Investigations of energy and flux of ions for diamond nucleation in a microwave plasma chemical vapor deposition

K. Nose and Y. Mitsuda

Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

Abstract: Flux and energy of hydrogen ion to a negatively-biased substrate were investigated in a microwave plasma chemical vapor deposition of diamond. Ion flux was exceptionally in-creased by a substrate biasing over 150 V at pressures greater than 3 kPa. It was estimated in a Monte-Carlo simulation that 95% of the energy input from biasing disperses to the thermal energy of neutrals. We propose that the substrate biasing mainly affect on the dissociation of carbon hydride species at the vicinity of the substrate, and the direct energy transfer to the surface is only the minor in the bias-enhanced nucleation of diamond. Keywords: microwave-plasma, chemical vapor deposition, bias enhanced nucleation, dia-mond, Monte-Carlo method

1. Introduction

In a microwave plasma chemical vapor deposition (MWP-CVD) of diamond, the bias enhanced nucleation (BEN) technique is used in order to achieve a high num-ber density of nucleation. BEN technique results in a nu-cleation density as high as 1010 cm-2 on silicon [1,2], which is six orders of magnitude higher than that on un-treated silicon surface. It is interesting to note that BEN technique is performed at pressures greater than 1 kPa, i.e., much higher than other low pressure processes with bias-ing treatments. It is expected that the substrate biasing is ineffective in this pressure region because of collisions against neutral species in the sheath. That is, substantial ion energy to the surface is limited by the mean free path, which might be much smaller than the sheath thickness in MWP. However, BEN is experimentally observed at pressures as high as 9 kPa [3]. In addition, direct energy transfer is often referred to as the driving force of the nu-cleation.[4] In this study, in order to clarify the mecha-nism of diamond nucleation at such high pressures, in-situ plasma diagnostics through I-V measurement, a conven-tional double probe and an optical emission spectroscopy were performed. In addition, ion energy distribution (IED) at the substrate surface was simulated by a Monte-Carlo (MC) method [5], in which some of basic parameters of plasma were given by experiments. On the basis of these experimental and theoretical results, we discuss the role of substrate biasing in the BEN of dia-mond. 2. Experimental 2-1. In-situ measurements A NIRIM(National institute for research in inorganic

materials)-type MWP-CVD chamber was used for evalua-tions of ion flux and plasma density [6,7]. A schematic diagram of the apparatus is shown in Fig. 1. Silicon sub-strate with a size of 10*10 mm2 was negatively-biased by a dc power supply. A counter electrode was inserted into

the plasma ball to keep the reference voltage to the plasma potential. Ion current and substrate bias voltages were measured by a pair of digital multimeters (ADCMT, TR6846 and R6441A) and a PC-based software for auto-matic measurements.

A conventional double-probe was used to analyze plasma density and electron temperature. Microwave power was 400 W. Hydrogen gas flow rate was 100 sccm. Total pressure was kept a constant in the range of 1 to 9 kPa. The substrate was placed at a position where the surface touches the plasma ball and heated to 1270 K by thermal radiation from plasma.

Optical emission from the plasma was analyzed by a spectrometer (JASCO, CT-25C) through an optic fiber directed to its center. In order to estimate the thermal en-ergy of species, emission intensity, vibration and rotation energies of C2 radicals were measured in the plasma of 1% methane diluted by hydrogen. No C-C bonds were included in the carbon source gas, CH4, but emission line

Fig. 1 Schematic diagram of a NIRIM-type MWP-CVD apparatus with a substrate biasing system and a conven-tional double probe measured in-situ by digital multi me-ters (DMMs).

from C2 generated in the plasma was clearly observed in this measurement. 2-2. Modeling-a Monte Carlo simulation

A simulation code based on the MC method was originally developed to calculate ion accelerations in the sheath [5,8]. It was assumed in this calculation that a hy-drogen ion travels in a mixture of hydrogen atom and molecule. Ratio of atom and molecule was calculated by the thermal equilibrium of 2H–H2 at 3000 K. Mean free path of each trajectory of ion was chosen from experi-mental cross sections in collisions of hydrogen ion against atomic or molecular states of hydrogen both in cases of elastic and inelastic scatterings as shown in Fig. 2. The distribution of the scattering angle can affect on the total energy transfer to the substrate in the case of anisotropic acceleration, we used a precise scattering model men-tioned below. The scattering phenomenon is calculated by analytic results of scattering in two-body collisions on the basis of Born-Mayer potentials by using numerical quad-ratures through double exponential formulas. Figure 3 shows closest approaches as functions of the incident en-ergy and the distance calculated by numerical integrations, and the distribution of scattering angle was calculated as shown in Fig. 4 for each collision.

