CN102289156B - Optimization method for NA-Sigma configuration of photoetching machine - Google Patents

Abstract

The invention provides an optimization method for the NA-Sigma configuration of a photoetching machine. The method provided by the invention comprises the following concrete courses: selecting a point with the greatest photoetching focal depth from two optimization directions which are set in advance; when the selected point does not meet the conditions, computing a new optimization direction and obtaining the corresponding point with the greatest photoetching focal depth in the new optimization direction to further judge whether the obtained point meets the conditions or not; and when the obtained point does not meet the conditions, updating the selected optimization direction until the obtained point with the greatest photoetching focal depth meets the conditions. The method provided by the invention can rapidly and effectively optimize to obtain the optimum NA-Sigma configuration, obtains the greatest photoetching focal depth and has high accuracy.

Description

A kind of optimization method of litho machine NA-Sigma configuration

Technical field

The present invention relates to the optimization method of a kind of projection lens of lithography machine numerical aperture and illuminator coherence factor (NA-Sigma) configuration, belong to litho machine parameter Cooperative Optimization field.

Background technology

Current large-scale integrated circuit generally adopts etching system manufacturing.Etching system mainly is divided into: light source, illuminator, mask, optical projection system and wafer five parts.Be incident on mask mask open part printing opacity after the light process illuminator shaping that light source sends; Through after mask, light is incident on the wafer that scribbles photoresist via optical projection system, so just mask graph is replicated on wafer.

The photoetching depth of focus is one of major parameter of estimating the etching system performance, it is defined as: in certain exposure latitude (exposure dose variation range), and be replicated under the constraint condition that mask graph on wafer satisfies certain dimension of picture error, pattern side wall angle, photoresist loss achieved maximum defocus amount.The larger explanation lithography performance of photoetching depth of focus is better.

In etching system, NA and Sigma are the key factors that affects the photoetching depth of focus.Wherein NA is directly proportional to photoetching resolution, and its square is inversely proportional to the photoetching depth of focus, therefore for to realize good photoetching resolution and large photoetching depth of focus, and must be to organically configuring between NA and Sigma.

Current, under different condition reasonably the NA-Sigma configuration had large quantity research (Li Yanqiu etc., the optical parametric configuration is on ArF lithography performance impact research [J]. electronics industry specialized equipment, 2004,33 (4): 36-39.).Above-mentioned research is mainly to determine the NA-Sigma configuration by the method for traversal emulation, namely the combination of all values in NA and Sigma scope is all traveled through one time, draw the graph of a relation of NA-Sigma and photoetching depth of focus, then select to obtain the NA-Sigma configuration of maximum photoetching depth of focus.But this method often needs to travel through the probable value in all NA and Sigma scope, and calculated amount is larger, and precision is lower, is difficult to find out optimum NA-Sigma configuration.

Summary of the invention

The optimization method that the purpose of this invention is to provide a kind of litho machine NA-Sigma configuration; The method can fast and effeciently be optimized the NA-Sigma configuration with maximum photoetching depth of focus.

Realize that technical scheme of the present invention is as follows:

A kind of optimization method of litho machine NA-Sigma configuration, concrete steps are:

The value of step 101, given initial point NA and Sigma is made as (NA, σ) ^(1,0), determine the direction d that two initial linear are irrelevant ^(1,1)And d ^(1,2), setting search precision ε makes k=1;

Step 102, from (NA, σ) ^{(k, 0)}Set out, along direction d ^{(k, 1)}Search for, obtain upwards having the party point (NA, σ) of maximum photoetching depth of focus ^{(k, 1)}, when wherein if the value of this direction all-pair photoetching depth of focus of answering all equates, optional a bit as point (NA, σ) of maximum photoetching depth of focus ^{(k, 1)}From (NA, σ) ^{(k, 1)}Set out, along direction d ^{(k, 2)}Search for, obtain upwards having the party point (NA, σ) of maximum photoetching depth of focus ^{(k, 2)}, when wherein if the value of this direction all-pair photoetching depth of focus of answering all equates, optional a bit as point (NA, σ) of maximum photoetching depth of focus ^{(k, 2)}

