Application of Molecular Dynamics Simulations to Plasma Etch Damage in Advanced Metal- Oxide-Semiconductor Field-Effect Transistors

According to "the international technology roadmap for semiconductors (ITRS)" (SIA, 2009), the shrinkage of silicon-based metal–oxide–semiconductor field-effect transistor (MOSFET) – an elemental device (unit) in ultra-large-scale integrated (ULSI) circuits – has been accelerating due to expanding demands for the higher performance and the lower power operation. The characteristic dimensions of current MOSFETs in mass productions are around 30 – 50 nm. Figure 1 shows the scaling trend of the key feature sizes in ULSI circuits predicted by Semiconductor Industry Association, USA. Various types of MOSFETs are designed for the specific purposes, i.e., low standby power (LSP), low operation power (LOP), and high performance (HP) operations, and built in ULSI circuits such as dynamic random access memory (DRAM) and micro-processing unit (MPU). New structured MOSFETs such as fully-depleted (FD) and metal-gate (MG) devices have been recently proposed. Since physical gate length (Lg) and source / drain extension depth (Ext) are the key feature sizes determining MOSFET performance (Sze & Ng, 2007), the shrinkage of Lg and Ext is a primal focus in the development of MOSFETs. These sizes have become a few nanometers, comparable to the scale of atomistic simulation domain.


Introduction
According to "the international technology roadmap for semiconductors (ITRS)" (SIA, 2009), the shrinkage of silicon-based metal-oxide-semiconductor field-effect transistor (MOSFET) -an elemental device (unit) in ultra-large-scale integrated (ULSI) circuits -has been accelerating due to expanding demands for the higher performance and the lower power operation.The characteristic dimensions of current MOSFETs in mass productions are around 30 -50 nm. Figure 1 shows the scaling trend of the key feature sizes in ULSI circuits predicted by Semiconductor Industry Association, USA.Various types of MOSFETs are designed for the specific purposes, i.e., low standby power (LSP), low operation power (LOP), and high performance (HP) operations, and built in ULSI circuits such as dynamic random access memory (DRAM) and micro-processing unit (MPU).New structured MOSFETs such as fully-depleted (FD) and metal-gate (MG) devices have been recently proposed.Since physical gate length (Lg) and source / drain extension depth (Ext) are the key feature sizes determining MOSFET performance (Sze & Ng, 2007), the shrinkage of Lg and Ext is a primal focus in the development of MOSFETs.These sizes have become a few nanometers, comparable to the scale of atomistic simulation domain.
To meet the requirements such as fabricating fine patterns with anisotropic features, plasma etching is widely used in mass production of MOSFETs.At present, the control of the pattern transfer by plasma etching needs to be within the variation of a few nanometers (SIA, 2009).In such regimes, the feature size of the region where plasma -etch reactions are occurring becomes no more negligible with respect to the scale of MOSFET.Thus, precise control of the surface reaction between plasma and device is strongly required.In plasma etch process, radicals (atoms or molecules in an excited state) react with surface material with a help of the energy of incident ions accelerated in the "sheath" between plasma and device surface.This reaction mechanism is commonly referred to as "reactive ion etching (RIE)" (Lieberman & Lichtenberg, 2005).In some plasma etch processes, an energy of the ion becomes larger than 1 keV to obtain high etch rate.In such schemes, an unexpected reaction may occur.This unexpected ("unwanted") reaction mechanism is usually called as "plasma process-induced damage" (Eriguchi & Ono, 2008;Lieberman & Lichtenberg, 2005;Oehrlein, 1989), which is bringing out many key problems in the development of MOSFETs.Plasma process-induced damage (PID) is one of the serious issues causing degradation of MOSFET performance and reliability.Figure 2 illustrates an example of PID during a typical plasma etch process.Si wafer is placed on a wafer stage in a plasma chamber.Reactive plasma is generated by power supply.This figure corresponds to an inductively coupled plasma (ICP) system (Lieberman & Lichtenberg, 2005), where powers with frequencies of f 1 and f 2 are supplied to a plasma source (f 1 ) and a wafer stage (f 2 ), respectively.During plasma etching, MOSFET is exposed to a plasma and energetic ions impact on the surface.This energetic ion bombardment results in creation of defects (ex.displaced Si atom) in the Si surface region of MOSFET.This mechanism is one of examples of PID (Eriguchi & Ono, 2008).During more than the last two decades, PID has been studied extensively to understand the mechanisms and to solve practical problems with various approaches.In order to obtain the statistical data in mass production and to clarify the source of PID, a use of specifically designed devices called "test elementary group (TEG)" (SIA, 2009) has been a major approach.In addition to the use of TEG, physical and electrical analyses have been conducted by using a bare Si wafer to gain fundamental understanding of PID.To realize future high-performance MOSFETs, understanding and controlling (minimizing) PID is crucial because the critical dimension of reaction-layer thickness and device feature size will be in conflict with the plasma-damaged-layer thickness governed by plasma parameters.In other words, the damaged-layer thickness does not scale with device-shrinkage trends shown in Fig. 1.
Several simulation techniques have been proposed so far for plasma etch process.There are two major schemes: (1) Plasma-etch feature-profile simulations employing a small cell (Jin et al., 2002;Tsuda et al., 2011) and (2) Surface-reaction simulations based on a molecular dynamics (MD) (Graves & Humbird, 2002;Ohta & Hamaguchi, 2001a, 2001b;Sankaran & Kushner, 2004).Since the number of particles to be simulated may be quite large (>10 10 cm -3 ) during plasma etching, classical MD simulations based on Newton's equation of motion (Graves & Humbird, 2002;Ohta & Hamaguchi, 2001a, 2001b) are now widely employed, compared to those using quantum mechanical calculations (Mazzarolo et al., 2001;Pelaz et al., 2009).Recently MD simulations have been used to understand formation of the surface "damaged" layer and displacement of Si atoms -PID (Graves & Humbird, 2002;Pelaz et al., 2009).However, the primary focus of these conventional MD simulations has been placed on the surface-reaction chemistry among ions, radicals, and the surface material.Since plasma etch processes are utilized for MOSFET fabrication, not only the surface reaction mechanism but also the effects of PID on MOSFET performance degradation should carefully be taken into account.Thus, MD simulations for PID should be incorporated with the prediction of electrical characteristics of MOSFETs.

