Development of Crystal Growth Simulator Based on Tight-Binding

We have developed a crystal growth simulator based on tight-binding quantum chemical molecular dynamics (TB-QCMD) method and applied it to ...
0 downloads 0 Views
Download PDF
Article pubs.acs.org/JPCC

Development of Crystal Growth Simulator Based on Tight-Binding Quantum Chemical Molecular Dynamics Method and Its Application to Silicon Chemical Vapor Deposition Processes Takuya Kuwahara, Hiroshi Ito, Yuji Higuchi, Nobuki Ozawa, and Momoji Kubo* Fracture and Reliability Research Institute (FRRI), Graduate School of Engineering, Tohoku University, 6-6-11 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan ABSTRACT: We have developed a crystal growth simulator based on tight-binding quantum chemical molecular dynamics (TB-QCMD) method and applied it to plasma-enhanced chemical vapor deposition (PECVD) processes for silicon thin-film growth via SiH3 radicals on hydrogen-terminated Si(001). We successfully simulated the abstraction of a surface hydrogen atom by irradiated SiH3 radical and the formation of a dangling bond on the hydrogen-terminated Si(001) surface. SiH3 radical was subsequently adsorbed on this dangling bond. When these processes were repeated, the thin film grew. Thus, a detailed mechanism was successfully found for the chemical reaction and electron transfer dynamics of silicon thin film growth by PECVD.

1. INTRODUCTION In recent years, the production of solar cells has significantly increased. Thin film amorphous silicon and microcrystalline silicon are two of the most promising materials for the largescale production of solar cells because of their low cost. However, silicon thin film solar cells suffer from photodegradation caused by the Staebler−Wronski effect.1 When the films are exposed to light for long periods of time, the weak Si− Si bonds and Si−H bonds are broken, which generates dangling bonds. These dangling bond defects decrease both photoconductivity and dark conductivity. The photodegradation is related to the hydrogen concentration, particularly the Si−H2 bond density; a high density of Si−H2 bonds is associated with photodegradation.2−4 It has also recently been discovered that nanoparticles (clusters) composed of high-order silanes are likely to form Si−H2 bonds. These nanoparticles are 0.5−10 nm in size and grow in the gas phase before they are deposited on the surface. Silicon thin films that contain fewer clusters show higher photostability.5 To prevent the efficiency loss caused by photodegradation, there is a pressing need to develop a thin film growth technique that minimizes the dangling bond concentration toward the practical use. There are two methods of silicon thin film growth: physical vapor deposition (PVD) and chemical vapor deposition (CVD). In PVD, silicon thin film growth is accomplished by physical adsorption to the surface, whereas in CVD, chemical reactions take place on the substrate surface or in the gas phase. Chemical reactions cause the decomposition of the source gases and the deposition on the film-growing surface. In various CVD processes,6−11 plasma-enhanced (PE) CVD is most widely used for silicon thin film growth. To increase the energy efficiency of silicon thin film solar cells, the processes involved in PECVD have been investigated.12−19 In PECVD, SiHx radicals, which © 2012 American Chemical Society

originate from the electron-impact dissociation of silane gas (SiH4) in the plasma, reach the film-growing surface, where many different processes occur, such as chemical reactions, adsorption, reflection, diffusion, and desorption.20 Silicon PECVD processes have been thoroughly explored in experiments;12−20 however, the detailed mechanisms of these complex processes have not been clarified. Computational simulation is a useful tool for elucidating the details of these surface phenomena on electronic and atomic scales. Numerous classical molecular dynamics simulations have been performed to investigate epitaxial crystal growth processes from liquid-,21 solid-,22 and vapor-phase silicon,23 as well as in PVD.24,25 We have also successfully simulated the epitaxial growth processes for electronics materials by using our original classical molecular dynamics code.26−30 However, classical molecular dynamics cannot simulate the chemical reaction and electron transfer dynamics of CVD processes because that method does not consider electrons. Many first-principles calculations have been performed to investigate the adsorption geometry of SiHx radical on a Si(001) surface31−37 because they can simulate chemical reactions. However, such calculations are static and cannot simulate the chemical reaction and electron transfer dynamics of CVD processes at a finite temperature. First-principles molecular dynamics calculation is a promising method for simulating CVD processes. Cheng et al. have performed pioneering works on atomic layer deposition (ALD) and CVD process simulations using first-principles molecular dynamics method38−41 and obtained very important atomicscale knowledge, which cannot be obtained by experiments. In Received: January 9, 2012 Revised: May 14, 2012 Published: May 21, 2012 12525

