Cite this Article
Sun Xiao-Yan, Zhang Yu-Ru, Li Xue-Chun, Wang You-Nian. Fluid simulation of the pulsed bias effect on inductively coupled nitrogen discharges for low-voltage plasma immersion ion implantation. Chinese Physics B, 2017, 26(1): 015201  
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Fluid simulation of the pulsed bias effect on inductively coupled nitrogen discharges for low-voltage plasma immersion ion implantation
Sun Xiao-Yan, Zhang Yu-Ru, Li Xue-Chun, Wang You-Nian †
Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China

 

† Corresponding author. E-mail: ynwang@dlut.edu.cn

Abstract

Planar radio frequency inductively coupled plasmas (ICP) are employed for low-voltage ion implantation processes, with capacitive pulse biasing of the substrate for modulation of the ion energy. In this work, a two-dimensional (2D) self-consistent fluid model has been employed to investigate the influence of the pulsed bias power on the nitrogen plasmas for various bias voltages and pulse frequencies. The results indicate that the plasma density as well as the inductive power density increase significantly when the bias voltage varies from 0 V to 4000 V, due to the heating of the capacitive field caused by the bias power. The fraction increases rapidly to a maximum at the beginning of the power-on time, and then it decreases and reaches the steady state at the end of the glow period. Moreover, it increases with the bias voltage during the power-on time, whereas the fraction exhibits a reverse behavior. When the pulse frequency increases to 25 kHz and 40 kHz, the plasma steady state cannot be obtained, and a rapid decrease of the ion density at the substrate surface at the beginning of the glow period is observed.

PACS: 52.30.Ex;52.65.-y;52.50.Qt
Keyword:fluid simulation;low-voltage plasma immersion ion implantation;N2 inductive discharge
1. Introduction

The low-voltage plasma immersion ion implantation (LPIII), which is characterized by low energy and high throughput, has been widely used in the semiconductor industry, e.g., for changing the surface chemistry and surface morphology of silicone,[1] fabricating shallow junctions,[2–5] as well as improving the microhardness and reducing the friction coefficient and wear rate of stainless-steel surfaces.[6,7]

Since the chemical structure of the surface is changed after a nitrogen treatment, nitrogen has been widely applied in the LPIII process.[1,5,8–10] For instance, Husein et al.[1] demonstrated that the surface chemistry of the silicon, i.e., the formation of SiO x , silicon oxynitrides and silicon nitrides, was changed after a nitrogen PIII treatment. Mukherjee et al.[8] revealed an enhancement of the surface microhardness, by implantation of the nitrogen in AISI 316 austenitic stainless steel. Moreover, Felch et al.[5] found that performing nitrogen plasma doping (PLAD) before ultra-low energy implantation, could reduce boron diffusion and produce shallower junctions.

Several pieces of equipment for LPIII have been proposed, for instance, the hot filament glow discharge configuration, the pulse- or direct current (DC)-biased electron cyclotron resonance (ECR) equipment, the pulse- or DC-biased ICP system, and so on.[7,11–17] In a pulse-biased ICP, a continuous inductive source is used to sustain the discharge, and a pulsed bias power is applied to the substrate to control the ion energy. Since this system offers higher ion densities at lower pressure, and the ion energy can be easily modulated by adjusting the bias power, the pulse-biased ICP has attracted growing interest.

Over the past few years, several theoretical studies[18,19] and experimental researches[1,15,16,20] have been published on a pulse-biased ICP. Agarwal et al.[18] applied a 2D hybrid model, and they found that the time averaged ion energy angular distribution (IEAD) was characterized by multi-energy structures, due to the contributions of the ions arriving during the pulse-on period (high energy) and the pulse-off period (low energy). Moreover, by using the same model, they revealed that the IEAD became asymmetric as the bias voltage increased from −1 kV to −10 kV, with the ICP power of 500 W.[19] Husein et al.[1] experimentally observed a rough silicon surface with deeper valleys during the PIII modification in N2 plasmas, when the bias voltage was low (i.e., 4 kV). In addition, Qin et al.[15] focused on the PLAD process in a pulsed radio frequency (RF)-excited B2H6/H2 plasma system, revealing that a deeper boron profile was produced, and the boron surface deposition decreased slightly at higher voltage. Subsequently, by using a time-delayed, time-resolved Langmuir probe, the higher plasma density and electron temperature were obtained in a continuous plasma with pulsed voltage than in a non-continuous plasma.[16] Chang et al.[20] achieved the liquid crystal (LC) alignment on the hydrogenated amorphous carbon (a-C:H) layer by an argon plasma ion immersion treatment. They attributed the formation of the LC alignment to the oblique incidence of the ions within the matrix sheath of non-uniform thickness near the a-C:H surface under a negative pulse bias.