If step 103 || (NA, σ) ^{(k, 2)}-(NA, σ) ^{(k, 0)}||≤ε makes (NA, σ)=(NA, σ) ^{(k, 2)}, enter step 109, wherein || || be modulo operation; Otherwise enter step 104;

Step 104, the new direction of search d of calculating ^{(k, 3)}=(NA, σ) ^{(k, 2)}-(NA, σ) ^{(k, 0)}From (NA, σ) ^{(k, 0)}Set out, along direction d ^{(k, 3)}Search for, obtain upwards having the party point (NA, σ) of maximum photoetching depth of focus ^{(k, 3)}

If step 105 || (NA, σ) ^{(k, 3)}-(NA, σ) ^{(k, 2)}||≤ε makes (NA, σ)=(NA, σ) ^{(k, 3)}, enter step 109; Otherwise enter step 106;

Step 106, as { f ((NA, σ) ^{(k, 0)})-f ((NA, σ) ^{(k, 1))}} 〉={ f ((NA, σ) ^{(k, 1)})-f ((NA, σ) ^{(k, 2)}) time, make m=1; As { f ((NA, σ) ^{(k, 0)})-f ((NA, σ) ^{(k, 1)})＜{ f ((NA, σ) ^{(k, 1)})-f ((NA, σ) ^{(k, 2))}The time, make m=2; F ((NA, σ) wherein ^{(p, q)}) expression point (NA, σ) ^{(p, q)}Corresponding photoetching depth of focus;

Step 107, order $\mathrm{\λ}=\frac{\left|\right|{(\mathrm{NA},\mathrm{\σ})}^{(k,3)}-{(\mathrm{NA},\mathrm{\σ})}^{(k,0)}\left|\right|}{\left|\right|{(\mathrm{NA},\mathrm{\σ})}^{(k,2)}-{(\mathrm{NA},\mathrm{\σ})}^{(k,0)}\left|\right|},$

If

Enter step 108; Otherwise, from (NA, σ) ^{(k, 1)}, (NA, σ) ^{(k, 2)}And (NA, σ) ^{(k, 3)}In choose the point with maximum photoetching depth of focus, make k add 1, and with selected point as initial point (NA, σ) ^{(k, 0)}, order direction of search d this moment ^{(k, 1)}And d ^{(k, 2)}Be former direction of search d ^(k-1,1)And d ^(k-1,2), return to step 102;

Step 108, the replacement direction of search: when m=1, this seasonal d ^(k+1,1)=d ^{(k, 2)}, d ^(k+1,2)=d ^{(k, 3)}When m=2, this seasonal d ^(k+1,1)=d ^{(k, 1)}, d ^(k+1,2)=d ^{(k, 3)}Make k add 1, order initial point (NA, σ) this moment ^{(k, 0)}Be initial point (NA, σ) originally ^(k-1,0), and return to step 102;

Value (NA, σ) and the best photoetching depth of focus f ((NA, σ)) of step 109, output NA-Sigma optimize and finish.

The present invention is in the described step 102, when along direction d ^{(k, 1)}Search the value of somewhat corresponding photoetching depth of focus when all equaling the photoetching depth of focus of this direction of search initial point, make (NA, σ) ^{(k, 1)}Equal (NA, σ) ^{(k, 0)}When along direction d ^{(k, 2)}Search the value of somewhat corresponding photoetching depth of focus when all equaling the photoetching depth of focus of this direction of search initial point, make (NA, σ) ^{(k, 2)}Equal (NA, σ) ^{(k, 1)}

The d of direction described in the present invention ^(1,1)Be edge [0,1] direction, described direction d ^(1,2)Be edge [1,0] direction.

Beneficial effect

The present invention optimizes directions by choosing two, and under constraint condition by being optimized optimizing direction, finally obtain the optimization direction with larger photoetching depth of focus gradient; Therefore adopt the present invention fast and effeciently to optimize and draw optimum NA-Sigma configuration, obtain maximum photoetching depth of focus, and higher precision is arranged.

Description of drawings

Fig. 1 is the process flow diagram of the optimization method of litho machine NA-Sigma configuration.