dx.doi.org/10.1021/jp3002542 | J. Phys. Chem. C 2012, 116, 12525−12531

The Journal of Physical Chemistry C

Article

ref 39, they studied CVD process of the copper films on the Ta surfaces with and without nitrogen termination. By using firstprinciples molecular dynamics method at the finite temperature, they clarified the difference of the Cu surface diffusion on the partially and fully passivated surfaces and the deposition mechanisms. In ref 40, they investigated the agglomeration process of Cu atoms on the fully nitrogen passivated metal surfaces during the ALD process. By using first-principles molecular dynamics method at the finite temperature, they clarified the difference of the agglomeration processes depending on the substrate temperature. As shown above, they successfully innovated ALD and CVD process simulations using first-principles molecular dynamics method. However, the continuous irradiation of CVD sources has not been performed in their simulations. Continuous irradiation of CVD sources is an essential approach to clarify the mechanism of the crystal growth processes during CVD processes. Other researchers also have not performed the quantum chemical molecular dynamics simulations on the crystal growth processes by the continuous irradiation of CVD sources in the world, to the best of our knowledge. Therefore, in the present study, we tried to advance their quantum chemical molecular dynamics simulations on CVD processes, by realizing the continuous irradiation of CVD sources. Concretely, we implemented a new algorithm into the quantum chemical molecular dynamics simulations, which realizes the increase and decrease in the number of molecules in the simulation cell for CVD process simulations. Here, in this moment, the first-principles molecular dynamics method is not suitable for simulating the continuous irradiation of many molecules in CVD processes because the long-time simulations of over 1,000,000 time steps are essential for that purpose. Such long-time first-principles molecular dynamics calculations on CVD processes have not been performed by Cheng et al. Here, we have developed a tight-binding quantum chemical molecular dynamics (TB-QCMD) code that is over 5000-fold faster than first-principles molecular dynamics method;42−45 thus, the developed code can be applied to larger systems and longer calculations as compared with first-principles molecular dynamics simulations. Moreover, we have already successfully applied our code to various systems such as etching, tribochemical reactions, and chemical mechanical polishing.46−53 However, the TB-QCMD code has not yet been applied to continuous irradiation processes of the CVD sources for the crystal growth simulations because the number of atoms in the simulation cell is fixed in the above-mentioned code. To simulate the continuous irradiation processes of the CVD sources, the number of atoms in the simulation cell must be changed. Therefore, we have developed a new crystal growth simulator based on the TB-QCMD code in which the number of atoms in the simulation cell can be changed. CVD source molecules can be emitted repeatedly, and the vaporized molecules produced by chemical reactions can be removed from the simulation cell. These new algorithms enable the chemical reaction and electron transfer dynamics of the CVD processes to be simulated; to the best of our knowledge, this is the first simulator to use quantum chemistry for this purpose. Our simulator can elucidate electronic-level mechanisms and help to optimize the process conditions for a wide variety of CVD methods, such as PECVD, thermal CVD, catalytic CVD, and metal−organic vapor phase epitaxy. In this article, we demonstrate the utility and effectiveness of our newly developed quantum chemistry crystal growth simulator in

predicting the chemical reaction and electron transfer dynamics for PECVD processes during silicon thin film growth.

2. DEVELOPMENT OF CRYSTAL GROWTH SIMULATOR FOR CVD PROCESSES BASED ON TB-QCMD METHOD In TB-QCMD method, the diagonal Hamiltonian Hrr is equal to the negative of the ionization potential (−Ir) of each atomic orbital. The corrected distance-dependent Wolfsberg−Helmholz formula for the off-diagonal Hamiltonian Hrs is used54 1 Hrs = K rsSrs(Hrr + Hss) (1) 2 where K rs = {1 + κ rs(1 − Δ4 ) + Δ2 } × exp[−δrs{rrs − drs}] (2)

and Δ=

Hrr − Hss Hrr + Hss

(3)

Here, Srs is the overlap integral matrix element and d is the summation of the orbital radii. Moreover, κ and δ are parameters for the chemical bonding interactions. The total energy in the system is calculated by using N

E=

∑ i=1

1 mivi 2 + 2

OCC

N

N

∑ εk + ∑ ∑ Eijrepul(R ij) k

i=1 j>i

(4)

where ⎛ aij − R ij ⎞ ⎟⎟ Eijrepul(R ij) = bij × exp⎜⎜ ⎝ bij ⎠

(5)

In these formulas, mi is the atomic weight, vi is the atomic velocity, and Rij is the interatomic distance. The parameters aij and bij are related to the size and stiffness of atoms, respectively. In eq 4, the first term corresponds to the kinetic energy of the atoms, the second term is the summation of the eigenvalues of all the occupied orbitals (calculated based on tight-binding electronic states), and the last term corresponds to the shortrange, exchange-repulsion energy. We improved this TB-QCMD code in order to simulate the CVD processes. Figure 1 shows the schematic model for the crystal growth process simulation. In previous QCMD code, the total number of atoms in the system was fixed, which meant that the continuous irradiation of source molecules for CVD processes could not be simulated. Therefore, we implemented a new algorithm for simulating the continuous irradiation and removal of molecules during the CVD process into our tightbinding quantum chemical molecular dynamics simulator. In the experimental CVD processes, molecules are irradiated far from the substrate, and the vaporized molecules fly away from the substrate. In order to simulate the above irradiation and vaporization events in the experimental CVD processes, the following algorithm is newly implemented. The number of atoms in the simulation cell changes by the continuous irradiation and the removal of molecules. The irradiated molecules with a constant kinetic energy appear far from the substrate by a certain interval. The initial X and Y coordinates of the irradiated molecules are determined randomly, and the initial Z coordinates of the irradiated molecules are far enough 12526

dx.doi.org/10.1021/jp3002542 | J. Phys. Chem. C 2012, 116, 12525−12531

The Journal of Physical Chemistry C

Article

processes. All the parameters for the TB-QCMD code were determined through first-principles density functional theory (DFT) calculations within the generalized gradient approximation (GGA) and the Perdew−Wang exchange correlation functional (PW91) using Accelrys DMol3 code.58 Parameters (δ, κ, a, and b) were set so as to reproduce the binding energy, bond distances, and bond angles of bulk silicon, H2, and SiH4 (Table 1). The TB-QCMD calculations using these parameters Table 1. Parameters for the Tight-Binding (TB) Simulation ζb (1/Å)

