In Situ Observation of Chemical Vapour Deposition Using Langasite Crystal Microbalance

A method of in situ observation using langasite crystal microbalance (LCM) is descri‐ bed for chemical vapour deposition (CVD). First, the frequency behaviour of the LCM is expressed using the equation having the optimized coefficients in a wide range of gas- phase conditions for the CVD. Next, by the LCM frequency behaviour, the existence of surface chemical reactions in a CVD reactor is determined. Additionally, the LCM can determine the lowest temperature for initiating the film deposition. In the last part, the temperature change related to the film formation process is described.


Introduction
Chemical vapour deposition (CVD) is currently a fascinating technology for producing thin films in various advanced industries [1]. The CVD process is a complicated one having transport phenomena linked with the gas-phase and surface chemical reactions. For clarifying and designing the CVD process, the phenomena in the CVD reactor should be understood and optimized. For this purpose, the computational fluid dynamics (CFD) has been significantly advanced [2] and is actually very useful. In contrast, an experimental approach is still not easy [3], because the sensors seriously suffer from thermal, mechanical and chemical damage by the reactive and high-temperature ambient.
The in situ monitoring technique by means of the langasite crystal microbalance (LCM) [4][5][6] can be an appropriate experimental solution, because the LCM can sensitively detect various changes in the CVD reactor, such as heat, flow and film deposition [5,6]. The information obtained by the LCM should be used for understanding the CVD phenomena. Here, the LCM frequency nonlinearly influenced by various parameters should be clarified. Additionally, a practical process for the measurement and analysis should be developed. In this chapter, the process to in situ observe the CVD is thus explained using the LCM.
In Section 1, the frequency behaviour of the LCM is discussed using ambient gas mixtures at atmospheric pressure and at various temperatures. In order to express the LCM frequency decrease with the increasing concentrations of various gases in ambient hydrogen, the LCM frequency difference between the gas mixture and the carrier gas is practically expressed by optimizing the coefficients accounting for the gas properties. In Section 2, a method for determining the existence of surface chemical reactions is explained. The parameter, C(T), of the equation is used for expressing the LCM frequency change in a hydrogen-monomethylsilane system. In Section 3, the lowest temperature for initiating the film deposition is evaluated using trichlorosilane gas and boron trichloride gas. In Section 4, the way to obtain the temperature change related to the film formation in a trichlorosilane-hydrogen system is described. First, the time constants for the LCM frequency change due to the surface and gas-phase temperature change are determined. Next, the continuous LCM frequency decrease is assigned to the weight increase by the film formation in a steady state. Based on an evaluation of the difference in the LCM frequency between those with and without the heat change related to the film formation, the surface temperature decrease caused by changing the precursor concentration is obtained.

Langasite crystal microbalance frequency behaviour over wide gas-phase conditions for chemical vapour deposition
In this section, a relationship between the LCM frequency and the gas properties is expressed [7] as a practical equation applicable to the CVD conditions using several gases at various temperatures and gas concentrations. Figure 1 shows the horizontal cold wall CVD reactor containing the langasite (La 3 Ga 5 SiO 14 ) crystal microbalance (LCM) [4,8]. This reactor consists of a gas supply system, a rectangularshaped quartz chamber and five infrared lamps. Hydrogen, nitrogen, trichlorosilane, monomethylsilane and boron trichloride gases are used. The carrier gas is hydrogen. The LCM (Halloran Electronics, Tokyo, Japan) having a fundamental frequency of 10 MHz is placed 5 mm above the silicon wafer surface. The LCM frequency decreases with the increasing temperature [5,6]. The silicon wafer and the LCM are simultaneously heated by infrared light from halogen lamps through the quartz chamber.

Experimental procedure
A typical process is shown in Figure 2. First, the LCM is heated to 160-600°C in hydrogen at atmospheric pressure. After waiting until the LCM frequency becomes stable, various gases are introduced at atmospheric pressure into the reactor chamber. The total gas flow rate is adjusted to 1 slm.

