SPread direction region specifics
The SPREAD line provides a way to distort rectangular grids in the vertical direction to follow surface and junction contours. SPREAD is very useful in reducing the amount of grid for some specific problems, most notably MOSFET's. The SPREAD line is somewhat complicated; it is suggested to follow the supplied examples very carefully (see the MOSFET example in the PISCES manual).
LEft = logical (default is false) Right = logical (default is false)
LEFT and RIGHT specify that the left and right-hand sides of the grid respectively be distorted.
region
Width = real Upper = integer LOwer = integer
WIDTH specifies the width from the left or right edge (depending on the LEFT and RIGHT parameters) of the distorted area. The actual x-coordinate specified by WIDTH ( min[x] + WIDTH for LEFT, max[x] - WIDTH for RIGHT) will lie in the middle of the transition region between the distorted and undistorted grid regions. UPPER and LOWER specify the upper and lower y-grid lines between which the distortion will take place.
specifics
Y.Lower = real
or
Thickness = real
and
Vol.ratio = real (default is 0.44)
Encroach = real (default is 1.0)
GRAding = real (default is 1.0)
GR1 = real (default is 1.0)
GR2 = real (default is 1.0)
Middle = real
Y.Middle = real
The Y.LOWER and THICKNESS parameters define the distorted grid region; only one should be supplied. Y.LOWER is the physical location in the distorted region at which the line specified by LOWER will be moved. The line specified by UPPER is not moved. THICKNESS is the thickness of the distorted region; THICKNESS will usually move the positions of both the UPPER and LOWER grid lines (unless VOL.RATIO is set to 0 or 1). VOL.RATIO specifies the ratio of the downward displacement of the lower grid line to the net increase in thickness. The default is 0.44 so that oxide-silicon interfaces are correct. VOL.RATIO is ignored if Y.LOWER is specified. ENCROACH is a factor which defines the abruptness of the transition between distorted and non-distorted grid. The transition region becomes more abrupt with smaller ENROACH factors (the minimum is 0.1). An important note: depending on the characteristics of the undistorted grid, very bad triangles (long, thin and obtuse) may result if ENCROACH is set too low. GRADING specifies a grid ratio (identical to the RATIO parameter on the X.MESH and Y.MESH lines) to produce a non-uniform grid in the distorted region. As alternative to a single grading parameter, GR1 and GR2 can be specified along with the y grid line MIDDLE and location Y.MIDDLE so that GR1 is used as the grading in the spread region from UPPER to MIDDLE and GR2 is the grading from MIDDLE to LOWER.
The following spreads what was previously a uniform 400 Angstroms of oxide to 1000 Angstroms on the left side of the device. This will result in a net increase in thickness of 600 Angstroms of oxide. Because the default VOL.RATIO is used, 0.44*(600) = 264 Angstroms of the net increase will lie below the original 400 Angstroms and 0.56*(600) = 336 Angstroms of the net increase will lie above the original 400 Angstroms. The width of the spread region is 0.5mm and the oxide taper is quite gradual because of the high encroachment factor. The grid is left uniform in the spread region.
$ *** Mesh definition *** MESH NX=30 NY=20 RECT X.M N=1 L=0 X.M N=30 L=2 Y.M N=1 L=-.04 Y.M N=5 L=0 Y.M N=20 L=1 R=1.4 $ *** Thin oxide *** REGION X.L=1 X.H=30 Y.L=1 Y.H=5 $ *** Silicon substrate *** REGION X.L=1 X.H=30 Y.L=5 Y.H=20 $ *** Spread *** SPREAD LEFT WIDTH=0.5 UP=1 LO=5 THICK=0.1 ENC=1.3
In the next example, the right side of the grid is distorted in order to follow a junction contour. Assume that the initial grid is defined as above. Y.LOWER is used so that there is no increase in the size of the device, just grid redistribution. With Y.LOWER set to the junction, the ENCROACH parameter should be chosen such that the lower grid line (LOWER=10) follows the junction as closely as possible. Note that the grid is graded so that the grid lines are spaced closer together as they approach the junction. Because the point specified by WIDTH on the SPREAD line lies in the middle of the transition region, it should be chosen to be slightly larger than the width of the doping "box" (WIDTH < X.LEFT - X.RIGHT = 0.5mm).
$ *** Doping *** DOPING UNIFORM N.TYPE CONC=1E15 DOPING GAUSS P.TYPE X.LEFT=1.5 X.RIGHT=2 + PEAK=0 CONC=1e19 RATIO=.75 JUNC=0.3 $ *** Spread *** SPREAD RIGHT WIDTH=0.7 UP=5 LO=10 Y.LO=0.3 + ENC=1.2 GRAD=0.7