THE SPECTRAL RADIATIVE EFFECT OF Si/SiO 2 SUBSTRATE ON MONOLAYER ALUMINUM POROUS MICROSTRUCTURE

Transcription

1 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer TE PECTRAL RADIATIVE EFFECT OF i/io 2 UBTRATE ON MONOLAYER ALUMINUM POROU MICROTRUCTURE by aiyan YU, aochun ZANG *, Chengshuai U, Kexin WANG, and Liang JIN chool of En ergy ci ence and En gi neer ing, arbin In sti tute of Tech nol ogy, arbin, China Orig i nal sci en tific pa per In this work, we have in ves ti gated the o ret i cally the spec tral ra di a tive prop er ties of a monolayer alu mi num po rous microstructure, in clud ing wave length-se lec tive trans mis sion, re flec tion, and ab sorp tion. The fi nite-dif fer ence time-do main method for electromagnetics has been used to cal cu late the spec tral ra di a tive prop er ties of the monolayer alu mi num po rous microstructure. It is found that the ab sorp tion spec tra of the alu mi num po rous microstructure will gen er ate two peaks within the wave length rang ing from 1.0 to 15.0 mm at nor mal in ci dence of light. Then the sur - face plasma polarition res o nance could be ob served clearly in the ob tained re sults of this work, es pe cially on the top sur face near the or i fice. In side the po rous struc - ture, mag netic polariton is the cru cial mech a nism to elu ci date for the power ab - sorp tion en hance ment. Fur ther more, the ab sorp tion ca pac ity of the alu mi num po - rous struc ture with i/io 2 sub strate has been an a lyzed, to ex plain the in flu ence of base on the monolayer po rous ma te rial. The find ings in di cate that the ab sorp tance peak at 3 mm in ci dent wave length sig nif i cantly im proved with sil i con sub strate, while that of sil ica sub strate has lit tle dif fer ence with alu mi num po rous plate. The sil i con and sil ica bases dis rupted the dis tri bu tion of the elec tro mag netic fields of the orig i nal alu mi num po rous struc ture, and form a new mag netic field within the subbases. Mean while the in ter nal microcavity polarition of the po rous struc ture has en hanced ob vi ously near the bases. Key words: po rous microstructure, ra di a tive, ab sorp tance, sub strate Introduction To achieve per fect ra di a tive char ac ter is tics of mi cro nanostructure in dif fer ent wave - length ranges is of vi tal im por tance in ap pli ca tions such as so lar en ergy har vest ing [1], air craft ra di a tive cool ing [2], and chem i cal sens ing [3]. Thor ough de vel op ment of the fun da men tals of microscale ra di a tion is avail able in re cent re search, such as sur face plasmon polaritons [4, 5], microcavity res o nance ef fect [6, 7], and pho ton tun nel ing ef fect [8, 9], etc. In the early 1970s, microscale ra di a tion ef fect was found by Zang and Tien et al. [10, 11]. Then sim u la tion re ceives more rec og ni tion with the rapid ex pand ing of com puter tech nol ogy in microscale ra di a tion. Mulet et al. [12] and Francoeur et al. [13] pointed out that the mag ni tude of microscale ra di a tion heat trans fer be tween two closely semi-in fi nite plates ex ceeded Planck's blackbody ra di a tion. Liu et al. [14] stud ied near-field ra di a tive heat trans fer of i based metamaterials us ing fluc tu a - tion elec tro dy nam ics method. The gen eral method to deal with microscale heat trans fer prob - * Corresponding author, ces@vip.126.com

