CN104866680B - The optimal spacing acquiring method of mirror body dorsal part cooling pipe in a kind of extreme ultraviolet collection system - Google Patents
The optimal spacing acquiring method of mirror body dorsal part cooling pipe in a kind of extreme ultraviolet collection system Download PDFInfo
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Abstract
The invention discloses a kind of optimal spacing acquiring method of mirror body dorsal part cooling pipe in extreme ultraviolet collection system, its step are as follows：S1：According to mirror body heat flux distribution feature, mirror body dorsal part cooling tube global alignment placement scheme is primarily determined that；S2：The heat transfer physical model of actual conditions can be reflected by establishing；S3：The mathematical calculation model of heat transfer between mirror body and cooling pipe is established, and tentatively tries to achieve the Temperature Distribution of mirror body in axial direction；S4：Tube wall temperature otherness caused by considering current heat absorption heating, adds one group of energy conservation relation formula, solves more accurate mirror body temperature again in the calculation；S5：Based on S1, S2, S3, S4 technical scheme steps, the optimal spacing optimization program of cooling tube is write, and each single tube spacing is added in sequential operation as last cyclic variable, tries to achieve the optimal solution of adjacent single tube spacing.The present invention can accurately calculate the optimal solution of cooling pipe spacing so that whole mirror body reaches uniform and stable Temperature Distribution in extreme ultraviolet collection system, so as to accurately design optimizing property of cooling pipe alignment placement.
Description
Technical field
The present invention relates to one kind in extreme ultraviolet photolithographic, extreme ultraviolet collection system reflector body cooling pipe alignment placement
Optimal spacing acquiring method.
Background technology
Proximal pole ultraviolet photolithographic (EUVL) is considered as one of photoetching technique most with prospects of future generation.In recent years,
The research and development institution of external several extreme ultraviolet lithographies achieves some breakthrough progress, if light source power is progressively and steadily and surely
Ground is improved, and collection system, lighting system, optical projection system constantly optimize, the preparation of mask plate and photoresist
Technique is continually improved.
However, in the extreme ultraviolet lithography early stage of development, R＆D work is the raising of emphasis light source power simply, and
Do not focus under working state of system high heat caused by high power light source and import problem, and the high temperature pair caused by intense radiation
The service life of follow-up system and performance influence to be fatal.
, can be tens of if the high heat of absorption cannot be discharged timely and effectively for extreme ultraviolet collection system
Mirror substrate temperature is steeply risen in second, on the one hand can cause the temperature distortion of collection system mirror body, cause through speculum
The light of reflection can not effectively be converged at intermediate focus, collection system collection efficiency is declined to a great extent, at intermediate focus
Hot spot also can gross distortion, Energy distribution is uneven, this be all to follow-up lighting system and exposure system it is extremely disadvantageous, finally
It can cause the of poor quality of photoetching chip, low output, can not meet the requirements；On the other hand, urgency is caused after mirror absorption high heat
Play heating, makes mirror substrate and film layer service life seriously reduce.
The content of the invention
It is an object of the invention to the heat dissipation problem for collection system mirror body in extreme ultraviolet photolithographic, it is proposed that a kind of extremely purple
The optimal spacing acquiring method of mirror body dorsal part cooling pipe in outer collection system.This method passes through axially non-homogeneous to cooling pipe
Distribution carries out theory analysis, under conditions of whole mirror body surface temperature difference scope minimum is required, utilizes the thermal conduction study such as heat conduction, convection current
Equation accurately calculates the optimal solution of cooling pipe spacing.
To achieve these goals, adopt the following technical scheme that：
S1：According to mirror body heat flux distribution feature, mirror body dorsal part cooling tube global alignment placement scheme is primarily determined that, such as
Shown in Fig. 1.
S2：The heat transfer physical model of actual conditions can be reflected by establishing, as shown in Figure 2.
S3：The mathematical calculation model of heat transfer between mirror body and cooling pipe is established, as shown in figure 3, simultaneously tentatively trying to achieve mirror body
Temperature Distribution in axial direction.
S4：Tube wall temperature otherness caused by considering current heat absorption heating, adds one group of conservation of energy in interative computation
Relational expression, as shown in figure 4, solving more accurate mirror body temperature again.