LCM frequency and fluid property
The relationship between the LCM frequency and the gas properties is described, accounting for the various relationships shown in Figure 3. Following a previous paper [9], the LCM frequency change, Δf Gas , at a fixed temperature, T (K), is expressed using the product of the gas density, ρ gas , and gas viscosity, η Gas as follows: where f c is the resonant frequency of the fundamental mode of the langasite crystal. ρ c and μ c are the density and shear modulus, respectively, of the langasite crystal. Based on Kanazawa et al. [9], the x, y and z values are 1.5, 0.5 and 0.5, respectively. In a vacuum, the Δf value becomes zero.
The LCM frequency change from the vacuum condition to the hydrogen and to the gas mixtures are shown in Figure 3 and are expressed by Eqs. (3) and (4).
Although the LCM frequency in the vacuum, as a initial value, should be determined, experiment by experiment, the LCM frequency measurement in the vacuum is often not easy in the atmospheric and low-pressure CVD system. Thus, the accurate measurement of the LCM frequency difference from the vacuum condition, such as Δ f H 2 and Δf Mix , is difficult. In contrast, the LCM frequency change at the CVD condition from the carrier gas ambient, such as hydrogen ambient, is easily measured by simple operation. The LCM frequency change from that in the hydrogen (100%), Δf Meas , is expressed by Eq. (5). 2 Meas Mix Following this, the Δf Meas value can be accurately determined, while the mass change of the LCM occurs by means of the multiple use of the LCM.
By evaluating the ratio of the measured LCM frequency in the gas mixture to that in hydrogen, Δf Meas is shown to have a relationship with the properties as described by Eq. (6).
The Δ f H 2 value can be sufficiently smaller than the first term in Eq. (6).
where A is a constant. Using Eq. (7) accounting for various LCM frequencies and the fluid properties, the y and z values can be optimized.
In Eq. (7), the gas density and the gas viscosity are obtained following the ideal gas law and the Chapman-Enskog equation [10], respectively. The viscosity of the gas mixture is calculated following Pollard and Newman [11]. Figure 4 shows the Δf Meas values obtained at 160, 400, 500 and 600°C using various gas mixtures, such as hydrogen-nitrogen, hydrogen-trichlorosilane, hydrogen-monomethylsilane. In this figure, the Δf Meas value is plotted as a function of ρ y μ z assuming that both the y and z values are 0.5 following a previous study [9]. As shown in this figure, the Δf Meas value follows a single trend and does not depend on the gas species. However, the behaviour shown in this figure is not linear.

Influenced of gas density and viscosity
Next, using Eq. (7), the y and z values are obtained. Using the measurement shown in Figure 4, both the y and z values are determined to be 1.3. As shown in Figure 5, the Δf Meas value has a linear relationship with ρ 1.3 μ 1.3 . Similar to Figure 4, the LCM frequency change in Figure 5 does not depend on the gas species.
Using Eqs. (1) and (2), the C(T) values at 160, 400, 500 and 600°C are obtained as shown in Figure 6. This figure shows that the C(T) value is expressed following the Arrhenius-type behaviour.

Method for determining chemical vapour deposition occurrence
In this section, the method for determining the surface chemical reaction occurrence [12] is explained. The silicon carbide film formation from monomethylsilane gas is discussed.