Fig. 2 is the coherent factor of photoetching machine lighting system schematic diagram.

Fig. 3 is the graph of a relation of NA-Sigma configuration and photoetching depth of focus.

Embodiment

Further the present invention is described in detail below in conjunction with accompanying drawing.

Fig. 1 is the process flow diagram of the optimization method of litho machine NA-Sigma configuration of the present invention, and its concrete steps are:

The value of step 101, initial point NA given according to the type of photo-etching machine illumination system and optical projection system and Sigma is made as (NA, σ) ^(1,0), (σ is the initial value of Sigma) determines the direction d that two initial linear are irrelevant ^(1,1), d ^(1,2), determine search precision ε＞0, wherein ε can determine according to the precision of NA and Sigma, for example, when the accuracy requirement of required NA and Sigma is higher, can arrange dilution of precision ε less; Make k=1.As shown in Figure 3, in the present embodiment, horizontal direction and vertical direction are set up coordinate axis, and wherein horizontal direction represents NA, and vertical direction represents Sigma; Make inceptive direction d ^(1,1)Be edge [0,1] direction, direction d ^(1,2)Be edge [1,0] direction.

Step 102, from (NA, σ) ^{(k, 0)}Set out, along direction d ^{(k, 1)}Be along [0,1] (vertically) direction is searched for, wherein said search is to carry out according to the vertical step-size in search of setting, even NA is constant, according to the vertical step-size in search of the setting σ that gradually changes, acquire the point (NA, σ) that in the vertical direction has maximum photoetching depth of focus in the desirable scope of σ ^{(k, 1)}, wherein, if when the value of the photoetching depth of focus that the vertical direction all-pair is answered all equates, choose any wantonly as point (NA, σ) of maximum photoetching depth of focus ^{(k, 1)}What the present invention was better is set as: if when the photoetching depth of focus of all some correspondences of in the vertical direction search all equates, and this season (NA, σ) ^{(k, 1)}Equal (NA, σ) ^{(k, 0)}

From (NA, σ) ^{(k, 1)}Set out, along direction d ^{(k, 2)}Be along [1,0] (level) direction is searched for, wherein said search is to carry out according to the horizon scan step-length of setting, even σ is constant, according to the horizon scan step-length of the setting NA that gradually changes, acquire the point (NA, σ) that has in the horizontal direction maximum photoetching depth of focus in the desirable scope of NA ^{(k, 2)}, when wherein if the value of the horizontal direction all-pair photoetching depth of focus of answering all equates, optional a bit as point (NA, σ) of maximum photoetching depth of focus ^{(k, 2)}What the present invention was better is set as: if when the photoetching depth of focus of all some correspondences of search all equates in the horizontal direction, and this season (NA, σ) ^{(k, 2)}Equal (NA, σ) ^{(k, 1)}The horizon scan step-length of choosing better in this enforcement equates with vertical step-size in search.

Step 103, judgement direction d ^{(k, 2)}Point (NA, σ) corresponding to upper maximum photoetching depth of focus ^{(k, 2)}With given initial point (NA, σ) ^{(k, 0)}Between the size of distance, if || (NA, σ) ^{(k, 2)}-(NA, σ) ^{(k, 0)}||≤ε makes (NA, σ)=(NA, σ) ^{(k, 2)}, enter step 109, wherein || || be modulo operation; Otherwise enter step 104.

Step 104, the new direction of search d of calculating ^{(k, 3)}=(NA, σ) ^{(k, 2)}-(NA, σ) ^{(k, 0)}From (NA, σ) ^{(k, 0)}Set out, along direction d ^{(k, 3)}Search for, wherein said search is in σ and the desirable scope of NA, carries out according to the step-length of setting, and obtains the point (NA, σ) with maximum photoetching depth of focus ^{(k, 3)}

Step 105, judgement direction d ^{(k, 3)}Point (NA, σ) corresponding to upper maximum photoetching depth of focus ^{(k, 3)}With direction d ^{(k, 2)}Point (NA, σ) corresponding to upper maximum photoetching depth of focus ^{(k, 2)}Between the size of distance, if || (NA, σ) ^{(k, 3)}-(NA, σ) ^{(k, 2)}||≤ε makes (NA, σ)=(NA, σ) ^{(k, 3)}, enter step 109; Otherwise enter step 106.

