in case 2 the mesh of fluid inside the chamber was assigned to the rotating frame to make the fluid rotating at an angular velocity of 5 rpm about a prescribed axis. Fig. 4.5 shows the airflow field for the chamber with the enclosed hood (case 2) when SF6 is released at the flow rate of 10 L/min, and the venting flow rate is at a maximum of 3130 L/min. It can be observed that downward airflow enters the chamber through the opening of the hood and upward airflow inside the chamber is confined by the hood. Both airflows inside the chamber and near the chamber top are seen to be sucked into the side window more completely. And there is no outward SF6
flow at the opening of the hood. A large circulation exists at the cross plane of the side window by the effect of the rotational fluid inside the chamber.
The concentration fields of SF6 at the SF6 release flow rate of 10 L/min, and the venting flow rate of 3130 L/min (100%) is shown in Fig. 4.6, for case2. In Fig. 4.6, it is observed that when there is an enclosed hood at the top of the chamber with the venting flow rate of 3130 L/min, the SF6 concentration near the opening of the hood is about zero, meaning there is no observable SF6 outflow through the opening of the hood then leaving from the chamber.
4.4 Comparison between experimental data and simulation results (case 2)
The measurements and the simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 3130 L/min is shown in Fig. 4.7, for case 2. When the venting flow rate is 3130 L/min, the simulated control efficiency is 100% at the SF6 release flow rate of 1, 5, 8, and 10 L/min. The measurements control efficiency is 97.5% or 98.8%
when the SF6 release flow rate is 5 L/min, as listed in Table 4.1. Based on the simulation results, the downward airflow patterns and the enclose hood that confine pollutant to stay in the chamber in combination with the side venting method can enhance the control efficiency.
breathing zone is lower than FTIR detection limit (< 5 ppb) when the SF6 release flow rate is 5 L/min and the venting flow rate is 3130 L/min, as listed in Table 4.1. Furthermore,
simulated SF6 concentration at the breathing zone is also lower than FTIR detection limit at different SF6 release flow rates when the venting flow rate is 3130 L/min.
4.5 Simulated airflow field and concentration field at different venting flow rates (case 1)
When the venting flow rate is reduced to 10% of the maximum value (or 313 L/min), the flow filed is changed completely, as shown in Fig 4.8. The flow near the side window is still converged into it while some of the flows at the far end of the side window escape the chamber top, leading to potential SF6 leaking into the clean room from the chamber. The concentration fields of SF6 at the SF6 release flow rate of 10 L/min, and the side venting flow rate of 313 L/min (10%) is shown in Fig. 4.9, for case2. In comparison, when the venting flow is small at 313 L/min, significant SF6 concentration exists at the top of the chamber,
indicating the leaking of SF6 from the chamber into the clean room. These results are
consistent with the flow fields seen in Fig. 4.8. Therefore, to prevent the contamination of the clean room during preventive maintenance, enough venting flow at the side window is
effective even when the chamber is open at the top (case 1). When the venting flow rate is too small to capture the air flow effectively, it is quite possible that the contaminant escapes the chamber and pollutes the clean room and the working personnel.
When the venting flow rate is zero, the flow fields for case 1 is shown in Fig. 4.10. It is observed that the downward clean room air flow enters the chamber, mixes with the SF6
release flow and then leaves at the top of the chamber. The SF6 concentration field in Fig. 4.11 further shows that SF6 leaves from the top of the chamber into the clean room creating
pollution of the room. Therefore, without the venting flow, contamination of the clean room is
dispersion, contamination still pose health risks to workers and causes wafer defects and process tool corrosion due to the air recirculation and change in the clean room. The
occupational hygiene of these workers and the problem how to apply the side venting method properly deserve attentions.
4.6 Simulation results at different venting flow rates (case 1)
The control efficiencies of side venting at different flow rates were investigated by changing the mass flow rate of sink in the simulation. Table 4.4 shows the simulated control efficiency when the side venting flow rate is 313 L/min for case 1. In smaller domain, the control efficiency are 81.9%, 72.7%, 74.7% and 73.5% at the inlet flow rate of 1, 5, 8, and 10 L/min, respectively. In larger domain, the control efficiency are 85.4%, 75.2%, 76.3% and 76.5% at the inlet flow rate of 1, 5, 8, and 10 L/min, respectively. These results are consistent with the flow and concentration fields seen in Fig. 4.8 and Fig. 4.9 that SF6 concentration exists at the top of the chamber when the side venting flow rate is reduced to 313 L/min.
