The numerical calculations evaluated the influences of the chamber wall temperature and the gas pressure on the gas phase temperature and the gas flow. In order to individually evaluate the heat transport by the thermal conduction and that by the gas recirculation, the calculation was first performed at a sufficiently low pressure producing no gas recirculation.

Figure 2 shows the overall gas flow motion and the gas velocity distribution at the chamber wall temperatures of (a) 200˚C, (b) 300˚C, (c) 350˚C and (d) 400˚C. For these calculations, the argon gas was supplied from the inlet at the gas flow rate of 100 sccm, the temperature of 25˚C and the pressure of 50 Pa. The temperatures of the gas distributor and the stage were fixed at 350˚C.

Figure 2(a) shows the gas flow when the chamber wall temperature was 200˚C. The argon gas flows downward through the gas distributor. In the center region of the chamber, the gas flows down to the stage and changes its direction to the outside edge of the stage. In the region around a half radius of the gas distributor, the gas seems to go straight to the space between the stage and the chamber wall. The gas from the outside region of the gas distributor also goes straight and downward to the exhaust.

As shown in Figure 2(b), Figure 2(c) and Figure 2(d) at the chamber wall temperatures of 300˚C, 350˚C and 400˚C, respectively, the gas flow directions are similar to those in Figure 2(a). Overall, the gases flow without recirculation in the reactor at 50 Pa and 100 sccm in the temperature range between 200 and 400˚C.

During the gas flow without any gas recirculation, such as those in Figure 2, the heat is transported between various parts mainly by thermal conduction. Thus, the influence of the chamber wall temperature on the gas phase temperature can be clearly evaluated. Figure 3 and Figure 4 show the gas phase temperature distribution at the chamber wall temperatures of (a) 200˚C, (b) 300˚C, (c) 350˚C and (d) 400˚C. The gas flow rate, gas temperature and pressure of the argon gas at the inlet are the same as those in Figure 2. The gas phase temperature was evaluated at the O, A, B and C positions. The maximum gas phase temperature difference from the stage temperature, ΔT, is defined by Equation (1).

Δ T = T Diff − T Stage . (1)

T_Stage is the stage temperature, that is, 350˚C. T_Diff is the greatest temperature difference from the T_Stage value between the O, A, B and C positions.

The gas phase temperature distribution at the chamber wall temperature of 200˚C is shown in Figure 3(a). The gas phase temperature at the C position is overall lower than those at the O, A and B positions, because of the heat conduction to the cold chamber wall. As shown in Figure 4(a), the gas temperature becomes the lowest value at the height near 80 mm above the stage. At the O, A, B and C positions, the lowest gas phase temperature is 340˚C, 325˚C, 315˚C and 300˚C, respectively. The ΔT value is −50˚C when the chamber wall temperature is 200˚C.

Figure 3(b) and Figure 4(b) show the temperature distribution when the chamber wall has the temperature of 300˚C. Because the temperature differences between the stage, the gas distributor and the chamber wall are less than those in Figure 3(a) and Figure 4(a), the decrease in the gas phase temperature becomes less than that in Figure 3(a) and Figure 4(a). The ΔT value is −16˚C, as shown in Figure 4(b).

When the chamber wall temperature is 350˚C, the gas phase temperature is overall around 350˚C, as shown in Figure 3(c) and Figure 4(c). The ΔT value is significantly low, such as −0.8˚C, as shown in Figure 4(c).

When the chamber wall temperature is 400˚C, the gas phase between the stage and the gas distributor is heated to the temperatures higher than 350˚C by the hot chamber wall, as shown in Figure 3(d) and Figure 4(d). The temperature increase is about 1˚C at the O position. The temperature difference from that of the stage increases with approaching the chamber wall. The highest temperature is 365˚C at the C position. The ΔT value in Figure 3(d) is +15˚C, as shown in Figure 4(d).

Figure 5 shows the relationship between the ΔT value and the chamber wall temperature. As shown in this figure, the ΔT value monotonously increases with the increasing chamber wall temperature. Based on this figure, the ΔT value is recognized to have a linear relationship with the chamber wall temperature when the heat transport is caused by the thermal conduction without gas recirculation, as shown in Figure 2.