Plasma
There are two major challenging parts in the development of future MOSFET and plasma etch process: (1) A systematic and quantitative understanding of PID -the thickness of the damaged layer and the density of the displaced Si atoms (defects), and (2) A comprehensive design framework for future plasma by considering the effect of PID on electrical characteristics of MOSFETs.By keeping these issues in mind, this chapter discusses PID mechanisms by a classical MD simulation.We compare the simulation results with experimental data obtained by various analysis techniques.Future key issues concerning the effects of PID on MOSFET performance are provided.This chapter is organized as follows: In Sec. 2, we review the PID mechanism (Si loss mechanism -Si recess structure formation as mentioned later).In Sec. 3, the MD simulation employed in this study is briefly described.In Sec. 4, the simulation results are presented.In Sec. 5, experimental results are compared to the simulation results.Concluding remarks are in Sec. 5.

Ion-bombardment damage to MOSFET during plasma processing
Figure 3 illustrates a PID mechanism induced by the ion bombardment on Si surface during an offset spacer (SIA, 2009) etching (one of manufacturing steps) for MOSFET.During plasma etching, an energetic ion impinges on the Si surface with an energy of E ion , leasing the energy by a series of collisions, then, it creates the defect sites under the exposed surface.This mechanism forms the damaged layer.In general, defect sites in Si substrate are referred to as displaced Si atoms, vacancies, and interstitials.As seen on the right in Fig. 3, the damaged structure consists of the surface (amorphous) and interfacial (a mixture of amorphous and crystalline structure) layers.Underneath these layers, there exist (latent) localized defect sites.(In this study, we denote these sites as "(local) defect sites".)The surface and interfacial layers can usually be monitored by an optical technique such as spectroscopic ellipsometry (SE) in production lines.The profile of defect site and the thickness of damaged-layer are determined by E ion as well as the potential between Si and the incident ion.In conventional MOSFET fabrication processes, a wet-etch step then follows the plasma etch process to remove the contaminated layer including the damaged layer.Since the damaged layer oxidizes due to an air exposure after the plasma etch, the portion is stripped off by the wet-etch.Then, the etched layer results in Si loss whose structure is observed as recessed Si surface, called "Si recess" (Ohchi et al., 2008;Petit-Etienne et al., 2010;Vitale & Smith, 2003).
Si recess is formed in the source / drain extension (SDE) region in a MOSFET.
It has been reported (Eriguchi et al., 2009a;Eriguchi et al., 2008a) that the Si recess structure by PID degrades MOSFET performance, i.e., induces the shift of threshold voltage (V th ) for MOSFET operation.Since V th (Sze, 1981;Sze & Ng, 2007) plays an important role in determining the performance, Si recess structure has become a primal problem in the present-day MOSFET development (SIA, 2009).To understand the formation of Si recess structure (PID), the damage creation mechanism should be clarified from both theoretical and experimental viewpoints.Moreover, to predict the effects of PID on the MOSFET electrical characteristics, the defect structures should be identified quantitatively with high accuracy.In this study, we performed a classical molecular dynamics simulation as well as quantitative analyses of the local defect site density.Then, we discuss the effects of PID on the electrical characteristics of MOSFET.