LCM frequency
The LCM frequency differences from ambient hydrogen in monomethylsilane-hydrogen system are shown in Figure 8. Immediately after opening the gas valve at 0 s, a high concentration of monomethylsilane gas, remained at 100% between the gas valve and the mass flow controller, is introduced into the reactor. During the high concentration gas passing through the reactor, the LCM frequency significantly decreases. Thereafter, the diluted monomethylsilane gas reaches the LCM in the reactor. Thus, the fluctuation of the LCM frequency becomes quite small.
As shown in Figure 8, the LCM frequency difference measured at 300°C is very stable after 20 s. This indicates that the gas temperature and the fluid properties, such as the gas density and gas viscosity, are in a steady state. This simultaneously indicates that there is no chemical reaction at 300°C, due to no thermal change caused by no reaction heat. The behaviour at 400 and 500°C is similar to that at 300°C. The trend in the LCM frequency difference at 300, 400 and 500°C is the same and parallel to each other. Thus, the MMS-H 2 system below 500°C is concluded to undergo no chemical reaction.
Although the LCM frequency difference at 550°C seems to be relatively stable, it very gradually increases after 20 s. Similar to this, the LCM frequency difference at 600°C also slightly increases with a larger gradient than that at 550°C. This gradual increase in the LCM frequency difference indicates that any transient change related to a chemical reaction, such as temperature, gas density and gas viscosity, occurred and continued in the reactor during the introduction of the monomethylsilane gas.
As shown in Figure 8, the LCM frequency increases with the decreasing temperature [13]. Additionally, the surface chemical reaction for the silicon carbide (SiC) film deposition from the monomethylsilane gas is endothermic [13]. The frequency decrease due to the weight increase by the film deposition is overcompensated by the frequency increase due to the temperature decrease by the endothermic reaction. Thus, the LCM frequency continues to increase till reaching a steady state. From Figure 8, the chemical reaction occurring at the LCM surface is considered to continue after 200 s.
The temperature change should be enhanced by the increasing reaction rate, due to the greater reaction heat. In order to clearly show this trend, the LCM frequency gradient at various temperatures for the monomethylsilane-hydrogen system is evaluated, as shown in Figure 9.
The LCM frequency gradient in the low-temperature range between 300-500°C is <0 Hz/s. This value is recognized to show the state with no chemical reaction. In contrast, the LCM frequency gradient increases at 550°C from a value <0 to the positive value of 2 Hz/s. It further increases to a value >4 Hz/s at 600°C. Because the LCM frequency gradient increases with the increasing temperature, the surface chemical reaction at the LCM surface is initiated in the temperature range between 500 and 600°C.  shows a linear relationship. The monomethylsilane-hydrogen system (triangles) at 400 and 500°C coincides with the behaviour of the nitrogen-hydrogen system. In contrast, the monomethylsilane-hydrogen system showed a slightly higher gradient in the low ρ 1.3 η 1.3 range. Thus, the C(T) value of Eq. (1) is expected to indicate the occurrence of a surface chemical reaction.

C(T) parameter
The C(T) values obtained using Eq. (1) are plotted versus 1/T. as shown in Figure 11. The C(T) values for the nitrogen-hydrogen system have a linear relationship following Arrhenius-type equation at temperatures from 300 to 600°C. In contrast, the monomethylsilane-hydrogen system shows an increase in the C(T) value at the higher temperatures.
In order to clearly recognize the difference, the C(T) value difference of the monomethylsilanehydrogen system from the nitrogen-hydrogen system are shown in Figure 12. The C(T) value difference at temperatures lower than 500°C is around zero. Thus, the monomethylsilane gas at <500°C behaves the same as that of nitrogen. The monomethylsilane-hydrogen system shows an increased C(T) value to >1 × 10 10 at temperatures between 500 and 550°C. Because these values are obtained separate from the fluid properties, the C(T) value change is understood as the surface chemical reaction for the CVD occurring at the higher temperatures. The obtained temperature is consistent with that from our previous study [6].

In situ observation of chemical vapour deposition using SiHCl 3 and BCl 3 gases
The film deposition behaviour using multiple precursors is explained [14]. The boron-doped silicon film is formed using the trichlorosilane (SiHCl 3 , TCS) gas and the boron trichloride (BCl 3 ) gas for the film deposition and boron doping, respectively.

Chemical reaction occurrence
The chemical reaction behaviour of boron trichloride gas is measured, as shown in Figure 13, at various boron trichloride concentrations and temperatures. At 400°C, the LCM frequency quickly decreases corresponding to the change in the fluid properties by an increase in the boron trichloride concentration. The LCM frequency is kept constant at each boron trichloride concentration. Thus, the boron trichloride gas does not have any chemical reaction and film deposition at this temperature. At 470°C, the LCM frequency sometimes shows flat and other times decrease. The film deposition occurrence is not obvious. In contrast, at 570°C, the LCM frequency decrease is clear at each boron trichloride concentration, as the typical behaviour showing the film deposition.
Similarly, the silicon film deposition from trichlorosilane gas is evaluated. Because the LCM frequency decrease occurs between 570 and 600°C, the silicon film deposition is determined to occur in this temperature range. Next, the LCM frequency behaviour during the boron-doped silicon film deposition is observed at various temperatures using the trichlorosilane and boron trichloride gases, as shown in Figure 14. The LCM frequency shows a gradual increase and decrease in a short cycle at 330-500°C. In contrast, at 530 and 570°C, the LCM frequency continuously decreases. Figure 15 shows the LCM frequency gradient in the temperature range between 330 and 570°C. At temperatures lower than 470°C, the frequency gradient values are near 0 Hz s −1 . At the temperatures higher than 500°C, the frequency gradient decreases to less than −3 Hz s −1 . This behaviour indicates the occurrence of a continuous film deposition. Because the LCM frequency decreases for a long period, the film deposition is determined to occur in the temperature range between 470 and 530°C, specifically higher than 530°C.