Ia (eV) atom H Si

s orbital 13.60 17.30 atom pair H−H H−Si Si−Si orbital pair H(s)−H(s) H(s)−Si(s) H(s)−Si(p) Si(s)−Si(s) Si(s)−Si(p) Si(p)−Si(p)

Figure 1. Schematic model of the crystal growth simulator based on TB-QCMD method.

p orbital

s orbital

9.20

1.5000 1.7534

p orbital 1.7539

aij

bij

1.362 2.136 2.902 κrs

0.156 0.160 0.156 δrs

0.496 0.908 0.894 0.840 0.840 0.840

0.130 0.130 0.130 0.130 0.130 0.130

a

Ionization energy from the valence orbital. bExponent for Slater-type atomic orbital.

from the substrate for realizing the zero interaction energy between the irradiated molecules and the substrate. However, the vaporized molecules, which fly away from the substrate and have zero interaction energy with the substrate, are removed from the simulation cell. These mean that the interaction energy between the molecules and the substrate atoms does not change after the appearance and removal of the molecules. In our algorithm, the appearance and removal of molecules are not correlated. The same algorithm for the appearance and removal of the molecules is already adopted in some classical molecular dynamics studies.26−30,55−57 Therefore, the validity of the above algorithm was already confirmed in the classical molecular dynamics simulations. However, the above algorithm has not been implemented in the quantum chemical molecular dynamics method. In the present study, we newly implemented the above algorithm for the change in the number of molecules into the tight-binding quantum chemical molecular dynamics method. To the best of our knowledge, this is the first implementation of the increase and decrease in the number of molecules for simulating the CVD process into the quantum chemical molecular dynamics method in the world. Furthermore, it is also possible to select the time interval, energy, rotation, number, and elements for the emitting molecules, as well as the temperature of the substrate. This means that quantum chemistry can be used to optimize various crystal growth conditions, which affect the crystallinity, deposition rate, and growth orientation. Although quantum chemistry is traditionally employed in material design, this new simulator demonstrates that quantum chemistry can be used effectively in process design.

gave a binding energy of −4.643 eV/atom and a bond distance of 2.351 Å for bulk silicon. These were consistent with the DFT values of −4.654 eV/atom and 2.352 Å. The binding energies of H2 were −4.466 eV as calculated using our TB-QCMD code and −4.639 eV as calculated using DFT. The bond length of 0.738 Å for H2 calculated using our TB-QCMD code is close to the DFT value of 0.748 Å. Furthermore, the Si−H bond length and H−Si−H angle in SiH4 calculated using the TB-QCMD code were 1.475 Å and 109.4°, respectively, which are similar to the DFT values of 1.489 Å and 109.5°. Thus, the geometry and the binding energy of bulk silicon, H2, and SiH4 were in good agreement with those calculated using DFT. This demonstrates that TB-QCMD coupled with the first-principles parametrization is effective for describing the geometry and energy of various fragments related to silicon PECVD growth processes. 3.2. Application to Silicon PECVD Processes. The TBQCMD simulator was then used to investigate silicon thin film growth by PECVD on a hydrogen-terminated Si(001) surface. The Si(001) substrate consisted of 80 atoms. Silicon and hydrogen atoms are 64 and 16 atoms, respectively. The above 16 hydrogen atoms terminate the top and bottom silicon atoms. The optimized parameters were used in simulating the continuous irradiation of 10 SiH3 radicals directed toward the Si(001) surface. Periodic boundary conditions were employed in the x, y, and z directions with lengths of 10.86, 10.86, and 29.50 Å, respectively. The 16 Si atoms in the lowest two layers and 8 hydrogen atoms terminating the bottom layer were fixed. SiH3 radicals with a constant energy of 0.1 eV were repeatedly irradiated every 2.0 ps onto the Si(001) substrate, and the first SiH3 radical appeared at 0.01 ps. The SiH3 radicals appeared at random positions above the substrate. The height at which the SiH3 radicals appeared and the vaporized molecules were removed was set at 7 Å from the surface. The Verlet

3. RESULTS AND DISCUSSION 3.1. Parameterization for TB-QCMD Simulations of Silicon PECVD Processes. The TB-QCMD code was needed to accurately describe the energetics and wave functions of the atomic fragments for the simulation of silicon PECVD 12527

dx.doi.org/10.1021/jp3002542 | J. Phys. Chem. C 2012, 116, 12525−12531

The Journal of Physical Chemistry C

Article

algorithm59 was used for atomic motion. We employed a very short time step of 0.01 fs in order to reproduce accurately the chemical reactions in the CVD processes under the high velocity conditions of irradiated atoms. Our tight-binding quantum chemical molecular dynamics simulation has timescale advantage compared to the first-principles molecular dynamics simulation, and then, we performed long-time calculations of 2,000,000 time steps in the present study. This corresponds to a 20 ps simulation. According to experimental observation, the silicon thin film shows the highest crystallinity at about 500 K.20 The temperature in the simulation was controlled by scaling the atom velocities to maintain a substrate temperature of 500 K, with the exception of the emitted molecules and fixed atoms. Figure 2 shows snapshots of the silicon thin film growth simulation by continuous SiH3 irradiation. At 0.01 ps, the first

