3D Simulation of Ion Enhanced Chemical Etching with VICTORY Process

Introduction

VICTORY Process is a tool for 3D simulation of the semiconductor industry’s technological processes. It allows stable and accurate modeling of the changes in a structure’s 3D geometry within etching reactors under various conditions. VICTORY Process achieves this by combining a powerful and robust hard-coded numerical engine, based on the Level Set method, with a flexible Open Modeling library which is extendable by users to suit their specific requirements.

The Open Modeling library, supplied with VICTORY Process, includes several predefined models one of which is the model for Ion Enhanced Chemical Etching (IECE model). This model assumes that the ambient within the plasma etching reactor consists of two distinct types of species:

  • Neutrals – uncharged thermal particles which chemically react with the surface.
  • Ions – charged, accelerated, non-reacting particles which facilitate reactions of the surface material with the neutrals by removing reaction by-products from the surface and hence exposing it for chemical reactions.

The IECE model does not take into account physical sputtering of substrate atoms by the ions. To be removed from the surface, a substrate atom has to react with the neutrals first.

In this paper we describe the model’s properties and assumptions on the basis of ion-assisted Si etching with F-radicals (neutrals). The model can be applied to any type of ion enhanced chemical etching as long as the enhancement is predominantly due to ions cleaning the substrate surface by removing the reaction by-products.

Note that VICTORY Process conducts the simulation on the feature-scale only. It assumes that reactor-scale conditions are already known and are constant within the feature-scale simulation domain. VICTORY Process does not simulate the conditions within the reactor-scale domain.

 

The Fundamental Assumptions of the IECE Model

Figure 1 illustrates the processes by which the substrate atoms are removed from the surface.

  • The neutrals (F-radicals) chemically attach themselves to dangling bonds of the silicon surface.
  • We assume that they react immediately with Si atoms forming SiFx molecules, where x is the number of fluorine atoms contained within one SiFx molecule.
  • Newly formed SiFx molecules stay at the surface. They cover Si bonds and prevent further chemical reactions.
  • The SiFx molecules can be removed from the surface by one of the following two physical processes:
    • Natural desorption of the SiFx molecules from the surface
    • When ion flux is present – sputtering of the SiFx molecules by ions
  • Once an SiFx molecule leaves the surface, the Si bonds are exposed again and can ‘catch’ fluorine radicals from the ambient.

Figure 1. Illustration of the particle flow for ion enhanced chemical etching of silicon by F atoms.

 

The IECE model considers the steady state, when the number of Si atoms reacting with F per unit time is equal to number of Si atoms leaving the substrate due to desor the ption and ion sputtering.

Note that you may count a Si atom as ‘etched’ from the surface either once it becomes a part of SiFx molecule or once this molecule leaves the surface. The rate of both processes is equal in the steady state, so the choice will not affect the resulting model equations. In the following explanation we have chosen the second option. Atoms of Si counted as removed from the substrate (etched) once they leave the surface as a part of an SiFx molecule

 

The Model Equations

The speed of the chemical reaction (and ultimately, the etch rate) is influenced by the following parameters:

  • the reactant flux towards surface or in other words, the amount of reactant arriving to the unit surface per unit time.
  • θ (dimensionless) the fraction of the surface covered by reaction’s by-products. Its value is within the range 0≤θ≤1 where

– θ=0 means that there are no SiFx molecules on the surface.

– θ=1 means that the surface is completely covered with SiFx molecules, so no surface chemical reaction can take place at all.

  • S0 (dimensionless) the probability of the fluoride atom to be captured by a Si atom at the clean (not covered by reaction’s by-products) (θ=0), surface. Hence the probability for capturing at a partially-covered surface S can be calculated as:

    (1)

  • b (dimensionless) an average number of F atoms consumed by a single Si atom. That is if, say, reaction by-products consist of 90% of SiF2 and 10% of SiF4 we have b = 0.9 . 2 + 0.1 . 4 = 2.2 .
  • the maximum desorption rate which is the number of reaction by-product molecules leaving the unit of fully covered (θ=1) surface per unit time. Consequently, the desorption rate from partially-covered surface can be expressed as:

(2)

Additionally there are parameters to characterize the influence of bombardment by ions on etching rate:

  • the ion flux towards the surface, or in other words, the amount of ions arriving to the unit surface per unit time.
  • β(Ei)(dimensionless) the ion sputtering efficiency (depends on ion energy), that is the probability that an ion, which hits a reaction by-product molecule, removes it from the substrate’s surface.

