Method of inspecting flatness of substrate
A method of inspecting flatness of substrate is provided and includes providing a substrate. N first inspecting points are selected from the surface of the substrate along a first straight line, where the coordinate of the i-th first inspecting point is (X i ,Y i ,Z i ). By using a formula “ D = ∑ i = 1 N - 1 ( X i + 1 - X i ) 2 + ( Y i + 1 - Y i ) 2 + ( Z i + 1 - Z i ) 2 ” , a first measurement length D is calculated. By using a formula “F=(D−S)/S”, a first flatness index F is calculated. S is the horizontal distance between 1st first inspecting point and N-th first inspecting point. When the first flatness index F is larger than a first threshold, the substrate is determined to be unqualified.
1. A method of inspecting flatness of a substrate, comprising:
providing the substrate having a surface;
selecting a plurality of first inspecting points from the surface along a plurality of side-by-side first straight lines by an optical dimension measuring device, wherein the optical dimension measuring device selects N first inspecting points (Xi, Yi) along each of the first straight lines in an X direction; measuring a plurality of heights Zi of the first inspecting points along each of the first straight lines in the X direction by the optical dimension measuring device; by using a formula:
D
=
∑
i
=
1
N
-
1
(
X
i
+
1
-
X
i
)
2
+
(
Y
i
+
1
-
Y
i
)
2
+
(
Z
i
+
1
-
Z
i
)
2
,
calculating a first measurement length D corresponding to each of the first straight lines;
by using a formula: F=(D−S)/S, calculating a plurality of first flatness indexes F, wherein one of the first flatness indexes F corresponds to one of the first straight lines, wherein S is a horizontal distance between 1 st first inspecting point and N-th first inspecting point along one of the first straight lines;
calculating a first average of the first flatness indexes F corresponding to the first straight lines; and
scrapping the substrate having the first average larger than a first threshold, determining that the substrate is unqualified.
2. The method of claim 1 , further comprising:
selecting a plurality of second inspecting points from the surface along a plurality of side-by-side second straight lines not parallel to the first straight lines by the optical dimension measuring device, wherein the optical dimension measuring device select M second inspecting points (Aj, Bj) from the surface along one of the second straight lines in a Y direction perpendicular to the X direction; measuring a plurality of heights Cj of the second inspecting points along each of the second straight lines in the Y direction by the optical dimension measuring device
by using a formula:
d
=
∑
j
=
1
M
-
1
(
A
j
+
1
-
A
j
)
2
+
(
B
j
+
1
-
B
j
)
2
+
(
C
j
+
1
-
C
j
)
2
,
calculating a second measurement length d corresponding to each of the second straight lines;
by using a formula: f=(d−R)/R, calculating a second flatness index f corresponding to each of the second straight lines, wherein R is a horizontal distance between 1 st second inspecting point and M-th second inspecting point along one of the second straight lines;
calculating a second average of the second flatness indexes f corresponding to the second straight lines; and
scrapping the substrate having the second average larger than a second threshold, determining that the substrate is unqualified.
3. The method of claim 2 , further comprising:
identifying the substrate as being qualified when the first average is less than or equal to the first threshold, and the second average is less than or equal to the second threshold.
4. The method of claim 2 , wherein a length of each of the first straight lines is larger than a length of each of the second straight lines, and N>M.
5. The method of claim 4 , wherein the first threshold is 2.
6. The method of claim 5 , wherein the second threshold is 2.
7. The method of claim 2 , wherein the first threshold is 2.
8. The method of claim 7 , wherein the second threshold is 2.
9. The method of claim 1 , wherein the first threshold is 2.
10. The method of claim 1 , wherein a horizontal distance between adjacent two of the first inspecting points is less than or equal to 1 cm.