Molecular dynamics simulation for plasma etching
Regarding to classical MD simulations for plasma etch process, many papers have been focusing on the surface reactions to understand details of silicon and silicon dioxide etch characteristics by energetic halogen (Abrams & Graves, 2000;Hanson et al., 1997;Humbird & Graves, 2004;Nagaoka et al., 2009;Ohta & Hamaguchi, 2001b) and fluorocarbon (Abrams & Graves, 1999) ions.The primal focuses are placed on estimation of etch yield by incident ions and the selectivity for RIE system.Regarding the ion bombardment damage, Graves and Humbird (Graves & Humbird, 2002) have reported in detail the formation of damaged layer in crystalline Si structures by Ar ion impacts.They estimated a stopping range of ions as well as a thickness of the amorphous (amorphized) layer formed near the surface.However, the detail mechanism of local defect site formation was not discussed.
As mentioned in Sec. 1, an RIE system includes the physical and chemical reactions triggered by 10 -10 3 eV high-energy ion impacts.Although ab initio MD simulations are now available, they cannot be applied in practice.This is because more than 10 3 atoms are necessary to construct a solid surface and the total number of incident ions is more than 10 10 cm -2 , resulting in more than 10 3 impacts on the surface with the area of 10 nm 2 (~ commonly simulated size).Therefore, at present, the only possible candidate for atomistic RIE simulations is a classical MD, in particular, with pre-constructed interatomic potential functions.
One of the commonly used interatomic potential functions for Si-containing systems is the one proposed by Stillinger and Weber (SW) (Stillinger & Weber, 1985) wherein the total potential energy consists of two-and three-body functions.The SW potential function was originally designed for Si/F systems.Afterwards various potential sets for Si/Cl (Ohta & Hamaguchi, 2001b), Si/O (Watanabe et al., 1999), Si/O/F (Ohta & Hamaguchi, 2001a), Si/O/Cl (Ohta & Hamaguchi, 2001a), and Si/O/C/F (Ohta & Hamaguchi, 2004;Smirnov et al., 2007) systems were provided.The other widely used function was proposed by Tersoff (Tersoff, 1988a(Tersoff, , 1988b) ) with bond-order parameters including multi-body interactions.This potential can be effectively applied to C-containing systems to understand the complicated behaviours by the strengths of double and triple bonds.The parameter sets were proposed for systems including Si, C, Si/C, C/H, C/F, and Si/C/F (Abrams & Graves, 1998;Tanaka et al., 2000).In addition to the SW and Tersoff potential functions, other potential functions (Biswas & Hamann, 1987;Dodson, 1987;Hanson et al., 1997) were also proposed.Although there have been many discussions on the validity of the functions (Balamane et al., 1992), all of these functions can effectively reproduce some structural and thermodynamic characteristics of the materials and the relevant structural chemistry for some selected molecules.In this study, to eliminate complicated surface reactions usually occurring in halogen-containing plasmas, we focus on Ar-Si-O system for studying PID.We used the SW potential function for the Si-Si and Si-O systems.

Interatomic potential functions used in this study
The Stillinger-Weber potential function (Stillinger & Weber, 1985) utilizes both two-body and three-body interaction terms to stabilize the diamond cubic structure of crystalline silicon.The potential function is given by 23 (, ) (, , ) where V 2 (i, j) is the two-body interaction term between i-th and j-th atoms expressed as , where a ij is the cut-off distance, and V 2 (i, j) = 0 otherwise.r ij is the interatomic distance between i-th and j-th atoms in the SW's length unit (0.20951 nm).The parameters , and a ij depend only on the species of i-th and j-th atoms.g ij (< 1) is the bondsoftening function introduced by Watanabe et al. (Watanabe et al., 1999), adjusting the contribution of the two-body term to reproduce the cohesive energies of Si-O bonds.The three-body interaction term has the following form.
where ijk  is the angle between two lengths of r ij and r jk , etc.Given that r ij and r ik are less than the cut-off distance, the function h is Regarding the two-body system with Ar, the Moliere-type repulsive pair potential function (Moliere, 1947;Torrens, 1972;Wilson et al., 1977) was employed.The potential function V 2 (i,j) includes a screening function f s (r ij ) combined with a Coulomb potential.The function is expressed as where e is the elementary charge,  0 is the permittivity of a vacuum, and Z i and Z j are the atomic numbers of the projectile (Ar) and target (Si, O, Ar) atoms, respectively.The expression of the screening function has been studied by many researchers (Torrens, 1972).So far, the repulsive interatomic potential between Ar and other elements has been modified (Wilson et al., 1977).In the expression of Moliere potential function, f s (r ij ) is described as where a' is the Firsov screening length (Firsov, 1957).The parameters proposed by Moliere (Moliere, 1947;Wilson et al., 1977) were used in this study.