Although a very small concentration is increased when the side venting flow rate is reduced to 313 L/min, simulated SF6 concentration at the breathing zone is also lower than FTIR
detection limit whether the venting flow rate is 3130 L/min or 313 L/min, as listed in Table 4.3. The side venting method is effective to control pollutant dispersion and improve the air quality in the clean room.
The simulated control efficienc y of SF6 versus total gas flow rate when the side venting flow rate is reduced to 50%, 10%, 5%, 3%, or 1% of the maximum value (1565 L/min, 313 L/min, 156.5 L/min, 93.9 L/min, or 31.3 L/min) are shown in Fig. 4.12, Fig. 4.13, Fig. 4.14, Fig. 4.15, and Fig. 4.16, respectively. In Fig. 4.12, the simulated control efficiency is still above 95% when the side venting flow rate is reduced to 50% (or 1565 L/min). However, the
side venting flow rate is reduced to 1% (or 31.3 L/min), as shown in Fig. 4.16. In Fig. 4.17, the control efficiency increases very close to 100% with the increasing of the side venting flow rate to 150% of the maximum value (or 4950 L/min).
Simulated control efficiency of SF6 versus different side venting flow rates when SF6
release flow rate is 10 L/min, 8 L/min, 5L/min, and 1L/min are shown in Fig. 4.18, Fig. 4.19, Fig. 4.20, and Fig. 4.21, respectively. Although there are many parameters and operation conditions that could influence the control efficiency of the chamber without the hood by side venting, this study has found that the side venting flow rate is the most important parameter.
For example, for the simulated control efficiency of SF6 shown in Fig. 4.18, when the side venting flow rate is less than about 700 L/min, the control efficiency increases with the increasing venting flow rate. When the side venting flow rate is higher than 1200 L/min, the control efficiency is found to be higher nearly 100% and becomes more or less a constant.
Similar trend also occurs for SF6 release flow rate is 8 L/min, 5L/min, and 1L/min. For case 1, the results show that side venting at a large flow rate should be an effective way to control pollutant dispersion and reduce the worker’s exposure during preventive maintenance.
4.7 Simulation results at different venting flow rates (case 2)
When the venting flow rate is reduced to 10% of the maximum value (or 313 L/min), the flow filed is similar to the results of the venting flow rate of 3130 L/min for the chamber with the hood, as shown in Fig 4.22. The flow near the side window is still converged into it. A large circulation exists at the cross plane of the side window by the effect of the rotational fluid inside the chamber. The concentration fields of SF6 at the SF6 release flow rate of 10 L/min, and the venting flow rate of 313 L/min (10%) is shown in Fig. 4.23, for case2. In comparison with the venting flow rate of 3130 L/min, it is also observed that when there is an
concentration near the opening of the hood is about zero, meaning there is also no observable SF6 outflow through the opening of the hood then leaving from the chamber. As shown in Fig.
4.24, when the venting flow rate is 313 L/min, the simulated control efficiency for case2 is 100% at the SF6 release flow rate of 1, 5, 8, and 10 L/min.
When the venting flow rate is zero, the flow and SF6 concentration fields for case 2 are shown in Fig. 4.25 and Fig. 4.26, respectively. In Fig. 4.25, it can be seen that without side venting the downward clean room air flow enters the chamber through the opening of the hood, then also mixes with the SF6 release flow and leaves from the opening of the hood. The SF6 concentration field in Fig. 4.26 further shows that SF6 can leaves from the opening of the hood and the rest of SF6 concentration accumulate at the lower side of the hood. Dispersion of SF6 is restricted to the downward airflow and the installation of the hood. It can be concluded that high degree isolation can effectively protect the worker’s exposure by the effect of installing the hood in combination with the side venting method at a large flow rate during preventive maintenance.
Table 4.1. Experimental data under different conditions when the side venting flow rate is 3130
b : SF6 concentration at the end point of the low vacuum venting line when SF6 is released inside the low vacuum line.
Table 4.2. Simulated control efficiency when the side venting flow rate is 3130 L/min, case 1.
