GRID

The GRID command defines a simple 1D,2D or 3D tensor product grid. The GRID (or LOAD) command must appear before any commands such as field, graph or bias.

The algorithm for creating non-uniform tensor product grid operates segment-by-segment, where the segments are defined by the values specified in the XLOC (or YLOC, ZLOC) keyword. Each XLOC value has an associated XDEL value, which is the grid spacing request that Prophet will try to accomodate. When a segment has the same XDEL values at both endpoints, the grid will be uniformly spaced at that value. When the XDEL values are different, Prophet will grade the grid spacing as smoothly as possible, minimizing the ratio of adjacent grid spacing. However, within a segment the ratio will never be greater than ``/library/math/grid/interval.ratio'' (set to 1.5 in the Prophet database currently). If the change in requested grid spacing within a segment is too extreme to meet this ratio, the smaller grid XDEL will be satisfied, and the larger ignored. To ensure that the requested spacing is possible, the user can check his/her input to see if the following is satisfied:

If the above inequality is not satisfied, it is possible that the grid spacings in adjoining segments will have a larger ratio than that specified by ``/library/math/grid/interval.ratio''. However, the maximum ratio is always met within each individual segment.

• MATERIAL=(s)
• ELEMENT=(s)
• [RESISTIVITY=(r)]
• [CONCENTRATION=(r)]
• [ORIENTATION=(i)]
• [DIMENSION=(i)]
• [XLOC=(r)]
• [XDEL=(r)]
• [YLOC=(r)]
• [YDEL=(r)]
• [ZLOC=(r)]
• [ZDEL=(r)]
• [MAP.MOSFET=(s)]
• [XMOLE=(r)]
• [YMOLE=(r)]

The following list itemizes the valid keywords, their units, and their meaning:

MATERIAL: [string]

type of material the substrate is made of. Possible values are found in the library in library/physics.

ELEMENT: [string]

impurity element initially in the substrate. If ELEMENT is not set, the substrate is assumed to be intrinsic. Either RESISTIVITY or CONCENTRATION must also be set.

RESISTIVITY: [real (ohms)]

substrate resistivity. Specify either RESISTIVITY or CONCENTRATION.

CONCENTRATION: [real ( )]

uniform concentration of ELEMENT in the substrate. Specify either CONCENTRATION or RESISTIVITY.

DIMENSION: [integer]

spatial dimension of the original grid of the simulation domain. Value may be 1, 2, or 3.

XLOC: [real (microns)]

array of grid locations in the vertical direction, separated by commas. The first and last values specify the beginning and end of the initial simulation domain. Intermediate values are used to specify a varying grid spacing.

XDELTA: [real (microns)]

grid spacing in the vertical direction. An array of the same length as XLOC can be given to specify the grid spacing at each XLOC. The grid is varied gradually between each XLOC.

YLOC: [real (microns)]

array of grid locations in the lateral Y direction, separated by commas. The first and last values specify the beginning and end of the initial simulation domain. Intermediate values are used to specify a varying grid spacing.

YDELTA: [real (microns)]

grid spacing in the Y direction. An array of the same length as YLOC can be given to specify the grid spacing at each YLOC. The grid is varied gradually between each YLOC.

ZLOC: [real (microns)]

array of grid locations in the Z direction, separated by commas. The first and last values specify the beginning and end of the initial simulation domain. Intermediate values are used to specify a varying grid spacing.

ZDELTA: [real (microns)]

grid spacing in the Z direction. An array of the same length as ZLOC can be given to specify the grid spacing at each ZLOC. The grid is varied gradually between each ZLOC.

MAP.MOSFET [string]

the fields from a MOSFET's pas file onto a new grid, flattening the silicon/gate-oxide interface in the process. THe basic purpose is to create a rectlinear grid, but using the fields from a MOS device with surface curvature created by process simulation This command assumes the silicon/gate-oxide interface is located at x=0. Fields in the silicon substrate are shifted vertically, if necessary. The new grid must be previously defined, and must not lie outside the domain of the mapped fields. The new grid must have its top at x=0. Typical usage:

grid dim=2 xloc=0,0.01,0.2 xdel=0.001,0.01,0.05
+ yloc=-0.2,0,0.2 ydel=0.01,0.01,0.01 mat=silicon
grid map.mosfet=myfile.pas

XMOLE [real]

``xmole'' (stochiometry) for region described by the grid statement. Value must be between 0.0 and 1.0.

YMOLE [real]

``ymole'' (stochiometry) for region described by the grid statement. Value must be between 0.0 and 1.0.

Examples::

1-D MOS Capacitor:

grid dim=1 mat=silicon
+ xloc=0.00000,0.0010,0.010,0.10,0.20,0.50
+ xdel=0.00005,0.0002,0.001,0.01,0.05,0.05
+ elem=boron conc=1.0e+18
deposit mat=oxide thickness=0.0,0.002 xdel=0.00005,0.0005

Note that in the deposit command above, the first ``xdel'' value refers to the bottom of the deposited layer. However in the grid command, the first ``xdel'' refers to the top of the initial structure. In order to have good accuracy, it is necessary to have vertical grid spacing on the order of an Angstrom adjacent to the silicon oxide interface.

2-D MOS:

grid dim=2 mat=silicon
+ xloc=0.00000,0.0010,0.010,0.10,0.20,0.50
+ xdel=0.00005,0.0002,0.001,0.01,0.05,0.05
+ yloc=-0.15,-0.07,-0.05,-0.04,0.040,0.050,0.07,0.15
+ ydel=0.02,0.005,0.002,0.005,0.005,0.002,0.005,0.02
+ elem=boron conc=1.0e+18
deposit mat=oxide thickness=0.0,0.002 xdel=0.00005,0.0005

For a MOS device, it is important to have sufficient lateral grid density at the source and drain junctions.

Less Used GRID Keywords

MASK.GRID [logical], EDGE.DELTA [real (microns)], SPACE.DELTA [real (microns)]

refinement around mask edges in a process flow can be automated using the MASK.GRID option. The logical MASK.GRID specifies that fine grid should be automatically allocated at the mask edges encountered in the input file, with coarser grid in between. The finest spacing at the edges is given by EDGE.DELTA. The coarsest spacing is given by SPACE.DELTA. The fine spacing is guaranteed to be honored, but depending on location of mask edges, the coarse spacing may be finer than requested. The spacing is automatically graded from coarse to fine areas. A SPACE.DELTA of 0.0 requests that the grid be made as coarse as possible between mask edges, consistent with not increasing the spacing more than a factor of 1.5 in any interval. The value of 1.5 comes from library/math/grid/interval.ratio.

ORIENTATION: [integer]

crystalline orientation of the substrate. Valid values are 100, 110 and 111.

TRIANGULATE [logical]

a triangular grid from a rectangular grid, or from a grid composed of rectangles and triangles.

QUALITY [logical]

and print a number of quality indicators for a 2-D triangular grid.

ADAPT [logical]

adaptation for 2-D triangular grid.

REFINE [logical]

refinement for 2-D triangular grid based on the field specified with FIELD keyword.

FIELD [string]

keyword specifies which field to use for refinement criteria when using the REDINE keyword.

RATIO [real]

parameter for REFINE keyword.

CLEANUP [logical]

-up 2-D triangular grid.

SHEAR [real]

x-coordinate of each point by an amount defined by SHEAR times that point's y-coordinate.

XSHIFT [real]

x-location of coordinates by specified amount.

YSHIFT [real]

y-location of coordinates by specified amount.

CURVE.MOS [logical]

a structure with a curved top surface by moving coordinate points, thus shifting the fields. Note that this will create a non-rectlinear grid.