From the literature mentioned above, it is clear that the bias power has a significant influence on the plasma properties in a pulse-biased ICP. Therefore, the bias effect should be systematically investigated, in order to understand the discharge characteristics and optimize the plasma performance for microelectronics applications. However, only a few researches have been carried out on the bias effect in an ICP discharge with a pulsed bias, and the plasma characteristics are still not well understood. Therefore, in this work, the so called Multiphysics Analysis for Plasma Soures-ICP (MAPS-ICP) solver has been employed to investigate the influence of the pulsed bias on the inductive nitrogen discharge behavior. The aim of this work is to elucidate the influence of the bias on the plasma characteristics, which is important for the improvement of the LPIII process.

This paper is organized as follows. In Section 2, the fluid model and the reaction set, together with the boundary conditions, are described. The effect of the pulsed bias on the plasma characteristics is shown in Section 3. Finally, a summary is given in Section 4.

2. Description of the fluid model

A schematic of the ICP reactor with a pulsed bias, studied in this work, is shown in Fig. 1. The nitrogen plasma is generated by a four-turn coil with radial positions at r = 3 cm, 5 cm, 7 cm, and 9 cm, respectively. The bottom electrode with a radius of 8 cm is fixed at a distance of 7 cm from the quartz window, and it is biased by a pulsed power to accelerate the positive ions towards the substrate. An insulator ring with a thickness of 1 cm is clamped around the substrate, and it is surrounded by a grounded thin metal layer.[21]

Fig. 1. (color online) Schematic diagram of the ICP immersion ion implantation instrument.

MAPS is a comprehensive modeling platform developed by Wang and his group for the multiphysics analysis of various plasma sources. It includes two solvers: the MAPS-CCP solver and the MAPS-ICP solver. This modeling platform has been used to simulation the ICP and capacitive coupled plasma (CCP) discharges.[22–28] The fluid model of the MAPS-ICP employed in this work is similar to that described in Refs. [24]–[26]. Therefore, only a brief description is included here.

2.1. Plasma module

The fluid equations for electrons are as follows:

(1)
(2)
(3)
Here, by ignoring the inertia term of the electron momentum equation, the electron flux is presented in the drift-diffusion approximation form. is the source term of electrons; , , , and are the density, temperature, mass, and energy flux of electrons, respectively; is the elastic collision frequency between electrons and neutrals; is the electrostatic field; is the energy transfer of electrons by collisions with other species; k is the Boltzmann constant; the period averaged inductive power deposition is described as , where T is the period of the coil current, J θ and E θ are the azimuthal electron flux and the electric field.

Since the ions are assumed to be at room temperature, only the continuity and momentum equations are needed,

(4)
(5)
where , , , and are the ion density, flux, mass, and velocity, respectively. represents the transfer of momentum from the ions by collisions with other species.

For the neutral species, the continuity equation is expressed as

(6)
where , , and are the density, diffusion coefficient, and source term of neutral species, respectively.

The gradients of the ion density and ion velocity at the boundaries are set to zero, i.e., , . Since the secondary electron emission induced by the ion impact becomes important when a high negative voltage is applied to the substrate,[19,29] the boundary condition for the electron flux is

(7)
where is the reflection coefficient of electrons.[30] The secondary electron emission coefficient at the surface of the substrate is expressed as a function of the incident ion energy[19]
(8)
where is the secondary electron emission coefficient when the incident ion energy is below eV, and eV is adopted, for higher ion energy.

The continuity and energy equations for electrons are discretized by the finite volume method in space and the Crank–Nicolson scheme in time,[31,32] and the electron flux is solved by the first-order upwind scheme. The flux-corrected transport method is used to solve the ion equations.[33]

2.2. Electromagnetic module

The electrostatic field due to the space charge within the plasma is determined by solving the Poisson equation

(9)
where is the permittivity of free space.

The spatial–temporal distributions of the electromagnetic fields are obtained by solving the Maxwell equations,

(10)
(11)
where is the electric field, is the magnetic field, is the vacuum permeability, and represents the relative dielectric constant of the dielectric window.