2 630 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer... lems was based on fluc tu a tion dis si pa tion the o rem [15]. The other gen eral method to solve microscale ra di a tive with out heat trans fer is based on dis crete Maxwell equa tions com bined with ma te rial equa tions [16]. Fu et al. [17] sim u lated reflectance of 1-D ran dom rough ness sur - face by us ing fi nite-dif fer ence time-do main (FDTD). Chen et al. [18] nu mer i cally in ves ti gated op ti cal re sponses of deep slits at trans verse mag netic by us ing rig or ous cou pled-wave anal y sis and found that the op ti cal re sponse was much dif fer ent for slits with dif fer ent at tached fea tures. Klimov et al. [19] re ported on the fun da men tal con straints per tain ing to the en hance ment of the ra di a tive emis sion rate achiev able with pla nar lamellar metamaterials of any kind. Zheng [20] fo cused on a meth od ol ogy about ad just ing the wave length se lec tiv ity of thin films em bed ded with nanoparticles. o far, cur rent re searches on the po rous ar ray micro struc tures mostly stay in the prep a - ra tion stage, while the com pre hen sive stud ies of their spec tral ra di a tive prop er ties are still de - manded. In this study, we in ves ti gated the o ret i cally the spec tral ra di a tive prop er ties of a po rous microstructure us ing the FDTD method for electromagnetics. Alu mi num was cho sen as the ma - te rial for its abil ity of tem per a ture sta bil ity and ease to elec tro chem i cal pro cess ing. The struc ture con tained the ar rays of uni formly sized spher i cal pores which or dered closely in side and the whole void spaces be tween the pores are filled up with alu mi num. More over, the spec tral ra di a - tive prop er ties of the po rous microstructure have been stud ied when the ba sis of dif fer ent ma te - ri als sub strate added. Fi nally we ex plored the en ergy ab sorp tion dis tri bu tion and how to en - hance the mech a nism of ab sorp tion of the alu mi num po rous microstructure. Physical model Alu mi num metal foam can be fab ri cated by some ma ture meth ods such as the prep a ra - tion meth ods of in verse opals. Among these meth ods, the col loi dal crys tal-templating ap proach has been used to pre pare 3-D or dered po - rous ma te ri als [21]. The alu mi num po - rous cell that was ob tained by means of in verse opals method can be sim pli fied into a spher i cal po rous el e ment cell model which was shown in fig. 1, with two fol low ing as sump tions: there is no metal ox i da tion on the sur face of alu mi - num and the el e ment is a smooth sur face. The po ros ity of each cell was 0.77, the Figure 1. The microporous configuration; (a) porous cell (b) porous monolayer structure Figure 2. The microporous substrate models configuration; (a) i substrate structure (b) io 2 substrate structure height of alu mi num po rous monolayer, l, and the edge length of alu mi num cell was 2.54 m and the ra dius of the in ner po - rous, r, was 1.5 m. The i and io 2 with their ex cel lent spec tral ra di a tion con trol - ling abil ity are com monly used in op ti cal com po nents es pe cially as sub strate ma te - rial which was shown in fig. 2. In this pa per, we use these mod els to study the ef fect of the sub strate on the alu mi num po rous monolayer struc ture. To sim plify the cal cu la tion, we as sume that the sub strate layer height, h, was in

3 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer di rect pro por tion to the height of alu mi num po rous monolayer, l, and the pro por tional co ef fi - cient was here a con stant equal to h/l = 1. Numerical details Governing equations The fi nite vol ume mod el ing was con ducted by ap ply ing the sim u la tion soft ware FDTD. The ba sic the ory of Maxwell func tion can gov ern the dis tri bu tion of electromag-netic phe nom ena, whose curl equa tions and con sti tu tive equa tions are writ ten: D J t (1a) B E M t (1b) B r e (1c) D r m (1d) where [V/m] is the mag netic field in ten sity, E [A/m] the elec tric field in ten sity, B [Wb/m 2 ] the mag netic flux den sity, D [C/m 2 ] the elec tric dis place ment vec tor, J [A/m 2 ] the cur rent den sity, t [s] the time, r [C/m 3 ] the de signed the vol ume charge den sity. The eqs. (1a) and (1b) de scribe, re spec tively, the in ter ac tion of elec tric field in ten sity and mag netic flux den sity in a vac uum. The ma te rial equa tions are given [20]: D e E (2a) B m (2b) J s E where e [F/m] is the permittivity, m [/m] the per me abil ity, s [/m] the con duc tiv ity. Fi - nally, the Maxwell func tion is ob tained by in sert ing eqs. (2) into eqs. (1) as eqs. (3): E e se t E m t (2c) (3a) (3b) 0 (3c) E r e In 3-D Car te sian co-or di nate sys tem, these equa tions can be writ ten as eqs. (4): E x 1 y E z s t m x z y y 1 E z E x t s m y z y x m m y x y (3d) (4a) (4b)