In steady state the amount of newly-formed reaction by-product atoms at unit surface per unit time is equal to the amount of by-products leaving the surface due to natural desorption and ion bombardment:

(3)

Note the coefficient b on the left side of the equation, which reflects the fact that several reactant atoms are required to form the single by-product molecule.

From (3) we can find the expression for steady-state surface coverage:

(4)

Note, that surface coverage is a local property, as the amount of reactant and ions arriving at particular location depends on the surface’s topography.

The etch rate of the Si substrate is equal to the rate with which Si atoms leave the surface as a part of the reaction by-product molecules divided by atomic density of ρSi (number of atoms per unit volume, ). In steady state the reaction and desorption rates are equal so, using (3) and (4), we can write the expression for the etching rate:

(5)

where Rsi is the etch rate (material removal rate) of silicon . (4) and (5) determine the local etch rate at the arbitrary point of the Si surface.

 

Implementation in VICTORY Process

For calibration purposes the VICTORY Process implementation of (4) and (5) uses normalized fluxes (all local fluxes are measured as fraction of flux of neutrals at the unshaded plane surface j ) and ideal etching rates:

(6)

(7)

With :

= – normalized flux of neutrals (F-radicals) towards a point of the surface

– normalized (relative to ) flux of ions towards a point of the surface

R = – ‘ideal’ etching rate of Si by the neutrals at the surface, corresponding to the case when reactions by-products are instantly removed from the surface.

(8)


–‘ideal’ etching rate of reaction by-products by the ion flux at the surface. It corresponds to the fully covered plane surface i.e. new reaction by-products immediately replace those just etched away – divided by the ratio between the plane ion and neutral fluxes (see below).

– ratio between ion flux to the neutral flux at the plane surface. It is introduced for technical reasons, as the numerical engine of VICTORY Process calculates ion flux as a fraction of the neutral flux at the plane.

(9)

– ratio of the SiFx molecules desorption rate to the rate of their formation on the plane.

Finally, we use the following empirical relationship for sputtering efficiency β(Ei) [1][2][3] :


and rewrite (8) in terms of the reference ideal ion etch rate:

(10)


where

Ei – the effective ion energy (eV)

Eth – the threshold ion energy (eV), below which no ion enhancement occurs.

Eref – the reference ion energy for which is specified (eV), Eref > Eth .

– the ion enhancement rate for the reference energy

 

Equations (6), (7), (9) and (10) are the actual implementation of the IECE model etching rate calculation in the VICTORY Process Open Modeling library function plasmaetch_iece_2part.

The model function depends on

The values of are calculated by the numerical engine of VICTORY Process on the basis of the geometrical configuration at the surface point where the IECE model function is evaluated. All the other parameters are set in the input deck.

 

Running the IECE Model Within VICTORY Process

VICTORY Process performs etching simulation on the feature scale level only. This means that several particle properties which must be fed as an input into the feature scale models of VICTORY Process should be obtained by one of the following methods:

  • By reactor-scale simulation, in order to find the conditions near the surface
  • By calibration, using a series of experimental measurements. Silvaco’s tool Virtual Wafer Fab (VWF) can be used to perform those calibrations.

On the basis of this information, the feature scale simulation produces an accurate three-dimensional topographical evolution of the wafer section being simulated.

