MULTI~FREQUENCY CAPACITIVELY COUPLED

The determined values ​​of the sheath parameters are compared with some published DF and TF models. Compared to collision time-independent models, this model estimates lower values ​​of the sheath parameters.

INTRODUCTION

Introduction

In the case of DF-CCP they also showed that the envelope width increases linearly with increasing low frequency power. It is found that when the HF voltage increases, the plasma density increases and the envelope width increases.

Organization of This Thesis

This model proposes an analytical solution of the sheath parameters of a multi-frequency source driven CCP, taking into account a collision sheath, an inhomogeneous ion distribution and a time-dependent electric field within the sheath. After modeling, the shroud parameters are determined and analyzed for two-frequency and three-frequency source-controlled CCP, respectively.

FUNDAMENTAL CONCEPTS OF PLASMA

Introduction

Definition of Plasma

In space, plasma is the most common aggregate state of ordinary matter, which is mostly found in rarefied intergalactic plasma and in stars [35]. Plasma is often called the fourth state of matter, as it is created by adding energy (heat) to a gas.

Fundamental Parameters of Plasma

• Plasma applications in industrial and metallurgical engineering
• Plasma application in electronics engineering
• Plasma for thin film deposition and etching
• Plasma sputtering
• Plasma in reactive sputtering
• Plasma enhanced chemical vapour deposition (PECVD)
• Plasma preparation of CNTs and grapheme

At equilibrium, the surface composition of the target is changed such that the composition of the elements in the sputtered flux is the same as the original alloy composition. In the deposition of these films, it is the chemical aspects of the plasma that are usually of greatest importance.

Figure 2.1 Electron density and temperature ranges for a variety of natural and man- man-made plasmas [35].

Types of Plasma

• Glow discharge plasma
• Capacitively coupled plasma
• Inductively coupled plasma
• Wave heated plasma

Generally, various gases such as Ar, O2, H2, N2, NH3 and CF4 have been used for plasma doping to induce the desired electronic structures. Much effort has been devoted to modifying the electronic properties of graphene by introducing heteroatoms (e.g., nitrogen) into its sheets through plasma processing.

Plasma Reactors

• Planar reactor

This is widely used in the microelectronics manufacturing and integrated circuit industries for plasma etching and plasma chemical vapor deposition [44]. However, the electrode consists of a coil wrapped around a discharge volume that inductively excites the plasma [40]. Perhaps the most ubiquitous class of plasma reactors is that in which the plasma is formed between plane-parallel electrodes [35].

The region inside the electrodes can be broken down into two regions: (i) the bulk plasma---the main body of the plasma where chemically reactive substances are generated and the electric field is low, and (ii) the cladding- the plasma-free zone near the electrode where the electric field is high. This is usually achieved by introducing a magnetic field nominally parallel to an electrode.

Figure 2.4 Schematic of planar plasma reactor [35].

Basic Plasma Properties

• Plasma breakdown
• DC breakdown
• Plasma oscillations
• Self bias and plasma potential

As a result of the acceleration due to the electric field, the electron will gain energy and cause ionization [35]. We can find a self-consistent solution for the electrostatic potential

The characteristic response of the plasma to a voltage V is given by the curve in Fig. The capacitor will be charged by the effective resistance of the plasma to electron current flow, and the plasma potential V2 will drop as in Fig.

Figure 2.6 Behaviour of the discharge at breakdown [35].

Definition and Properties of Sheath and Pre-sheath

• Bohm sheath criterion
• Pre-sheath

Setting nes=njs =ns at the mantle edge (x =0) and substituting nj and ne in Poisson's equation, we have. Equation (2.24) is the fundamental non-linear equation governing the sheath potential and the ion and electron density. 2.24) can be obtained by multiplying the equation by d

To give the ions a directed velocity Un, there must be a finite electric field in the plasma over a region, usually much wider than the sheath, called the pre-sheath (Fig. 2.16). The transition can arise from geometric contraction of the plasma, from frictional forces of the ions in the pre-sheath, or from ionization in the bulk plasma [40].

Figure 2.15 Schematic of RF plasma and sheath [40].

Summary

ANALYTICAL MODELLING OF SHEATH PARAMETERS

Introduction

Why Multi-frequency?

Analytical Modelling

Assumptions

The plasma chamber is filled with Ar plasma driven by a current source with one low and N number of high frequencies, where N is a positive integer. ii) All harmonic frequencies are integer multiples of the fundamental frequency. iii). The ion sheath is inhomogeneous, i.e. the ion density decreases towards the electrode. iv) Ions passing through the sheath can respond to the instantaneous electric field. v) The mean free path of the ions is less than the width of the sheath, i.e. the ion sheath is colliding. vi). The boundary between ion sheath and plasma is stationary and ions enter the sheath with a Bohm velocity in front of the sheath. vii).

