CN109753718B - PECVD color difference improvement method based on least square method - Google Patents
PECVD color difference improvement method based on least square method Download PDFInfo
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- CN109753718B CN109753718B CN201811629432.3A CN201811629432A CN109753718B CN 109753718 B CN109753718 B CN 109753718B CN 201811629432 A CN201811629432 A CN 201811629432A CN 109753718 B CN109753718 B CN 109753718B
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Abstract
The invention relates to the field of solar cell generation, in particular to the field of solar cell tube PECVD technology. The PECVD chromatic aberration improving method based on the least square method comprises the following steps of firstly, measuring the average film thickness of each batch of silicon wafers in every q times of cyclic use in the using process of a graphite boat; average value of film thickness of each batch in s-time cyclic measurement process=M is the total number of batches of silicon wafers in the using process of each graphite boat, i is the ith cyclic measurement, and s is the total number of cyclic measurement; average value of film thickness of each batch by least square methodBatch fitting with silicon wafers in each graphite boat use process, and obtaining a fitting function phi (u 𝑖 ) The method comprises the steps of carrying out a first treatment on the surface of the According to the target film thickness and the fitting function phi (u 𝑖 ) Deriving a function of corrected deposition time from the differenceThe method comprises the steps of carrying out a first treatment on the surface of the At the current deposition timeThe correction deposition time is added to obtain the deposition time G=with improved chromatic aberration+The deposition is performed according to the color difference improving deposition time G.
Description
Technical Field
The invention relates to the field of solar cell generation, in particular to the field of solar cell tube PECVD technology.
Background
The solar cell coating technology is mature, and the problem of uniformity and chromatic aberration of the appearance color of the silicon wafer is always plagued by PECVD technology. There are many factors affecting the uniformity of the coating film, in which the number of times of use of the graphite boat increases, and the problem of color difference, which causes a decrease in uniformity due to the increase of silicon nitride films deposited on the surface of the graphite boat, is one of the important factors affecting the uniformity of the coating film. The method mainly adopted for the factors is to limit the use times of the graphite boat and clean the graphite boat in time, but even if the surface electric field of the graphite boat is changed due to the continuous increase of the silicon nitride film on the surface of the graphite boat within the range of the normal use times, the chromatic aberration problem still can be caused.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: how to reduce the chromatic aberration problem caused by the decrease of uniformity due to the increase of the silicon nitride film on the surface of the graphite boat.
The technical scheme adopted by the invention is as follows: PECVD color difference improvement method based on least square method is carried out by installing the following steps
Step one, measuring the average film thickness of each batch of silicon wafers when the graphite boat is recycled every q times in the using process;
step two, the average value of the film thickness of each batch in the s-time cyclic measurement process is obtainedm is the total number of batches of silicon wafers in the using process of each graphite boat, i is the ith cyclic measurement, and s is the total number of cyclic measurement;
step three, using a least square method to average the film thickness of each batchBatch fitting with silicon wafers in each graphite boat use process, and obtaining a fitting function phi (u i )；
Step four, according to the target film thickness and the fitting function phi (u) i ) The difference derives a function ψ (u i )；
Step five, supplementing the current deposition time G' withCorrecting the deposition time to obtain a color difference improvement deposition time g=g' +ψ (u) i ) The deposition is performed according to the color difference improving deposition time G.
The beneficial effects of the invention are as follows: and fitting a function which abandons the traditional artificial segmentation of a plurality of segmentation functions and changes the coating time of the nodes along with the use times of the graphite boat by using a least square method. The accuracy between the use times of the graphite boat and the coating time is improved, the coating compensating time is optimized, the coating color difference is greatly improved, and the industrial production popularization is facilitated.
Drawings
FIG. 1 is a graph showing the variation of film thickness with the number of uses of a graphite boat;
FIG. 2 is a graph showing a modified deposition time function ψ (u i ) A drawing.
Detailed Description
As shown in fig. 1, since the graphite boat has a certain service life, it must be removed from the cleaning machine for cleaning until a certain service life is reached. Therefore, the invention counts the data of the silicon wafer film thickness corresponding to the times of using the graphite boat for a plurality of times, and tries to predict the silicon wafer film thickness under the arbitrary times of using the graphite boat by using the data.
The PECVD color difference improvement method based on the least square method comprises the following steps:
step one, measuring the film thickness of each batch of silicon wafers every q times, wherein one graphite boat is a complete cycle from starting measurement to cleaning by a cleaning machine, so that the graphite boat needs to be used for s cycles (s is larger and better), the batches measured in the using process of the graphite boat are P, p+q, p+2q, p+3q and … p+ (m-1) q respectively, m is the total number of the batches of the silicon wafers in each graphite boat using process, namely m batches are measured in the complete cycle of the graphite boat, and P and q are set to be natural numbers smaller than 10 (P and q are smaller and more accurate).
