An Atomic Scale Model of Multilayer Surface Reactions and the Feature Profile Evolution during Plasma Etching

Abstract

A phenomenological model has been developed to simulate the feature profile evolution for nanometer-scale control of the profile and critical dimension during plasma etching. Attention was focused on the feature profile evolution of infinitely long trenches etched in Si with chlorine chemistries. The model takes into account the transport of ions and neutrals in microstructures, multilayer surface reactions through ion-enhanced etching, and the resulting feature profile evolution, where the transport is analyzed by a two-dimensional particle simulation based on successively injected single-particle trajectories with three velocity components. To incorporate an atomistic picture into the model, the substrates are taken to consist of a large number of small cells or lattices in the entire computational domain of interest, and the evolving interfaces are modeled by using the cell removal method; the Si atoms are allocated in the respective two-dimensional square lattices of atomic scale. Moreover, the Monte Carlo calculation is employed for the trajectory of incident Cl+ ions that penetrate into substrates. The present model has a prominent feature to phenomenologically simulate the multilayer surface reaction, the surface roughness, and also the feature profile evolution during etching. The etching of planar Si substrates was simulated for a test of validity of the present model, showing the structure of surface reaction layers, the distribution of Cl atoms therein, and the surface roughness that depend on incident neutral-to-ion flux ratio and ion energy. The etch yield as a function of neutral-to-ion flux ratio for different ion energies gave a similar tendency to the known experimental data, indicating that the present model properly reflects synergistic effects between neutral reactants and energetic ions in the ion-enhanced etching. The feature profile evolution during etching was then simulated for sub-100 nm line-and-space patterns of Si, exhibiting the reactive ion etching (RIE) lag that occurs depending on neutral-to-ion flux ratio and ion energy. The degree of RIE lag was found to be more significant at higher flux ratios and higher energies, being associated with the difference in surface chlorination at the feature bottom; in effect, for narrow pattern features of the order of sub-100 nm, the bottom surfaces tend to starve for neutral reactants owing to severe effects of the geometrical shadowing.

Surface roughening and rippling during plasma etching of silicon: Numerical investigations and a comparison with experiments

“…The ASCeM-3D methodology has been described in part in our previous papers, 46,47 together with the surface chemistry and kinetics concerned, which is basically an extension of the ASCeM-2D. [40][41][42][43][44][45] In more detail, the simulation domain is a square W ¼ 50 nm on a side with a depth of 630 nm, consisting of a number of small cubic cells of atomic size L ¼ q Si À1/3 ¼ 2.7 Å (185 Â 185 Â 2333 % 8 Â 10 7 cells in total), where q Si ¼ 5.0 Â 10 22 cm À3 is the atomic density of Si substrates. The substrates initially occupy a lower 620-nm-deep layer therein (or the substrate surfaces are initially flat, being located 10 nm downward from the top of the domain).…”

“…The particles are assumed to move straight from the top of the simulation domain onto substrate surfaces and then into microstructures thereon, without collisions with other particles in vacuum, where their transport is calculated every movement of step L, taking into account geometrical shadowing effects of the structure; then, the particles are assumed to reach the surface if there is a Si atom in any of the 26 cells neighboring the cell which the particle concerned is in. The local surface normal and thus the local angle h of incidence on microstructural feature surfaces is calculated by using the extended four-point technique 40,42,46,48 for 5 Â 5 Â 5 neighboring cells (125 cells in total) at around the substrate surface cell that the particle reaches, as shown in Fig. 1; this is one of the key procedures in the cell-based simulations such as ASCeM, because the surface chemistry and kinetics calculations rely crucially on the local incidence angle h, as mentioned below.…”

“…21 We have developed a semi-empirical, atomic-scale cellular model (ASCeM) for simulating plasma-surface interactions and the resulting feature profile evolution during plasma etching of Si, based on the Monte Carlo algorithm with the cell removal method for interface evolution; [40][41][42][43][44][45][46][47] in effect, a two-dimensional ASCeM model (ASCeM-2D) reproduced the evolution of nanometer-scale profile anomalies on sidewalls and bottom surfaces of the feature, together with pattern-size or aspect-ratio dependences of them, during Si trench etching in Cl 2 and Cl 2 /O 2 plasmas. [40][41][42][43][44][45] However, the ASCeM-2D was found to be insufficient to reproduce the nanoscale surface roughness formed during plasma etching, probably because the formation and evolution of roughness is 3D as well as stochastic. 24,28 Therefore, we have recently developed a 3D ASCeM model (ASCeM-3D) to simulate the evolution of 3D feature profiles, including nanoscale surface features such as roughness, during Si etching in Cl-based plasmas.…”

Atomic-scale cellular model and profile simulation of poly-Si gate etching in high-density chlorine-based plasmas: Effects of passivation layer formation on evolution of feature profiles

“…The substrates are taken to consist of cells or lattices of atomic size, and the evolving interfaces are modeled by the so-called cell removal method, as in our previous study. 17 The present atomic-scale cellular model, which is a phenomenological model at an intermediate between the MD simulation and continuum models, gives a nanometer-scale representation of the feature profile evolution during etching along with reaction and passivation layers on feature surfaces, their chemical constituents, and surface roughness. Figure 1͑a͒ illustrates the simulation domain with the coordinate system ͑x , z͒ presently employed, where Cl + ions, Cl neutrals, O neutrals, and etch byproducts of silicon chlorides SiCl x and oxychlorides SiCl x O y are taken to be injected from the plasma into microstructural features on substrates; moreover, etch products such as SiCl x and SiCl x O y are desorbed or sputtered from the feature surfaces during etching.…”

“…The model is based on our previous atomic-scale model for the ion-enhanced etching, 16,17 taking into account not only Cl + ions and Cl neutrals but also O neutrals and etch products/byproducts of SiCl x and SiCl x O y in microstructural features. The simulation domain is taken to consist of a number of square cells or lattices of atomic size, and the evolving interfaces are represented by removing Si atoms from and/or allocating them at the cells concerned.…”