Numerical Study on Thermal Design of a Large-Area Hot Plate with Heating and Cooling Capability for Thermal Nanoimprint Lithography

Abstract

A numerical study is conducted on the thermal performance of a large-area hot plate specifically designed as a heating and cooling tool for thermal nanoimprint lithography processes. The hot plate has the dimensions 240 mm × 240 mm × 20 mm, in which a series of cartridge heaters and cooling holes are installed. Stainless steel has been selected to endure the high molding pressures. A numerical model based on ANSYS Fluent is employed to predict the thermal behavior of the hot plate in both the heating and cooling phases. The proportional–integral–derivative (PID) thermal control of the device is modeled by adding user defined functions. The results of the numerical computations demonstrate that the use of cartridge heaters provides sufficient heat-up performance and the active liquid cooling in the cooling holes provides the required cool-down performance. However, a crucial technical issue is raised, namely that the proposed design poses a large temperature non-uniformity in the steady heating phase and in the transient cooling phase. As a remedy, a new hot plate in which heat pipes are installed in the cooling holes is considered. The numerical results show that the installation of heat pipes could enhance the temperature uniformity both in the heating and cooling phases.

1. Introduction

A hot plate is a heating device which indirectly heats material through surface heating. Hot plates are used in a wide range of applications from cooking surfaces, to devices which maintain constant temperature for chemical experiments where temperature uniformity is important, to semiconductor processing equipment which requires rapid and uniform heating performance. General hot plate design reflects the current level of industrial technology, and it does not have a high level of difficulty. As such, there are already a variety of products on the market for various uses, and they are rarely discussed in recent academic studies.

The target of this study is a hot plate for thermal nano-imprint lithography (TH-NIL below) equipment. In other words, the topic of this hot plate study is the challenging technical demands that are uniquely required by the TH-NIL process. The key focus for improving the performance of electronic parts and improving manufacturing productivity is mass production technology which can create a variety of nano-scale shapes. Up to the present, photolithography has led the ultra-miniaturization of shapes in the field of semiconductor processing [1]. This manufacturing process uses the photoreactive qualities of resins, and it has evolved to the point where it can create 10 nm line widths during memory semiconductor processing [2]. However, because the manufacturing process is complex, the cost of production is high and it is difficult to manufacture a variety of shapes. In addition, progress in miniaturization is encountering limitations due to constraints caused by light wavelengths [3,4,5]. One alternative which has been proposed for resolving this problem is nano imprinting. This is a mechanical etching method in which a polymer substrate is softened by heating it to higher than the glass transition temperature [6,7,8,9,10,11,12,13] and then a stamp with a nano-shape is pressed on the surface to transfer the opposite shape [14,15,16]. This manufacturing method is classified according to the method by which the resin is hardened, and it includes the photocuring method which uses ultraviolet radiation on the resin and the TH-NIL method which cools the resin to harden it. TH-NIL is not subject to the limitations caused by the photocuring method’s ultraviolet ray wavelengths, and it can create high aspect ratio shapes [17], but it requires fine thermal control due to the characteristics of the continuous heating-pressurizing-cooling process.

Even in the earliest publications from Chou et al., [2,18,19] this simple concept showed high-resolution capabilities down to the 10-nm regime. Various NIL methods are differentiated depending on the curing process applied, which will also set the required specifications for mold and resist materials. NIL methods with corresponding materials used are summarized in

Table 1. NIL methods summarized from reference [18,19,20,21,22,23].

