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由于具有极低的噪声等效功率, 超导转变边沿探测器(transition edge sensor, TES)近年来被广泛地应用于国际各个宇宙微波背景辐射(cosmic microwave background, CMB)极化观测项目中. 为保证探测器工作在性能最佳区间, 探测器饱和功率值需根据观测地点气象条件及观测波段进行调整, 而探测器梁架结构尺寸直接决定了饱和功率大小. 因工艺差异等原因, 不同加工方案下得到的梁架尺寸参数往往不能直接用于横向比对. 在之前的观测项目中, 一般先加工出一系列不同尺寸器件并逐一测量, 然后通过拟合实测饱和功率与梁架尺寸的关系推测实际需要尺寸. 为了与目标值匹配, 往往需要多次加工迭代过程. 本文使用边界限制的声子输运模型, 成功整合了之前观测项目中的器件参数, 对TES梁架尺寸进行预估. 并按照预估值首次在国内制备了用于探测CMB极化信号的TES探测器芯片. 测量表明参数与目标值相差较小. 该方法可以很好地对同类TES探测器尺寸进行估计, 对之后TES探测器的设计有指导性意义.Owing to its extremely low noise equivalent power, superconducting transition edge detectors have been widely used in various international cosmic microwave background polarization observation projects in recent years. In order to ensure that the detector works in the best performance range, the saturation power value of the detector needs to be adjusted according to the meteorological conditions of the observation site and the observation band, and the structural size of the detector beam directly determines the saturation power. Owing to process differences and other reasons, the beam sizes obtained under different processing schemes often cannot be directly used for horizontal comparison. In previous observation projects, a series of devices with different sizes were generally processed and measured one by one, and then the actual required size was inferred by fitting the relationship between the measured saturated power and the beam size. In order to match the target value, multiple machining iterations are often required. In this work, the boundary-restricted phonon transport model is used to successfully integrate the device parameters from previous observation projects to estimate the size of the transition edge sensor (TES) beam. According to the estimated value, the TES detector chips for detecting cosmic microwave background polarization signal are fabricated for the first time in China. Measurements show that its parameters deviate slightly from the target value. This method can well estimate the sizes of similar TES detectors, and thus has guiding significance for designing TES detectors in the future.
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Keywords:
- superconducting transition edge sensor /
- cosmic microwave background /
- phonon transport /
- phonon effective mean free path
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图 1 (a)超导薄膜理想R-T曲线; (b) AlMn材料实测R-T曲线
Fig. 1. (a) Ideal R-T curve of superconducting thin films; (b) measured R-T curve of AlMn alloy
图 3 (a) TES探测器立体结构图; (b)梁架结构横截面示意图
Fig. 3. (a) Three dimensional (3D) structure of TES detector; (b) cross section of beam structure
图 4 不同梁架宽度下声子有效平均自由程与材料表面漫反射概率的关系
Fig. 4. Relationship between the effective mean free path of phonons and the probability of diffuse reflection on the material surface under different beam widths
图 5 TES探测器加工过程横截面示意图
Fig. 5. Schematic diagram of cross-section of TES detector fabricating process
图 6 (a) TES探测器芯片整体实物照片; (b) TES探测器局部放大照片
Fig. 6. (a) Overall physical photo of TES detector chip; (b) partially enlarged photo of TES detector
图 7 (a)绝热去磁制冷机照片; (b)装载TES的样品托的照片; (c)样品托在制冷机内安装状态的照片
Fig. 7. (a) Adiabatic demagnetization refrigerator; (b) sample holder loaded with TES; (c) sample holder installed in the refrigerator
图 8 不同尺寸TES探测器发热功率