The potential drop in the sheath was described by a collisional form of the Child law [9]. The boundary value was given by the applied negative bias to the substrate. Parameters for the collisional sheath condition were given by experimental data. That is, ion densities in the plasma and ion flux to the substrate were measured by above-mentioned double probe method and as currents to the substrate, respectively. The mean free path used for the calculation of the sheath thickness was firstly given by a conventional cross section of the hydrogen molecule, and an average of free path in a calculation was used regressively as a parameter for the next calculation. The calculation was repeated until the average energy of ion and mean free path were converged. That is, the relation between mean free path and sheath thickness is consistent even though parameters of gas and electron temperature and plasma density are given arbitrarily and experimen-tally.

The electron temperature was fixed to be 4000 K in order to discuss effects of substrate bias and gas pressure on ion energy distribution (IED), although it might be variable against substrate bias. Motions of 100 thousands ions were calculated one by one, and the IED at the sub-strate surface was calculated. A random number sequence was given by the Mersenne Twister [15], and used to choose original velocities, free paths and collisional fac-tors, that are ruled by distribution functions mentioned above. Pressures, 1 to 9 kPa, and substrate negative bias, 25 to 350 V, were given as experimental parameters. 3. Results 3-1. In-situ plasma diagnostics Current to the substrate is plotted against the substrate

bias in Fig. 5. I-V characteristic at 1 and 3 kPa showed

smaller gradients at higher negative biasing, which is similar to that observed by a single probe in a low pres-sure plasma at around a few Pa. On the other hand, when the pressure is greater than 3 kPa, currents increased ex-traordinary by increasing the bias over 150 V. On the ba-sis of the collisional sheath condition, sheath thickness was estimated from the ion current as shown in Fig. 6. The sheath thickness without bias was estimated to be 0.2 to 0.3 mm, which was almost independent of the pressure.

Fig. 3 Normalized distances of the closest approach as func-tions of incident energy of hydrogen ion and incident dis-tances noamralized by a Born Mayer potential. Two sets of Born Mayer potentials, aBM= 253 and 428 eV, bBN= 31 and 37 nm-1 were used for the collision between H-H and H-H2, respectively.

Fig. 2 Collision cross section functions used in this study. H+-H and H+-H2 collisions both in cases of elastic and ine-lastic. Refer to [10-14].

Fig. 4 A distribution of the scattering angle as functions of incident energy and distances, which were simulated on the basis of closest approaches shown in Fig. 3.

This might be due to the comparable ion flux/mean free path in this pressure range, that is, lower ionization ratio and smaller mean free path at higher pressures in the case of no biasing. The sheath thickness increased to 0.7 mm by increasing the bias voltage to 250 V at the pressure less than 6 kPa. When the pressure was greater than 3 kPa, we found peaks of the sheath thickness at a negative bias around 150 V. It is interesting to note that BEN of dia-mond is effective under this biasing condition at 6 kPa and the higher pressures. In order to explain this sheath compression, which is equivalent to current enhancement in this measurement, we need to take account of the in-crease of the plasma density by biasing.

On the contrary, we observed a clear reduction of the optical emission intensity from C2 under the condition of sheath compression mentioned above. As shown in Fig. 7, biasing greater than 150 V at the pressure of 6 kPa re-sulted in the lower intensity from C2 radical. It was also observed that vibration energy of C2 radical at 250 V was twice larger than that at no biasing. These results indicate that electron energy and/or the gas temperature increased by the substrate biasing.

The electron temperature (Te) evaluated at 6 kPa was in the range of 7 to 11 eV. On the other hand, plasma density (Np) corresponds to 6×1017 m-3. The plasma density is consistent to 8×1017 m-3 at 1.6 kW at 21 kPa recently simulated by Yamada et al. [16] Both of Te and Np values decreased slightly by increasing the substrate negative bias, but this change might be smaller than the measure-ment error. The increase of the plasma density could not directly observed by this method. This might be due to the nature of the probe method. That is, we only detect the change of the plasma parameters at a point where the probe was inserted, which was not always consistent to the mean plasma density, and affected easily by the posi-tion of the plasma/ 3-2. MC simulation A velocity development of ion in three dimensions at 2

kPa is plotted against the distance from the substrate sur-face in Fig. 8. It is observed that velocities normal to the acceleration, Vx and Vy, do not exceed 3 eV even when the ion approaches the substrate. On the other hand, Vz increases in each free path, as is expected, and every col-lision makes the energy almost thermalized. The IEDs at the substrate are shown in Fig. 9. We can observe a long tail at the higher energy at low pressures, but the ions with the energy greater than 10 eV is scarce when the pressure is greater than 4 kPa.