To perform a simulation of ion enhanced chemical etching (as with any general etching process) you should setup the model by defining the following in your input deck:

  • The fluxes for all particles (reactants) participating in the etching step by using a separate FLUX statement for each particle. For the IECE model two FLUX statements are required, one FLUX statement for ions and one for neutrals
  • The surface reaction model for the ion enhanced chemical etching by using the REACTION statement. By means of the REACTION statement you also set the values for all model parameters of the surface reaction model which are not material specific
  • The topography model, which combines fluxes with the surface reaction model. The topography model describes the general way how reactants affect the surface. This is performed by the TOPOGRAPHYMODEL statement
  • How each species affects each exposed material. You do this by using ETCHDEPOPROPERTIES statements. You can also view the ETCHDEPOPROPERTIES statements as means to set the material specific model parameters of the surface reaction model. You have to use one ETCHDEPOPROPERTIES statement per species. This means that two statements are required for the IECE model
  • Finally, you should use the defined model in the ETCH statement in order to perform the actual process step simulation

Example

Let us use the IECE etching model to etch the structure shown in Figure 2. We assume that conditions in the reactor chamber are such, that for silicon:

= 17.0 µm/min

= 1.0

= 90.0 µm/min with Eref = 44 eV

= 0.2 for all materials

= 0.026

and the mask is not etched at all.


Figure 2. 3D shape of the structure before etching.

 

We want to simulate an etching process step for 1.2 seconds (0.02 min). It can be achieved by means of the deck shown in Decksequence 1.

Decksequence 1

 

We want to simulate etching of the structure shown in Figure 2 as follows:

  • etching without ion acceleration (dcVoltage = 0)
  • etching with ion acceleration where the effective ion energy is 44 eV (dcVoltage = 44).

For the above mentioned reactor conditions, the steady state surface coverage according to (6) on a plane unshaded silicon surface is:

θss (Eeff = 0) = = 0.500

θss (Eeff = 44) = = 0.468

and the effective etch rate on a plane silicon surface according to (7) is:

RSi(Eeff = 0) = 17 . 0.500 = 8.500 µm/min

RSi(Eeff = 44) = 17 . 0.532 = 9.044 µm/min .

Therefore for a plane silicon wafer for the etching time mentioned above, the etch depth is:

dSi(Eeff = 0) = 8.500 . 0.02 = 0.170 µm

dSi(Eeff = 44) = 9.044 . 0.02 = 0.181 µm .

Due to the mask which blocks parts of the incoming fluxes the etch depth for the structure shown in Figure 2 is slightly less than this. You have to keep in mind that the flux density of both particle fluxes is reduced by the mask. Due to the modified fluxes the local surface coverage is also changed.

Figure 3 shows a comparison of the etching profiles obtained by the IECE model within a cross section at the domain boundary (side where the mask is open). The dotted lines in Figure 3 indicate how deep the etching would proceed if no mask were put on top of the silicon layer. The black dotted line corresponds to the case without ion acceleration while the red dotted line corresponds to the case with ion acceleration.


Figure 3. Etch profile obtained by the IECE model for different ion acceleration energies. Dotted lines indicate the etching depth for the plane wafer.

For the low sticking efficiency of the neutrals as used in this example, the IECE model is close to an ‘isotropic’ etching model at least when no ion acceleration is taken into account. By increasing the effective energy of the ions, the aspect ratio of the etching profile is increased. This is due to the fact that reaction-accelerating ion flux is:

  • more focused than the neutral flux
  • has sticking efficiency 1.0, so ions ‘bouncing’ from the surface cannot contribute to sputtering again somewhere else

As a result, the ion flux is concentrated at unshaded / partly shaded areas of the structure (i.e. trench bottom under the mask opening), and leads to an increased etching rate in this region.

 

Conclusions

VICTORY Process allows simulation of complex etching processes by extending the Open Modeling library. In this paper we have shown how to derive and setup the Ion Enhanced Chemical Etching (IECE) model, for which a model function is supplied with VICTORY Process. supplied with VICTORY Process. Moreover it was demonstrated that VICTORY Process accurately takes into account shading effects, caused by masks, and ion enhancement, caused by removal of reaction’s by-product from the exposed surface by ion flux.

 

References

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