S5：Based on S1, S2, S3, S4 technical scheme steps, the optimal spacing optimization program of cooling tube is write.It is total in cooling tube
Under the premise of body layout is known, minimum temperature difference is reached as optimization aim using mirror body, by input light source power, mirror body face type, cold
But the related physical property parameter of pipe size, cooling water cooling parameter and material, present invention optimization program can automated execution coolings
The optimization of tube spacing operates, and after loop iteration, can provide each adjacent cooling tube pitch after optimization.Afterwards, by between each single tube
Away from being added to as last cyclic variable in sequential operation, the optimal solution of adjacent single tube spacing is tried to achieve.Present invention optimization program
After the completion of writing, after tested, meet to be applicable in requirement, verification result can be referring to embodiment.
The concrete operation method of the step 2 is as follows：For certain layer of mirror body provided, the row of its dorsal part cooling pipe is determined
Cloth situation, G1, G2, G3 are end to end same root coiled pipes, and G4, G5 are another end to end coiled pipes, along mirror body
Axis direction can regard 5 single tubes as, and each single tube is wound with half of circumference of mirror body.S1, S2, S3, S4 be successively G1,
Arc length direction spacing between the adjacent cooling tube of G2, G3, G4, G5.
The concrete operation method of the step 3 is as follows：By the use of two angles be θ (θ is used as computing intermediate variable, it may not be necessary to
Provide numerical values recited) axial plane from the next fillet body of mirror body cutting, this fillet body is stretched vertically, forms one
Length is the narrow bar cuboid of S (S is the arc length of former fillet body vertically), this cuboid is divided into the small length that length is p
Cube, it is clear that p is smaller, and numerical stability is higher.If the width of small cuboid is u, the thickness of thickness d, d namely mirror body.
Mirror body is in contact with cooling pipe small cuboid (the small cuboid of black in Fig. 3), is referred to as " camera bellows ", temperature is followed successively by
T1, T2, T3, T4, T5 in stating.
Each small cuboid be applied in respectively on two surfaces using radial direction as normal direction mirror body minute surface heat flow density and
Mirror body dorsal part heat flow density, due to small cuboid dimensions very little, the heat flow density on two small surfaces can regard constant value as；Each small length
Cube carries out the transmission of hot-fluid by the face element that is in contact, these face elements energy transmission with the Inner Constitution of each small cuboid
" passage ", the heat for entering each small cuboid is flowed into " camera bellows " by this " passage ", and cooled water is taken away,
When whole diabatic process enters stable state, if neglecting the radiation between mirror body and environment, according to the conservation of energy, identical
In time, the sum of heat that each small cuboid is absorbed is equal to the heat that cooling water is taken away in " camera bellows ".
For the vivider above-mentioned physical process of description, each small cuboid is imagined as small with water inlet one by one
" water tank ", and mirror body dorsal part and cooling tube contact position (camera bellows) be equivalent to there is one " suction pump ", entering each small " water
The water of case " is all taken away in time, and whole system is in the process of a dynamic equilibrium.Two adjacent water pumps are between them
Water tank draws water, and the pumpage of each water pump pair and its similar water tank is strong, it therefore follows that in two pump houses, must deposit
In a location point, the current of each water tank on the left of this location point are made all to flow to the water pump in left side, positioned at this position
The current of each water tank on point right side all flow to the water pump on right side.
For convenience's sake, the heat flow density of mirror body both sides is first added summation, be re-applied in two surfaces wherein
One of.Assuming that N number of small cuboid is shared between adjacent two " camera bellows ", wherein there are the n1 heats by absorption to conduct to the left
" camera bellows ", has " camera bellows " of the n2 heat conduction by absorption to the right, there is n1+n2=N.And by these small cuboids by Ln1,
L (n1-1) ... L3, L2, L1, R1, R2, R3 ... R (n2-1), Rn2 are numbered, the total border hot-fluid of each small cuboid
Density is the heat of fz (i), i=Rn1 ... Rn2, each small cuboid absorption：
Q (i)=fz (i) * u*p (16)
Q (i) is when the small cuboid axially inside conducts, its heat flow density：
Fx (i)=Q (i)/(u*d)=fz (i) * p/d (17)
The total axial heat flux density of i-th small cuboid is：
Obtained by Fourier heat equation：
Wherein k is the thermal conductivity of material, qnIt is that direction vector isCertain section on heat flow density,For in this direction
Rate of temperature change.
