Simulation of 3D Anisotropic Crystal Etching with VICTORY Process

1. Introduction

Anisotropic crystal etching is the common technique used in Micro Electromechanical systems (MEMS) manufacturing. It uses the property of some single crystal materials, like silicon, of having different etching rates in different crystal directions when the material is etched in special chemicals, such as potassium hydroxide (KOH). Predicting the resulting shape of the structure under such conditions requires full three-dimensional simulation of the evolution of the etched surface.

Silvaco’s 3D process simulator VICTORY Process is perfectly suitable for such task. The numerical engine of VICTORY Process is able to accurately model physical etching with complicated distributions of etch rates over the surface even for initial structures with complex three-dimensional topographies.

2. Defining the Anisotropic Etch Rates

In order to model anisotropic crystal etching you have to specify

• a reference etch rate (in VICTORY Process this applies to the {100} crystal plane) and
• relative rates for the principal crystal axes.

Etching rates for intermediate directions are obtained by interpolation. VICTORY Process uses a linear interpolation as proposed in [1], which maintains C0 continuity across the crystal planes. Note, that there is no need to demand higher order continuity, as it would prevent formation of sharp edges as observed in experiments [2].

When simulating anisotropic crystal etching, VICTORY Process takes into account the silicon crystal’s symmetry. Therefore, it is enough to interpolate the etch rates not for the whole sphere (over all possible etching directions) but for its segment 0≤θ≤/2, 0≤φ≤/4 where θ and φ are elevation and azimuth in polar coordinates. This segment is divided into ‘spherical triangles’. The number of spherical triangles which are used by the interpolation routine, depends on the number of the principal axis for which relative etching rates are provided in the input deck. Within each of those spherical triangles linear interpolation is used. See [1] for more details.

At the moment VICTORY Process allows user to specify relative etch rates either along

• 3 - ({100}, {110}, {111}) or
• 4 - ({100}, {110}, {111}, {311})

principal axis.

Within the input deck, you can provide those relative etch rates by means of the ETCHDEPOPROPERTIES statement. For example,

ETCHDEPOPROPERTIES name=”KOH_3” \
material=”silicon” rate=0.797 \
r100=1.0 r110=1.855 r111=0.0073 \
material=”resist” rate=0.00 \

defines etching properties for anisotropic crystal etching of silicon. The name ‘KOH_3’ is assigned to these properties so that they can be used (referred to) later on in the deck for performing the actual etching simulation. Those etching properties contain:

• the anisotropic etch rates for crystalline silicon
• with a reference etch rate in {100} direction of 0.797 µm/min
• with different rates in two other directions set as Rate{110} = 1.855*Rate{100} and Rate{111} = 0.0073 * Rate{100}
• and the isotropic etch rate for resist of 0.00 µm/min

The statement:

ETCHDEPOPROPERTIES name=”KOH_4” \
material=”silicon” rate=0.797 \
r100=1.0 r110=1.855 r111=0.0073 r311=1.801 \
material=”resist” rate=0.00

defines etching properties which contain

• the anisotropic etch rates for crystalline silicon
• with a reference etch rate in {100} direction of 0.797 µm/min
• with different rates in three other directions set as Rate{110} = 1.855*Rate{100} and Rate{111} = 0.0073 * Rate{100} and additionally for the plane {311} set as Rate{311} = 1.801*Rate{100}
• and the isotropic etch rate for resist of 0.00 µm/min

The input deck name ‘KOH_4’ is assigned to those etching properties so they can be referred to later on in the input deck. Note that you can specify multiple etching properties within a single input deck. They may be valid for different processing conditions, like different temperatures.

The etching rates in the above examples are taken from [3] and correspond to the etching rates for silicon in a 30% solution of KOH at 70°C (note, that in the paper the reference direction is {110}).

It should also be noted here, that whenever you perform an anisotropic crystal etching, obviously, the wafer orientation and the wafer rotation, which you can set by means of the INIT statement by the parameters

• ORIENTATION
• ROT.SUB

are taken into account during etching.

3. Performing the Anisotropic Crystal Etching

Once you have defined the etching properties by means of the ETCHDEPOPROPERTIES statement, you can perform the actual anisotropic crystal etching step by calling the ETCH input deck statement as shown in Section 4. Within the ETCH input deck statement,

• You refer to previously defined etching properties by means of the parameter ETCHDEPOPROPERTIES
• Next you must select a model for etching simulation. The model which is suitable for anisotropic crystal etching is the “anisotropic” model
• You must also specify the etching time (in minutes by default in version 3.5.0.R) within the ETCH statement
• In order to optimize the numerical accuracy, we also recommend to set the SOLVER parameter, which selects the numerical scheme for moving the interfaces, to LAX_FRIEDRICH since this solver is more suitable for the etch rate profiles of anisotropic crystal etching than the default solver used in version 3.5.0.R of VICTORY Process
• Additionally you should also limit the size of the time steps by setting the parameter MAXCFL to 0.5 in order to minimize the numerical error of the solver which moves the interfaces

4. Examples

In all examples shown in this section we have used the etching properties as defined in section 2.

