The hot filament chemical vapor deposition (HFCVD) process was first employed by Matsumoto et al. [1] to produce diamond film under low pressure. Thereafter, research related to the HFCVD process has been conducted to produce large amounts of diamond film [2] because this film has excellent characteristics such as high strength and low conductivity [3,4]. In the HFCVD process, a filament that has been heated above 2,000 °C is used to activate hydrocarbons, precursors to diamonds, and raise the temperature of the substrate. Due to the excellent performance of diamond film and economical HFCVD process, it has an advantage over other processes in large-scale and mass thin film production. So, the HFCVD process has been intensively investigated to produce diamond film in large quantities [2].

Although many researchers have studied diamond thin film deposition using the HFCVD process, the diamond thin film growth mechanism remains unclear. However, it was confirmed that the temperature gradient produced by thermal energy generated from the filament has a large influence on the growth of diamond thin film [4–9]. For this reason, it is very important to accurately predict the filament temperature and the temperature distribution surrounding the worktable, both of which depend on the operating conditions of the system.

Therefore, three-dimensional computational analysis of the HFCVD process, employing ANSYS-FLUENT (Ver. 20.1), a commercial computational fluid dynamic (CFD) code, was conducted under various input power levels. In addition, filament surface temperature was optically investigated using two-color pyrometry technique. The results from each method were compared to verify these methods. Through the results of three-dimensional fluid modeling, moreover, the worktable temperature was analyzed because it is an important parameter in the growth of diamond film.

2.1. Simulation method

Several assumptions were used to simplify the simulation and reduce the computing time. First, the laminar and steady-state flow was adopted, and the chemical reaction was negligible due to the lowpressure environment. Finally, the Discrete Ordinate model was employed to consider radiative heat transfer.

The mass, momentum, energy, and radiation transport equations used in this simulation are as follows:

where ρ, $\overrightarrow{v}$, u, v, ω, P, μ, g_y, C_p, k, T, S_Rad, I($\overrightarrow{r}$, $\overrightarrow{s}$), a, and σ represent the mass density, velocity vector, velocity components in the x direction, velocity components in the y direction, velocity components in the z direction, pressure, mixture viscosity, gravity force, specific heat, mixture thermal conductivity, gas temperature, energy source due to thermal radiation, radiation intensity depending on position ($\overrightarrow{r}$) and direction ($\overrightarrow{s}$), absorption coefficient, and Stefan–Boltzmann constant.

Both experiment and simulation considered the reactor designed by Song et al. [10]. Figures 1(a) and 1(b) are a schematic and the threedimensional geometry of the HFCVD reactor, which consists of filaments, worktable, heat shield, copper, graphite, and steel. Hydrogen (H₂) was used as the processing gas; its properties were calculated using Khimera software. Table I shows the properties of the materials used in the simulation. And the properties of these used materials are shown in Table II which also indicates the descriptions of boundary conditions. The heat emitted from the filaments was considered by using the heat flux boundary condition, of which the values, which depend on the power, were determined by dividing the input power applied to the filament by filament surface area. The input power was changed from 0.9 to 2.9 kW at fixed operating pressure of 2 Pa. Heat was transferred to the stainless steel through the graphite and copper plate through the copper worktable, and the heat was dissipated by water flowing into the stainless steel. The numbers of cells and nodes were 2,487,894 and 438,545, respectively.

Table 1 . Materials used in analysis and properties of each material..

Material	Density (kg/m3)	Cp (Specific Heat) (J/kg⋅K)	Thermal conductivity (W/m⋅K)	Viscosity (kg/m⋅s)
Hydrogen (H2)	Incompressible ideal gas $\rho =\frac{P}{RT/M_{\omega }}$	According to temperature (Cp=a1+a2T+a3T+a4T3+a5T4)	Calculated by Khimera	Calculated by Khimera
Tantalum (Ta)	16690	140	57.5	N/A
Aluminum (Al)	2719	871	202.4	N/A
Copper (Cu)	8978	381	387.6	N/A
Graphite (C)	2490	771	8.7	N/A
Silicon (Si)	2329	700	149	N/A
Steel (Fe)	8030	502.48	16.27	N/A

*a₁ = 1.360245E+05, a₂ = 3.402317E+00, a₃= -3.358423E-03, a₄= -3.907953E- 07, a₅= 1.705345E-09(300 ≤ T (K) < 1,000).

a₁ = 1.233753E+05, a₂= 2.887275E+00, a₃= -2.323560E-03, a₄= -3.807379E- 07, a₅= 6.527742E-09(1,000 ≤ T (K) < 5,000).