The electron Debye length, AD, everywhere inside the sheath is much smaller than the ion sheath thickness Sm, that is, AD « sm. Thus, the electron density drops sharply from ne '" ni at the plasma side of the electron boundary to ne=0 at the electrode side.

Modelling

The one-dimensional spatial variation of the ion density, ni (x, f), the ion velocity, ui (x,t), the electric potential, V(X,f), and the instantaneous electric field, E(x, t) are described from the ion continuity equation, . For the plasma sheath, the crucial parameter determining the dynamics of the plasma sheath is (0/ (Oi where, (0 is the RF frequency and (OJ =2rc /'oi, is the frequency of ion oscillations inside the sheath and 'Oi is the time of ion transition 0» (OJ: The ion density is independent of time, and the ions respond only to the time-averaged electric field.

0« (Oi: The ion density is time dependent and ions respond instantaneously to the electric field. To control the ion energy by a low frequency source, the low frequency voltage Vlow is much larger than the high frequency voltage.

Summary

From here the value of

RESULTS AND DISCUSSION

Operating condition

In determining the parameters of the envelope, we have taken into consideration the Ar plasma with standard values ​​of the input parameters which have also been used in various published works.

Comparison with Jiang's model

Comparison with Boyle's model

This is due to the presence of initial non-zero electric field at plasma sheath boundary in this model which is not considered in Boyle's model. This is because the assumption of instantaneous electric field assumes more ion-neutral collisions than that of Boyle's model where time-dependent effects are not taken into account. Thus, we expect similar behavior of sheath potential estimated by this model while comparing it with Boyle's model.

We see that the maximum sheath width and potential calculated by this model are always lower than those of Boyle's model. Again it is worth noting that the sheath parameters decrease with the increase in pressure in this model as well as in the Boyle's model.

Figure 4.3 Normalized sheath motion as function of normalized phase for a, = 51, [3,

Effects of plasma density

This is because, the time-dependent effect on the ion density considered in this model causes lower envelope width and potential. In the case of Jiang's model, we see that pressure has no effect on the envelope parameters. To understand the effect of frequency coupling, we plotted the envelope width and peak potential as functions of the frequency ratio, ex (=Wj/~f) which are shown in Figs.

It is clear that as the frequency ratio increases, the envelope width becomes less sensitive to the frequency change. To investigate the effects of phase difference on the envelope parameters, we plot the parameters at different phase differences in Fig.

Figure 4.7 A; / Sm as function of plasma density at different chamber pressures for a=51, {3=10, and T, =3 eV

Triple Frequency Case

• Expressions for the sheath parameters
• Operating conditions
• Comparison with time independent TF model
• Effects of pressure and plasma density
• Effects of frequency ratio

In the higher phase, the envelope parameters of this model are estimated to be lower than those of the Rahman model. In all pressure ranges, this model estimates lower values ​​of the mantle parameters than the Rahman model. Also due to high and mid frequency modulation effects, the envelope parameters show maxima and minima at certain combinations of frequencies.

Compared to Rahman's model, this model shows the lower values ​​of the mantle parameters in all the figures mentioned. For the same reason, the peak values ​​of the mantle parameters are also much higher than those of the DF-driven mantle.

Figure 4.12 Normalized sheath motion as function of normalized phase for a,=21 , 0;,=61, /3,=5, [3,,=10 and p = 100 mTorr.

Summary

Since the ion energy is directly related to the sheath potential, compared to the DF sheath, it would be more flexible to control the ion energy inside the sheath by controlling the current parameters of the TF source.

CONCLUSION

Conclusion

The sheath parameter found to decrease with the increase in pressure as well as plasma density. Jiang's model has no pressure effect since it does not assume collision in the mantle. Proper choice of phase difference can be used to control the peak position and the value of the envelope parameters.

The dependence of sheath parameters on pressure and plasma density showed similar behavior as in the DF CCP case. Compared to the DF CCP case more oscillatory behavior is found in both the sheath motion and the potential in the TF CCP case.

Suggestions for Future Work

Because this model takes into account the instantaneous ion motion and the instantaneous electric field, this model is more accurate compared to other models that take into account the time-averaged electric field. Multi-frequency modeling of CCP will thus help to estimate the sheath parameters more accurately using this model, giving the plasma users better control over the etching properties.

Shon, “Control of ion energy distribution in single and dual frequency plasma sources,” Plasma Sources Sci. Voloshin, "Ion energy distribution function in capacitively coupled double-frequency rf discharges: Analytical model," Pys. Wang, “Numerical investigation of ion energy distribution and ion angle distribution in a dual-frequency plasma combined with a hybrid model,” Phys.

Schiingel “The Effect of Secondary Electrons on the Separate Control of Ion Energy and Flux in Dual Frequency Capacitively Coupled Radio Frequency Discharges,” Appl. Lee, “Control of ion energy distribution in low-pressure and triple-frequency capacitive discharge,” Plasma Sources Sci.