Simulation procedure
We prepared a crystalline Si structure of squared Si (100) surface with a side length of 3.258 nm (six times of lattice constant ~ a squared 6-unit cell).The MD code used in this study was originally developed by Ohta and Hamaguchi (Ohta & Hamaguchi, 2001b).Each layer contained 72 atoms (= 1 monolayer (ML)).The bottom layer of the simulation cell (72 atoms) was rigidly fixed throughout the simulations.Initial depth of the simulation domain is 9unit cells (nine times of lattice constant or 36 MLs).Periodic boundary condition was employed along the horizontal direction.Since a typical MOSFET structure has an SiO 2 layer on the Si substrate, the initial Si structure (6  6  9 cell) was "oxidized" before the Ar ionbombardment.The oxidation was done by the 500-consecutive impacts of O atoms at 50 eV and followed by a subsequent cooling step with a set-point temperature of 400 K (See below).This step can create a surface oxidized layer corresponding to SiO 2 film formed on a source / extension region of MOSFET.Using the obtained SiO 2 /Si structure, we injected Ar atoms with various incident energies.Ar atoms were injected from randomly selected horizontal locations above the surface of the cell at normal incidence.(In this study, we injected Ar ions with a constant E ion , although, in practical plasma etching processes, the energy of ions obeys an ion energy distribution function (IEDF) dependent on a frequency of applied bias power (Lieberman & Lichtenberg, 2005) as illustrated in Fig. 2.However, a recent study (Eriguchi et al., 2010) showed that, in low applied bias voltages (< 500 eV), the average ion energy can be used as a primal measure for the damaged-layer thickness.Therefore, in the present MD simulation, we employed a mono-energetic ion impacts.)Note that, in plasma etching, an ion plays an important role in the reactions.However, in conventional MD simulations, charge-neutral atoms are used as incident particles.This is based on the assumption that incident ions are expected to be neutralized near the target surface due to a resonance or Auger process.Thus, in this study, we employed the above potential functions for charge-neutral Ar atom.
In the present-day RIE, plasma densities of the order of 10 9 -10 11 cm -3 are widely used.
These densities lead to a (Bohm) flux of incident ions of 10 13 -10 16 cm -2 s -1 , depending on the plasma density and the electron temperature (Lieberman & Lichtenberg, 2005).The interval between two successive ion impacts in the case of the present simulation domain (~ 10 nm 2 ) is much longer than the simulation time range.Therefore, each ion impact is thought to be an independent single event.To simulate such single events, for the first 0.7 ps after an energetic particle hits the surface, the motion of all particles in the domain are solved numerically by a classical mechanics except for those in the rigidly fixed bottom layer.Then, we applied "artificial" cooling step to all the particles for 0.3 ps using Berendsen's heat removal scheme (Berendsen et al., 1984) with a cooling constant of 2.0 x 10 -14 s -1 .The set-point temperature of the simulation cell was 400 K to reproduce the practical surface-temperature range during plasma etching.After the end of cooling step, a new energetic particle was directed again to the surface, and the whole simulation cycle was repeated.Details of the present MD simulation procedure were published elsewhere (Ohta & Hamaguchi, 2001b).
To evaluate the damage creation mechanisms, the defect structure formed by the ion impacts should be identified.Since comprehensive discussions on the defect structures may be beyond the scope of this article, we focus on the displaced Si atoms from the initial lattice site and the representative defect structures obtained by the simulations.To assign the displaced atoms, the Lindemann radius (r L ) was used as a measure of the displacement threshold (Hensel & Urbassek, 1998;Nordlund et al., 1998).The Lindemann radius is defined as the vibration amplitude of Si atoms at their melting point.For the SW potential function for Si, the radius is r L = 0.45 Å.After the MD simulations, we inspected the displacements of all the Si atoms.Then, we identified all those atoms as defects if they were outside of the cubic cell (with an edge of 2  r L ) whose center was located at an original lattice site.The number of the displaced atoms was counted to investigate an overall trend of PID in the course of successive ion impacts.

Simulation results and discussion
Figures 4 display typical damaged-layer/Si structures after 500 impacts by Ar ions with various energies.In these figures, Ar ions are omitted from the structures to clearly show the damaged layer and Si substrate.From other simulation results, we found that Ar atoms are usually present in the tetrahedral interstitial site underneath the interfacial layer.As seen in Fig. 4, the damaged layer thickness increases with an increase in E ion .The heavily damaged surface layer and mixing layer with a rough interface (interfacial layer) are observed, in particular, for higher E ion cases (≥ 200 eV).The surface layer has been usually identified as "an amorphous layer" in the view of simulation as discussed in previous literatures (Graves & Humbird, 2002;Oehrlein, 1989).However, when samples (wafers) are processed to the next manufacturing step, oxidation of the surface occurs due to an air exposure.As mentioned in the next section, the partially oxidized layer is detected by an optical technique as SiO 2 layer, and the residual damaged layer is evaluated as a mixing layer.In the following discussion, based on the experimental data, we define the surface amorphous layer and the rough interfacial region (including local defect sites) as the surface and interfacial layers, respectively.One should also pay careful attention to the local defect sites underneath the rough interface as highlighted in Fig. 4.
Regarding the local defect sites observed in Fig. 4, many respective structures have been proposed so far (Baraff et al., 1980;Batra et al., 1987;Cheng & Corbett, 1974;Estreicher et al., 1997;Hastings et al., 1997;Leung et al., 1999;Schober, 1989;Tang et al., 1997).In addition to vacancy, various interstitials have been studied extensively by ab initio calculations using clustered Si atoms.Tetrahedral and hexagonal interstitials as well as "dumbbell" and the bond-centered interstitial are commonly proposed structures (Batra et al., 1987;Leung et al., 1999).Figure 5 shows the profile of an increase in the number of Si atoms located in each atomic plane along the depth of [100] direction (The space between the planes is 0.13575 nm).72-Si atoms are originally located in each plane for the present cell structure (6 × 6).In this figure, only Si atoms were inspected and counted.The difference in the interstitial structures mentioned in the above was not considered.The positive value presumably implies the presence of interstitials and the negative, that of vacancy.This means that the local defect sites are consisting of vacancies as well as Si interstitials.(Note that one can see cumulatively the net positive value when integrating the data from the bottom.This implies that the Si interstitials are more probable than vacancies in those cases.)The interstitial Si atoms were formed by knock-on process.