Growth rate
The film growth rate is shown in Figure 16, obtained following that the frequency decrease of 1 Hz corresponds to the weight increase of 6 ng cm −2 [9,13,15]. Here, the molecular weight and the density of the boron-doped silicon film are tentatively assumed to be an average of the silicon and boron.
The boron film growth rate at 570°C is near 1.5 × 10 −9 mol cm −2 s −1 at the boron trichloride gas concentrations from 1 to 4%. Additionally, the silicon growth rate shows no obvious trend versus the trichlorosilane gas concentration from 1 to 4%. Similarly, the growth rate of the boron-doped silicon film formed from both the trichlorosilane and boron trichloride gases has no obvious trend, being about 1 × 10 −9 mol cm −2 s −1 . This growth rate behaviour is consistent with the saturation in the low-temperature silicon epitaxial growth process [16].
The change in the growth rate with the increasing temperature is shown in Figure 17 as the Arrhenius plot. The boron growth rate is near 1 × 10 −9 mol cm −2 s −1 and 1.5 × 10 −9 mol cm −2 s −1 at 470 and 570°C, respectively. The silicon growth rate from trichlorosilane gas is about 5 × 10 −10 mol cm −2 s −1 at temperatures lower than 530°C. It is too low value for determining the film deposition occurrence. Because the growth rate increases to nearly 10 −9 mol cm −2 s −1 at 600°C, the silicon film deposition occurs at temperatures higher than 570°C.
At temperatures lower than 530°C, the film growth rate is about 5 × 10 −10 mol cm −2 s −1 . Because this value is similar to that of silicon, the film deposition is negligible. In contrast, the growth rate increases at temperatures higher than 530°C. It reaches 1 × 10 −9 mol cm −2 s −1 at 570°C. The boron-doped silicon film is expected to be obtained at 570°C.

Film formation on substrate
The boron-doped silicon film is formed at 570°C using the trichlorosilane gas and boron trichloride gas at 5 and 3%, respectively. The depth profile of the boron concentration is evaluated by secondary ion mass spectrometry (SIMS), as shown in Figure 18. While the boron concentration in the substrate is about 5 × 10 16 atoms cm −3 , it increases to that higher than 10 20 atoms cm −3 near the film surface. Because the obtained film thickness is about 100 nm, the film growth rate is about 6-7 nm min −1 . This value is comparable to 4 nm min −1 estimated from Figures 16 and 17. Thus, the growth rate obtained by the LCM is consistent with that by the film growth on the substrate.

Surface process
The behaviours of film growth and doping are explained using Eqs. (9)- (12). The symbol '*' indicates the chemisorbed state. Trichlorosilane is chemisorbed at the surface to produce *SiCl 2 and hydrogen chloride gas; *SiCl 2 is decomposed by hydrogen to form silicon at the surface [15]. Similarly, *BCl 2 is considered to be formed at the surface; it reacts with hydrogen to produce boron. the slower process, that is by the silicon film growth rate. Because the LCM detects such details of the various behaviours, it can work as a sensitive monitor for studying the film growth behaviour.

Temperature change related to film formation process
The surface temperature is one of the most important parameters for the CVD. In this section, the LCM is used in order to reveal and clarify the temperature behaviour related to the film formation [17]. For this purpose, the silicon film formation in a trichlorosilane-hydrogen system is used as one of the most popular systems.