Step 106, judgement { f ((NA, σ) ^{(k, 0)})-f ((NA, σ) ^{(k, 1)}) and { f ((NA, σ) ^{(k, 1)})-f ((NA, σ) ^{(k, 2)}) size, f ((NA, σ) wherein ^{(p, q)}) expression point (NA, σ) ^{(p, q)}Corresponding photoetching depth of focus;

As { f ((NA, σ) ^{(k, 0)})-f ((NA, σ) ^{(k, 1)}) 〉={ f ((NA, σ) ^{(k, 1)})-f ((NA, σ) ^{(k, 2)}) time, show that this moment is along direction d ^{(k, 1)}The variable quantity of photoetching depth of focus is larger, this seasonal m=1;

As { f ((NA, σ) ^{(k, 0)})-f ((NA, σ) ^{(k, 1)})＜{ f ((NA, σ) ^{(k, 1)})-f ((NA, σ) ^{(k, 2)}) time, show that this moment is along direction d ^{(k, 2)}The variable quantity of photoetching depth of focus is less, this seasonal m=2.

Step 107, order

Judge current search direction d by λ ^{(k, 1)}And d ^{(k, 2)}With new direction of search d ^{(k, 3)}Linear independence, determine whether that according to the result of judgement needs are with new direction of search replacement current search direction d ^{(k, 1)}And d ^{(k, 2)}The process of judgement is as follows:

If Show the direction of search d that this is stylish ^{(k, 3)}Have better linear independence with in the first two direction of search one, enter step 108 this moment, with of the new original direction of search of direction of search replacement; Otherwise, from (NA, σ) ^{(k, 1)}, (NA, σ) ^{(k, 2)}And (NA, σ) ^{(k, 3)}In choose the point with maximum photoetching depth of focus, make k add 1, and with selected point as initial point (NA, σ) ^{(k, 0)}, order direction of search d this moment ^{(k, 1)}And d ^{(k, 2)}Be former direction of search d ^(k-1,1)And d ^(k-1,2), return to step 102.

Step 108, the replacement direction of search:

When m equals 1, this seasonal d ^(k+1,1)=d ^{(k, 2)}, d ^(k+1,2)=d ^{(k, 3)}Guarantee two direction of search linear independences that determine this moment, and along with the continuity of iteration, the direction of search increases gradually near the degree of conjugation.

When m equals 2, this seasonal d ^(k+1,1)=d ^{(k, 1)}, d ^(k+1,2)=d ^{(k, 3)}Guarantee two direction of search linear independences that determine this moment, and along with the continuity of iteration, the direction of search increases gradually near the degree of conjugation.

Make k add 1, order initial point (NA, σ) this moment ^{(k, 0)}Be initial point (NA, σ) originally ^(k-1,0), and return to step 102.

The value (NA, σ) of step 109, output NA-Sigma and corresponding best photoetching depth of focus f ((NA, σ)) optimize and finish.

The invention process example:

The below is configured to example explanation optimizing process of the present invention to optimize 45nm node litho machine NA-Sigma.

To the intensive lines of 45nm node, adopt liquid immersion lithography, the immersion liquid refractive index is 1.44, numerical aperture of projection objective is [1,1.35] interior adjustable, exposure wavelength is 193nm, improve its resolution and increase the photoetching depth of focus with resolution enhance technology, mask-type is selected attenuated phase-shifting mask, lighting system is selected ring illumination, in order to guarantee productive rate, the ring width of ring illumination mode is chosen as 0.15, is also that the difference between the external coherence system factor and interior coherence factor is 0.15 (Δ σ=σ when improving resolution _out-σ _in=0.15), as shown in Figure 2.In order further to increase the photoetching depth of focus, used the linearly polarized light identical with line orientations during lithography simulation.For a kind of like this photoetching configuration, the hunting zone of the external coherence system factor is [0.15,1], and the search precision of NA and Sigma is 0.001, and initial NA-Sigma is configured to (1.1,0.8), and initial search direction is [0,1; 1,0].Determine best NA-Sigma configuration below by method of the present invention, to obtain maximum photoetching depth of focus.