Plasma
By keeping in mind the results in Fig. 5, we investigated in detail some of typical defects in From Fig. 4, we roughly categorize the defect structures (the interstitial atoms) as Type-A, Type-B, and Type-C.Type-A is like a tetrahedral interstitial, and Type-B, a hexagonal interstitial (Batra et al., 1987;Leung et al., 1999;Schober, 1989).In both cases, neighbouring Si atoms are not displaced considerably.Type-C is like a "dumbbell" structure where bonded Si atom was displaced from the lattice sites due to the presence of an interstitial Si permeating from other regions.It is widely believed that these structures are probable and found to be stable in terms of the formation energies calculated from a quantum mechanics scheme (Colombo, 2002;Leung et al., 1999;Tang et al., 1997).Typical structures reported so far are also illustrated on the right of Fig. 5.For details including other structures, please see the literatures (Batra et al., 1987;Cheng & Corbett, 1974;Leung et al., 1999).In terms of the effect of the presence of these structures on electrical characteristics of crystalline Si structure, it is also believed that these defects can create additional energy levels in the band gap ("band-gap states") (Estreicher et al., 1997;Hastings et al., 1997;Schultz, 2006).Therefore, one can speculate that the local defects by PID degrade MOSFET performance because the band-gap state plays a role as a carrier trap site inducing an increase in leakage current due to hopping conduction (Koyama et al., 1997) and/or an increase in a channel series-resistance (Eriguchi et al., 2009b) due to coulomb scattering by the trapped carrier.In general, it is difficult to identify those local defects by conventional analysis techniques such as TEM observation, in particular, to quantify the density of these defects.In the next section, by using novel analysis techniques, we quantify the density of the defects and discuss the electrical characteristics of these defects.
Since the observed defect structures are indeed derived from our MD simulations, we have to pay careful attention to the effects of the simulation procedure on our findings.In the present case, the number of defect sites (~ the density) might be dependent on both the simulation cell size and the number of Ar impacts.Conventional MD simulations for plasma etch processes employ; (1) periodic boundary condition and (2) the rigid fixed Si atoms at the bottom plane of the cell.Both technical restrictions may make the defect generation mechanism being dependent on the cell-size.It was reported (Abrams & Graves, 2000;Graves & Humbird, 2002) that the formation of amorphous layer is time-dependent, i.e., the number of ion impacts determines whether the damaged-layer formation process is in a growth or a saturation phases.Previous reports showed that the thickness of amorphous layer by Ar ion impacts became in a steady state after 1.5-monolayer (ML) impact (Graves & Humbird, 2002) and also that the reaction layer thickness by F ion impacts, after 10 MLs (Abrams & Graves, 2000).
Figure 7 shows at first the cell-size dependence of Si ion penetration depth.Si was selfimplanted repeatedly with the energy of 150 eV into the initial simulation cells of various sizes.Due to a stopping process (Lindhard et al., 1963;Wilson et al., 1977), the injected Si atom loses the energy by a series of collisions and finally comes to rest in Si substrate.After 1000 impacts of Si atoms, the profiles of penetration depth ("projection range") were determined and compared for various cell sizes.As shown, one can see a small difference among the peak positions, i.e., the ion penetration depth is almost independent on the cell size.The result may suggest that one can use a smaller cell-size for plasma-etch MD simulation to reduce a "simulation cost" for estimating the ion penetration depth.However, as mentioned later, for investigating the density of local defect site, a smaller cell-size statistically contains a smaller number of local defect sites under the same number of ion impacts.Hence, although the estimation of ion penetration depth can be done by using a smaller cell size, a larger number of impacts should be conducted to investigate an overall feature of local defect site structures.In Sec. 4, we compare the number of defect sites in Fig. Figure 8 shows time evolutions of the number of displaced Si atoms (n Si ) determined from the algorithm based on the Lindemann radius, for the case of the present cell size of 6 × 6 × 9.
As seen, at the initial stage, the counted n Si increases with fluence until ~ 100 impacts, and then saturates after approximately 500 impacts for both E ion cases.The 500-impact corresponds to ~ 7-ML injections in the case of the present (100) surface (6 × 6).Compared to previous reports (Abrams & Graves, 2000;Graves & Humbird, 2002), this saturation value is in the reasonable range.Thus, it can be concluded that by considering the saturation phenomena, the number of impacts should be properly optimized in advance when performing plasma-etch MD simulations.(In Fig. 4, we have shown the results by 500 impacts for discussions on the defect sites.)