There is following relation between two neighboring small cuboid：
Since two fz (i) and T (Ln1), T (Rn2) boundary temperatures are it is known that need to only circulate the apportioning cost for bringing n1 and n2 into,
Using above-mentioned iterative relation, when α=T (L1)-T (R1) ＜ 0.001 (or higher precision), iteration terminates, and at this moment thinks to solve
Go out the actual temperature of each small cuboid, also obtain the Temperature Distribution of whole mirror body in axial direction immediately.
The concrete operation method of the step 4 is as follows：If the heat that every single tube is taken away is Qi, i=1,2,3,4,5,
Obtained by heat transfer equation：
Qi=hA Δs TLM (22)
Obtained by the heat power equation of the conservation of energy and coolant：
Wherein, A is inner surface of tube wall area, cpFor the specific heat capacity of cooling water, m is the mass velocity of current, Δ T=Tout-
TinFor the temperature rise of current, TinWith ToutRespectively current water inlet and water outlet temperature, for the convenience calculated in engineering,
Logarithmic mean temperature difference (LMTD) is replaced using geometric mean temperature：
ΔTAM=Ti-(Tin+Tout)/2 (24)
H is the convective heat-transfer coefficient of cooling water,
H=λ * Nu/D
Nu=0.012* (Re^0.87-280) * Pr^0.4
Re=D*w/v (25)
Pr=v/ [λ/(ρ * cp)]
Wherein, λ is the thermal conductivity factor of cooling water；Nu is nusselt number, and what is provided in formula is between laminar flow and turbulent flow
Transition region when rule-of-thumb relation；Re is Reynolds number；Pr is planck number, during in transition region, Pr=7；D is straight for water pipe
Footpath, w are the mean flow rate of current, and v is kinematic viscosity, and ρ is density.
Single tube pipe wall average temperature is obtained by equation (22), (23), (24), (25)：
In cooling water physical parameter, flow parameter, pipe size is cooled down and under conditions of five single tube spacing give, formula (26)
In only Qi be loop iteration variable, again according to the conservation of energy understand, conducted through tube wall, the heat that cooling water convection current is taken away
A part of region of mirror bodies of the Qi near the single tube.When giving five single tubes, one initial value respectively, using formula (16)~
(21) it can obtain n1, n2, after effective heat sink region of each single tube determines, hot-fluid is carried out to these mirror body surface regions successively
The curve surface integral of density, can obtain the heat that each single tube is absorbed：
Qi=∫ ∫sfz(i)ds (27)
After Qi is determined, according to formula (26), one group of new each single tube temperature for being different from initial value is can obtain, by the new temperature
Number of degrees group brings formula (16)~(21) progress computing into again after being brought directly to or being done together with last initial value certain algorithm process, such as
This circulation is gone down, untill the tube wall temperature solved converges to the precision met the requirements.
Above although obtained tube wall temperature is correct, but is not also the final result that we want, because for
Above-mentioned solution procedure, the spacing between each single tube be assumed to be at the very start it is known that and give certain initial value, this hardly may be used
Can be optimal solution, so, also sequential operation is added to using spacing as last cyclic variable.So far, adjacent single tube
Between spacing optimal solution solution procedure finish.
The invention has the beneficial effects that according to the overall principle of cooling tube layout designs, by axial to cooling pipe
The theory analysis and program calculation of non-uniform Distribution, can accurately calculate the optimal solution of cooling pipe spacing so that extremely purple
Whole mirror body reaches uniform and stable Temperature Distribution in outer collection system, so as to accurately be carried out to cooling pipe alignment placement excellent
The property changed design.
Brief description of the drawings
Fig. 1 is mirror body dorsal part cooling pipe general arrangement scheme；
Fig. 2 is mirror body dorsal part cooling pipe arrangement schematic diagram；
The mathematical calculation model of Fig. 3 heat transfer between mirror body and cooling pipe；
Fig. 4 solves flow chart for adjacent single tube spacing optimal value.