Table 2 . Boundary conditions applied in simulation..

Boundary	Boundary condition	Surface emissivity	Material
Filament	Steady Heat Flux	0.4	Tantalum
Chamber	Isothermal (350 K)	0.1	N/A
Stainless steel	Isothermal (350 K)	0.1	steel
Heat Shield	Coupled	0.5	Copper
Worktable	Coupled	0.5	Copper
Graphite	Coupled	0.75	Graphite
Copper	Coupled	0.1	Copper

Figure 1. (a) Mesh and three-dimensional (3-D) geometry used for HFCVD simulation and (b) schematic diagram of HFCVD system.

2.2. Optical diagnosis method for hot filament surface

Heat is transferred in three ways, by radiation, conduction, and convection. Radiation transfers heat through electromagnetic wave, even in the absence of an object or medium. Thus, all objects with temperatures above absolute 0 K emit thermal radiation. The amount transferred by this method can be written as Eq. (7), according to Planck’s Law.

where u (W/m³) is the thermal radiation intensity, T (K) is the temperature, c (m/s) is the light speed, and h (J ⋅ s) is the Planck constant, and k (J/K) is the Boltzmann constant. This method of estimating the temperature using the ratio of two equations for different wavelengths is called two-color pyrometry, of which the formulations are as follows:

This method is very useful because it is possible to estimate the temperature of a hot surface with uncertain emissivity. A schematic of two-color pyrometry for the HFCVD system is presented in Fig. 2, in which it can be seen that the filament surface temperature was measured by fixing the position of the optical fiber in the center of the filament. The temperature, estimated based on the input power, was compared with the temperature calculated in the simulation.

Figure 2. Schematic diagram of two-color pyrometry for HFCVD system.

3.1. Numerical simulation results

Figure 3 shows the calculated temperature distribution for the zaxis plane of the chamber. The filament surface temperatures for each input were 1365.7, 1495.9, 1547.8, 1719.9, 1792.8, and 1835.4 K, respectively.

Figure 3. Temperature distribution in vertical direction of chamber for each input: (a) 0.9, (b) 1.2, (c) 1.6, (d) 2.1, (e) 2.4, and (f) 2.9 kW.

The temperature of the worktable has been reported to be an important parameter for diamond deposition [11]. However, it is difficult to measure the worktable temperature using an infrared thermometer, because the amount of light from the filament is very strong. We used three-dimensional numerical simulation to predict the worktable temperature. The calculated temperatures of the worktable were 501.8, 526.9, 625.5, 658.9, 675.9, and 700.8 K, as shown in Fig. 4. As the input increased, both the filament surface temperature and the worktable temperature increased, showing that heat is transferred efficiently; the spatial temperature distribution on the worktable side increased as well. The fact that the temperature of the cooling zone was lower than the temperature of the worktable indicates that cooling was properly achieved. It was confirmed that the increased rate of the calculated temperature gradually decreased with increasing input power. This is because heat from the filament was more quickly transferred because the temperature gradient was more severe with increasing filament temperature. It was found that worktable temperature had a similar trend.

Figure 4. Temperature distribution of worktable for each input: (a) 0.9, (b) 1.2, (c) 1.6, (d) 2.1, (e) 2.4, and (f) 2.9 kW.

3.2. Optical diagnosis results

Figure 5 shows the absolute thermal radiation from the filament based on the input power. It was confirmed that thermal radiation increased along with increasing input power. Applying the two-color pyrometry, two wavelengths and corresponding thermal radiation values were required to estimate the temperature. To minimize the mechanical error of the spectrometer, 11 wavelengths were chosen between 800 and 900 nm at increments of 10 nm. Within this range, error caused by emissivity was minimized by reducing the difference in emissivity of the wavelength values. By applying two-color pyrometry to each of the 11 selected wavelengths, 55 results about temperature were calculated; these diagnostic values were obtained by averaging them.