4 632 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer... E E z 1 x y s t m z z y m z E x 1 z y s x e E t e x y z E y 1 x z e s y E t ey z x E z 1 y x s e z E t e z x y where x, y, and z are the axis in the Car te sian co-or di nate sys tem. Equa tions (4) es tab lishes the re la tion ship be tween Maxwell function and phys i cal model me dia. Dur ing the cal cu la tion, the top and bot tom are treated as the per fectly matched bound ary-layer con di tions. Ab sorp tion scat ter ing cross-sec tion In elec tro mag netic the ory, the ab sorp tion scat ter ing cross-sec tion is de fined: ( i ) c Re { E ( i ) ( i )*} (5) 8p c W ( a ) Re [ E ( i ) ( s )* E ( s ) ( ( i )* ( s )* )] ndxd y (6) 8p where is the Poynting vec tor, n the unit out ward nor mal, W (a) [W/s] the rate of ab sorp tion scat ter ing, the sys tem av er age, su per script (i) the in ci dence, (s) the scat ter ing, * the con ju gate com plex vec tor, and Re the real part. Ra tio W (a) / (i) is: x z y z (4c) (4d) (4e) (4f) Q ( a) W ( a) ( i) Re [ E ( i) ( s)* E ( s) ( ( i)* ( s)* )] ndxdy Re( E ( i ) ( i )* ) (7) where Q (a) [m 2 ] is the ab sorp tion cross-sec tion. When it co mes to monolayer microstructure is com posed its ab sorp tive ca pac ity can be ex pressed as the ab sorp tive ca pac ity: A 1 ( ( r ) ( t ) ) gndxdy ( i) gndxdy where (r) rep re sents the en ergy of re flec tion, while (t) is the trans mis sion en ergy flow. The A is the ab sorp tance. In the same way, reflectance R and trans mit tance T can be ex pressed as eqs. (9) and (10): R T ( r) ( i) ( t) ( i) gndxdy gndxdy gndxdy (8) (9) gndxd y (10)

5 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer In this pa per eqs. (9)-(11) were used to study the spec tral ra di ant char ac ter is tics of high po ros ity alu mi num po rous monolayer struc ture with dif fer ent bases. Re sult and dis cus sion These com pu ta tions were car ried out on a 3.4 Gz Intel 8-Core E v3 pro ces sor Win dows 7 server and 16 GB RAM. The in ci dence was TEM wave rang ing of 0.1 m l 15 m, which was di vided into 300 in ter vals for spec tral cal - cu la tions. In this study, a mesh size of l/100 was used, de pend ing the check ing of the grid in de pend ence. The pre vi ous di elec tric con stant was cal cu lated by us ing the n, k model. The absorbance of the monolayer alu mi num cell struc ture was avail able ac cord ing to the Drude model [22]. The dif fer ent Drude mod els were used to cal cu late the ab sorp - tance of the monolayer spher i cal po rous alu mi num struc ture as shown in fig. 3. The di elec tric con stant of the ma te rial was dif - fer ent when the Drude model was used to de scribe the change of the ab sorp tion curve. In the range of 1~3 m, there was an ir reg u lar ab sorp tion peak, which was rel a tively smaller com pared to 4.3 m wave length, and the peak at 4.3 mm does not change with the Drude model chang - ing. It can also be found that the absorbance of the model was the same, and the ab sorp tion rate of the n and k mod - els was the small est. ow ever, at 0.43 m, the ab sorp tion rate of the n and k mod els was 0.3, with the absorbance of the Drude model in creas ing to 0.6. Fig ure 4 showed that in the in fra red band range of 1~15 m, the in fi nite alu mi - num plate ab sorp tance was 0. The elec tro - mag netic waves are al most all re flected when ver ti cal in ci dence. The alu mi num plate showed full re flec tion char ac ter is tic in the mid dle and near in fra red band. For the alu mi num po rous monolayer struc - Figure 3. Absorbance of different drude models (for color image see journal web site) Figure 4. The spectral radiative properties; (a) aluminum plate (b) aluminum porous monolayer structure (for color image see journal web site)