LCM frequency behaviour
The LCM frequency decreases corresponding to the weight increase on the LCM surface, following the Sauerbrey equation [15].
( ) where Λf is the measured resonant frequency decrease, f 0 is the intrinsic crystal frequency, Δm is the elastic mass change, A is the electrode area, ρ c is the density of the crystal, and μ c is the shear modulus of the crystal.
where ρ and η are the density and the viscosity, respectively, of the gas mixture. The η value is obtained from the literature [11]. The x value is 1.3 [7] in this section.
These parameters produce various changes in the LCM frequency during the CVD process. The change in the LCM frequency related to the film deposition by the trichlorosilane gas is classified by Parameters (i)-(viii) schematically shown in Figure 19. Figure 19 is the pressure and concentration of the gas remaining in the gas system. The LCM frequency very quickly and slightly increases due to the pressure increase in the reactor when opening the trichlorosilane gas valve. Immediately after this, the LCM frequency decreases and soon recovers by the trichlorosilane gas, which is remained at a high concentration in the gas line, reaching and passing the reactor. Parameter (ii) is the (ρη) 1.3 value of the gas mixture. Corresponding to this, the LCM frequency decreases from the initial frequency. Parameter (iii) is the heat capacity and the heat conduction. The increase in the heat capacity gradually causes the gas-phase temperature to decrease, resulting in an increase in the LCM frequency. Parameter (iv) is the reaction heat. The silicon film formation is an endothermic reaction [19]. This decreases the temperature and thus increases the LCM frequency. With the addition of the trichlorosilane gas, the film formation quickly begins and continues till termination of the trichlorosilane gas supply. Parameter (v) is the weight increase due to the film deposition. After a sufficient time for reaching a steady state, the weight increase by the film formation on the LCM appears as a continuous and linear decrease in the LCM frequency. Parameter (vi) is the (ρη) 1.3 value. The decrease in this value immediately causes the LCM frequency to shift to a high value when the trichlorosilane gas supply is terminated. Parameter (vii) is the heat capacity and the heat conduction. Due to the heat capacity decrease because of the lack of trichlorosilane gas, the gas-phase temperature gradually increases and causes a decrease in the LCM frequency. Parameter (viii) is the weight increase due to the film deposition. After a sufficient period for achieving a steady state, the LCM frequency shift from that before the trichlorosilane gas supply corresponds to the increased weight of the film formed on the LCM. If the temperature change due to the trichlorosilane gas did not exist, the temperature during the early stage of the film formation behaves like the thick dotted line, as shown in Figure 19.

Parameter (i) in
Thus, the LCM frequency difference between the solid line and the thick dotted line is considered to be a function of the temperature shift.

Reaction heat and heat transport
By introducing the trichlorosilane gas into the reactor, the silicon film formation occurs along with the endothermic reaction heat and change of the physical properties of the gas mixture, as shown in Figure 20. Thus, the multiple thermal processes change the surface temperature.
Here, the influence of each parameter is evaluated, following Steps 1, 2 and 3, as shown in Figure 21, taking into account the time constant for heat transport.
During Step1, the time constant for the surface temperature shift is evaluated without introducing a precursor in the ambient hydrogen. The quick lamp power decrease is assumed to show a significantly quick surface temperature decrease similar to that by the endothermic surface chemical reaction, as shown in Figure 20. After this, the gas-phase temperature of the near-surface region gradually decreases. These two processes are expected to have different time constants, such as very short and slightly long.

During
Step 2, the influence of the change in the heat capacity and the heat conduction of the gas mixture are explained. The time constant for the gas-phase temperature shift induced by the precursor introduction, as shown in Figure 20, is evaluated at sufficiently low temperatures at which no chemical reaction occurs. The time constant for this process is expected to be longer than those for Step 1, because the gas-phase temperature shift occurs in the entire region of the reactor and not limited to the region near the surface.

During
Step 3, the temperature change related to the film deposition is explained, accounting for the time constants obtained in Steps 1 and 2. During Step 3, the trichlorosilane concentration is stepwise changed from 0 to 3%. After the period corresponding to the time constants obtained in Steps 1 and 2, the LCM frequency behaviour expresses the film formation in a steady state. By extrapolation, the LCM frequency immediately after changing the precursor concentration is used for evaluating the temperature shift related to the film formation.

Temperature and frequency
The entire frequency dependence on the temperature is shown in Figure 22. This shows the frequency difference at various temperatures from that at room temperature. With the increasing temperature, the LCM frequency decreases, as shown in Figure 22a. At the higher temperatures, the LCM frequency more rapidly decreases than that at the lower temperatures.
The temperature gradient is shown in Figure 22b. The gradient decreases with the increasing temperature. The frequency change due to the temperature change is about −400 Hz/K in the temperature range between 500 and 650°C.