Step two, carrying out average value calculation on the relation data of a plurality of using times of the graphite boat circulation s times and film thickness to list the data corresponding to the using times and the film thickness one by one,wherein the method comprises the steps of/>Is the average value of the film thickness per batch. As shown in Table 1 below
Step three, using a least square method to average the film thickness of each batchFitting batches of silicon wafers with each graphite boat in the using process, drawing a scatter diagram under a rectangular coordinate system, and obtaining normalized batch times u i And film thickness->Fitting function of +.>The concrete solution is as follows:
for any group u i And (3) withData points>Are m experimental points. Is provided withTogether m sets of data and m > n, where a 1 ，a 2 ，a 3 ，…a k For the coefficients of the fitting function, k is a natural number and n is a natural number. Assuming that the absolute error between the fitting value and the actual value is xiLet absolute error vector (residual)/(residual)> As long as the euclidean norm of the absolute error vector is minimized.
The norm of vector 2, the least squares method, is employed for ease of calculation. I.e. the minimum of the sum of squares of the residuals, i.eThe fitting function can be obtained>To obtain min ζ i Only min ζ is required i And 0. Only need to be to xi i Deviation-inducing, i.e.)>
Introduction of inner product
The above method can be rewritten as
Then there is
…
The least squares method equation is
A can be obtained by solving the positive definite matrix k (k=0, 1,2 …, n) so that the polynomial can be found
And step four, deducing a function expression display for correcting the deposition time according to the difference value of the target film thickness and the fitting function. Let the target film thickness be delta,
by depositing 1nm from the known empirical relationship of silicon nitride deposition 8s, the deposition time function ψ (u i )＝8[δ-Φ(u i )]
And fifthly, supplementing correction time to the current deposition time G' to improve chromatic aberration caused by the use of the boat. Let the current deposition time be T ', the new deposition time function with corrected deposition time after chromatic aberration improvement be g=g' +ψ (u) i )。
In this example, p=5 and q=5, and the number of times of use of the graphite boat and the thickness of the silicon wafer were counted as shown in the following table.
The normalized fitting function of the number of times of use and film thickness variation is realized by EXCEL, and the relation diagram is shown in figure 1, and R can be seen 2 The ratio of the regression square sum to the total dispersion square sum is expressed as the ratio of the total dispersion square sum to the regression square sum, and the larger the ratio is, the better the model is, and the more obvious the regression effect is. Where R is 2 The ratio = 0.9831 is large and the regression effect is good.
The functional expression for deriving the corrected deposition time from the difference between the target film thickness 83nm and the fitting function is shown as:
Ψ(u i )＝8[δ-Φ(u i )]
＝8[83-(-0.0002u i 2 +0.06u i +80.327)]
＝8[0.0002u i 2 -0.06u i +2.673]
＝0.0016 u i 2 -0.48u i +21.384
as shown in fig. 2
Supplementing correction time on the current deposition time G 'to obtain a normalized fitting expression of chromatic aberration caused by the number of times of use of the improved boat, wherein G=G' +0.0016u is shown i 2 -0.48u i +21.384。
Claims (1)
1. The PECVD color difference improvement method based on the least square method is characterized by comprising the following steps of: the steps of installation are as follows
Measuring the average film thickness of each batch of silicon wafers every q times in the using process of the graphite boat, wherein one graphite boat is a complete cycle of the graphite boat from starting measurement to cleaning by a cleaning machine, so that the graphite boat needs to be used for s times of cycles, the batches measured in the using process of the graphite boat are p, p+q, p+2q, p+3q, … p+ (m-1) q respectively, m is the total number of the batches of the silicon wafers in the using process of the graphite boat each time, namely, m batches are measured in the complete cycle of the graphite boat, p is the using number of the graphite boat in the first test, and p and q are natural numbers smaller than 10;
step two, the average value of the film thickness of each batch in the s-time cyclic measurement process of the graphite boat is obtainedm is the total number of batches of silicon wafers in each graphite boat use process, d mi For the film thickness during the ith cycle measurement in each batch, i is the ith cycle measurement, s is the total number of cycle measurements;
step three, using a least square method to average the film thickness of each batchBatch fitting of silicon wafers in each graphite boat use process, and obtaining normalized batch times u i Average value of film thickness->Fitting function of +.> Wherein a is 0 ，a 1 ，a 2 ，a 3 ，…a k K epsilon natural number and n epsilon natural number are coefficients of the fitting function;
step four, according to the target film thickness and the fitting function phi (u) i ) The difference derives a function ψ (u i )＝8[δ-Φ(u i )]Wherein δ is the target film thickness;
step five, at the current deposition time G ′ The upper supplement is used for correcting the deposition time,obtaining a color difference improving deposition time g=g ′ +Ψ(u i ) The deposition is performed according to the color difference improving deposition time G.
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