The plasma current is given by

(12)
and it is set to zero in the vacuum and dielectric window regions.

The radial magnetic field at the interface of the dielectric window and vacuum is , where is the current density. At the interface of the dielectric window and plasma region, the radial magnetic field and the azimuthal electric field are continuous.

The successive-over-relaxation method is applied to solve the Poisson equation, and the Maxwell equations are solved with the finite difference time domain (FDTD) method.[34]

The chemical reactions taken into account in the model are listed in Table 1. For ions, only and are included, because their densities are much higher than other ions, such as and .[35] Besides, the ground-state N atoms, as well as three excited levels of N2 molecules, i.e., , , and , are also considered in this model.

Table 1.

The reactions for the N2 plasma taken into account in the model.

.
3. Results and discussion

In this section, the influence of the pulsed bias on the inductively coupled nitrogen discharge has been investigated at a fixed ICP current of 16 A and an RF frequency of 10 MHz. The simulations are performed at a pressure of 10 mTorr. For the base case, the frequency and duty cycle of the pulsed bias is 8 kHz and 40%, respectively, and the waveform is shown in Fig. 2.[44]

(13)
where , is the rise time, is the plateau time, is the fall time, and the power-off time is s. The voltage of the pulsed bias varies from 0 V to −4000 V.

Fig. 2. Schematic of the pulsed voltage waveform.
3.1. Pulsed bias voltage effect

In the nitrogen LPIII process, the ions have an important influence on the implantation depth due to their high energy. Since the ions can recombine with electrons and then produce two nitrogen atoms, they are responsible for the high nitrogen atom concentration in the implanted sample. Therefore, it is of significant importance to understand the behavior of the ions and their ratio in the discharge. The evolutions of the ion density at the reactor center (r = 0 cm, cm) and at the substrate surface (r = 0 cm, z = 6 cm), for various bias voltages, are presented in Fig. 3. When the bias power is turned on, the ion density at the reactor center increases rapidly, and then it reaches the steady state, as shown in Fig. 3(a). When the bias power is turned off, the ion density at the reactor center decays to a very low value in a short time. The evolution of the ion density at the substrate surface is similar to that at the reactor center, except that the ion density first increases to a peak value, and then it decays to a lower value at the beginning of the after-flow period (see Fig. 3(b)). This peak can be explained by the fact that when the pulse power is off, electrons move rapidly to the substrate, and the sheath region becomes thin. Therefore, the bulk plasma region is closer to the substrate, and more ions move to the substrate. Moreover, the secondary electron emission becomes less pronounced, hence the ion consumption due to the recombination is limited, and this is also attributed to the increase of the ion density at the substrate. In addition, the ion density increases significantly when the bias voltage varies from 0 V to −4000 V, both at the reactor center and at the substrate surface. This is because the plasma is heated not only by the inductive field, but also by the capacitive field caused by the pulsed bias. Therefore, the electrons gain more energy from the bias power, and this gives rise to the enhanced ionization.

Fig. 3. (color online) N ion density (a) at the reactor center, (b) at the substrate surface, as a function of time for various bias voltages for a pulse frequency of 8 kHz and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.

The ion densities at the reactor center and substrate surface as a function of time for different pulse voltages are shown in Figs. 4(a) and 4(b). The evolution of the N ion density with time is similar to that of the ion density, except that the ion density at the steady state is about three times higher than the ion density. Compared to the ion density, the peak of the N ion density at the beginning of the pulse-off period appears at a later time (i.e., 52.6 for the ion density, and 51.1 for the ion density, see Figs. 4(b) and 3(b)). Moreover, the ion density increases slower to the steady state at the beginning of the glow period, and similarly, the decay time of the density is also longer than the ion density. This indicates that the ions are more sensitive to the pulsed power than the ions. This is because the ions are mainly produced by the electron impact ionization of the feedstock N2 gas, and the ions are mainly formed by the ionization of the N atoms. In this paper, we assume that the density of the feedstock is constant, which is because only a very small part of the background gas is ionized or excited at the low pressure, whereas the N atom density is modulated by the bias source. Therefore, the ion density exhibits a quicker response to the pulsed power.

Fig. 4. (color online) N ion density (a) at the reactor center, (b) at the substrate surface, as a function of time for various bias voltages for a pulse frequency of 8 kHz and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.