Embodiment
Technical scheme is further described below in conjunction with the accompanying drawings, but is not limited thereto, it is every to this
Inventive technique scheme technical scheme is modified or replaced equivalently, without departing from the spirit and scope of technical solution of the present invention, should all cover
In protection scope of the present invention.
In EUV light source collection system, given light source and individual layer mirror body, the total heat flow density of its minute surface is：
Hyperboloid portion：Fz (x)=3557*exp (- 0.02009*x) -814.7*exp (- 0.2342*x)；
Ellipsoid part：Fz (x)=0.00687*x.^3-2.149*x.^2+217.8*x-5381；
(equation origin is mirror body axis and the intersection point of mirror body front end face)
Cooling water pipe internal diameter 5mm, outside diameter 8mm；Cool down water flow velocity 0.5889m/s, reynolds number Re=2944, water inlet temperature
20 DEG C of degree.
Assuming that N number of small cuboid is shared between adjacent two " camera bellows " (mirror body dorsal part and cooling tube contact position), wherein having
" camera bellows " of the n1 heat conduction by absorption to the left, has " camera bellows " of the n2 heat conduction by absorption to the right, there is n1+
N2=N.And by these small cuboids by Ln1, L (n1-1) ... L3, L2, L1, R1, R2, R3 ... R (n2-1), Rn2 carry out
Numbering, each total border heat flow density of small cuboid are the heat of fz (i), i=Rn1 ... Rn2, each small cuboid absorption
Amount：
Q (i)=fz (i) * u*p (16)
Q (i) is when the small cuboid axially inside conducts, its heat flow density：
Fx (i)=Q (i)/(u*d)=fz (i) * p/d (17)
The total axial heat flux density of i-th small cuboid is：
Obtained by Fourier heat equation：
Wherein k is the thermal conductivity of material, qnIt is that direction vector isCertain section on heat flow density,For in this direction
Rate of temperature change.
There is following relation between two neighboring small cuboid：
Since two fz (i) and T (Ln1), T (Rn2) boundary temperatures are it is known that need to only circulate the apportioning cost for bringing n1 and n2 into,
Using above-mentioned iterative relation, as α=T (L1)-T (R1) ＜ 0.001, iteration terminates, and at this moment thinks to have solved each small length
The actual temperature of cube, also obtain the Temperature Distribution of whole mirror body in axial direction immediately.
In the step 4, if the heat that every single tube is taken away is Qi, i=1,2,3,4,5, obtained by heat transfer equation：
Qi=hA Δs TLM (22)
Obtained by the heat power equation of the conservation of energy and coolant：
Wherein, A is inner surface of tube wall area, cpFor the specific heat capacity of cooling water, m is the mass velocity of current, Δ T=Tout-
TinFor the temperature rise of current, TinWith ToutRespectively current water inlet and water outlet temperature, for the convenience calculated in engineering,
Logarithmic mean temperature difference (LMTD) is replaced using geometric mean temperature：
ΔTAM=Ti-(Tin+Tout)/2 (24)
H is the convective heat-transfer coefficient of cooling water,
H=λ * Nu/D
Nu=0.012* (Re^0.87-280) * Pr^0.4
Re=D*w/v (25)
Pr=v/ [λ/(ρ * cp)]
Wherein, λ is the thermal conductivity factor of cooling water；Nu is nusselt number, and what is provided in formula is between laminar flow and turbulent flow
Transition region when rule-of-thumb relation；Re is Reynolds number；Pr is planck number, during in transition region, Pr=7；D is straight for water pipe
Footpath, w are the mean flow rate of current, and v is kinematic viscosity, and ρ is density.
Single tube pipe wall average temperature is obtained by equation (22), (23), (24), (25)：
In cooling water physical parameter, flow parameter, pipe size is cooled down and under conditions of five single tube spacing give, formula (26)
In only Qi be loop iteration variable, again according to the conservation of energy understand, conducted through tube wall, the heat that cooling water convection current is taken away
A part of region of mirror bodies of the Qi near the single tube.When giving five single tubes, one initial value respectively, using formula (16)~
(21) it can obtain n1, n2, after effective heat sink region of each single tube determines, hot-fluid is carried out to these mirror body surface regions successively
The curve surface integral of density, can obtain the heat that each single tube is absorbed：
Qi=∫ ∫sfz(i)ds (27)
After Qi is determined, according to formula (26), one group of new each single tube temperature for being different from initial value is can obtain, by the new temperature
Number of degrees group brings formula (16)~(21) progress computing into again after being brought directly to or being done together with last initial value certain algorithm process, such as
This circulation is gone down, untill the tube wall temperature solved converges to the precision met the requirements.