While the temperatures of all parts in the reactor should be the same for achieving a uniform temperature distribution, Figure 5 is expected to be useful to finely adjust and solve the temperature gradient which is unintentionally formed due to any unavoidable reasons.

The gas flow and the temperature were next studied when the gas recirculation exists in the chamber. Figure 6 shows the gas flow and the velocity distribution at the gas pressures of (a) 500 Pa, (b) 1000 Pa, (c) 2000 Pa and (d) 5000 Pa. The chamber wall temperature is set to 200˚C so that the influence of the gas pressure on the gas phase temperature is clearly recognized.

At the gas pressure of 500 Pa, as shown in Figure 6(a), the gas overall flows are downward through the gas distributor. In the region near the stage surface, there is a small and significantly slow gas recirculation as indicated by the arrows.

The gas recirculation is enhanced by the increasing gas pressure. At 1000 Pa, as shown in Figure 6(b), the dimension of the gas recirculation is enhanced to reach the center region of the stage, at which the gas velocity is even significantly low. Figure 6(c) and Figure 6(d) show that the gas recirculation has the gas velocity of about 0.1 m/s and about 0.2 m/s at 2000 Pa and 5000 Pa, respectively, in the wide gas region from the stage to the gas distributor. Overall, the gas velocity and the dimension of the gas recirculation increase with the increasing gas phase pressure.

The gas recirculation shown in Figure 6 influences the gas phase temperature, as showed in Figure 7 and Figure 8. Figure 7(a) and Figure 8(a) show that the mid height at the A, B and C positions has the lowest temperature, similar to those in Figure 3(a), Figure 4(a), Figure 7(b) and Figure 8(b). In contrast, as shown in Figure 7(c) and Figure 7(d), the gas cooled by the cold chamber wall flows to the stage, following the enhanced recirculation indicated by Figure 6(c) and Figure 6(d), the gas phase in the lower half of the chamber is colder than the upper half region.

As shown in Figure 8(a), Figure 8(b) and Figure 8(c), the temperature decreases caused at the O, A, B and C positions are similar at the gas phase pressures between 500 Pa and 2000 Pa. The ΔT values are between −47˚C and −49˚C. While the height showing the lowest temperature at the C position slightly shifted to near 60 mm at 2000 Pa, the overall temperature profiles are considered to be unchanged at the gas phase pressure less than 2000 Pa; the gas recirculation produced at 500 - 2000 Pa does not significantly worsen the gas temperature uniformity. In contrast, at 5000 Pa, the enhanced gas recirculation indicated by Figure 6(d) significantly takes the heat away from the center region of the gas phase to decrease the gas phase temperature. At the C position, the ΔT value is −76˚C at 5000 Pa.

The ΔT values are −47˚C, −48˚C, −49˚C and −76˚C at the pressures of 500, 1000, 2000 and 5000 Pa, respectively, as shown in Figure 9. This figure shows that the influence of the gas recirculation on the temperature distribution is slight at a pressure lower than 2000 Pa when the gas flow rate is 100 sccm. Because the influence of the gas recirculation may become significant at the gas pressures higher than some specific value, the relationship between the gas pressure and the formed film quality should be carefully evaluated.

The gas phase temperature distributions were further evaluated for various parameters, such as the stage temperature, T_Stage (˚C), the gas distributor temperature, T_GD (˚C), the chamber wall temperature, T_CW (˚C), the gas pressure, P (Pa), and the gas flow rate, F (sccm). The temperature of the gas inlet was 25˚C. Next, the gas phase temperature uniformity at the i position, X_i, (%) was evaluated by Equation (2) using the maximum and minimum temperature, T_Max,i (˚C) and T_Min,i (˚C), respectively.

X i ( % ) = 1 00 × ( T Max , i − T Min , i ) ÷ ( T Max , i + T Min , i ) . (2)

The influences of the various parameters on the X_O, X_A, X_B and X_C values are expressed by Equations (3)-(6) which are obtained by the least squares method.