Experimental setup, test sample structure, and evaluation techniques
To verify the above MD simulation results, we carried out plasma treatments of Si wafers by using two plasma reactors.N-type (100) Si wafer with 0.02 cm was exposed to an inductively coupled plasma (ICP) reactor (See Fig. 2) and a DC plasma reactor.In the ICP reactor (Eriguchi et al., 2008a), the plasma was generated by a source power supply unit.The applied power was 300 W. The plasma density can be controlled by changing this source power.On the other, a bias power applied to the wafer stage determines the energy of ion incident on the wafer surface.In the present study, the bias power was varied from 50 to 400 W. The frequencies of source and bias power were 13.56 MHz for both.Ar was used and the pressure was 20 mTorr.Unless otherwise specified, the process time was 30 s.By using an oscilloscope, we determined self dc bias (V dc <0) and plasma potential (V p ), resulting in an average ion energy E ion (eV) (= e(V p -V dc )) ranging from 56 to 411 eV.From a Langmuir probe measurement, the electron density and the electron temperature were estimated to be 3.3  10 11 cm -3 and 2.6 eV, respectively.Since Ar plasma is electropositive, the ion density is approximately equal to the electron density 3.3  10 11 cm -3 , giving the flux of ions ( ion ) of 1.2  10 17 cm -2 s -1 .Note that this ICP configuration results in a constant  ion to the wafer for all bias power conditions in the present experiments.
In SE analysis, the damaged layer is assumed to consist of two regions, i.e., the surface and interfacial layers (abbreviated as SL and IL, respectively).The SL is composed of SiO 2 , as a result of oxidation of heavily damaged regions by exposure to an air as well as the presence of knock-on oxygen from the surface oxide layer.(This is confirmed from the MD simulation results.)The IL is partially oxidized or disordered Si, which is identified by SE as a mixed layer consisting of crystalline Si and SiO 2 phases.Thus, an optical model assuming four layers (ambient, surface SiO 2 layer, interfacial layer, and Si substrate) was employed (Eriguchi et al., 2008a;Matsuda et al., 2010).In this analysis, the thicknesses of the surface (SL: d SL ) and interfacial [IL (SiO 2 + crystalline-Si): d IL ] layers and the composition (f Si : component of crystalline-Si) were determined.
PRS is one of modulation spectroscopic techniques (Aspnes, 1973;Pollak & Shen, 1990), where the surface of the sample is modulated by a laser beam.The reflectance change by using a probe beam was monitored.In the present PRS, the amplitude of reflectance change (R/R) for the damaged sample was measured.A decrease in R/R means the defect generation in the surface region of Si substrate (< 10 nm) (Murtagh et al., 1997;Wada et al., 2000).Details for the basics of PRS analysis and experimental procedures were described elsewhere (Eriguchi & Ono, 2008).From the laser-power dependence of spectra, the areal defect site density (N dam (cm -2 )) can be estimated (Eriguchi & Ono, 2008;Nakakubo et al., 2010a).
For Capacitance -Voltage (C-V) analysis (Sze, 1981), we used a mercury probe system.The bias frequency was 1 MHz.To estimate the local defect site density, we investigated 1/C 2 -V curves of the damage samples (Eriguchi et al., 2008a).Details are mentioned later.

Thickness of the damaged-layer
Figure 9 shows the surface and interfacial thicknesses (d SL and d IL ) identified by SE with an optimized four-layer model.The samples were treated by the ICP system by changing an applied bias power.The SE analysis assigns an increase in d IL with the average ion energy E ion , while d SL does not exhibit a clear increase.This may be due to surface sputtering mechanism.Rutherford backscattering spectrometry (not shown here) identifies the presence of stoichiometric SiO 2 region in the SL, and the IL consisting of SiO 2 and c-Si phases (Eriguchi et al., 2008a).Figure 10 shows TEM observation results for various bias powers.Although it is difficult for the case of higher E ion to assign the details of the damaged structures, one can observe the presence of interfacial layer below the surface layer.The estimated thickness was found to be consistent with the SE data (Eriguchi et al., 2008a;Matsuda et al., 2010).The roughness in the interfacial layer is confirmed to increase, in particular, for the 400-W case.The increase in roughness may agree with MD simulation results in Fig. 4. Therefore, it is concluded that the presence of both the surface and interfacial layers should be taken into account when evaluating the damaged-layer thickness by SE and/or TEM.Note that, from these TEM observation results, one can see no local defect site which was assigned by MD simulations.To identify these local defect sites, other novel techniques are required.In the subsection 4.2.3, we provide the results by these techniques.From a Langmuir probe measurement, the electron temperature and the electron density were estimated to be 3.0 eV and ~ 10 9 cm -3 , respectively, giving  ion of ~ 2 × 10 14 cm -2 s -1 in these experiments.Thus, the total dosage (fluence) is approximately 2 × 10 15 cm -2 for 10 s.Based on the results by the MD simulations in Fig. 8, 500-impact in the present cell size corresponds to a fluence of ~ 5 × 10 15 cm -2 .
Although the E ion in the DC plasma processes was not measured precisely (only deduced from applied DC bias voltages), we can speculate that the saturating behaviour of d IL in Fig.
11 corresponds to the results in Fig. 8.In other words, once  ion is properly determined by plasma diagnostics, the MD simulation can predict the time evolution of damaged-layer formation in practical plasma etching process.
In general, the number of ion impacts combined with the cell size is a more practical and useful measure rather than MLs for MD simulations, because the density of local defect site is a key parameter determining the effects of PID on MOSFET performance degradation.
Figure 12 provides the relationship among the number of ion impacts,  ion , and t pro .Figure 12 guides how many ion impacts are necessary in MD simulations to predict correctly the local defect site generation during practical plasma etching.For a given  ion , the number of impacts in a MD simulation should be increased with an increase in t pro .For example, in the case of  ion = 10 15 cm -2 s -1 and t pro = 10 2 s, approximately a 10000-impact is needed in the MD evolution of damaged-layer formation as in Fig. 8, one can expect that a smaller size is better (more efficient).However, as discussed in the next, in terms of local defect site density, one has to increase a cell size as much to understand accurate pictures and overall features of the defect structures for the precise prediction of MOSFET performance degradation.

