Specification establishing method for controlling semiconductor process
View Patent ↗A specification establishing method for controlling semiconductor process, the steps includes: sampling a plurality of sample groups from a population, each sample group being a non-normal distribution; filtering the sample groups; summarizing the filtered sample groups to form a non-normal distribution diagram; getting a value-at-risk and a median by calculating from the non-normal distribution diagram; getting a critical value by calculating the value-at-risk and the median with a critical formula; getting a plurality of state values by calculating the filtered sample groups with a proportion formula; and getting an index value by calculating the non-normal distribution diagram with the proportion formula. Thus, the state values indicate the states of the sample groups are abnormal or not by comparing the state values to the index value.
1. A specification establishing method for controlling semiconductor process, comprising the steps of:
providing a database and choosing a population from the database;
sampling a plurality of sample groups from the population, each sample group being a non-normal distribution and having a plurality of samples;
filtering the sample groups;
summarizing the filtered sample groups to form a non-normal distribution diagram;
getting a value-at-risk and a median by calculating from the non-normal distribution diagram;
getting a critical value by calculating the value-at-risk and the median with a critical formula;
getting a plurality of state values by calculating the filtered sample groups with a proportion formula; and
getting an index value by calculating the non-normal distribution diagram with the proportion formula;
thereby the state values present the states of the sample groups are abnormal or not by comparing the state values to the index value,
wherein the critical formula is
VaR
+
M
n
=
V
cri
(
n
∈
R
,
n
>
0
)
,
VaR is the value-at-risk, M is the median and V cri is the critical value.
2. The specification establishing method as claimed in claim 1 , wherein the database is a data group of wafer process.
3. The specification establishing method as claimed in claim 1 , wherein the population is a defect group or a yield group.
4. The specification establishing method as claimed in claim 1 , wherein the sample groups are a plurality of sample groups of different equipments.
5. The specification establishing method as claimed in claim 1 , wherein the non-normal distribution diagram is a beta distribution diagram.
6. The specification establishing method as claimed in claim 1 , further limited for controlling semiconductor wafer process.
7. A specification establishing method for controlling semiconductor wafer process, comprising the steps of:
providing a non-normal distribution population;
sampling at least two sample groups from the population, each sample group has a plurality of samples;
filtering the at least two sample groups;
summarizing the at least two filtered sample groups to get a value-at-risk;
getting a critical value by calculating the value-at-risk;
getting a plurality of state values by calculating the at least two filtered sample groups with a proportion formula; and
getting an index value by calculating the at least two summarized sample groups with the proportion formula;
thereby the state values present the states of the sample groups are abnormal or not by comparing the state values to the index value,
wherein the proportion formula is
H
cri
H
cri
+
L
cri
=
V
(
V
=
V
state
or
V
index
)
or
L
cri
H
cri
+
L
cri
=
V
(
V
=
V
state
or
V
index
)
,
H cri is the number of samples with values higher than the critical value, L cri is the number of samples with values lower than the critical value, V state is the state value, and V index is the index value.
8. The specification establishing method as claimed in claim 7 , wherein the population is a defect group or a yield group.
9. The specification establishing method as claimed in claim 7 , wherein the sample groups are a plurality of sample groups of different equipments.
10. A specification establishing method for controlling semiconductor process, comprising the steps of:
providing a database and choosing a population from the database;
sampling a plurality of sample groups from the population, each sample group being a non-normal distribution and having a plurality of samples;
filtering the sample groups;
summarizing the filtered sample groups to form a non-normal distribution diagram;
getting a value-at-risk and a median by calculating from the non-normal distribution diagram;
getting a critical value by calculating the value-at-risk and the median with a critical formula;
getting a plurality of state values by calculating the filtered sample groups with a proportion formula; and
getting an index value by calculating the non-normal distribution diagram with the proportion formula;
thereby the state values present the states of the sample groups are abnormal or not by comparing the state values to the index value,
wherein the proportion formula is
H
cri
H
cri
+
L
cri
=
V
(
V
=
V
state
or
V
index
)
or
L
cri
H
cri
+
L
cri
=
V
(
V
=
V
state
or
V
index
)
,
H cri is the number of samples with values higher than the critical value, L cri is the number of samples with values lower than the critical value, V state is the state value, and V index is the index value.
11. The specification establishing method as claimed in claim 10 , wherein the database is a data group of wafer process.
12. The specification establishing method as claimed in claim 10 , wherein the population is a defect group or a yield group.
13. The specification establishing method as claimed in claim 10 , wherein the sample groups are a plurality of sample groups of different equipments.
14. The specification establishing method as claimed in claim 10 , wherein the non-normal distribution diagram is a beta distribution diagram.
15. The specification establishing method as claimed in claim 10 , further limited for controlling semiconductor wafer process.