NIL Method	Process Details	Mold/Substrate	Resist Materials
Thermal NIL [20,21]	Thermal annealing of polymers at temperatures up to 50 °C above the glass transition temperature.	High hardness molds (Young’s modulus should be higher than that of resist): silicon, glasses, quartz, nickel, ceramics, Al oxideNote: thermal expansion coefficient of mold and substrate should match	Only thermoplastic polymers: polystyrene (PS), poly(methyl-methacrylate) (PMMA), polycarbonate (PC), polyethylene terephthalate (PET), siloxane copolymers (PDMS-b-PS, PDMS-g-PMMA), specified spin-on polymers
UV NIL at room temperature [3,4,5,22,23]	UV, EUV exposure	UV-transparent materials: quartz glass; soft stamps are more common for UV NIL: polydimethylsiloxane (PDMS), polyvinyl chloride (PVC), PMMA	Low viscosity UV-sensitive materials, ideally with low volume shrinkage after polymerization—usually liquid functionalized monomers or oligomers, CARs
UV NIL + thermal annealing [18,19]	Simultaneous UV exposure and substrate heating	UV-transparent materials	UV-curable polymers with better surface coverage and lower imprint temperatures as for T-NIL can be used

.

The following requirements must be considered in the design of TH-NIL hot plates.

(1) The hot plate must have the ability to perform rapid heating and rapid cooling to efficiently melt and solidify the resin. (2) The hot plate must be expandable to a large area. (3) The hot plate must maintain a high temperature uniformity to minimize deformation caused by non-uniform thermal expansion and allow for easy separation from the stamp. (4) The hot plate material must have high strength and hardness to minimize deformation caused by pressing during pressurization. (1) and (2) are productivity-related requirements, and (3) and (4) are quality-related requirements. After a study by Chou et al. [2], research on TH-NIL etching began to gather momentum, but most of it was focused on physical phenomena that occur during processing such as filling, the material properties of the substrate and other materials, stamp manufacturing, and the quality and applications of manufactured shapes [23,24,25,26,27,28,29,30]. Meanwhile, studies on hot plates were conducted as the development of TH-NIL equipment moved forward [31,32,33,34,35]. Kwak et al. [32] proposed the concept of a hot plate with horizontally extensible cooling and heating sources that use long rod-shaped cartridge heaters and cooling holes for flowing refrigerant that are staggered vertically. They verified the validity of the concept through computational analysis and experiments. In a later study, Park et al. [33] made a specific version of a concept model presented in preceding studies by designing a 240 mm × 240 mm × 20 mm hot plate and analyzing its thermal behavior with computational analysis. They reported that the hot plate provided heating performance and temperature uniformity which satisfied the design requirements. This study created and used an adjunct program which can model PID control to recreate the thermal behavior of a hot plate that is equipped with an actual feedback controller. To ensure temperature uniformity, the study used aluminum, which has a very high thermal diffusion coefficient, as the hot plate material. However, the aluminum, which has a low surface hardness, was not found to be a suitable material for TH-NIL processing in which it is exposed to high pressure pressing. Aware of this problem, Yang [36] fabricated a hot plate from stainless steel, which has high surface hardness, and performed heating experiments. However, these did not include cooling experiments that used flowing refrigerant in the cooling holes, and therefore the overall process’ thermal performance could not be evaluated. The present paper focuses on a hot plate that is fabricated from stainless steel, which has high strength and hardness, so that it can withstand the pressurizing process. It numerically analyzes abnormal thermal behavior in the heating and cooling process and evaluates the suitability of the thermal design. The goal is to understand the thermal problems which can occur during this process due to the stainless steel material which has a low thermal conductivity and to find methods for resolving these problems.

2. Model

2.1. Physical Model

Figure 1 shows the hot plate which is discussed in this study. Its basic structure is the same as the hot plates discussed in previous studies [37,38,39]. The hot plate has a square plate structure with a side length of L and a thickness of d. The actual working area where work is possible is a square area with a side length of L-2g which excludes the hot plate perimeter region with a width of g. On the hot plate’s sides, there are 2 rows of staggered circular holes with a diameter D in the length (z) direction, one row above the other. The circular holes are arranged horizontally at intervals of S, and one of the core advantages of the hot plate is its extensibility, by which it can easily be extended to a large area by increasing the number of holes. As shown in Figure 1, a heat source is provided in heating mode by inserting circular cartridge heaters in the lower circular holes, and the upper circular holes are used for cooling. The main dimensions of the hot plate used in this study are as follows.

