Simulating Redeposition During Etch Using a Monte Carlo Plasma Etch Model



The shrinking critical dimensions of modern technology place a heavy requirement on optimizing the etching of narrow mask opening. In addition the aspect ratio of etches has been increased requiring deeper etches along with the small CDs. The simulation of these process requires more advanced techniques than the directional rate-based etching found in the current versions of Elite. A more complete treatment involving calculation of the plasma distribution is required.

The new Monte Carlo etch module is implemented into ATHENA/Elite. The main application of the module is simulation of plasma or ion assisted etching. The module can take into account the redeposition of the polymer material generated as a mixture of incoming ions with etched (sputtered) molecules of substrate material. In addition, the module has interface to the C interpreter which allows simulation of several other processes like wet etch and deposition, ion milling and sputtering deposition of various materials.

Simulation of Incoming Ions and Neutrals

Direct modeling of the plasma sheath is not included into this release and will be added later. It is assumed that ions and neutrals fluxes leaving plasma sheath are represented by bimaxwell velocity distribution function along the direction determined by user specified incident angle:


where uII is the ion velocity component parallel to the incident direction, u^ is the ion velocity component perpendicular to the incident direction, I ion (or neutral) current density, TII is the dimensionless parallel temperature and T^ is the dimensionless lateral temperature.


Calculation of Ion and Neutral Fluxes

During each time step the simulation consists of the three stages:

1. calculation of ion, neutral, and polymer fluxes

2. calculation of etch, polymer ejection and redeposition rates

3. surface movement

On the first stage, the fluxes of incoming and reflected ions and neutrals are calculated on the each segment of the surface. Computation of the ion fluxes is done by tracing of user defined number of particles (Figure 1a). Each particle is generated at the random position on the top of the simulation area with normal and lateral velocities randomly determined from the bimaxwell distribution function (Eq. 1). Then each particle trajectory is traced until the ion is either absorbed by the surface or back scattered out of the simulation area.

Figure 1. Diagram of Plasma Flux algorithm (a) including zoom-in of ion reflection models (b and c).


Interaction of the ion with material surface is governed by two parameters: reflection coefficient Prefl and roughness of the surface R both of which depend on the surface material and the type of ion. Reflection coefficient is the probability of the particle to be reflected from the surface. Roughness determines how the ion is reflected. If R = 0 the reflection is specular (Figure 1b), if R = 1 the reflection is random with uniform angular distribution (Figure 1c). In general case, the velocity of the ion after a collision with a surface segment could be presented as follows:


Where X is random number, and |Vsp| = |Vrelf| = |Vi|

Each absorbed ion contributes to the incoming flux Fi at the surface segment. The following characteristics describe the flux:

  • normalized number of absorbed particles Ni

    where Nabs number of absorbed particles, I is current density for the given type of the incident ion, N traj number of trajectories;

  • normalized normal and tangential velocity components of the absorbed particle before the encounter with the surface:


  • normalized kinetic energy of absorbed particles:


Calculation of Polymer Fluxes

After ion and neutral fluxes are determined, the fluxes of the polymer particles are calculated as follows. As the result of ion flux interaction with the surface segment the polymer particles are generated. The angular distribution of the polymer particles is uniform and the current density of these particles is determined by the etch model (see below) and the sum of the fluxes from incoming ions, neutrals, and from polymer particles ejected from other surface segments. Obviously, the latter flux needs to be pre-calculated.

This flux is computed as follows. First, the configuration (or geometrical)factors are calculated. These factors are the fractions of the number of particles ejected from one segment and absorbed by the other one. These are calculated using the same trajectory tracing algorithms which are described above for the incident ions and neutrals with the only one difference that starting points are not at the upper boundary of the simulation area but at the surface segments. After this an iteration process is initialized. At the first iteration only the incoming ion and neutral fluxes are used for calculation of the ejection rates from each surface segment. Knowing the current densities of ejected particles and the configuration factors the polymer fluxes are calculated. At the subsequent iterations the polymer fluxes calculated at the previous iteration are used to update the etch and ejection rates. The iterations are repeated until etch and ejection rates converge.