The average number of times collision occurs for one ion in a travel to the substrate, the sheath thickness di-vided by the mean free path, is shown in Fig. 10. The change of the collision frequency is similar to that of the sheath thickness because the mean free path weakly de-pend on the velocity. That is, the sheath compression en-hances the final energy of ion. The average energy and the

energy of the top 1 % of all ions are also plotted against the bias. It is interesting to note that the average energy was 6.8 eV even in the case of 200 V biasing at 6 kPa, indicating that 95 % or more of the energy input through substrate biasing dispersed to the neutral species in the sheath.

Fig. 7 Optical emission intensity of C-C bonds plotted against the substrate negative bias at 6 kPa.

Fig. 6 Sheath thickness evaluated by a mean free path of hydrogen molecule and the ion flux on the basis of colli-sional sheath condition of the Child law, s=((2/3)(5/3)1.5 ε0(2eλi/πM)V0

1.5/J0)0.4.

Fig. 5 Current-voltage characteristics measured by using the substrate as a single probe.

4. Discussions Typical methane concentration is 1 to 5 % of hydrogen

in the BEN of diamond. On the other hand, the ionization ratio of hydrogen is from 2 to 10×10-6 as estimated in the double probe method in this study. In addition, the simu-lated IED revealed that the energy of ion at 6 kPa is less than 1/20 of the energy of the free electric acceleration, indicating that substrate biasing in a MWP-CVD resulted in much smaller number and energy flux in comparison with other low pressure plasmas. This fact suggests that the effect of the physical energy transfer to the surface by the ion irradiation is minor on the nucleation of diamond especially at 4 kPa and the higher pressures. On the con-trary, we propose, on the basis of both direct observation of dissociation of C2 molecule and sheath compression under the condition of typical BEN, that the substrate biasing raises the thermal energy of neutrals and ioniza-tion at the vicinity of plasma, which further enhance the dissociation of hydrocarbon species. That is, the substrate biasing only affects the net power input to plasma, which generates higher density of precursors of diamond nuclei. The power input to the plasma by biasing at 6 kPa reaches 0.1 A*200 V=20 W in our case, comparable to the net power input from MW, which is smaller than 400 W measured at the power source. 5. Conclusion

Most of the energy of ions accelerated by substrate negative bias disperses into the thermal energy of neutrals in the sheath in a typical condition of BEN of diamond in MWP-CVD. We propose that power input from the sub-strata bias into plasma causes dissociation of hydrocarbon species at the vicinity of the substrate, further causing nucleation of diamond. 6. Acknowledgements

This work was financially supported by Kakenhi No. 18360348 for the in-situ measurement and No. 20760489 for developing the MC code. Authors thank Prof. T. Ito of Osaka Univ. and Dr. K. Shinoda of Stony Brook Univ. for the helpful discussions about the modeling. References [1]S. Yugo et al., Appl. Phys. Lett. 58 1036 (1991) [2]S. P. McGinnis et al., Appl. Phys. Lett. 66 3117 (1995). [3]Y. Kaenel et al., Phys. Stat. Sol. (a) 154 219 (1996). [4] J. Robertson et al., Appl. Phys. Lett. 66 3287 (1995). [5]T. Ito, et al., Phys. Rev. E 73 No. 046401 (2006) [6]M. Kamo, et al., J. Crystal Growth. 62 642 (1983). [7]Y. Mitsuda J. Mater. Sci. 22 1557(1987). [8]T. Nakano, et al., Appl. Surf. Sci. 113/114 642 (1997). [9]M. A. Liberman, A. J. Lichtenberg, “Principles of

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[10]J. H. Newman et al., Phys. Rev. A 25 2967 (1982). [11]M. R. C. McDowell, Proc. Phys Soc. 72 1087 (1958). [12]M. W. Gealy et al., Phys. Rev. A 36 3091 (1982). [13]J. H. Simons et al., J. Chem. Phys. 11 307 (1943). [14]A. V. Phelps, J. Phys. Chem. Ref. Data 19 653 (1990).

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Fig. 8 A motion of a hydrogen ion in the sheath accelerated by substrate bias of -250 V at 2 kPa plotted against the dis-tance from the substrate. The direction z is normal to the substrate. The calculated sheath thickness was converged to 0.65 mm on the basis of mean free path in this simulation.

Fig. 9 Ion energy distribution at the bias of -250V as a func-tion of the pressure, 1 to 9 kPa.

Fig. 10 Average ion energy and mean collision times in the sheath, sheath thickness / mean free path is plotted against the substrate negative bias at 6 kPa..