Computer-aided design and analysis of circuits and semiconductor – Nanotechnology related integrated circuit design
Reexamination Certificate
1998-07-07
2002-11-19
Siek, Vuthe (Department: 2768)
Computer-aided design and analysis of circuits and semiconductor
Nanotechnology related integrated circuit design
Reexamination Certificate
active
06484305
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an impurity quantity transfer device which conducts, in numerical analysis of a semiconductor device, integral interpolation of impurity quantities among meshes generated on a semiconductor device to be processed for use in process device simulation and an impurity interpolation method thereof.
2. Description of the Related Art
At the oxidation and diffusion steps of a semiconductor manufacturing process, configuration of a semiconductor to be processed changes through the steps. For reproducing such a phenomenon by using a process simulator, configuration and a diffusion time are discretized, respectively. Discretization is employed because a diffusion equation used for oxidation and diffusion is non-linear and also because such a strong non-linear physical phenomenon as initial accelerating oxidation exists.
As a conventional technique of space discretization by a two-dimensional (2D) process simulator, the control volume method (hereinafter referred to as C.V. method) having excellent configuration-adaptability is widely used. In the C.V. method, space is represented by triangular meshes on which a control volume is defined with respect to each grid point (mesh point). Control volume denotes a polygon obtained by finding circumcenters of triangular elements having a relevant mesh point as a vertex and sequentially connecting the circumcenters of adjacent triangles (i.e. triangle sharing a side). Such a control volume obtained as a polygon is a grid-based control volume. In the C.V. method, a flow of physical quantities (e.g. current) on a mesh edge is represented as a quantity obtained by multiplying a density of the flow (e.g. current density) on the edge in question by a length of a side of a control volume which side crosses with the mesh edge in question (in general, referred to as a cross section also in two-dimensional space).
Depending on the configuration of a triangular mesh, however, sequentially connecting circumcenters of adjacent mesh triangles in a manner as mentioned above fails to have one (convex) polygon. In other words, sides of a control volume cross with each other. In this case, a cross section of the control volume takes a negative value in calculation, so that a flow of physical quantities on a mesh edge will be in the opposite direction to a density of the flow, causing increase in analysis errors.
To prevent such a situation, Delaunay division is employed. A line connecting circumcenters of mesh triangles fails to form a (convex) polygon when within a circumcircle of a predetermined triangular element on meshes, a vertex of other triangular element exists. It is therefore necessary to divide the meshes such that inside each circumcircle of every triangular element on the meshes, there falls none of the mesh points of other triangular elements. Such division is called Delaunay division. In the simulation employing the C.V. method, ensuring a calculation precision requires the Delaunay division to be ensured for a mesh as a unit of discretization of configuration.
In the simulation of an oxidation process, configuration of a semiconductor changes with time as mentioned above. When the configuration changes during the simulation due to oxidation processing, regeneration of a mesh is needed for ensuring the Delaunay division. On this occasion, it is necessary to transfer an impurity value defined with respect to a mesh yet to be regenerated to a regenerated mesh. In the C.V. method, an impurity concentration is defined with a mesh point (grid point) existing one in a control volume as a representative point.
Methods of defining an impurity concentration at a regenerated mesh include a method by analytical calculation of an impurity concentration as is used for log alignment and a method employing integral interpolation in which dose is preserved. For highly precise diffusion simulation, the integral interpolation method in which dose is preserved is employed. At a pn junction portion where an impurity concentration difference between grids is large, however, pseudo diffusion occurs which is a phenomenon of transfer of impurity quantities toward a grid of low impurity value caused as a result of impurity interpolation.
FIG. 8
is a flow chart showing a procedure of an integral interpolation method. First, with respect to a regenerated mesh, a grid-based control volume is defined (Step
801
). Next, with respect to a mesh yet to be regenerated, a grid-based control volume is defined (Step
802
). A grid-based control volume is a polygonal region obtained by connecting a circumcenter of each triangular element sharing a grid point as described above.
Next, the grid-based control volume for the mesh yet to be regenerated is converted into a control volume triangle (hereinafter referred to as C.V. triangle) on a triangular mesh basis (Step
803
). A triangular-mesh-based C.V. triangle represents a region divided by the respective sides of triangular elements on triangular meshes and the respective sides of the above-described grid-based control volume (polygon). Impurity concentration at each C.V triangle is made equal to an impurity concentration at an original grid-based control volume. Impurity quantities is therefore distributed in proportion to an area of a C.V. triangle.
Next, an area of overlap (hereinafter referred to as overlap area) is calculated between a pattern of a grid-based control volume on the regenerated mesh and a triangular-mesh-based C.V. triangle on the mesh yet to be regenerated (Step
804
). After the calculation of an overlap area, an impurity quantity within the C.V. triangle proportional to the calculated overlap area is transferred to the grid-based control volume on the regenerated mesh (Step
805
). After the transfer, determination is made whether the impurity quantities of all the C.V. triangles have been transferred to the grid-based C.V. on the regenerated mesh (Step
806
), and when the transfer is yet to be completed, Steps
804
and
805
will be repeated and when it is completed, integral interpolation of impurities is finished.
Consideration will be given to change of an impurity concentration, that is, pseudo diffusion, occurring when integral interpolation of impurities is conducted by the above-described conventional impurity interpolation method. Here, vertical profiles are obtained assuming that with a space between meshes fixed on the premise of one-dimensional structure, integral interpolation is conducted with only a position of a mesh staggered by half a cycle. The obtained result is shown in FIG.
9
. In
FIG. 9
, a curve
901
represents an initial impurity profile, a curve
902
represents an impurity profile obtained after the integral interpolation is conducted once by the above method, and curves
903
and
904
represent impurity profiles obtained after the integral interpolation is conducted ten times and 100 times by the above method, respectively.
In the above-described conventional method, when a region of a control volume on a regenerated mesh bridges a control volume region of extremely high impurity concentration and a control volume region of low impurity concentration on a mesh yet to be regenerated due to impurity interpolation, so a large quantity of impurities will be transferred from the region of high impurity concentration toward the region of low concentration, that transfer of the impurity quantities within the region of lower impurity concentration is negligible. As a result, the impurity quantity is propagated toward the region of lower impurity concentration to cause large pseudo diffusion. As can be seen from
FIG. 9
, as few as ten times of repetition of impurity interpolation causes large pseudo diffusion.
In the simulation of oxidation steps, one oxidation step is divided into several time-steps to calculate time required for one oxidation step. Since one step is in common divided into approximately ten for calculation, the conventional method in which obvious pseudo diffusion appears by appr
Siek Vuthe
Thompson A. M.
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