Calculation of Rates

The second stage involves calculation of the etching rates as well as ejection and redeposition rates of the polymer particles. During each time step the two processes simultaneously take place on each surface segment. The first is redeposition of the polymer with the rate equal to the polymer flux. The second is etching by incoming ions and neutrals. The combination of these two processes can be treated as deposition of a virtual polymer layer with subsequent etching of the two-layer structure. If the etch rate of polymer by incoming ions and neutrals is less than the polymer deposition rate the result is redeposition of a polymer layer on the surface. If the etch rate of polymer by incoming ions and neutrals is larger than the polymer deposition rate the result is actual etch of the underlying material. In the case of the linear model the etch rate is calculated as:


If EtchRate (polymer) is less than the polymer flux (redeposition rate) the actual etch rate is negative which corresponds to redeposition:


EtchRate(polymer) is larger than polymer flux the actual etch rate is positive:



C-interpreter can be used for introduction of different etch and ejection models.The following parameters are passed to the C-interpreter file and can be used for implementing the models: number of ion types, the four characteristics of ion fluxes for each ion type (Eq 3 - Eq 5), PolymerFlux,and surface material. Returned parameters are EtchRate and EjectionRate.

For example, the wet etching can be simulated by setting the etch rate to a constant positive value depending only on the surface material. In this case the trajectory tracing part of the model is not needed, the number of trajectories can be set to one.

Uniform deposition can be simulated by setting of negative constant etch rate and specifying the redeposited material other than polymer in the etch statement. If the fluxes are not used as in the wet etching simulation the void formed will be eventually filled with the deposited material because inside the C-interpreter there is no way to determine if the current surface segment belongs to the void or not. This obstacle can be overcome by simulating ion fluxes and setting the etch rate equal to zero if the flux on the surface segment is less than some small threshold value.


Surface Movement

A sophisticated string algorithm is used to move all segments according to the rates(positive or negative) calculated at each time step. If the rate is negative the surface moves outside and the area is filled with redeposited material(by default, polymer). If the rate is positive the surface moves inwards and the area is filled with vacuum.



This model can be used to simulate the redeposition of material during etches for:

- deep and narrow trench etches

- via etches

- loading effects

Figure 2 shows the etch of a deep narrow trench in silicon. It shows a comparison between the case with no redeposited material and the case including redeposition. Redeposition can be defined as selective between the silicon, mask and other materials. The redeposited materials continually etched during subsequent timesteps in the etch simulation according to the plasma flux.


Figure 2. Comparison of Silicon trench etch with and without polymer redeposition.


Figure 3 shows the loading effects during etch where the depth of the etch depends on the size of the mask opening. The reflection parameter R can be used to tune this effect.


Figure 3. Demonstration of loading effects using the MC plasma
etch model. No redeposition was considered here.


The physics of the polymer redeposition can be controlled by the user. Figure 4 illustrates the effect of changing the polymer redeposition rate on the final etch profile. The case with no redeposition produces a 'barrel' shaped etch. The polymer acts to passivate the sidewalls of the trench, reducing the lateral etch rate. This leads to trenches with more vertical sidewalls as shown in experimental work such as [1].


Figure 4. User control over the redeposition parameters is important for tuning.
Redeposition converts a 'barrel' shaped trench into a straight sidewall trench.



Figure 5 shows the effect of mask size opening on the etch characteristics when polymer re-deposition is considered. Both the 0.25 micron and 0.5 micron mask openings are processed with the same etch conditions. The polymer redeposition in the 0.25 micron case inhibits the etch rate at the bottom of the etched area. The same redeposition physics applied to a larger mask opening shows a larger etch rate as the polymer is unable to inhibit the plasma in the center of the mask opening.


Figure 5. Etch depth varies with the size of the mask opening as the
redeposited material restricts etching the bottom of the trench.



A new model for Monte Carlo plasma etching has been implemented into ATHENA. It allows physically based modeling of the mechanism of polymer deposition during etches. The application of this model to aid process optimization of deep narrow trench or via etches.



[1] "Simulation Study of Micro-Loading Phenomena in Silicon Dioxide Hole Etching", Misaka and Harafuji, IEEE Electron Devices May 1997.