Heat at surface
In order to evaluate the LCM frequency behaviour caused by the quick surface temperature decrease, such as that by the reaction heat, the LCM frequency influenced by the stepwise lamp power shift is evaluated, as shown in Figure 23. The lamp power corresponding to about 1 K quickly decreases at 450 and 660°C.

Figure 23a
and 23b shows the normalized LCM frequency change caused by the stepwise lamp power shift at 450 and 660°C, respectively. In both figures, the LCM frequency very quickly increases immediately after changing the lamp power. It then moderately increases and reaches the steady state.

Heat transport around surface in gas phase
The LCM frequency changes due to the thermal properties, such as the heat capacity and the heat conductivity, are evaluated at the low temperatures, which do not cause the film deposition [14]. Figure 24 shows that the LCM frequency change is due to the stepwise concentration change of hydrogen gas and trichlorosilane gas at 380°C. At conditions C A -C E , the hydrogen concentration and the trichlorosilane concentration decrease and increase, respectively.
At the beginning of condition C A , the LCM frequency quickly drops to less than −3000 Hz and recovers to −1000 Hz. The LCM frequency shift from 0 Hz to −1000 Hz corresponds to the increase in the gas density and the gas viscosity. Next, it gradually recovers to near −400 Hz. Till 500 s, the LCM frequency reaches the steady state. The gradual recovery of the LCM frequency is a result of the temperature decrease mainly due to the increase in the heat capacity of the gas mixture. Additionally, the temperature decrease at the surface is moderated by the heat balance with the gas phase via the heat conduction.
These heat transports overlaps and gives the gradual recovery of the LCM frequency. The LCM frequency at 380°C and at condition C D is expressed, as shown in Figure 25, using the following equation.
From the temperature shift width shown in Figure 25, the temperature decrease by the trichlorosilane gas concentration change at 380°C is about 1 K. The time constant of these process is about 120 s. The time constant in Eq. (17) is longer than that of the second term in Eqs. (15) and (16). The time constant is assumed to have a similar value at the higher temperatures, such as 600-700°C.

Film formation
The silicon film is formed at 640°C along with measuring the LCM frequency, as shown in Figures 26 and 27. The hydrogen gas concentration decreases from 100 to 97%, while the trichlorosilane gas concentration increases from 0 to 3%. Because the silicon film growth rate is saturated at this temperature [16], the reaction heat remains the same for conditions C A -C E . At condition C A , the trichlorosilane gas is added to the hydrogen gas. The LCM frequency shows a significant drop and a quick recovery within several seconds. After the quick recovery, the LCM frequency gradually increases. After the peak appearance, the LCM frequency gradually decreases accompanying the fluctuation due to a temperature fluctuation. Conditions C C , C D and C E show a similar LCM frequency behaviour without a significant drop, unlike that at the beginning of condition C A .
Taking into account the time constant corresponding to the various heat processes, the LCM frequency behaviour is evaluated, as shown in Figure 27. This shows the LCM behaviour at condition C D , as an example. Immediately after increasing the trichlorosilane concentration from 1.8 to 2.4%, the LCM frequency quickly decreases to about −550 Hz due to the increase in the gas density and the gas viscosity. Next, it shows a broad bottom for about 20 s. The LCM frequency gradually increases from 50 to 180 s. After showing a peak, the LCM frequency begins to decrease. This decrease is due to the film formation during the steady state.
Next, the LCM frequency gradient is evaluated. The maximum and minimum values are 1.6 Hz/s between Points A and B and 0.77 Hz/s between Points A and C, respectively. By this operation, the LCM frequency immediately after changing the trichlorosilane concentration is 245 to 410 Hz, as shown in Figure 27.
In addition, the flat bottom of the LCM frequency to 20 s after changing the trichlorosilane concentration may be caused by the balance among the changes in the gas density, the gas viscosity, the heat capacity and the heat conductivity. In order to obtain the possible minimum frequency value, the increasing trend in the LCM frequency between 20 and 180 s is extrapolated to that near several seconds. By this estimation, the frequency of about 50 Hz may be lower than that at the bottom. By adding these values, the LCM frequency change due to the temperature change by changing the trichlorosilane concentration from 1.8 to 2.4% is between 295 and 460 Hz. The surface temperature shift caused by changing the precursor concentration is considered to be about one degree. Figure 27. Evaluation of frequency change caused by the stepwise change from condition C C to C D in Figure 26.