(Figure 2f). It was then stabilized on the surface, which generated the first S−Si bond. At 10.5 ps, the sixth SiH3 radical approached the surface and abstracted a surface hydrogen atom, generating another dangling bond at a different site. At 11.1 ps, the seventh SiH3 radical approached the surface, and at 12.5 ps, it was adsorbed on the dangling bond, which was generated by the fourth SiH3 radical (Figure 2g,h). Two SiH3 radicals were adsorbed on adjacent dimers in neighboring dimer rows. We suggest that this adsorption structure acts as a nucleation center for forming a hexagonal silicon structure, and thus generating a new silicon layer upon further deposition of SiH3 radical. The eighth SiH3 radical abstracted a surface hydrogen atom, whereas the ninth and tenth SiH3 radicals were repelled back into the gas phase. Table 2 summarizes the surface events for the 10 SiH3 radicals calculated by using the TB-QCMD simulator. Table 2. Surface Reactions for Irradiated SiH3 Radicals irradiated SiH3

surface reaction

first second third fourth fifth sixth seventh eighth ninth tenth

repelling hydrogen abstraction repelling hydrogen abstraction adsorption hydrogen abstraction adsorption hydrogen abstraction repelling repelling

The atomic bond populations for the Si and H atoms, which were based on the Mulliken population analysis,61 were calculated to determine the bond breaking and bond formation dynamics during the chemical reactions quantitatively. The atomic bond population is defined by on X on Y OCC

Figure 2. Snapshots of silicon PECVD by continuous irradiation of SiH3 with constant energy of 0.1 eV. The first SiH3 radical (a) before and (b) after repelling; the second SiH3 radical (c) before and (d) after hydrogen abstraction; the fifth SiH3 radical (e) before and (f) after adsorption; and the seventh SiH3 radical (g) before and (h) after adsorption.

MXY = 4

r

s

j

(7)

where Cjr is an eigenvector element. Figure 3 shows the time evolution of the atomic bond populations on SiA−HA, SiB−HA, and SiA−SiC. SiA is a silicon atom on the top layer, HA is a surface hydrogen atom connected to SiA, SiB is the silicon atom from the second SiH3 radical, and SiC is the silicon atom from the fifth SiH3 radical (Figure 2d,f). Figure 3 shows that, at 2.5

SiH3 radical emerged and approached the Si(001) surface (Figure 2a). It reached the surface and, at 0.36 ps, was repelled with no chemical reaction (Figure 2b). At 2.20 ps, the second SiH3 radical approached the surface (Figure 2c), then abstracted a surface hydrogen atom, which generated a molecule of SiH4 (Figuer 2d). The SiH4 was then desorbed back into the gas phase, and a dangling bond was generated on the surface. This is known as the Eley−Rideal mechanism,60 which corresponds to the following reaction: SiH3 + Hsurf → SiH4 gas + dbsurf

∑ ∑ ∑ CjrCjsSrs

(6)

where db indicates a dangling bond on a silicon atom, and the subscript surf and gas indicate surface species and gas-phase species, respectively. At 4.8 ps, the third SiH3 radical reached the surface and was repelled and desorbed back into the gas phase. At 7.00 ps, the fourth SiH3 radical abstracted a surface hydrogen atom, and a second dangling bond was generated on the Si(001) surface. At 8.08 ps, the fifth SiH3 radical approached the surface (Figuer 2e), reacted with the dangling bond, and was adsorbed on the dangling bond at 9.85 ps

Figure 3. Time course of the atomic bond population for SiA−HA, SiB−HA, and SiA−SiC when the second and fifth SiH3 radicals were irradiated onto the hydrogen-terminated Si(001) substrate. 12528