In order to understand the influence of the pulsed bias power on the electron heating, the spatiotemporal distributions of the inductive power density next to the reactor symmetry axis at different bias voltages for a whole pulse period are plotted in Fig. 5. In a pure inductive discharge without the pulsed bias source, the electrons are heated only by the inductive azimuthal electric field, and hence the inductive power density is very low (i.e., at maximum about 7.4×10 kW/cm3, see Fig. 5(a)), leading to lower plasma densities (see Figs. 3 and 4). At the bias voltage of −500 V, the inductive power density during the power-on time (i.e., 0–50 s) increases remarkably (i.e., at maximum about 36.3×10 kW/cm , which is about five times higher than that during the power-off period. This is because during the glow period, the electrons gain more energy from the capacitive electric field induced by the bias power. Therefore, the plasma density and the azimuthal electron flux increase considerably, which gives rise to the higher (see Fig. 5(b)). When the pulsed bias voltage is equal to −2000 V and −4000 V (see Figs. 5(c) and 5(d)), a higher power density during the pulse-on time is observed, which is again due to the higher azimuthal electron flux. Moreover, the inductive power density during the off period also becomes higher (i.e., at maximum about 17×10 kW/cm3 at a bias voltage of −4000 V).

Fig. 5. (color online) Spatiotemporal distributions of the inductive power density next to the reactor symmetry axis at different bias voltages: (a) 0 V, (b) −500 V, (c) −2000 V, and (d) −4000 V, for a pulse frequency of 8 kHz and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.

Ratios of the and ion densities to the total ion density at the surface of the substrate as a function of time for various bias voltages are shown in Fig. 6. It is clear that the fraction is much higher than the fraction in the case without a bias power, i.e., /N . When the bias power is applied to the substrate, the fraction increases rapidly to a maximum at the beginning of the power-on time, and then it decreases and reaches the steady state at the end of the glow period. However, the fraction first decreases to its minimum, and then it increases to the steady state. When the bias power is turned off, the fraction drops rapidly to its minimum, and at a later time, it increases to the steady state. However, a reverse behavior of the fraction is observed. This is because when the bias power is turned on, the ion density increases faster than the ion density, so the fraction reaches its maximum in about 10 s. At a later time during the glow period, the ion density keeps constant, whereas the ion density increases till about 19 (see Fig. 4(b)). This gives rise to a decrease in the fraction and an increase in the fraction. When both the and N ion densities reach the steady state, i.e., after about 25 s, the fractions of the and ions become constant. The minimum of the fraction and the maximum of the fraction at the beginning of the after-glow are again due to the quick response of the ions. Moreover, during the power-on time, the fraction becomes higher when the bias voltage increases from 0 V to −4000 V, whereas the fraction decreases with the bias voltage. This is because the ion density rises more rapidly (i.e., from 0.02×1011 cm at 0 V to 0.27×1011 cm at −4000 V, see Fig. 3(b)) than the ion density (i.e., from 0.09×1011 cm at 0 V to 0.77×1011 cm at −4000 V, see Fig. 4(b)). However, when the pulsed power is turned off, the fraction decreases with the bias voltage, whereas the fraction exhibits an increased trend due to a similar reason. These phenomena are similar to that observed in Refs. [45] and [46], i.e., the ion density increases faster with the RF power than the ion density.

Fig. 6. (color online) Ratios of the and ion densities to the total ion density, as a function of time for various bias voltages for a pulse frequency of 8 kHz and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.

The radial distributions of the total ion flux at the substrate surface for various bias voltages averaged over one pulse period are shown in Fig. 7. The total ion flux is characterized by a center high profile at all selected bias voltages, and the ion flux above the substrate increases significantly with the bias voltage due to the high plasma density (see Figs. 3(b) and 4(b)).

Fig. 7. (color online) Radial distributions of the total ion flux at the substrate surface averaged over one pulse period, for various bias voltages for a pulse frequency of 8 kHz and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.
3.2. The pulse frequency effect