Finally, based on S1, S2, S3, S4 technical scheme steps, the optimal spacing optimization program of cooling tube is write, and by spacing
Sequential operation is added to as last cyclic variable.So far, the spacing optimal solution solution procedure between adjacent single tube finishes.
By optimization, G1, G2, G3, G4, G5 single tube axial coordinate value are respectively：
8.00 19.64 31.28 50.68 73.96 105 [mm]
The bulk temperature distribution of mirror body surface meets reality, and temperature value difference is less than 1 DEG C.
Claims (1)
- A kind of 1. optimal spacing acquiring method of mirror body dorsal part cooling pipe in extreme ultraviolet collection system, it is characterised in that the side Method step is as follows：S1：According to mirror body heat flux distribution feature, mirror body dorsal part cooling tube global alignment placement scheme is primarily determined that；S2：The heat transfer physical model of actual conditions can be reflected by establishing, and concrete operation method is as follows：For certain layer of mirror body provided, the arrangement situation of its dorsal part cooling pipe is determined, G1, G2, G3 are end to end same Root coiled pipe, G4, G5 are another end to end coiled pipes, regard 5 single tubes, each single tube winding as along mirror body axis direction Half of circumference of mirror body, S1, S2, S3, S4 are the arc length direction spacing between the adjacent cooling tube of G1, G2, G3, G4, G5 successively；S3：The mathematical calculation model of heat transfer between mirror body and cooling pipe is established, and tentatively tries to achieve the temperature of mirror body in axial direction Degree distribution, concrete operation method are as follows：Using the axial plane that two angles are θ from the next fillet body of mirror body cutting, this fillet body is stretched vertically, shape The narrow bar cuboid for being S into a length, is divided into the small cuboid that length is p, width u, thickness is by this cuboid D, mirror body and the region of each cooling tube joint, are referred to as " camera bellows ", temperature is followed successively by T1, T2, T3, T4, T5；Assuming that N number of small cuboid is shared between adjacent two " camera bellows ", wherein there are the n1 heats by absorption to conduct to the left " camera bellows ", there is " camera bellows " of n2 by the heats conduction of absorption to the right, there is a n1+n2=N, and by these small cuboids by Ln1, L (n1-1) ... L3, L2, L1, R1, R2, R3......R (n2-1), Rn2 are numbered, each total border of small cuboid Heat flow density is fz (i), i=Ln1, L (n1-1) ... L3, L2, L1, R1, R2, R3......R (n2-1), Rn2, each The heat that small cuboid absorbs is：Q (i)=fz (i) * u*p (16)；When the small cuboid axially inside conducts, its heat flow density is Q (i)：Fx (i)=Q (i)/(u*d)=fz (i) * p/d (17)；The total axial heat flux density of i-th small cuboid is：<mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>i</mi> </munderover> <mi>f</mi> <mi>x</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>p</mi> <mi>d</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>i</mi> </munderover> <mi>f</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>Obtained by Fourier heat equation：<mrow> <msub> <mi>q</mi> <mi>n</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>k</mi> <mfrac> <mrow> <mo>&part;</mo> <mi>T</mi> </mrow> <msub> <mo>&part;</mo> <mi>n</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>There is following relation between two neighboring small cuboid：<mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mi>k</mi> <mfrac> <mrow> <mi>&Delta;</mi> <mi>T</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mi>p</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow><mrow> <mi>T</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>&Delta;</mi> <mi>T</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mrow> <mi>k</mi> <mo>*</mo> <mi>d</mi> </mrow> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>i</mi> </munderover> <mi>f</mi> <mi>z</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>Due to fz (i) and T (Ln1), two boundary temperatures of T (Rn2) it is known that need to only circulate substitute into n1 and n2 apportioning cost, utilize The iterative relation of above-mentioned formula (21), when α=T (L1)-T (R1) is sufficiently small, iteration terminates, and at this moment thinks to have solved each The actual