dx.doi.org/10.1021/jp3002542 | J. Phys. Chem. C 2012, 116, 12525−12531

The Journal of Physical Chemistry C

Article

ps, the SiA−HA bond population decreased from ∼0.6 to 0.0, and the SiB−HA bond population increased from 0.0 to ∼0.6. This indicates that the second SiH3 radical abstracts the surface hydrogen atom (HA) and generates a dangling bond on the top-layer silicon atom (SiA) and a SiH4 molecule. In Figure 3, the dashed line, which represents the SiB−HA bond population, disappears at 4.0 ps. This is because the vaporized SiH4 molecule moved upward and reached the point where it was removed from the simulation cell (Figure 1). At 9.0 ps, the SiA−SiC bond population increased from 0.0 to ∼0.5. This indicates that the fifth SiH3 radical is adsorbed on the dangling bond generated by the second SiH3 radical. Figure 3 confirms that our crystal growth simulator successfully clarifies the chemical reaction and the electron transfer dynamics between the SiH3 radicals and the hydrogen-terminated Si(001) substrate during silicon PECVD. The abstraction of a surface hydrogen atom by a SiH3 radical has previously been studied by Cereda et al., using static firstprinciples calculations.62 They reported that the energy barrier is ∼0.005 eV and the exothermic energy is 0.5 eV, and that this reaction is almost barrierless because the energy barrier is smaller than the thermal energy (0.04 eV at 500 K). This energy barrier was also calculated by our TB method, and we obtained the energy barrier of 0.004 eV. This result is in good agreement with that of 0.005 eV obtained by the above firstprinciples calculations.62 Therefore, this result shows that the accuracy of our tight-binding parameters is sufficient to describe the nonequilibrium state of the chemical reactions. They also showed that the Si−H bonds in the SiH4 molecule are stronger than those on the hydrogen-terminated Si(001) surface, which suggests abstraction reactions are likely to occur. Although these static first-principles calculations have shown that the abstraction process is almost barrierless, it has been observed experimentally that many SiH3 radicals are repelled from the hydrogen-terminated Si(001) surface.20 Our TB-QCMD simulations successfully simulated both the repelling of the SiH3 radicals and the abstraction of the surface hydrogen atom by SiH3 radicals. Our simulation also suggests that the repelling and abstraction depends on how the SiH3 radicals collide with the surface atoms. The static first-principles calculations by Cereda et al. also showed that the adsorption of a SiH3 radical to a Si(001) surface dangling bond is barrierless and exothermic.62 The energy difference of 2.4 eV between the initial and final states for the adsorption process is large.62 This suggests that a strong attractive force acts between the SiH3 radical and the dangling bond of the Si(001) surface, allowing the SiH3 radical to be easily adsorbed on the dangling bond. Conversely, our TBQCMD simulation shows that the third SiH3 radical was repelled by the surface, although there is a dangling bond on the Si(001) surface, which is generated by the second SiH3 radical. The ninth and tenth SiH3 radicals are also repelled, even though there are two dangling bonds on the Si(001) surface. The repelling of the SiH3 radicals on the partially hydrogen-terminated Si(001) surface depends on how the SiH3 radicals collide with the surface atoms. In contrast to the static first-principles calculations, our TB-QCMD simulation suggests that the SiH3 radicals can be repelled even when there are dangling bonds on the Si(001) surface. Furthermore, a spin analysis has been performed. In particular, we focused on the spin variations on two specific chemical reactions: (1) the abstraction of surface hydrogen atom and (2) the adsorption of SiH3 radical on the surface

dangling bond. Concretely, we performed a spin analysis of the state after the second SiH3 radical abstracted a surface hydrogen atom, and then, we revealed that the spin remained at the dangling bond. We also performed a spin analysis of the state after the fifth SiH3 radical was adsorbed on the dangling bond, and then, we revealed that the spin disappeared from the dangling bond. In order to confirm the repeatability and validity of our calculation results, further ten calculations with the different initial positions of ten SiH3 radicals are performed. The initial X and Y coordinates of the irradiated SiH3 radicals were determined randomly in the further ten calculations. In all the calculations, almost the same phenomena were observed. Concretely, the same repelling, abstraction, and adsorption processes were observed. The repeat of the abstraction and adsorption processes leads to the film growth. Then, from further ten calculations on the different initial irradiation positions, we confirmed the repeatability and validity of our CVD process simulations. Our TB-QCMD code is effective for examining the mechanisms involved in CVD, compared with the static firstprinciples calculations, because the simulation reproduces all the surface events, such as the repelling, abstraction, and adsorption reactions. The results also suggested that our TBQCMD code can be used to estimate the sticking coefficient of the source molecules in the CVD processes, which is the most important experimental factor in determining the source gases and growth conditions. The sticking coefficient of the source molecules cannot be calculated by the static first-principles method, thus demonstrating the utility of our TB-QCMD code in the theoretical design of CVD processes. 3.3. Chemical Reaction and Electron Transfer Dynamics in Silicon PECVD Processes. During silicon PECVD, electrons are transferred between the SiH3 radical and the Si surface atoms during the chemical reactions; therefore, it is necessary to understand the electron transfer dynamics in order to determine the reaction mechanisms. Figure 4 shows the surface geometries and atomic charge obtained by using our TB-QCMD code before and after the hydrogen abstraction by the second SiH3 radical (Figure 4a,b), before and after the adsorption by the fifth SiH3 radical (Figure 4c,d) and before and after the hydrogen abstraction by the sixth SiH3 radical (Figure 4e,f). Between 0.0 and 2.5 ps, the atomic charge on the SiL was almost the same as that on the SiR (Figure 4a). Between 2.5 and 2.6 ps, the atomic charge on SiL changed from 0.250 to 0.054; this indicates that the electron was transferred from the surface hydrogen atom to SiL. However, the atomic charges on the second-layer silicon atoms did not change significantly and showed bilateral symmetry (Figure 4a,b), which suggests that the electron transfer takes place between a top-layer silicon atom and a surface hydrogen atom during hydrogen abstraction. Between 8.7 and 8.8 ps, when the fifth SiH3 radical was adsorbed on the dangling bond, the electron was transferred from the SiH3 radical to SiL. The atomic charge on SiL changed from 0.072 to −0.025 (Figure 4c,d), and the charge on the adsorbed SiH3 radical was positive. However, the atomic charge on SiR did not change significantly. The atomic charges of SiL and SiR were different, and the atomic charges on the second-layer silicon atoms also changed, which means that the atomic charges were asymmetric (Figure 4d). The Si dimer in the top layer was tilted, and the z-coordination value of SiL increased until it exceeded that of SiR because the adsorbed SiH3 radical strongly attracted SiL. In Figure 4e,f, between 10.4 and 10.5 ps, the electron was transferred from a surface 12529