L = 240 mm, D = 6 mm, g = 10 mm, d = 20 mm, S = 12 mm. Using this as a reference, 20 cartridge heaters were installed in the lower part and 19 cooling holes were made in the upper part. Each cartridge heater has a heating capacity of 300 W. The heating plate material is stainless steel STS304, and the density is 8030 kg/m³. The thermal conductivity is 15.1 W/m K. The thermal diffusion coefficient is 3.75 × 10⁻⁶ m²/s, which is considerably smaller than the thermal diffusion coefficient of the aluminum used in previous studies, which is 7.10 × 10⁻⁵ m²/s. This study considered two hot plate models with different methods of using the cooling holes. Model I is a model which uses the cooling holes as flow channels for refrigerant as in an existing study [36]. The coolant flows in cooling mode only, and the hot plate is cooled directly. Model II is a model with a heat pipe attached to the cooling holes. It was considered as a method for improving the temperature uniformity problems which can occur in Model I. In this model, a heat pipe that is longer than the hot plate is used, and the heat pipe is indirectly cooled by cooling the end of the heat pipe which protrudes outside of the hot plate. The outer diameter of the heat pipe is 6 mm, and the length is 340 mm. Of the 100 mm part that protrudes outside of the hot plate, the 30 mm at the end is cooled.

Feedback control is performed on the cartridge heater’s heat generation to allow the hot plate temperature to optimally approach the set temperature and stabilize. As done in a previous study [33,34], 6 PID controllers are used to control the 20 heaters. Six temperature monitoring points are arranged as shown in Figure 1a. The two heaters near each perimeter monitoring point are combined into single groups, and the 4 heaters near the internal temperature monitoring points are combined into single groups to achieve independent temperature control for a total of 6 groups.

2.2. Computation Analysis Model

To examine the hot plate’s abnormal thermal behavior, ANSYS Fluent V15.0, which is commercial CFD code, was used to perform computational analysis. The analysis area was the entire hot plate as shown in Figure 1, and 2 million grid cells were used.

The RNG k − ε model [35] is a method of modeling the turbulence phenomenon based on a mathematical statistical technique called RNG (Renormalization Group) method. The transportation equation for k, ε of RNG model is as follows:

$$\rho \left(U_i\frac{\partial k}{\partial x_i}\right)=\frac{\partial }{\partial x_i}\left({\sigma }_k{\mu }_{eff}\frac{\partial k}{\partial x_i}\right)+{\mu }_t\left(\frac{\partial U_i}{\partial x_j}+\frac{\partial U_j}{\partial x_i}\right)\frac{\partial U_i}{\partial x_j}-\rho \epsilon$$

(1)

$$\rho \left(U_i\frac{\partial \epsilon }{\partial x_i}\right)=\frac{\partial }{\partial x_i}\left({\sigma }_{\epsilon }{\mu }_{eff}\frac{\partial \epsilon }{\partial x_i}\right)+C_{\epsilon 1}\frac{\epsilon }{k}\left[{\mu }_t\left(\frac{\partial U_i}{\partial x_j}+\frac{\partial U_j}{\partial x_i}\right)\frac{\partial U_i}{\partial x_j}\right]-\left(C_{\epsilon 2}+\frac{C_{\mu }\eta \left(1-\frac{\eta }{{\eta }_0}\right)}{1+\beta {\eta }^3}\right)\rho \frac{{\epsilon }^2}{k}$$

(2)

where, $\eta =Sk/\epsilon$, $S={\left(2S_{ij}{S}_{ij}\right)}^{1/2}$.

The coefficient values applied in the above equation are as follows:

${\sigma }_k=0.7194$, ${\sigma }_{\epsilon }=0.7194$, $C_{\epsilon 1}=1.42$, $C_{\epsilon 2}=1.68$, $C_{\mu }=0.0845$, ${\eta }_0=4.38$, $\beta =0.012$.

