The present invention relates to an abrasion method of a semiconductor device, and especially, to an abrasion method of a semiconductor device using a Chemical Mechanical Polishing (CMP) technique.
A conventional abrasion method of a semiconductor device using the CMP is described in JP-A-8038/1997. FIG. 3A and FIG. 3B are views illustratively showing an abrasion method described in this publication, and FIG. 3A is a plain view of one small region, and FIG. 3B is a cross sectional view along a bxe2x80x94b line of FIG. 3A.
In the above-described conventional abrasion method, for abrading steps of an oxidized film formed on wiring of aluminum and so forth on a wafer 13, first as shown in FIG. 3A, a region to be simulated of a layout data is divided into a plurality of rectangular small regions. Further, when a sum total of tip areas of a plurality of convex patterns 12 corresponding to a convex shape of the wiring of the same small region is B, an area of a small region (i,j) which is the i-th in an x direction and the j-th in a y direction in dividing the region to be simulated into a matrix is A, density (=B/A) of the convex patterns 12 in the small region (i,j) is d(i,j), a gradient of an abrasive pad is g(i,j), and a proportional constant is r0, a movement rate (refer to an abrasion rate also, hereinafter) r(i,j) of the abrasive pad in abrasion of the small region (i,j) is calculated by the following equation:
r(i,j)=r0xc2x7g(i,j)/d(i,j).
Here, when a proportional constant is c, and height of the convex patterns 12 is h(i,J), assuming that there are four convex patterns 12 around one convex pattern 12, the gradient g(i,j) in the abrasive pad is obtained by the following equation:
g(i,j)=1+c{4h(i,j)xe2x88x92h(i+1,j)xe2x88x92h(ixe2x88x921,j)xe2x88x92h(i,j+1)xe2x88x92h(i,jxe2x88x921)}.
Thereby, a step on the wafer 13 is predicted.
By the way, in case that the density of the convex patterns 12 is high, as shown in FIG. 3B, the abrasive pad 11 is in contact with only tip surfaces of a number of convex patterns 12 without bending so much, and is not in contact with a concave pattern 14 around the convex patters. In this case, average stress applied to the plurality of convex patterns 12 is in inverse proportion to the density of the convex patterns 12. In accordance with this, in the conventional abrasion method, an abrasion rate is calculated simply on the assumption that it is in inverse proportion to the density of the convex patterns 12.
However, in case that the density of the convex patterns is low for example, the abrasive pad 11 is also in contact with the concave pattern 14 around the convex patterns 12, and thereby, stress from the abrasive pad acts on the convex patterns 12, and due to this, the abrasion rate generates an error between a measurement value and a simulation value, and a task that an abrasion accuracy is reduced occurs.
The present invention is made to solve the above-mentioned problems.
Moreover, the objective of the invention is to provide an abrasion method of a semiconductor device, in which, even in case that the density of the convex patterns (convex portions) on the semiconductor substrate is low, an abrasion accuracy can be improved by setting an appropriate abrasion rate.
In order to accomplish the above-described objective, an abrasion method of a semiconductor device of the present invention, in which concavity and convexity of an oxidized film surface on a semiconductor substrate are abraded using an abrasive pad, is characterized in that it includes steps of:
dividing a region to be simulated in a layout data of a wiring process of the above-described semiconductor device into a plurality of small regions; and
calculating approximate average height of the above-described abrasive pad from concave portions in the above-described small regions based on a sum total of areas of tip surfaces of the above-described convex portions, average height of the above-described convex portions, and a sum total of an area of a surrounding region around each convex portion.
In the abrasion method of a semiconductor device of the present invention, since the approximate average height of the abrasive pad is newly added as a parameter for calculating an abrasion rate by taking account of a point that whole stress in the surrounding region, which is applied from the abrasive pad, acts on the convex portions, it becomes to be possible to calculate an appropriate abrasion rate, and especially, it is possible to avoid a task that, in case that the density of the convex portions is low, an actual abrasion rate is higher than a rate by means of a simulation, and to improve an abrasion accuracy.
Here, in the preferable abrasion method of a semiconductor device of the present invention, when the sum total of areas of tip surfaces of each convex portion is B, the average height of the above-described convex portions is h(i,j), and the sum total of an area of the above-described surrounding region is C, the approximate average height H(i,j) of the above-described abrasive pad in the small regions (i,j) within the above-described plurality of small regions is obtained by the following equation:
H(i,j)=h(i,j)xc2x7B/(B+C).
In this case, since the approximate average height of the abrasive pad is obtained by the simple equation, it is possible to suppress the increase of calculation time by a computer apparatus and so forth.
Also, it is a preferable form of the present invention to obtain a gradient G(i,j) of the above-described abrasive pad in the above-described surrounding region by means of the following equation when a proportional constant is k:
G(i,j)=1+k{4H(i,j)xe2x88x92H(i+1,j)xe2x88x92H(ixe2x88x921,j)xe2x88x92H(i,j+1)xe2x88x92H(i,jxe2x88x921)}.
In this case, since a solution of a difference equation can be used for a calculation part that needs time, it is possible to suppress the increase of calculation time by a computer apparatus and so forth.
Furthermore, it is preferable to obtain effective density D(i,j) of the above-described convex portions, and a movement rate R(i,j) of the above-described abrasive pad by the following equations, respectively, when an area of the above-described small regions (i,j) is A, and a proportional constant is R0:
D(i,j)=A/(A+C),
and
R(i,j)=R0xc2x7G(i,j)/D(i,j).
In this case, it is possible to correctly calculate an abrasion rate, and especially, to effectively prevent a task that there is a difference in an abrasion rate between a measurement value and a simulation value in case that the density of the convex portions is low.
An abrasion method of a semiconductor device of the present invention, in which concavity and convexity of an oxidized film surface on a semiconductor substrate are abraded using an abrasive pad, is characterized in that it includes steps of:
dividing a region to be simulated in a layout data of a wiring process of the above-described semiconductor device into a plurality of small regions;
calculating coordinates of the concavity and convexity of the above-described oxidized film surface based on average height of each convex portion in the above-described small region; and
obtaining a movement rate of the above-described abrasive pad based on a stress analysis which is conducted by pressing the above-described abrasive pad against the above-described oxidized film surface, and a value of coordinates of the above-described concavity and convexity.
In the abrasion method of a semiconductor device of the present invention, it is possible to simulate a shape with high accuracy, which is to be abraded by the CMP and so forth, to correctly obtain an abrasion rate, and especially, it is possible to avoid a task that there is a difference in an abrasion rate between a measurement value and a simulation value in case that the density of the convex portions is low.