One of the most notorious problems one faces in topography simulations is the determination of the erosion/growth rates of materials exposed to a variety of complex physico-chemical processes. The latter evolve continually to satisfy the needs of the ever advancing microelectronic industry, while understanding about these processes is often incomplete and insufficient for their description. Existing theoretical models, which are often semi-empirical, include sets of fitting parameters which are generally unknown and their determination is in most cases pure guess work.
2Dinese has adopted a very pragmatic way of interfacing this problem. Instead of assuming the validity of a certain model or models for a particular process (which also brings with it the uncertainties of various fitting parameters - sticking coefficients, reaction probabilities and the like) and calculating the etch rates itself, it expects the user to specify the erosion/deposition rate and its angular dependence for any particular material. This makes 2Dinese an open Simulator independent the process characteristics. In other words, the user is at the liberty to determine the etch/erosion rates in any way he/she finds appropriate and 2Dinese will do the simulation with invariable robustness. For example, if the user wishes to simulate ion beam erosion of a given material(s), he/she might choose to use another computer program (TRIM, MARLOWE, etc) to determine the angular dependence of the sputtering yield (resp. the erosion rate), which is the only input data needed in this case. Alternatively, the user may experimentally determine this angular dependence in his/her own equipment and processing conditions. In another instance, if a given theoretical (or computer) model for a given process is shown to be adequate, the user can freely use its results as input to 2Dinese.
As mentioned above, however, the processes used in IC production today are much more complex and experimental determination in many cases may be difficult and/or translation of the results from one equipment to another may be inadequate (even if the processing conditions appear to be the same). Having recognised that, we have recently developed (see the Proceedings from the 1995 meeting of the American Vacuum Society in Minneapolis) and are further refining a general method for the experimental determination of the erosion/deposition rate and its angular dependence and which method is IC compatible. The idea is to determine these rates under the actual processing conditions and not outside in another experimental chamber, so that the obtained values, and hence the simulation that subsequently uses these values, are as realistic as they can possibly be.
The fact that 2Dinese is an open simulator, and not confined to any specific class of processes or process characteristics, means that it can be used for a large variety of processes, even processes and technologies that are yet to be devised.
Generally a Directional process is also anisotropic, since the etch/deposition rate depends on the angle between the surface normal and the incidence direction, that is this is also a kind of anisotropy. But it is also important to note that in a Directional process a surface element is ONLY etched if it is DIRECTLY seen (visible) by the incident flux, that is, if it is NOT shadowed by another surface element. For this reason, the angular dependence is defined for an angular range (-90,90) degrees with respect to the incidence direction. In fact the user only defines data in the range (0,90) degrees since the behaviour is assumed to be symmetric about the incidence direction. The etch/deposition rate at 90 degrees is always zero since by definition the flux is zero. It is mandatory that a data point at 0 degree is always specified. If the user chooses to use spline interpolation the minimum number of data points is four.
All angles are coordinate system independent and are scalars representing the angle between the incidence direction and the surface normal.
Typical examples for directional processes are: Ion Beam Etching, Reactive Ion Beam Etching, Reactive Ion Etching, Low Pressure Sputter Deposition, a number of Physical Vapor Deposition Processes, Ion Beam Activated Processes, etc.
N.B. A process can have isotropic characteristics and still be classified as 'Directional'. For instance, if we have an erosion/deposition process in which the flux distribution of the eroding/depositing particles is isotropic but their mean free path is much larger than the dimensions of microstructures etched/grown, then such a process will be 'Directional' with 90 degree divergence. Conversely, if their mean free path is much smaller than the microstructure dimensions, then such a process is simply isotropic (provided that transport effects are insignificant).
2. Anisotropic processes:
In an Anisotropic process, however, the etch/deposition rate is a function of the surface orientation ONLY (the coordinate system is defined by the user when he/she defines the initial structure - see "I/O Formats"). No shadowing or proximity of other surface elements play any role. The anisotropy can be complete, that is, the etch/deposition rate can and must be specified in the whole (0,360) degree interval. It is mandatory that data points for 0,90,180 and 270 degrees are specified, but since the user may use spline interpolation it is also mandatory that at least two additional data points in each sub-interval are also specified.
All angles are defined with respect to the positive y-axis.
Typical examples for anisotropic processes are: Wet and Dry etching of monocrystalline materials, Plasma Etching, Crystal growth and dissolution, Combined (etching and deposition) processes, etc.
The user may find the definition of the etch/deposition rate somewhat confusing for cases with non-zero divergence. The confusion arises from the fact that the user defines an erosion/deposition rate and not a flux as would have been more appropriate for directional processes. The notion of divergence is implemented in the following way.
1. Directional deposition:
The user defines a deposition rate in the appropriate field (see the "Deposition" command in the Process Menu). This rate is effectively equivalent to a deposition from a collimated flux J of particles onto a planar surface perpendicular to the flux direction. When the user specifies a non-zero divergence the same flux is "redistributed" uniformly in an angular range, which is equal to twice the divergence and is symmetric about the deposition flux direction. In other words, the flux distribution is uniform in the above angular interval and the flux in any given direction within that interval is equal to J/(2*divergence).
2. Directional erosion:
Here the user defines an etch rate in the appropriate field (see the "Etching" command in the Process Menu) as well as specifies and angular dependence of the etch rate. The net etch rate is the product of the two and similarly to the Directional deposition case above this net etch rate is effectively equivalent to a collimated flux J of eroding species with a user specified incident direction. Similarly, when the user further specifies a non-zero divergence, the same flux is uniformly "redistributed" in an angular range, which is equal to twice the divergence and is symmetric about the incident flux direction. In other words, the flux distribution is uniform in the above angular interval and the flux in any given direction within that interval is equal to J/(2*divergence). It is further assumed that the angular dependence specified by the user is valid for all incident flux directions, or in simple terms, the etch rate is a function of the angle of incidence onto the surface only and not explicitly on the surface orientation.
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IV. Memory and Speed Considerations
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Remember that the memory required by the program depends strongly on the size of the structure, which in turn determines the number of points that constitute the surface. Generally, the segment length is kepth between 5 and 10 Spatial Units (see Preferences). If the latteral dimension of the structure, for instance, is 2000 Spatial Units, then the surface will contain at least 200 points. Of course, if the topography is non-planar this number can be much higher. The point made here is that both execution speed and memory consumption depend on your choice of both structure size and Spatial Unit used.
This is seen from the following simple example. Suppose you have a planar structure which is 20000 Angstroms wide and you have selected the Spatial Unit to be 'Angstroms' (see Preferences). The program will automatically divide the surface into 2000 segments (segment length equal to 10 Angs.). Suppose now you have the same structure and have selected the same process but have chosen 'nanometers' as the Spatial Unit (segment length equalt to 10 nm). The program will now divide the structure into 200 segments resulting in a ten-fold shorter execution time as well as ten-fold smaller memory requirements for surface related variables.
The most time consuming processes are 'Directional' with non-zero divergence. The larger the divergence the slower the execution is.
Copyright 1996 I.V.Katardjiev. All rights reserved.