6 634 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer... Figure 5. The current density distribution when the incidence wavelength is 2.86 mm ture, keep ing the in ci dent con di tions un - changed, its ab sorp tance, trans mis sion than the flat struc ture has un der gone great changes. What is more, at 3 m wave length, the value of ab sorp tance can reach 0.28, while at 4.5 m wave length, it was up to 0.3. In gen eral, the sur face plasma for ma - tion of the polarition was easy to pro duce ir - reg u lar peaks, and a wide peak can be found eas ily in the mag netic polarition for ma tion of the res o nance. To il lus trate this phe nom - e non more clearly, we drawn the elec tric field dis tri bu tion and mag netic field in ten - sity at these two places. Figure 5 showed the cur rent den sity dis - tri bu tion and sche matic of the alu mi num po - rous monolayer microstructure at nor mal in - ci dence of wave-length l = 2.86 m. There are three sec tions along y-axis, lo cat ing at, y = 635 nm, y = 0 nm, and y = 635 nm, re - spec tively. The color con tour shows the am - pli tude of the mag netic field, while the ar rows de note the in stan ta neous the di rec tion of the cur rent den sity. It was ob vi ous that there are two closed loops formed by the in duced cur rent near the up - per and lower sur faces of po rous struc ture. On the ba sis of Lenz's law, these two new mag netic fields are ac ti vated by the in duced cur rent along the di rec tion of x-axis which was op po site to the di rec tion of the in ci dent mag netic field. It can be seen that this res o nance ex ists only near sur face area and at tenu ates rap idly, which was a typ i cal char ac ter is tic of the sur face plasma res o nance (PR). In or der to con sider the in flu ence of the base on the struc ture, the base of the alu mi - num was added to i/io 2 sub strate un der the monolayer. In this re search, the thick - ness of i and io 2 sub strates was 2.54 m. At the wave length rang ing from 1~15 m, i is a non-dispersive ma te rial, whose re frac - tive in dex is usu ally 3.4, com par ing with io 2. The re frac tive in dex of the real and imag i nary parts [22] with the wave length of the re la tion ship is shown in fig. 6. The io 2 ma te rial is a di elec tric, as well as a dis per sion ma te rial in the in fra red band. The real part re duced with the in crease in wave length of 1~ 6 m, while the imag i nary part was kept at 0. When the wave length Figure 6. The io 2 refractive index with the wavelength of the relationship rang ing from 6.5~9 m, the real part also pro duced a sharper change, while the imag i - nary part raised a large pro tru sions and rapid

7 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer de clined. Us ing these char ac ter is tics of io 2 ma te rial, a con trol de vices with ra di a tion char ac ter is tics can be well de signed. Based on the previous data, we ob tained the i sub - strate and io 2 sub strate ab sorp tion trans - mis sion and re flec tion di a gram as shown in fig. 7. From fig. 7, the continuous irregular peaks are gen er ated in the 1~6 m band. The peaks are sharper and the width is nar rower, in this band, the res o nant state was strong, and the curve was al most no change in the 6~15 m band. The trend was con sis tent with that of the flat plate, in di cat ing that the change of the struc ture in the band will not af fect the op ti cal radiation characteristics of the material. The dif fer ence was that the trans mit tance and reflectance curves of the graph are sharper in the range of the wave length from 1-5 m. The ab sorp tance curve of the peak was not so sharp. Fig ure 8 showed the re la tion ship be tween the ab sorp tance of the monolayer spher i cal porous aluminum structure, i monolayer spherical porous aluminum structure, and io 2 monolayer spherical porous aluminum struc ture with wave length. The ab sorp tion rates of three struc tures are fluc tu at ing in the range of 1~6 m, while these three ab sorp tion curves co in cide with each other, in the 6~15 m band. The trend was con sis tent with the alu mi num plate on in creas ing and chang ing. The ab sorp tance of i sub strate had lit tle dif - fer ence with that of po rous alu mi num plate. To further analyze the mechanism reason of ab sorp tion peaks, figs. 9 and 10 were mapped to de scribe the elec tric field and mag netic in - ten sity in these two places. Fig ure 9 showed the cur rent den sity dis - tri bu tion and sche matic of the alu mi num po - rous monolayer microstructure and i/io 2 sub strate monolayer struc ture at nor mal in - ci dence of wave-length l = 3 m, lo cat ing the cross-sec tion at y = 0 mm. The color con - tour shows the am pli tude of the mag netic field, while the ar rows de note the in stan ta - neous the di rec tion of the cur rent den sity. Con trast with the figs. 10(a)-10(c), the dis - Figure 7. Absorption, transmission and reflection of i and io 2 substrate structures; (a) i substrate structure, (b) io 2 substrate structure (for color image see journal web site) Figure 8. The absorptance of three models (for color image see journal web site)