temperature of small cuboid, also obtain the Temperature Distribution of whole mirror body in axial direction immediately；S4：Tube wall temperature otherness caused by considering current heat absorption heating, adds one group of energy conservation relation in interative computation Formula, solves more accurate mirror body temperature again, and concrete operation method is as follows：If the heat that every single tube is taken away is Qi, i=1,2,3,4,5, obtained by heat transfer equation：Qi=hA Δs TLM(22)；Obtained by the heat power equation of the conservation of energy and coolant：<mrow> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>c</mi> <mi>p</mi> </msub> <mo>&CenterDot;</mo> <mover> <mi>m</mi> <mo>&CenterDot;</mo> </mover> <mo>&CenterDot;</mo> <mi>&Delta;</mi> <mi>T</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>Wherein, A is inner surface of tube wall area, cpFor the specific heat capacity of cooling water, m is the mass velocity of current, Δ T=Tout-TinFor The temperature rise of current, TinWith ToutRespectively temperature of the current in water inlet and water outlet；Logarithmic mean temperature difference (LMTD) is replaced using geometric mean temperature：ΔTAM=Ti-(Tin+Tout)/2 (24)；H is the convective heat-transfer coefficient of cooling water, then has：Wherein, λ is the thermal conductivity factor of cooling water；Nu is nusselt number；Re is Reynolds number；Pr is planck number；D is straight for water pipe Footpath, w are the mean flow rate of current, and v is kinematic viscosity, and ρ is density；Single tube pipe wall average temperature is obtained by equation (22), (23), (24), (25)：<mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>c</mi> <mi>p</mi> </msub> <mover> <mi>m</mi> <mo>&CenterDot;</mo> </mover> </mrow> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mi>h</mi> <mi>A</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>;</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...5</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>When giving five single tubes, one initial value respectively, n1, n2, effective heat absorption area of each single tube are obtained using formula (16)~(21) After domain all determines, successively these mirror body surface regions are carried out with the curve surface integral of heat flow density, obtains the heat that each single tube is absorbed Amount：Qi=∫ ∫sfz(i)ds (27)；After Qi is determined, according to formula (26), one group of new each single tube temperature for being different from initial value is obtained, by the new temperature array It is brought directly to or brings formula (16)~(21) progress computing, so circulation into again after certain algorithm process is done together with last initial value Go down, untill the tube wall temperature solved converges to the precision met the requirements；S5：Based on S1, S2, S3, S4 step, the optimal spacing optimization program of cooling tube is write, and using each single tube spacing as last Cyclic variable be added in sequential operation, try to achieve the optimal solution of adjacent single tube spacing.
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| CN102175427A (en) * | 2010-12-31 | 2011-09-07 | 中国科学院光电技术研究所 | Method for comprehensively testing stability of deep ultraviolet optical element |
| CN103433507A (en) * | 2013-09-23 | 2013-12-11 | 哈尔滨工业大学 | Finish machining method of direct lathe machining of optical collecting mirror in EUV (extreme ultra-violet) lithography light sources |
| CN103869633A (en) * | 2014-04-11 | 2014-06-18 | 哈尔滨工业大学 | Extreme ultraviolet lithography light source collection and illumination system |
| CN104345570A (en) * | 2013-07-24 | 2015-02-11 | 中芯国际集成电路制造(上海)有限公司 | Extreme ultraviolet lithography machine light source system and extreme ultraviolet exposure method |
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| CN102175427A (en) * | 2010-12-31 | 2011-09-07 | 中国科学院光电技术研究所 | Method for comprehensively testing stability of deep ultraviolet optical element |
| CN104345570A (en) * | 2013-07-24 | 2015-02-11 | 中芯国际集成电路制造(上海)有限公司 | Extreme ultraviolet lithography machine light source system and extreme ultraviolet exposure method |
| CN103433507A (en) * | 2013-09-23 | 2013-12-11 | 哈尔滨工业大学 | Finish machining method of direct lathe machining of optical collecting mirror in EUV (extreme ultra-violet) lithography light sources |
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