Density of defect sites
So far, PID has been evaluated by a wide variety of techniques (Awadelkarim et al., 1994;Egashira et al., 1998;Kokura et al., 2005;Mu et al., 1986;Oehrlein et al., 1988;Yabumoto et al., 1981).However, there have been not so many reports quantifying the density of created local defects by PID.In this study, we employed two different quantification techniques, photoreflectance spectroscopy (PRS) and capacitance-voltage (C-V) measurement.Details are presented in other literatures (Eriguchi et al., 2008a;Eriguchi & Ono, 2008).
Figure 13 shows the estimated local defect site density from photoreflectance spectra of the test structures damaged by the ICP system (closed squares, on the left axis).By using a modified PRS model for estimation of the density of defect sites (Eriguchi et al., 2008b;Eriguchi & Ono, 2008), one can determines the areal defect site density (N dam ) as a function of E ion .From this figure, one can observe N dam of the order of 10 12 cm -2 for the present plasma conditions.
Figure 14 shows examples of 1/C 2 -V analysis results. Figure 14 on the right illustrates the basics of this C-V technique, where w and q are the depletion layer width and the elementary charge, respectively.By using a mercury probe system, a bias voltage applied to Si substrate was swept, and the capacitance was measured.We performed this C-V measurement for both the control (without plasma exposure) and the damaged samples.
When the value 1/C 2 is plotted along the bias voltage (V b ) for a fresh Si substrate (the control), the slope of 1/C 2 -V b becomes constant since the slope corresponds to the impurity (dopant) concentration n D (Goodman, 1963;Sze & Ng, 2007).For the plasma-damaged sample, one can see the distortion of 1/C 2 -V b curves in the inversion region as seen on the left figure.In this experiment, we used n-type Si substrate, thus, the negative bias voltage (V b < 0)) corresponds to the inversion layer formation region.The presence of the local defect site (carrier trapping site) causes doping loss (a decrease in n D ) by intermixing with subsequently-implanted ions (Kokura et al., 2005).Therefore, the distortion (a decrease in the slope of 1/C 2 -V b plot) indicates a defect site creation in the Si substrate.On the right in Fig. 14, the schematic view of these defect sites in the inversion scheme is also shown.From a change of the slope, we can estimate the volume density of the defect site (n dam cm -3 ) by assuming that the effect impurity concentration equals to (n D + n dam ) (Eriguchi et al., 2008a;Nakakubo et al., 2010b).The calculated n dam is plotted on the right axis in Fig. 13 (open circles).The n dam on the order of 10 18 -10 19 cm -3 is assigned.Since the thickness of d IL containing n dam is estimated to be a few nanometers as seen in Fig. 9, the areal density calculated from the E ion -dependence of n dam is consistent with N dam b y P R S .( E x a c t l y speaking, the depth profile of n dam should be taken into account, though.)One of the other important findings in Figs. 13 and 14 is the fact that the identified local defect sites are electrically active and may induce the MOSFET performance degradation.The defect site structures observed in Fig. 6 are fatal and should be investigated with carefully attention.
The estimated range of n dam or N dam gives an important interpretation to the MD simulations for PID as follows.The areal density of defect site ranging from 10 12 to 10 13 cm -2 in practical samples is equivalent to the number of defect site of 0.1 to 1 in the present 6 × 6 simulation cell (~ 10 nm 2 ), although it depends on t pro and plasma parameters.In Fig. 4, the observed local defect sites are indeed a few in the number.This number corresponds to approximately 10 13 cm -2 in practical samples, which is in consistent with the experimental results in Fig. 13.If one uses a smaller simulation size such as 3 × 3 cell to reduce the simulation cost, one can not find any defect sites statistically.In other words, a simulation scheme using a smaller size (for reducing the calculation time) may bring an erroneous conclusion (no observation of local defect sites).Regarding PID by MD, an optimization of the cell size in accordance with the plasma etching parameter such as  ion is quite important.) Fig. 13.Estimated defect site densities as a function of (V p -V dc ) by two different analysis techniques; PRS and CV.From PRS, the areal density was determined, while, from CV, the volume density.

Defect site
Hg F

Prediction framework for MOSFET performance degradation by MD
Finally we discuss the effects of PID observed in the MD simulations and experimental data on MOSFET performance degradation.From the findings in the above, we can summarize the following key issues: 1.The damaged layer is found to consist of two layers, the surface and the interfacial layers.By considering this oxidation process, this thickness of Si loss (Si recess depth d R ) can be predicted by MD simulations.2. Underneath the interfacial layer, local defect sites are present.The local defect structures can be assigned from MD simulations.
3. The local defect sites (observed in the MD simulation) are confirmed to be electrically active from the experimental data.
As proposed by Eriguchi et al.(Eriguchi et al., 2009a;Eriguchi et al., 2009b), Si recess depth d R and the local defect sites degrades MOSFET-operation parameters such as V th and I d , where I d is drain current determining the operation speed (Sze, 1981).These mechanisms are analytically expressed as, th R g where V th and 0 d I are the shift of threshold voltage and the drain current of a fresh device, respectively.A and B are the process-and device-structure-dependent parameters which can be determined from Technology Computer-Aided-Design (TCAD) simulations (Eriguchi et al., 2008a).A prediction of MOSFET performance from process parameters such as E ion was demonstrated by using experimental relationship between E ion and d R (or n dam ).Moreover, from the present studies, one presumes that d R and n dam can be determined from MD simulations.At present, the statistical distribution functions for the local defect structures by PID are not clarified yet.A future work is hoped to assign the defect generation mechanisms and the statistical distribution functions with a help of MD simulations.Since the size of MOSFET is shrinking aggressively, a prediction framework of future device design can be organized by an atomistic technique such as MD simulations.