dx.doi.org/10.1021/jp3002542 | J. Phys. Chem. C 2012, 116, 12525−12531

The Journal of Physical Chemistry C

Article

code,58 under GGA-PW91 using numerical basis sets, a periodic supercell, and effective core potential. Table 3 shows that the atomic charges on SiL and SiR obtained by using the TB-QCMD code are in good agreement with those obtained from static first-principles calculations. This result demonstrates that the TB-QCMD code and the first-principles parametrization produce reliable results. Figure 4c−f indicates that the polarization of the atomic charges on the Si dimer causes the Si dimer to tilt when the SiH3 radical is adsorbed on one side. This tilting has also been reported when firstprinciples calculations were used.37 Smardon et al. reported that differences in the Si dimer tilt depend on the adsorption structure and that the unsaturated Si dimer is particularly likely to be stabilized by tilting to one side.37 In our calculations, the Si dimer tilts when the SiH3 radical is adsorbed on the dangling bond of the Si dimer. Our TB-QCMD results are also consistent with previous first-principles calculations.37 Our newly developed crystal growth simulator based on TB-QCMD method successfully clarified surface reactions involving electron transfer dynamics and is an effective tool for elucidating the chemical reaction and electron transfer dynamics in CVD processes on electronic and atomic levels.

4. CONCLUSIONS We have developed a crystal growth simulator based on TBQCMD method. This is a first simulator to elucidate details of CVD processes, including chemical reaction and electron transfer dynamics. We have introduced new algorithms such as continuous irradiation of source molecules and the removal of vaporized molecules, which enabled the simulation of CVD processes on electronic and atomic levels. When silicon PECVD processes were simulated, the underlying chemical reaction and electron transfer dynamics were revealed for the first time. SiH3 radicals were repeatedly irradiated onto a hydrogen-terminated Si(001) surface and various surface events, such as the abstraction of a surface hydrogen atom, the repelling of SiH3 radical, and the adsorption of SiH3 radical at the dangling bond on the hydrogen-terminated Si(001) surface, were observed. Although static first-principles calculations have previously shown that the abstraction and the adsorption processes are barrierless, the repelling of the SiH3 radical is frequently observed experimentally. The static firstprinciples calculations cannot reproduce and describe the repelling of the SiH3 radicals, whereas our TB-QCMD code accurately reproduced this repelling. Moreover, our TB-QCMD code can estimate the sticking coefficient of the SiH3 radical, which is the most important factor in selecting the source gases and experimental conditions for PECVD. The sticking coefficient cannot be estimated by the static first-principles calculations, and the capability to calculate it is another major advantage of our method. Moreover, our TB-QCMD code and the first-principles parametrization quantitatively reproduced the results of the static first-principles calculations, confirming its accuracy and reliability. Our crystal growth simulator based on TB-QCMD method is an effective, reliable tool for elucidating the chemical reaction and electron transfer dynamics of CVD processes on electronic and atomic scales.

Figure 4. Change in the surface geometry and atomic charges before and after the chemical reactions. The second SiH3 radical 4.1 (a) before and 4.1 (b) after the hydrogen abstraction, the fifth SiH3 radical 4.2 (a) before and 4.2 (b) after the adsorption, the sixth SiH3 radical 4.3 (a) before and 4.3 (b) after the hydrogen abstraction.

hydrogen atom to SiR and the atomic charge on SiR changed from 0.274 to 0.112. The atomic charges on the silicon atoms in the second layer also changed significantly (Figure 4f), and the Si dimer was more tilted. The z-coordination value of SiR decreased until it was smaller than that of SiL because SiR was strongly attracted by the second layer of Si atoms. We suggest that the unsaturated Si dimer is stabilized by tilting. In addition, single-point energy calculations were performed for each structure shown in Figure 4 by using static first-principles calculations for comparison with the results from the TBQCMD code. Table 3 shows the electron charge on SiL and SiR in Figure 4 before and after the surface reactions calculated using the TB-QCMD code and the first-principles method. The DFT calculations were performed using Accelrys DMol3 Table 3. Atomic Charges on Top-Layer Silicon Atoms (SiL and SiR) before and after Chemical Reactions Obtained by the TB-QCMD and First-Principles Methods SiL

■

SiR

atom

1 (a)

1 (b)

2 (a)

2 (b)

3 (a)

3 (b)