The heating mode, which raises the hot plate’s temperature from room temperature to 200 °C, and the cooling mode which lowers the temperature from 200 °C to room temperature, were calculated separately. The computation conditions were set to be similar to a previous study [37]. For Model I, it was assumed that the cooling holes were empty during heating mode. For cooling mode, it was assumed that the refrigerant was flowing into the cooling holes at a temperature of 17.2, and the computations were done at velocity boundary conditions. To increase temperature uniformity, the neighboring cooling holes’ refrigerant flows were set to be in opposite directions. For coolant, nitrogen gas and water were used. The coolant’s turbulent flow was calculated using the RNG k-ε model and an enhanced wall function. The key to Model II is in modeling the heat pipe. The heat pipe’s axial effective thermal conductivity is considered to be around 80 times that of copper [20], and the heat pipe was simply modeled as a solid which has 80 times the thermal conductivity of copper. In cooling mode, the cooling of the 30 mm at the end of the heat pipe was performed at boundary conditions with a convective heat transfer coefficient h_heatpipe of 1768.4 W/m²K and an external temperature of 17.2. Based on the initial cooling conditions, the cooling capacity corresponds to 150 W, and this study used a maximum electric heat capacity [39] that satisfies the capillary limit of the heat pipe with a 6 mm diameter that was found in a previous study [19]. The hot plate’s bottom surface was treated as insulated, and natural convection cooling conditions were applied to the top surface and side surfaces. The laminar natural convection heat transfer correlation equation for the square structure’s side and top surfaces is as follows [38].

$${\mathrm{Nu}}_{\mathrm{side}}= 0.59R{a}_d^{1/4} \left({10}^4\le Ra\le {10}^9\right)$$

(3)

$${\mathrm{Nu}}_{\mathrm{upper}}= 0.54R{a}_{\delta }^{1/4} \left({10}^4\le Ra\le {10}^9\right)$$

(4)

$$\mathrm{Nu}={\left\{06+\frac{0.387R{a}^{\left(\frac{1}{6}\right)}}{1+{\left({\left(\frac{0.559}{Pr}\right)}^{\frac{9}{16}}\right)}^{\frac{8}{27}}}\right\}}^2 \left({10}^5\le Ra\le {10}^{12}\right)$$

(5)

Here, ${Ra}_d$ and ${Ra}_{\delta }$ are the Rayleigh numbers found using the hot plate’s height and the surface’s characteristic length $\delta =\mathrm{L}/4$. The heating mode is ${Ra}_d=4.4\times {10}^4, R{a}_{\delta }=1.2\times {10}^6$ in a normal state, and the natural convection on the side surfaces and the top surface can be seen as laminar flow. The convection heat transfer coefficients of ${\mathrm{h}}_{\mathrm{side}}=13.4$(W/m²·K), ${\mathrm{h}}_{\mathrm{upper}}=9.35$ (W/m²·K) were found from this value, and they were used to process the side surface and top surface cooling boundary conditions. In reality, the heating and cooling heat flux applied to the hot plate from the heat sources and cooling sources is more than 100 times this, and therefore the effect of these boundary conditions is not great. To model the supplied heat quantity, which is adjusted in real time by the controller during heating mode, the PID control logic was made into a user-defined function (UDF) and linked to Fluent. The UDF was created using a macro provided by Fluent, and was used via interpretation. In the same fashion as the PID controller that is normally used, the target temperature was set, and the gain index for proportional control (P_gain), the integral control gain index (I_gain), and the differential control gain index (D_gain) were inputted; then the amount of heat supplied by the heater was controlled based on the temperature obtained from the temperature monitoring portion. A normal controller controls the time during which the current or voltage is interrupted, but this is difficult to reflect in the computational analysis. As such, it was changed into an adjustment of the amount of heat supplied to the cartridge heaters. The numerical model was created so that 6 controllers independently controlled 6 regions centered on the 6 temperature monitoring points shown in Figure 1, as described in Section 2.1.