Fig. 3 draws the graph of a relation of NA-Sigma configuration and photoetching depth of focus under above-mentioned condition for the method by traversal emulation.As can be seen from Figure 3, NA and Sigma only can obtain the photoetching depth of focus in the sub-fraction zone, as wanting the NA-Sigma configuration of accomplished maximum photoetching depth of focus, must accurately travel through this graph of a relation of emulation in NA and Sigma variation range.Accurately traveling through this graph of a relation of emulation consuming time is 17 hours.

following table is for adopting search iteration process of the present invention, from iterative process, initial point NA-Sigma configuration (1.1, 0.8) the photoetching depth of focus located is 0, along [0, 1] still can not get the photoetching depth of focus after the direction search, return to (1.1, 0.8) point, again along [1, 0] direction search, can be (1.3496, 0.8) the some place can get maximum photoetching depth of focus 0.15442 μ m, the edge is from initial point (1.1 again, 0.8) and (1.3496, 0.8) between line direction (0.2496, 0.8) search for, still (1.3496, 0.8) the some place obtains maximum depth of focus 0.15442 μ m, judge that it does not satisfy the condition that finishes of optimizing, beginning the second search of taking turns.second takes turns search from (1.3496, 0.8) put and set out, first along [0, 1] direction search, can be (1.3496, 0.90184) the some place can get maximum photoetching depth of focus 0.38657 μ m, again along [1, 0] direction search, can be (1.3004, 0.90184) the some place can get maximum photoetching depth of focus 0.46063 μ m, the edge is from initial point (1.3496 again, 0.8) and (1.3004, 0.90184) between line direction (0.0492, 0.1447) search for, (1.2797, 0.9447) the some place obtains maximum photoetching depth of focus 0.52215 μ m, it does not satisfy the condition that finishes of optimizing, the search of beginning third round, so move in circles, until satisfy the condition of convergence, till, drawing at last at (1.2214,0.97017) some place has maximum photoetching depth of focus 0.62192 μ m, and search finishes, and this invention is consuming time is 8 minutes, specifically as shown in table 1:

Table 1 is chosen the number of times that adopts search iteration of the present invention

	NA	Sigma	DOF(μm)
				First round search
	1.1	0.8	0
					1.3496	0.8	0.15442
	1.3496	0.8	0.15442
				Second takes turns search
	1.3496	0.90184	0.38657
					1.3004	0.90184	0.46063

	1.2797	0.9447	0.52215
				The third round search
	1.2797	0.9447	0.52215
					1.2518	0.9447	0.55768
	1.2518	0.9447	0.55768
				The fourth round search
	1.2518	0.9546	0.56742
					1.2369	0.9546	0.58217
	1.2214	0.96493	0.61567
				The 5th takes turns search
	1.2214	0.97017	0.62192
					1.2214	0.97017	0.62192
	1.2214	0.97017	0.62192

Although described by reference to the accompanying drawings the specific embodiment of the present invention, for those skilled in the art, under the premise of not departing from the present invention, can also do some distortion, replacement and improvement, these also are considered as belonging to protection scope of the present invention.

Claims (3)

1. the optimization method of litho machine NA-Sigma configuration, described NA is numerical aperture of projection objective, and described Sigma is the illuminator coherence factor, it is characterized in that, and concrete steps are:

The value of step 101, given initial point NA and Sigma is made as (NA, σ) ^(1,0), determine the direction d that two initial linear are irrelevant ^(1,1) and d ^(1,2), setting search precision ε makes k=1;

Step 102, from (NA, σ) ^{(k, 0)}Set out, along direction d ^{(k, 1)}Search for, obtain upwards having the party point (NA, σ) of maximum photoetching depth of focus ^{(k, 1)}, when wherein if the value of this direction all-pair photoetching depth of focus of answering all equates, optional a bit as point (NA, σ) of maximum photoetching depth of focus ^{(k, 1)}From (NA, σ) ^{(k, 1)}Set out, along direction d ^{(k, 2)}Search for, obtain upwards having the party point (NA, σ) of maximum photoetching depth of focus ^{(k, 2)}, when wherein if the value of this direction all-pair photoetching depth of focus of answering all equates, optional a bit as point (NA, σ) of maximum photoetching depth of focus ^{(k, 2)}