8 636 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer... Figure 9. The current density distribution when the incidence wavelength is 3 m Figure 10. The current density distribution when the incidence wavelength is 4.5 mm tri bu tion of the elec tric field in side the alu mi num was con sis tent, how ever, the strength of the PR ef fect of the microstructure was sig nif i cantly en hanced. Due to the ad di tion of the sub - strate, the mag ne ti za tion ef fect of the up per sur face of the alu mi num layer was en hanced, es pe - cially in te rior the alu mi num po rous monolayer, while the nether elec tric field was in the op po - site di rec tion, form ing a com pletely closed loop. The for ma tion of two groups of in duc tion elec tric filds af fects the ini tial cur rent dis tri bu tion in the po rous in te rior. For i and io 2, the rel - a tive of the ma te rial, namely n and k, caused the in ter nal elec tric field de flect ing di rectly, which formed the in duc tion mag netic field in dif fer ent di rec tions. Fig ure 10 shows the cur rent den sity dis tri bu tion and sche matic of the alu mi num po - rous monolayer microstructure and i/io 2 sub strate monolayer struc ture at nor mal in ci dence of wave length l = 4.5 m, lo cat ing the cross-sec tion at y = 0 mm. At this in ci dent fre quency, con trast ing fig. 9 with fig. 10, the dis tri bu tion of the elec tric field in side the alu mi num was con - sis tent, how ever, the strength of the PR ef fect of the microstructure en hance sig nif i cantly. Due to the ad di tion of the sub strate, the mag ne ti za tion ef fect of the up per sur face of the alu mi num layer en hance, es pe cially in te rior the alu mi num po rous monolayer, while the nether elec tric field was in the op po site di rec tion, form ing a com pletely closed loop. The for ma tion of two groups of in duc tion elec tric fields af fects the ini tial cur rent dis tri bu tion in the po rous in te rior. It was ob vi ous that the two closed loops formed by the in duced cur rent near the up per and lower sur faces of po rous struc ture en hance sig nif i cantly. Mean while, these small new mag netic loops formed within the base of the sub strate fur ther strengthen the sur face plas mas of the po rous struc ture. Con clu sions In this pa per, the spec tral char ac ter is tics of the spher i cal po rous alu mi num monolayer struc ture in the in fra red band with wave length rang ing from 1-15 m was cal cu lated by FDTD. The dis tri bu tions of the elec tric field and mag netic in ten sity were an a lyzed. Then the ab sorp tive ca pac ity of i and io 2 sub strate struc tures was con sid ered, re spec tively. We have con sulted the fol low ing con clu sions.