3. Hot Plate Concept Model Comparison Evaluation

The maximum possible temperature in the upper part of the hot plate according to the arrangement of the heating and cooling sources is shown as a straight line with a fixed slope in both Case I and Case II of Figure 1c, as described above. This is because the heated areas of the unit heat sources were modeled as being the same. Therefore, when there is no PID controller, the phenomenon of temperature convergence does not occur. This phenomenon is the reason why the controller is necessary. In other words, it can be seen that the controller is needed to reflect the physical behavior in which the temperature converges on a fixed temperature over time as it does in reality.

The abnormal temperature behavior of the hot plate was analyzed in regard to cases where the cooling was in one direction or in both directions for the 2 kinds of hot plates according to the arrangement of the heating and cooling sources as shown in Figure 2. Nitrogen with a flow rate of 30 m/s and a temperature of 17 °C was used as the refrigerant. In the modeling, the hot plate material was aluminum, and the hot plate dimensions were modeled so that the horizontal and vertical lengths were the same. The heated area of each cartridge heater was fixed. The results of cooling with a nitrogen flow in one direction and in both directions are as follows.

Figure 3 shows the maximum and minimum temperatures of the hot plate when it is cooled with refrigerant flow in a single direction. Considering the fact that heat loss occurs through the hot plate’s sides, measurements were taken at 9 points that were 1 cm in from the sides. The measuring points were set at 5 cm intervals left, right, above, and below the center of the hotplate. It can be seen that the difference between the maximum temperature and the minimum temperature is maintained to some degree.

To analyze this more clearly, Figure 4 shows a graph of the temperature differences in each hot plate. Case II’s temperature difference was the largest at 22.4 degrees. Next, Case I’s temperature difference was less than 16.1 degrees, but it is considerably different from the target temperature deviation.

Figure 5 shows the hot plate’s maximum and minimum temperatures during bidirectional cooling in which the refrigerant flowed in intersecting directions. When compared to Figure 3, the difference between the maximum and minimum temperatures shows a decreasing trend, but it can be seen that a fixed interval is still maintained.

Figure 6 shows the temperature difference between the maximum and minimum temperatures for each hot plate. Case II’s temperature difference was the largest at 11.3 degrees. Case I was next in order at less than 3.9 degrees, but it was still different from the target temperature deviation. Compared to the single direction cooling, the bidirectional cooling temperature showed a trend of being lower by a maximum of 12.6 degrees. Therefore, when bidirectional cooling is used, the deviation between the maximum and minimum temperatures can be reduced.

Computational analysis was used to perform a heating and cooling analysis. The hot plate’s temperature changes in each case were analyzed, and the results show that there were similar trends during heating. Case I consists of heating on the top plate and cooling on the bottom plate, while Case II consists of heating and cooling alternating plates. The heat transfer characteristics of heating and cooling for these two plates were analyzed. During cooling, Case I showed better thermal performance than Case II. Since Case II of Figure 1c was modeled so that the heat sources’ heated areas were the same, the cooled volume of each unit cooling hole became small, and the cooling performance dropped. Therefore, Case I was selected as the shape model that was found during the hot plate concept design.

4. Results and Investigations

4.1. Heating Analysis Characteristics

A numerical analysis was performed to determine the usability of the hot plate heating model which includes a controller, i.e., the proposed model, and the hot plate cooling model according to the presence of the heat pipe. There were 11 controllers in the hot plate heating model which includes controllers. Considering the loss caused by convective heat transfer to the hot plate’s sides, the 2 heaters on the side walls were controlled by a single controller. Three middle heaters were controlled by 1 controller, and a total of 5 controllers were used. In the computational analysis, the UDF was applied to the 5 controllers, and an interpretation method was used. As for the measurement points, the temperature was observed from 9 points in the forward, backward, left, and right directions from the hot plate’s center. The hot plate’s material was aluminum, and the cartridge heaters were stainless steel.