If step 103 || (NA, σ) ^{(k, 2)}-(NA, σ) ^{(k, 0)}||≤ε makes (NA, σ)=(NA, σ) ^{(k, 2)}, enter step 109, wherein || || be modulo operation; Otherwise enter step 104;

Step 104, the new direction of search d of calculating ^{(k, 3)}=(NA, σ) ^{(k, 2)}-(NA, σ) ^{(k, 0)}From (NA, σ) ^{(k, 0)}Set out, along direction d ^{(k, 3)}Search for, obtain upwards having the party point (NA, σ) of maximum photoetching depth of focus ^{(k, 3)}

If step 105 || (NA, σ) ^{(k, 3)}-(NA, σ) ^{(k, 2)}||≤ε makes (NA, σ)=(NA, σ) ^{(k, 3)}, enter step 109; Otherwise enter step 106;

Step 106, as { f ((NA, σ) ^{(k, 0)})-f ((NA, σ) ^{(k, 1)}) 〉={ f ((NA, σ) ^{(k, 1)})-f ((NA, σ) ^{(k, 2)}) time, make m=1; As { f ((NA, σ) ^{(k, 0)})-f ((NA, σ) ^{(k, 1)})＜{ f ((NA, σ) ^{(k, 1)})-f ((NA, σ) ^{(k, 2)}) time, make m=2; F ((NA, σ) wherein ^{(p, q)}) expression point (NA, σ) ^{(p, q)}Corresponding photoetching depth of focus;

Step 107, order $\mathrm{\λ}=\frac{\left|\right|{(\mathrm{NA},\mathrm{\σ})}^{(k,3)}-{(\mathrm{NA},\mathrm{\σ})}^{(k,0)}\left|\right|}{\left|\right|{(\mathrm{NA},\mathrm{\σ})}^{(k,2)}-{(\mathrm{NA},\mathrm{\σ})}^{(k,0)}\left|\right|}$

If

Enter step 108; Otherwise, from (NA, σ) ^{(k, 1)}, (NA, σ) ^{(k, 2)}And (NA, σ) ^{(k, 3)}In choose the point with maximum photoetching depth of focus, make k add 1, and with selected point as initial point (NA, σ) ^{(k, 0)}, order direction of search d this moment ^{(k, 1)}And d ^{(k, 2)}Be former direction of search d ^{(k-1, 1)}And d ^(k-1,2), return to step 102;

Step 108, the replacement direction of search: when m=1, this seasonal d ^(k+1,1)=d ^{(k, 2)}, d ^(k+1,2)=d ^{(k, 3)}When m=2, this seasonal d ^(k+1,1)=d ^{(k, 1)}, d ^(k+1,2)=d ^{(k, 3)}Make k add 1, order initial point (NA, σ) this moment ^{(k, 0)}Be initial point (NA, σ) originally ^(k-1,0), and return to step 102;

Value (NA, σ) and the best photoetching depth of focus f ((NA, σ)) of step 109, output NA-Sigma optimize and finish.

2. optimization method according to claim 1, is characterized in that, in described step 102, when along direction d ^{(k, 1)}Search the value of somewhat corresponding photoetching depth of focus when all equaling the photoetching depth of focus of this direction of search initial point, make (NA, σ) ^{(k, 1)}Equal (NA, σ) ^{(k, 0)}When along direction d ^{(k, 2)}Search the value of somewhat corresponding photoetching depth of focus when all equaling the photoetching depth of focus of this direction of search initial point, make (NA, σ) ^{(k, 2)}Equal (NA, σ) ^{(k, 1)}

3. optimization method according to claim 1, is characterized in that, described direction d ^(1,1)Be edge [0,1] direction, described direction d ^(1,2)Be edge [1,0] direction.

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