Calculation domain
Table 4.3. Simulated SF6 concentration at the breathing zone when the side venting flow rate is 3130 L/min or 313 L/min, case1.
Calculation domain (X*Y*Z)
Flow rate (L/min)
SF6 concentration at the breathing zone, side venting flow rate of 3130 L/min (ppb)
SF6 concentration at the breathing zone, side venting
Table 4.4. Simulated control efficiency when the side venting flow rate is 313 L/min, case 1 Calculation domain
(a)
(b)
Fig. 4.1. Velocity vector for SF6 release flow rate of 10 L/min, venting flow rate of 3130
(a)
(b)
Fig. 4.2. Concentration distribution for SF6 release flow rate of 10 L/min, venting flow rate of 3130 L/min in the 2x2x3m domain, case 1 (a) plane across the chamber top (b) plane
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % ) SF
6
Control Efficiency
SF
6=1000ppm (exp. results)
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.3. Measurements and simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 3130 L/min, case 1.
(a)
(b)
Fig. 4.4. Concentration distribution at the breathing zone for SF6 release flow rate of 10 L/min, venting flow rate of 3130 L/min in the 2x2x3m domain, case 1 (a) xz plane (b) the
(a)
(b)
Fig. 4.5. Velocity vector of the chamber with the hood for SF6 release flow rate of 10 L/min,
(a)
(b)
(c)
Fig. 4.6. Concentration distribution of the chamber with the hood for SF6 release flow rate of
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % ) SF
6
Control Efficiency
SF
6=1000ppm (exp. results)
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.7. Measurements and simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 3130 L/min, case 2.
(a)
(b)
Fig. 4.8. Velocity vector for SF6 release flow rate of 10 L/min, venting flow rate of 313 L/min
(a)
(b)
Fig. 4.9. Concentration distribution for SF6 release flow rate of 10 L/min, venting flow rate of
(a)
(b)
Fig. 4.10. Velocity vector for SF6 release flow rate of 10 L/min, venting flow rate of 0 L/min
(a)
(b)
Fig. 4.11. Concentration distribution for SF6 release flow rate of 10 L/min, venting flow rate of 0 L/min in the 2x2x3m domain, case 1 (a) plane across the chamber top (b) plane
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.12. Simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 1565 L/min, case 1.
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.13. Simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 313 L/min, case 1.
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.14. Simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 156.5 L/min, case 1.
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.15. Simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 93.9 L/min, case 1.
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.16. Simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 31.3 L/min, case 1.
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.17. Simulated control efficiency of SF6 versus total gas flow rate when the side venting flow rate is 4695 L/min, case1.
0 1000 2000 3000 4000 5000 Q
venting(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n cy ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.18. Simulated control efficiency of SF6 versus different side venting flow rates when SF6 release flow rate is 10 L/min, case1.
0 1000 2000 3000 4000 5000 Q
venting(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n cy ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.19. Simulated control efficiency of SF6 versus different side venting flow rates when SF6 release flow rate is 8 L/min, case1.
0 1000 2000 3000 4000 5000 Q
venting(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n cy ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.20. Simulated control efficiency of SF6 versus different side venting flow rates when SF6 release flow rate is 5 L/min, case1.
0 1000 2000 3000 4000 5000 Q
venting(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n cy ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.21. Simulated control efficiency of SF6 versus different side venting flow rates when SF6 release flow rate is 1 L/min, case1.
(a)
(b)
Fig. 4.22. Velocity vector of the chamber with the hood for SF6 release flow rate of 10 L/min, venting flow rate of 313 L/min in the 2x2x3m domain, case 2 (a) xz plane (b) xy
(a)
(b)
(c)
Fig. 4.23. Concentration distribution of the chamber with the hood for SF6 release flow rate of 10 L/min, venting flow rate of 313 L/min in the 2x2x3m domain, case 2.
0 2 4 6 8 10 Q
SF6(L/min)
0 20 40 60 80 100
C o n tr o l E ff ic ie n c y ( % )
SF
6Control Efficiency
SF
6=1000ppm (sim. results, domain 2x2x3) SF
6=1000ppm (sim. results, domain 4x4x5)
Fig. 4.24. Simulated control efficiency of SF6 versus total gas flow rate when the side venting
Fig. 4.24. Simulated control efficiency of SF6 versus total gas flow rate when the side venting