Figure 7 shows the abnormal temperature behavior in the upper part of the small hot plate as time passed. The abnormal temperature behavior is shown in 2 groups. There is a slight temperature difference between temperature measurement points P2, P5, and P8 in the center portion and points P1, P3, P4, P6, P7, and P9 on the edges, and this shows a trend of increasing as time passes. Except for P5, which is located in the perimeter portion, the measurement points were located 1 cm inside the end of the plate. As time passed, the heat from the heater spread evenly throughout the entire solid hot plate. Because there was no heat loss except at the sides and the top, the heat accumulated in the center portion. Therefore, there were high temperatures at P2, P5, and P8, which were the temperature measurement points located in the center portion. The temperature deviation between the center portion temperatures and the temperature measurement points located on the sides was less than 1.5 degrees. Since the phenomena occur symmetrically from the center, it can be seen that there is no problem in analyzing temperature behavior even when comparing only 2 horizontal axis and vertical axis lines in the experiments.

Figure 8 shows the temperature difference between the maximum temperatures and minimum temperatures measured from P1 to P9. There was a maximum temperature difference at around 50 s, and the temperature difference was less than 2 degrees after 200 s. From these results, it can be seen that during the entire process, the deviation between the maximum and minimum temperatures was not less than 2 degrees, but after 90 s it was less than 3 degrees. Even though aluminum, which has a high heat conduction coefficient, was used as the hot plate material, there is a need for additional measures to increase the temperature uniformity during the overall heating process.

Figure 9 shows the temperature field on the top surface of the hot plate after 200 s when control is performed using the shape in Figure 1, which is the hot plate heating model that includes the proposed controller. It can be seen that the entire temperature field is maintained within 2 degrees.

4.2. Cooling Analysis Characteristics

The hot plate cooling used a direct cooling method in which cooling holes are created and coolant is employed, as well as an indirect cooling method in which a heat pipe is used. First, the results of the direct cooling method are described as follows. Figure 10 shows the maximum temperature and minimum temperature of the hot plate during analysis of uni-directional cooling using nitrogen as a refrigerant, and Figure 11 shows the difference between the minimum and maximum temperatures. The analysis used the same 9 measuring points that were initially used. The analysis’ fluid inlet speeds were 10, 20, and 30 m/s, and the UDF code was used to enter a fully developed flow profile of the inlets and outlets. As the refrigerant temperature increased, the maximum and minimum temperatures showed a decreasing trend, and the amount of heat transport increased, causing the cooled places to become cooler faster. As shown in Figure 10 there was a great temperature difference between the maximum and minimum, and then as time passed, the temperature difference showed a decreasing trend. Even when flow occurred for 300 s, the initial target cooling speed and temperature deviation were not achieved. In this study, it was found that stability is secured as the speed increases as a result of rapid stabilization in the temperature drop according to the inflow speed.

Figure 12 shows the hot plate’s maximum and minimum temperatures during analysis using uni-directional cooling and water as a refrigerant, and Figure 13 shows the differences between maximum and minimum temperatures. Using the same method as before, measurements were taken at 9 points, and fluid inlet speeds of 10, 20, and 30 m/s were used. When water is used as a refrigerant, its heat transport capacity is greater because the density of water is greater than that of nitrogen. Therefore, the temperature fell relatively rapidly within 5 s, and the temperature deviation occurred within 10 s. In the initial 5 s, the target values were achieved except when the temperature deviation was different than the target value.

Figure 14 shows the hot plate’s maximum and minimum temperatures as found by the computational analysis during bi-directional cooling using nitrogen as a refrigerant, and Figure 15 shows the differences between maximum and minimum temperatures. Using the same method as before, measurements were taken at 9 points, and fluid inlet speeds of 10, 20, and 30 m/s were used. The overall trends were similar to when uni-directional cooling was performed with nitrogen. However, it is difficult to make the judgment that relatively even cooling and fast cooling were achieved by performing bi-directional cooling. During cooling, a maximum temperature deviation of 4 degrees occurred, and a deviation of less than one degree was maintained after 300 s. Compared to uni-directional cooling, the temperature deviation was reduced.