Figure 5. Absolute thermal radiation dose from filament according to wavelength for input values of 0.9, 1.2, 1.6, 2.1, 2.4, and 2.9 kW.

Figure 6 shows the filament temperature with its error for each input power, estimated by applying two-color pyrometry. It was found that both temperature and error increased along with increasing input power; this was attributed to severe fluctuation of the emissivity, which was removed when applying two-color pyrometry.

Figure 6. At 0.9, 1.2, 1.6, 2.1, 2.4, and 2.9 kW of input, filament surface temperature diagnosed using two-color pyrometry.

3.3. Discussion

Table III shows the temperature of the filament surface and the difference rate by input. Figure 7 shows the diagnosed filament surface temperature with their standard deviations and the calculated filament surface temperature. For each input, the values measured by optical diagnosis were 1515, 1548, 1571, 1620, 1640, and 1731 K, and the calculated results were 1424, 1564, 1711, 1856, 1929, and 2037 K. The difference rates were 5.9, 1.01, 8.9, 14.52, 17.65, and 17.69 % at the various levels of input power, respectively. As the input increased, the difference rate increased because the standard deviation of the measurement wavelength increased as input increased. Nevertheless, based on the difference rates of approximately 18 % or less, it was identified that temperatures estimated or calculated with each method were reasonable values. As the result, the validity of the calculation was verified.

Table 3 . According to the input, measured values and simulation results of filament surface temperature and their difference rates..

Power (kW) 0.9	1.2	1.6	2.1	2.4	2.9
Measured temperature (K) 1514.72	1548.46	1570.77	1620.24	1639.76	1730.6
Calculated (K) temperature 1424.23	1564.24	1710.63	1855.57	1929.28	2036.86
Difference rate (%) 5.9	1.01	8.9	14.52	17.65	17.69

Figure 7. Comparison between filament surface temperature diagnosed using two-color pyrometry and using calculated temperature.

Because asmall spectrometer with flexible optical fiber is used to diagnose temperature, this method of estimating temperature by analyzing radiation measured through optical equipment and applying two-color pyrometry can be used without restrictions in locations or structures of objects to be measured. Therefore, the method can be applied as a substitute for commercial dichroscope pyrometry to estimate the temperature. In addition, the thermal fluid analysis method can be applied to the actual HFCVD process and used to estimate the temperature of filaments and base material, which are important variables for diamond thin film.

In the HFCVD process used to synthesize high-quality diamond film, it is important to precisely control the worktable temperature. Since thermal radiation from filaments with high temperature of about 2,000 K has a great effect on worktable temperature, however, it is a challenge to measure and predict the temperature under various operating conditions. Therefore, in this study, a simulation of the HFCVD process using the commercial CFD code ANSYS-FLUENT was conducted to calculate the filament and worktable temperature as well as the thermal flow in the process. In addition, the filament temperature was diagnosed by employing two-color pyrometry; then, the results were compared with calculated temperature values. This comparison showed that the difference between estimated and calculated temperatures was under 18 %. The difference of the filament temperature increases as the output increases; this is attributed to an increase in measurement noise along with increasing thermal radiation. Nevertheless, it seems that both methods can be applied to measure and calculate the filament temperature within a reasonable error range. Moreover, it was possible to predict the gas temperature and worktable temperature through three-dimensional analysis considering radiative heat transfer. The worktable temperature was calculated and found to be 502, 527, 626, 659, 676, and 701 K for the individual inputs. This simulation can be used to suggest design and operating parameters when HFCVD process is scaled up.

This work was supported by the Global Frontier R&D Program of the Center for Hybrid Interface Materials (HIM) (2013M3A6B1078874) and the National Research Foundation (NRF) (2021M3I3A1084958), funded by the Korean Government (MIST).

The authors declare no conflicts of interest.