Conclusion
We applied classical MD simulations to investigate plasma-etch damage mechanisms.The simulated structures were found to consist of two layers, the surface and the interfacial layers.Due to oxidation by an air exposure, these two layers were identified in practice as SiO 2 and a mixed layer consisting of crystalline Si and SiO 2 phases, respectively.Underneath the interfacial layer, we assigned local defect sites, and the structures were confirmed to include typical Si interstitials.From the experiments, these sites were found to be electrically active.Combined with plasma diagnostics and quantitative analysis techniques of the local defect site density, the number of required ion impacts and the cell size for MD simulations were optimized for PID.Finally, a prediction framework for MOSFET design was discussed.An optimized MD simulation will be a promising candidate for predicting MOSFET performance degradation by PID.

Acknowledgment
The author greatly thanks Dr. H.

Fig. 1 .
Fig. 1.Scaling trend of feature sizes in a metal-oxide-semiconductor field-effect transistor (MOSFET) in an ultra-large-scale integrated circuit.

Fig. 2 .
Fig. 2. Illustrations of plasma process reactor and plasma etch damage.

Fig. 3 .
Fig. 3. Mechanism of plasma-etch damage to Si substrate and "Si loss" formation.Energetic ion bombardment creates a damaged layer underneath the Si surface.As shown on the right, localized defect sites are formed.A portion of the damaged layer with defect sites is stripped off during a subsequent wet-etch process, resulting in Si loss.(For details, see the text.)


are parameters for the j-i-k triplet.ij jik a and ik jik a are the cut-off distances in the three-body configuration.For the "ideal"

Fig. 4 .Fig. 5 .
Fig. 4. SiO 2 /Si structures after 500 impacts of Ar with different incident energies.The injected Ar ions are omitted from the cells for easy comparison.Local defect sites are highlighted.

Fig. 4
to clarify the structures of these defects formed by PID.Figures 6 present some of typical structures -we chose three representative structures.On the left are shown the views of the defects on the (100) plane (along [100]).In the middle, the bird's views to the respective defects (Si atoms) are shown.Interstitial Si atoms are highlighted in the views.

Fig. 6 .
Fig. 6.Typical structures of Si-interstitial defects created by energetic ion bombardments.On the left are the views along [100] and the bird's-view are shown in the middle.On the right, typical structures assigned by previous reports are shown.(See also Fig. 4.)

Fig. 7 .
Figure7shows at first the cell-size dependence of Si ion penetration depth.Si was selfimplanted repeatedly with the energy of 150 eV into the initial simulation cells of various sizes.Due to a stopping process(Lindhard et al., 1963;Wilson et al., 1977), the injected Si atom loses the energy by a series of collisions and finally comes to rest in Si substrate.After 1000 impacts of Si atoms, the profiles of penetration depth ("projection range") were determined and compared for various cell sizes.As shown, one can see a small difference among the peak positions, i.e., the ion penetration depth is almost independent on the cell size.The result may suggest that one can use a smaller cell-size for plasma-etch MD simulation to reduce a "simulation cost" for estimating the ion penetration depth.However, as mentioned later, for investigating the density of local defect site, a smaller cell-size statistically contains a smaller number of local defect sites under the same number of ion impacts.Hence, although the estimation of ion penetration depth can be done by using a smaller cell size, a larger number of impacts should be conducted to investigate an overall feature of local defect site structures.In Sec. 4, we compare the number of defect sites in Fig.4with that obtained by the experiments.

Fig. 8 .
Fig. 8. Time evolutions of the number of displaced Si atoms.

Fig. 9 .
Fig. 9. Thicknesses of surface and interfacial layers obtained by spectroscopic ellipsometry with a four-layer optical model.Total optical thickness is also shown (closed circles).
Fig. 10.TEM observation results for the Si wafer surface damaged by various bias powers.

Fig. 11 .Fig. 12 .
Fig. 11.Thicknesses of surface and interfacial layers as a function of process time.A DC plasma reactor was used.

Fig. 14 .
Fig. 14.Illustrations of an example for 1/C 2 -V plots and the energy band diagram during the CV measurement.
Ohta for his great support of the MD simulation in this work.Acknowledgements are also given to Mr. Y.Nakakubo, Mr. A. Matsuda, Dr. Y. Takao, and Prof. K. Ono at Kyoto University, and Drs.M. Yoshimaru, H. Hayashi, S. Hayashi, H. Kokura, T. Tatsumi, and S. Kuwabara at STARC (Semiconductor Technology Academic Research Center) for their helpful discussions.This work was financially supported in part by STARC and a Grant-in-Aid for Scientific Research (B) from the Japan Society for the Promotion of Science.