TB-QCMD first-principles

0.250 0.158

0.054 0.084

0.072 0.084

−0.025 −0.119

0.274 0.186

0.112 0.097

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 12530

dx.doi.org/10.1021/jp3002542 | J. Phys. Chem. C 2012, 116, 12525−12531

The Journal of Physical Chemistry C

Article

Notes

(33) Lim, F. C. H.; Tok, E. S.; Kang, H. C. Phys. Rev. B 2006, 74, 205333. (34) Bakos, T.; Valipa, M. S.; Maroudas, D. J. Chem. Phys. 2005, 122, 054703. (35) Ceriotti, M.; Bernasconi, M. Phys. Rev. B 2007, 76, 245309. (36) Kang, J. K.; Musgrave, C. B. Phys. Rev. B 2001, 64, 245330. (37) Smardon, R. D.; Srivastava, G. P. J. Chem. Phys. 2005, 123, 174703. (38) Cheng, H.; Pez, G. P.; Kern, G.; Kresse, G.; Hafner, J. J. Phys. Chem. B 2001, 105, 736. (39) Machado, E.; Kaczmarski, M.; Ordejon, P.; Garg, D.; Norman, J.; Cheng, H. Langmuir 2005, 21, 7608. (40) Han, B.; Wu, J.; Zhou, C.; Li, J.; Lei, X.; Norman, A. T. J.; Gaffney, R. T.; Gordon, R.; Roberts, A. D.; Cheng, H. J. Phys. Chem. C 2008, 112, 9798. (41) Han, B.; Wu, J.; Zhou, C.; Chen, B.; Gordon, R.; Lei, X.; Roberts, A. D.; Cheng, H. Angew. Chem., Int. Ed. 2010, 49, 148. (42) Kubo, M.; Ando, M.; Sakahara, S.; Jung, C.; Seki, K.; Kusagaya, T.; Endo, A.; Takami, S.; Imamura, A.; Miyamoto, A. Appl. Surf. Sci. 2004, 223, 188. (43) Elanany, M.; Selvam, P.; Yokosuka, T.; Takami, S.; Kubo, M.; Imamura, A.; Miyamoto, A. Phys. Rev. B 2003, 107, 1518. (44) Suzuki, A.; Selvam, P.; Kusagaya, T.; Takami, S.; Kubo, M.; Imamura, A.; Miyamoto, A. Int. J. Quantum Chem. 2005, 102, 318. (45) Masuda, T.; Tsuboi, H.; Koyama, M.; Endo, A.; Kubo, M.; Broclawik, E.; Miyamoto, A. Jpn. J. Appl. Phys. 2006, 45, 2970. (46) Sasata, K.; Yokosuka, T.; Kurokawa, H.; Takami, S.; Kubo, M.; Imamura, A.; Shinmura, T.; Kanoh, M.; Selvam, P.; Miyamoto, A. Jpn. J. Appl. Phys. 2003, 42, 1859. (47) Yokosuka, T.; Sasata, K.; Kurokawa, H.; Takami, S.; Kubo, M.; Imamura, A.; Miyamoto, A. Jpn. J. Appl. Phys. 2003, 42, 1897. (48) Rajendran, A.; Takahashi, Y.; Koyama, M.; Kubo, M.; Miyamoto, A. Appl. Surf. Sci. 2005, 244, 34. (49) Koyama, M.; Hayakawa, J.; Onodera, T.; Ito, K.; Tsuboi, H.; Endou, A.; Kubo, M.; Del Carpio, C. A.; Miyamoto, A. J. Phys. Chem. B 2006, 110, 17507. (50) Alam, M. K.; Farouq, A.; Nakamura, K.; Suzuki, A.; Sahnoun, R.; Tsuboi, H.; Koyama, M.; Hatakeyama, N.; Endou, A.; Takaba, H.; Del Carpio, C. A.; Kubo, M.; Miyamoto, A. J. Phys. Chem. C 2009, 113, 7723. (51) Ahmed, F.; Alam, K.; Suzuki, A.; Koyama, M.; Tsuboi, H.; Hatakeyama, N.; Endou, A.; Takaba, H.; Del Carpio, C. A.; Kubo, M.; Miyamoto, A. J. Phys. Chem. C 2009, 113, 15676. (52) Onodera, T.; Morita, Y.; Suzuki, A.; Koyama, M.; Tsuboi, H.; Hatakeyama, N.; Endou, A.; Takaba, H.; Kubo, M.; Dassenoy, F.; Minfray, C.; Pottuz, L. J.; Martin, J. M.; Miyamoto, A. J. Phys. Chem. B 2009, 113, 16526. (53) Hayashi, K.; Tezuka, K.; Ozawa, N.; Shimazaki, T.; Adachi, K.; Kubo, M. J. Phys. Chem. C 2011, 115, 22981. (54) Wolfsberg, M.; Helmholz, L. J. Chem. Phys. 1952, 20, 837. (55) Lee, G. S.; Chung, C. Y. J. Appl. Phys. 2006, 100, 074905. (56) Zientarski, T.; Chocyk, D. Mol. Phys. 2007, 105, 3099. (57) Mungan, M.; Weisskopf, Y.; Erbudak, M. Phys. Rev. B 2007, 76, 195443. (58) Delley, B. J. Chem. Phys. 2000, 113, 7756. (59) Verlet, L. Phys. Rev. 1967, 159, 98. (60) Eley, D. D.; Rideal, E. K. Nature 1940, 146, 401. (61) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1841. (62) Cereda, S.; Ceriotti, M.; Montalenti, F.; Bernasconi, M.; Miglio, L. Phys. Rev. B 2007, 75, 235311.

The authors declare no competing financial interest.