9 Yu,., et al.: The pectral Radiative Effect of i/io 2 ubstrate on Monolayer The ab sorp tive ca pac ity of the po rous struc ture of i and io 2 sub strate was cal cu lated. It was found that in wave length of 1~6 m, the sin gle layer of alu mi num cell struc ture with i sub strate could pro duce higher ab sorp tion peak, while the io 2 based struc ture could not at the wave length from 6 to 15 m. The ab sorp tive ca pac ity of these two struc tures and monolayer spher i cal po rous alu mi num cell struc ture had no dif fer ence. The high est ab sorp tance of sil i con sub strate was 0.76, which was three times higher than that of the po rous alu mi num plate. Acknowledgment This work is sup ported by the Na tional Nat u ral ci ence Foun da tion of China (Grant No , No ). Nomenclature A ab sorp tance, [ ] B mag netic flux den sity, [Wbm 2 ] D electric displacement E elec tric field in ten sity, [Am 1 ] mag netic field in ten sity, [Vm 1 ] J the cur rent den sity, [Am 2 ] n the unit out ward nor mal, [ ] Q (a) the ab sorp tion cross-sec tion, [m 2 ] R reflectance, [ ] poynting vec tor, [Wm 2 ] T trans mit tance, [ ] t time, [s] W (a) the rate of ab sorp tion, [Ws 1 ] x, y, z the axis in Car te sian co -or di nate, [ ] Greek sym bols e the permittivity, [Fm 1 ] m the per me abil ity, [m 1 ] r vol ume charge den sity, [Cm 3 ] u per script a s ab sorp tion scat ter ing References [1] choles, G. D., et al., Les sons from Na ture about o lar Light ar vest ing, Nature Chemistry, 3 (2011), 10 pp [2] uang, Z., et al., Nanoparticle Em bed ded Double-Layer Coating for Daytime Radiative Cooling, Interna - tional Jour nal of eat and Mass Trans fer, 104 (2017), Jan., pp [3] Wang,., et al., CFD tud ies of Dual Cir cu lat ing Fluidized Bed Re ac tors for Chem i cal Loop ing Com bus - tion Pro cesses, Chem i cal En gi neer ing Journal, 236 (2014), Jan., pp [4] Bolger, P., et al., Am pli fied pon ta ne ous Emis sion of ur face Plasmon Polaritons and Lim i ta tions on the In crease of Their Prop a ga tion Length, Op tics Let ters, 35 (2010), 8, pp [5] Nakkach, M., et al., Angulo-pec tral ur face Plasmon Res o nance Im ag ing of Nanofabricated Grat ing ur faces, Op tics Let ters, 35 (2010), 13, pp [6] Jha, R., et al., igh-per for mance en sor Based on ur face Plasmon Res o nance with Chalcogenide Prism and Alu mi num for De tec tion in In fra red, Op tics Let ters, 34 (2009), 6, pp [7] uang, J. G., et al., Nar row-band pec tral Fea tures of truc tured il ver ur face with Rect an gu lar Res o - nant Cav i ties, Jour nal of Quan ti ta tive pectroscopy and Radiative Transfer, 112 (2011), 5, pp [8] Fu, C. J., et al., emi con duc tor thin Films Combined with Metallic Grating for elective Improvement of Ther mal Ra di a tive Ab sorp tion/emis sion, Jour nal of eat Trans fer, 131 (2009), 3, [9] Chen, Y. Y., et al., Un usual Pho ton Tunneling in the Frustrated Total Internal Reflection tructure Includ - ing In def i nite Metamaterials, Jour nal of Op tics, 12 (2010), 4, pp [10] Zhang, Z. M., et al., Un usual Pho ton Tun nel ing in the Pres ence of a Layer with a Neg a tive Re frac tive In - dex, Ap plied Phys ics Let ters, 80 (2002), 6, pp [11] Tien, C. L., Ther mal Ra di a tion Prop er ties of Gases, Ad vances in eat Trans fer, 5 (1969), Dec., pp [12] Mulet, J. P., et al., En hanced Ra di a tive eat Trans fer at Nanometric Dis tances, Microscale Thermophysical En gi neer ing, 6 (2002), 3, pp [13] Francoeur, M., et al., Role of Fluctuational Elec tro dy nam ics in Near-Field Ra di a tive eat Trans fer, Jour - nal of Quan ti ta tive pec tros copy and Radiative Transfer, 109 (2008), 2, pp

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