For a better understanding of the pulsed bias effect on the nitrogen RF discharge properties, the calculations are performed for pulse frequencies of 8 kHz, 16 kHz, 25 kHz, and 40 kHz, at a duty cycle of 40% and a bias voltage of −2000 V. Since the behavior of the ion density during one pulse cycle is similar to the ion density, only the evolutions of the ion density at the reactor center and at the substrate surface are shown here. At the pulse frequency of 25 kHz and 40 kHz, the power-on time is only 16 and 10 s, which is insufficient for the ions to achieve the steady state. Therefore, the ion density at the reactor center increases to its peak value at the end of the glow period, and then it decreases when the power is turned off, as shown in Fig. 8(a). Note the ion density at the substrate surface has a significant decrease at the beginning of the glow period, especially at higher pulse frequencies (see Fig. 8(b)). This is because during the ramp-up period, although the total power deposition increases with bias voltages, the bias power dissipation caused by the ion acceleration is more dominant, especially in the sheath region where the capacitive field is very strong, and this gives rise to a considerable decrease in the plasma density. As the bias voltage increases further, the electrons gain more energy from the higher capacitive bias power, and therefore, these energetic electrons enhance the plasma generation. Moreover, at higher pulse frequencies, the plasma density could not decay to a very low value in the limited after-glow period. Therefore, the average electron energy at the beginning of the glow period is low, which limits the ionization process, and leads to a more rapid decrease in the N ion density. When the pulse frequency is lower than 16 kHz (i.e., with a power on time of 25 s), the ion density can reach the steady state, and a peak value appears at the beginning of the after-glow period, which is similar to that shown in Fig. 4.

Fig. 8. (color online) N ion density (a) at the reactor center, (b) at the substrate surface, as a function of time for various pulse frequencies for a bias voltage of −2000 V and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.

The influence of the pulse frequency on the ratios of the and ion densities to the total ion density is shown in Fig. 9. It is clear that at the beginning of the power-on time, the fraction decreases with pulse frequency. This can be attributed to the lower electron energy at higher pulse frequency at the beginning of the glow period. Since the ions are mainly formed by the ionization of the N atoms, and the N atom density decreases with pulse frequency due to the lower dissociation rate of N2 caused by the lower electron energy, the fraction increases slower at higher pulse frequencies.

Fig. 9. (color online) Ratios of the and ion densities to the total ion density, as a function of time for various pulse frequencies for a bias voltage of −2000 V and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.

The influence of the pulse frequency on the total ion flux at the surface of the substrate is shown in Fig. 10. It is clear that the pulse frequency has no significant influence on the radial distribution of the total ion flux, i.e., a center-high profile is observed at all selected pulse frequencies. However, the absolute value of the total ion flux has a slight decrease at 25 kHz. When the pulse frequency increases to 40 kHz, a remarkable decrease is observed (i.e., maximum of about 10.6×1016 cm s at 8 kHz and 5.2×1016 cm s at 40 kHz). This is again because the steady state cannot be reached at higher pulse frequencies, and the ion density is lower.

Fig. 10. (color online) Radial distributions of the total ion flux at the substrate surface averaged over one pulse period, for various pulse frequencies for a bias voltage of −2000 V and duty cycle of 40%, in an ICP nitrogen discharge sustained at a current of 16 A and 10 MHz.
4. Conclusions

In this paper, a 2D self-consistent fluid model is applied to investigate the influence of the pulsed bias power on the nitrogen inductively coupled discharge for various pulse voltages and pulse frequencies.

From the simulation results, it can be found that the plasma density increases with bias voltage due to the heating of the capacitive field caused by the pulsed bias, and accordingly, the higher azimuthal electron flux leads to the higher inductive power density. The ion density at the substrate surface exhibits a peak at the beginning of the after-glow period due to a thin sheath and the reduction of the secondary electrons. The fraction shows a maximum at the beginning of the power-on time, and then it decreases and keeps constant. When the bias power is turned off, the fraction drops rapidly to its minimum, and at a later time, it increases to the steady state. Moreover, the fraction increases with the bias voltage during the power-on time, whereas the fraction exhibits a reverse behavior. The radial distribution of the axial total ion flux above the substrate is characterized by a center high profile, and the absolute value increases with the bias voltage.

We also found that the steady state cannot be obtained for higher pulse frequencies, i.e., 25 kHz and 40 kHz due to the shorter power-on time. In addition, the ion density at the substrate surface has a rapid decrease at the beginning of the glow period, especially at higher pulse frequencies. The maximum of the fraction at the beginning of the power-on time decreases with pulse frequency, and the minimum when the pulsed power is off at a pulse frequency of 40 kHz is slightly higher than those at lower pulse frequencies. The ion flux above the substrate becomes slightly lower at 25 kHz, and the decreasing trend becomes more evident at 40 kHz.

In conclusion, the plasma density and ion species ratio can be modulated by the bias voltage and pulse frequency. This is very important to realize, as it can help us to optimize the LPIII process.

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