4.1 Specifying Etch Rates for 3 or 4 Principal Axis
The first example illustrates the effect of specifying the rate in the {311} direction in addition to the main {100}, {110} and {111} rates. We start from the structure shown on Figure 1 and etch it for 0.5 min using both etching properties “KOH_3” and “KOH_4” as defined in section 2.

 Figure 1. Initial structure.

The structures shown on Figures 2a) and 2b) are obtained by applying the commands

ETCH etchdepoproperty=KOH_3 model=”anisotropic” time=0.5 \
maxcfl=0.5 solver=LAX_FRIEDRICH

and

ETCH etchdepoproperty=KOH_4 model=”anisotropic” time=0.5 \
maxcfl=0.5 solver=LAX_FRIEDRICH

to the structure shown on Figure 1. You can see, that setting rates in 4 directions adds another facet to the etched surface, which is particularly visible on the hemisphere.

 a) Etching with the etching properties defined as KOH_3 a) Etching with the etching properties defined as KOH_3 Figure 2: The difference between setting rates in 3 and 4 directions.

In the example shown in Figure 2 the default wafer orientation of version 3.5.0.R of VICTORY Process was applied. This means that:

• a {100} wafer (z-axis is {100} crystal direction) is used
• the wafer rotation is 0 degree (x-axis is {100} crystal direction).

4.2 The Effect of Wafer Rotation
The next example illustrates the effect of wafer rotation, which you can set in the INIT statement. Figure 3a) shows the initial structure. A silicon substrate with the square-shaped mask on the top is used for demonstration purposes. We have conducted two simulations with crystal anisotropic etching, whereby the same ETCH statement was applied.

ETCH etchdepoproperty=KOH_4 model=”anisotropic” time=2 \
maxcfl=0.5 solver=LAX_FRIEDRICH

However, in first case the initial substrate was not rotated. Therefore, the mask’s sides were aligned with the crystal direction {100}, while for second simulation the initial structure was generated with the parameter ROT.SUB set to 45° in the INIT statement. Although this does not change the visible shape of the initial structure it affects the position of the mask relative to the crystal’s axis (as the crystal was rotated relative to domain’s coordinate). That is why in the second case, the mask’s edges were aligned with the {110} crystal direction.

As you can see in Figure 3, the rotation of the substrate had a dramatic effect on the resulting shape. Note, that substrate orientation and rotation can be set only at the beginning of the deck in the INIT statement and cannot be changed during the process simulation. In order to provide also a experimental verification, we have taken Figure 3d), from [2], where the SEM photograph of the structure as analyzed in this section, after anisotropic crystal etching is shown. The SEM image corresponds very well to the structure obtained by simulation (Figure 3c).

 a) Initial structure b) No substrate rotation c) Substrate rotation 45° d) SEM photograph of anisotropically etched structure [2]. Figure 3.Influence of the initial substrate rotation on anisotropic crystal etch and comparison with experimental results.

4.3 Etching of a Beam Structure
The last example in this article shows another comparison of simulation with experimental results for a frequently used benchmark. Anisotropic crystal etching is used to create a {100} oriented beam structure on {110} substrate.

Figure 4 shows very good agreement between simulated and experimentally obtained shapes.

 a) Anisotropic crystal etching of a {100} oriented beam structure on a {110} substrate. b) SEM photograph of the experiment [2]. Figure 4. Comparison of simulation with experimental results.

5. Conclusions

VICTORY Process can accurately simulate the anisotropic crystal etching of silicon by setting the relative etch rates for different crystal directions. The results of simulation closely match experimental data.

Since anisotropic etching is a highly non-linear process, simulating it requires careful adjustment of the time step. We recommend to set the ETCH statement parameters MAXCFL to 0.5 or less and to use the LAX_FRIEDRICH solver for the etching process.

References

1. Hubbard, T.J, MEMS design: the geometry of silicon micromachining, PhD thesis, California Institute of Technology, 1994.
2. Schröeder, H. Obermeier, E., Horn, A., Wachutka, G.K.M. Convex Corner Undercutting of {100} Silicon in Anisotropic KOH Etching: the New Strp-Flow Modl of 3-D Structuring and First Simulation Results. J. of Microelectromechanical Systems, Vol. 10(1), 2001, pp. 88-97.
3. Sato, K., Shikida, M., Matsushima, Y., Yamashiro, T., Asaumi, K., Iriye, Y., Yamamoto M., Characterization of orientation-dependent etching properties of single-crystal silicon: effects of KOH concentration. Sensors and Actuators A 64, 1998, pp. 87-93.