At the O position:

X O ( % ) = − 0. 324 T GD + 4 . 2 0 × 1 0 − 4 T GD 2 − 7 . 78 × 1 0 − 3 T CW − 2 . 49 × 1 0 − 4 P     + 4 . 28 × 1 0 − 3 F + 65 . 7 . (3)

At the A position:

X A ( % ) = − 0. 295 T GD + 3 . 7 0 × 1 0 − 4 T GD 2 − 1 . 38 × 1 0 − 2 T CW + 4 . 67 × 1 0 − 4 P     + 3 . 27 × 1 0 − 3 F + 63 . 9 . (4)

At the B position:

X B ( % ) = − 0. 262 T GD + 3 . 17 × 1 0 − 4 T GD 2 − 1 . 96 × 1 0 − 2 T CW + 6 . 7 0 × 1 0 − 4 P     + 2 . 27 × 1 0 − 3 F + 61 .0. (5)

At the C position:

X C ( % ) = − 0. 211 T GD + 2 . 35 × 1 0 − 4 T GD 2 − 3 .0 5 × 1 0 − 2 T CW + 7 . 32 × 1 0 − 4 P     + 1 . 35 × 1 0 − 3 F + 57 . 6 . (6)

Utilizing Equations (3)-(6), the temperature uniformities, X_i, at the O, A, B and C positions are drawn as contour diagrams, as shown in Figure 10. In Figure 10, the temperatures of the gas distributor, chamber wall and stage are fixed at 350˚C. Figure 10(A) shows that the X_O value is overall less than 3%. As shown in Figure 10(A), Figure 10(B) and Figure 10(C), the X_A, X_B and X_C values increase with the increasing gas pressure and the increasing gas flow rate, while the trends of the A, B and C positions are slightly different from each other.

Based on Figure 10, the gas phase temperature uniformity can be adjusted by the process parameters, such as the gas flow rate and the gas pressure. When the gas phase temperature uniformity is less than 3%, the gas pressure and the gas flow rate are adjusted to those in the left bottom region of the 3% line.

The gas residence time, t_RT (s), was obtained, as shown in Figure 11, by tracing the virtual particles from the inlet to the exhaust in the reactor utilizing the Fluent software. For this calculation, the temperatures of the gas distributor, chamber wall and stage are fixed at 350˚C.

As shown in Figure 11(a), the maximum gas residence time, t_RT,Max (s), at 1000 Pa decreases with the increasing gas flow rate, because of the increase in the gas velocity over the gas phase in the reactor. While the t_RT,Max value is about 500 s at 50 sccm, it decreases to 400 s at the gas flow rate of 100 sccm. At 500 sccm, the t_RT,Max value becomes significantly short to achieve the quick removal of the precursor and the byproducts.

When the gas flow rate is fixed, the high gas pressure makes the t_RT,Max value long, as shown in Figure 11(b), due to the significant gas recirculation, as shown in Figure 6(d). For preparing the t_RT,Max value shorter than 400 s, the gas pressure should be lower than 1000 Pa at the gas flow rate of 100 sccm.

Accounting for the X_i and t_RT,Max values, shown in Figure 10 and Figure 11, respectively, the process parameters can be determined. By adjusting the parameter values with evaluating the t_RT,Max value, the ALD process is expected to become fast.

While the cross-shaped table, shown in Figure 1(b), is placed on the stage, its influence on the maximum gas residence time is considered to be negligible. When many tables are stacked on the stage in order to increase the number of samples, the gas residence time should be evaluated for avoiding any unexpected gas stagnation behind the table.

A practical design method using the CFD for the ALD gas conditions is summarized as shown in Figure 12. It consists of the four steps. 1) At the low gas pressure producing no gas recirculation, the ΔT values are obtained taking into account the various parameters, such as the temperatures of the sample stage, the gas distributor and the chamber wall. 2) The influence of the gas pressure on the ΔT value is studied taking into account the existence of the gas recirculation. 3) The contour diagrams of the temperature uniformity are obtained for determining the applicable combinations of the process conditions utilizing the temperature uniformity equations consisting of various parameters. 4) The relationships of the maximum gas residence time with the gas flow rate and the gas pressure are obtained for determining the range of the process conditions for achieving a fast process.

The evaluation of the gas flow and the temperature in the gas phase without the recirculation shows the potential capability for temperature uniformity in the reactor. By adding the analysis taking into account the gas recirculation and the gas residence time, the applicable ranges of the various parameters are determined without degrading the temperature uniformity and the processing time.