Figure 16 shows the hot plate’s maximum and minimum temperatures as found by the computational analysis during bi-directional cooling using water as a refrigerant, and Figure 17 shows the differences between the maximum and minimum temperatures. Using the same method as before, measurements were taken at 9 points, and fluid inlet speeds of 10, 20, and 30 m/s were used. The overall trends were similar to when uni-directional cooling was performed with water, but relatively even cooling was achieved by using bi-directional cooling, and the cooling was quick compared to when nitrogen was used. During cooling, a maximum temperature deviation of 4 degrees occurred, and a deviation of less than 0.2 degrees was maintained after 300 s. Compared to uni-directional cooling, there was no marked difference in temperature deviation, unlike when nitrogen was used.

In the case of bidirectional cooling, even when nitrogen was used, a temperature difference of less than 2 degrees was achieved at a rate of 10 m/s. When water was used, a temperature difference of less than 2 degrees was not achieved in less than 5 s regardless of the rate.

In an actual small hot plate, sufficient cooling is only possible through direct cooling with a cooling fluid. Up to this point, the results for direct cooling have been described. The results for indirect cooling are as follows. For the hot plate model that uses a heat pipe, the loss was less than 10% of the total supplied heat in the results found by using Equation (3). As such, the calculations were performed assuming that 90% cooling was performed using the heat pipe and assuming that the supplied heat was 150 W. It can be determined that the emitted heat was excessive. However, the heat pipe case was the same as the case in which cooling was performed on a 340 mm long portion at 200 mm using 15 °C air at 30 m/s. The cooling time was calculated for up to 200 s. The measurement points were P1 and P6 from the same 9 points shown in Figure 1. Figure 18 shows the abnormal temperature behavior at 6 points. Since the end of the heat pipe is cooled by convection, it showed an overall monotone decrease. Figure 19 shows the difference between the maximum and minimum temperatures over time in order to quantitatively analyze the temperature difference shown in Figure 18. Overall, the temperature difference at the hot plate’s upper surface was maintained at less than 6.5 °C over time. In order to observe the temperature field of the upper surface in areas outside of the measurement points, Figure 20 shows the upper surface temperature at a cooling time of 200 s. It can be seen that the overall temperature field has a temperature deviation of less than 2.55 °C. The analysis that was performed up to this point has confirmed the usability of the hot plate heating model that uses the proposed controller and the hot plate cooling model that uses a heat pipe.

5. Conclusions

This study used computational analysis methods to examine the thermal behavior of a large-area hot plate with a working area of 240 mm × 240 mm that was equipped with straight cartridge heaters arranged vertically, as well as cooling holes through which refrigerant flowed. The hot plate was made from stainless steel which has a low thermal diffusion coefficient but also has high surface hardness and strong pressure resistance. Computational analysis methods were used to assess whether the hot plate has thermal characteristics which satisfy the demands of usage as TH-NIL equipment. When PID control was used and 20 cartridge heaters with 300 W heat generation capacity were arranged in parallel, the hot plate could be heated in a stable manner to the target temperature of 200 degrees within 5 min, but the temperature deviation within the hot plate during its normal state was fairly large. In the cooling tests, the temperature deviation was large in the transient states of both air cooling and water cooling using the cooling holes, and the process requirements were not satisfied. To resolve this problem, a new hot plate model was proposed in which a heat pipe is installed on the cooling holes and part of the heat pipe is cooled during cooling mode, and the thermal characteristics of this model were assessed. The hot plate with the heat pipe installed reduced the temperature deviation during heating mode to within the allowable range. During cooling mode, it reduced the temperature deviation greatly compared to the hot plate that was directly cooled using air holes. This study has confirmed that there is a need for additional improvements to the usefulness of the heat pipe-equipped hot plate in terms of temperature uniformity, as well as improvements to the hot plate’s cooling performance and temperature uniformity through optimization of the heat pipe.