■

REFERENCES

(1) Staebler, D. L.; Wronski, C. R. J. Appl. Phys. 1980, 51, 3262. (2) Shimizu, S.; Matsuda, A.; Kondo, M. Sol. Energy Mater. Sol. Cells 2008, 92, 1241. (3) Nakamura, N.; Takahama, T.; Isomura, M.; Nishikuni, M.; Yoshida, K.; Tsuda, S.; Nakano, S.; Ohnishi, M.; Kuwano, Y. Jpn. J. Appl. Phys. 1989, 28, 1762. (4) Kageyama, S.; Akagawa, M.; Fujiwara, H. Phys. Rev. B 2011, 83, 195205. (5) Shiratani, M.; Koga, K.; Kaguchi, N.; Bando, K.; Watanabe, Y. Thin Solid Films 2006, 506, 17. (6) Konagai, M.; Tsushima, T.; Kim, M.-K.; Asakusa, K.; Yamada, A.; Kudriavtsev, Y.; Villegas, A.; Asomoza, R. Thin Solid Films 2001, 395, 152. (7) Tsugawa, K.; Ishihara, M.; Kim, J.; Koga, Y.; Hasegawa, M. J. Phys. Chem. C 2010, 114, 3822. (8) Lee, C. J.; Park, J.; Huh, Y.; Lee, J. Y. Chem. Phys. Lett. 2001, 343, 33. (9) Shi, Y. J.; Li, X. M.; Toukabri, R.; Tong, L. J. Phys. Chem. A 2011, 115, 10290. (10) Vasant Kumar, C. V. R.; Sayer, M.; Pascual, R.; Amm, D. T.; Wu, Z.; Swanson, D. M. Appl. Phys. Lett. 1991, 58, 1161. (11) Wang, Q. Thin Solid Films 2009, 517, 3570. (12) Koga, K.; Kai, M.; Shiratani, M.; Watanabe, Y.; Shikatani, N. Jpn. J. Appl. Phys. 2002, 41, 168. (13) Myong, S. Y.; Sriprapha, K.; Yashiki, Y.; Miyajima, S.; Yamada, A.; Konagai, M. Sol. Energy Mater. Sol. Cells 2008, 92, 639. (14) Jia, H.; Kuraseko, H.; Kondo, M. J. Appl. Phys. 2008, 103, 024904. (15) Sumiya, S.; Mizutani, Y.; Yoshida, R.; Hori, M.; Goto, T.; Ito, M.; Tsukada, T.; Samukawa, S. J. Appl. Phys. 2000, 88, 576. (16) Jia, H.; Kondo, M. J. Appl. Phys. 2009, 105, 104903. (17) Smit, C.; Hamers, E. A. G.; Korevaar, B. A.; van Swaaij, R. A. C. M. M.; van de Sanden, M. C. M. J. Non-Cryst. Solids 2002, 299, 98. (18) Bronneberg, A. C.; van de Sanden, M. C. M.; Creatore, M. J. Non-Cryst. Solids 2012, 358, 379. (19) Mai, Y.; Klein, S.; Carius, R.; Wolff, J.; Lambertz, A.; Finger, F.; Geng, X. J. Appl. Phys. 2005, 97, 114913. (20) Matsuda, A. Jpn. J. Appl. Phys. 2004, 43, 7909. (21) Landman, U.; Luedtke, W. D.; Ribarsky, M. W.; Barnett, R. N.; Cleveland, C. L. Phys. Rev. B 1988, 37, 4637. (22) Motooka, T.; Nishihara, K.; Munetoh, S.; Moriguchi, K.; Shintani, A. Phys. Rev. B 2000, 61, 8537. (23) Schneider, M.; Schuller, I. K.; Rahman, A. Phys. Rev. B 1987, 36, 1340. (24) Gawlinski, E. T.; Gunton, J. D. Phys. Rev. B 1987, 36, 4774. (25) Hensel, H.; Urbassek, H. M. Phys. Rev. B 1998, 58, 2050. (26) Kubo, M.; Oumi, Y.; Miura, R.; Fahmi, A.; Stirling, A.; Miyamoto, A.; Kawasaki, M.; Yoshimoto, M.; Koinuma, H. J. Chem. Phys. 1997, 107, 4416. (27) Kubo, M.; Oumi, Y.; Miura, R.; Stirling, A.; Miyamoto, A.; Kawasaki, M.; Yoshimoto, M.; Koinuma, H. Phys. Rev. B 1997, 56, 13535. (28) Kubo, M.; Oumi, Y.; Miura, R.; Stirling, A.; Miyamoto, A.; Kawasaki, M.; Yoshimoto, M.; Koinuma, H. J. Chem. Phys. 1998, 109, 8601. (29) Kubo, M.; Oumi, Y.; Miura, R.; Stirling, A.; Miyamoto, A.; Kawasaki, M.; Yoshimoto, M.; Koinuma, H. J. Chem. Phys. 1998, 109, 9148. (30) Kubo, M.; Oumi, Y.; Takaba, H.; Chatterjee, A.; Miyamoto, A.; Kawasaki, M.; Yoshimoto, M.; Koinuma, H. Phys. Rev. B 2000, 61, 16187. (31) Pandey, S. C.; Singh, T.; Maroudas, D. J. Chem. Phys. 2009, 131, 034503. (32) Chen, H.-T.; Hwang, C.-C.; Chiang, H.-J.; Chang, J.-G. J. Phys. Chem. C 2011, 115, 15369.

■

NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on June 1, 2012, with errors to the Abstract and References. The corrected version was reposted with the Issue on June 14, 2012.

12531

dx.doi.org/10.1021/jp3002542 | J. Phys. Chem. C 2012, 116, 12525−12531