$ P_{\rm TES} $ 随热沉温度变化曲线 (a)样品梁架长度为1100${\text{μm}}$ ; (b)样品梁架长度为900${\text{μm}} $ ; (c)样品梁架长度为700${\text{μm}} $ .Fig. 8. Curves of heating power as a function of heat sink temperature with different beam sizes: (a) The length of beams is 1100 μm; (b) the length of beams is 900 μm; (c) the length of beams is 700 μm
图 9 不同尺寸下TES探测器饱和功率
$ P_{\rm \text{饱和}} $ 随热沉温度变化曲线 (a) 样品梁架长度为1100$ {\text{μm}}$ ; (b)样品梁架长度为900${\text{μm}}$ ; (c)样品梁架长度为700$ {\text{μm}}$ Fig. 9. Curve of saturation power of TES detector with heat sink temperature under different sizes: (a) The length of beams is 1100 μm; (b) the length of beams is 900 μm; (c) the length of beams is 700 μm
图 10 (a)不同尺寸TES探测器实际饱和功率与预测饱和功率之比随热沉温度的变化; (b)不同尺寸TES探测器实际饱和功率与修正后预测饱和功率之比随热沉温度的变化
Fig. 10. (a) Ratio of actual saturation power to predicted saturation power for TES detectors of different sizes as a function of heat sink temperature; (b) the ratio of the actual saturation power to the corrected predicted saturation power of TES detectors with different sizes as a function of heat sink temperature
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[1] Mather J C, Fixsen D J, Shafer R A, Mosier C, Wilkinson D T 1999 Astrophys. J. 512 511
Google Scholar
[2] Hinshaw G, Spergel D N, Verde L, Hill R S, Meyer S S, Barnes C, Bennett C L, Halpern M, Jarosik N, Kogut A 2003 Astrophys. J. Suppl. Ser. 148 135
Google Scholar
[3] Ade P A R, Aghanim N, Armitage-Caplan C, Arnaud M, Ashdown M, Atrio-Barandela F, Aumont J, Baccigalupi C, Banday A J, Barreiro R B, Bartlett J G, Battaner E, Benabed K, Benoît A, Benoit-Lévy A, Bernard J P, Bersanelli M, Bertincourt B, Bethermin M, Bielewicz P 2014 A&A 571 16
[4] Abazajian K, Addison G, Adshead P, Ahmed Z, Allen S W, Alonso D, Alvarez M, Amin M A, Anderson A, Arnold K S, Baccigalupi C, Bailey K, Barkats D, Barron D, Barry P S, Bartlett J G, Thakur R B, Battaglia N, Baxter E, Bean R 2019 arXiv: 1908.01062 [astro-ph]
[5] Hu W, White M 1997 New Astron. 2 323
Google Scholar
[6] Ade P A R, Aghanim N, Alves M I R, Armitage-Caplan C, Arnaud M, Ashdown M, Atrio-Barandela F, Aumont J, Aussel H, Baccigalupi C, Banday A J, Barreiro R B, Barrena R, Bartelmann M, Bartlett J G, Bartolo N, Basak S, Battaner E, Battye R, Benabed K 2014 A&A 571 A1
[7] Ade P A R, Ahmed Z, Amiri M, Barkats D, Basu T R, Bischoff C A, Beck D, Bock J J, Boenish H, Bullock E, Buza V, Cheshire IV J R, Connors J, Cornelison J, Crumrine M, Cukierman A, Denison E V, Dierickx M, Duband L, Eiben M 2022 Astrophys. J. 927 77
Google Scholar
[8] Enss C 2005 Cryogenic Particle Detection (Heidelberg: Springer) pp2–5
[9] 张青雅, 董文慧, 何根芳, 李铁夫, 刘建设, 陈炜 2014 物理学报 63 200303
Google Scholar
Zhang Q Y, Dong W H, He G F, Li T F, Liu J S, Chen W 2014 Acta Phys. Sin. 63 200303
Google Scholar
[10] Gao H, Liu C, Li Z, Liu Y, Li Y, Li S, Li H, Gao G, Lu F, Zhang X 2017 Radiat. Detect. Technol. Methods 1 12
Google Scholar
[11] Kuo C L, Bock J J, Bonetti J A, Brevik J, Zmuidzinas J 2008 Millimeter and Submillimeter Detectors and Instrumentation for Astronomy IV SPIE Marseille, France, August 18, 2008 p415
[12] Ahmed Z, Amiri M, Benton S J, Bock J J, Bowensrubin R, Buder I, Bullock E, Connors J, Filippini J P, Grayson J A, Halpern M, Hilton G C, Hristov V V, Hui H, Irwin K D, Kang J, Karkare K S, Karpel E, Kovac J M, Kuo C L 2014 Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VII SPIE Montréal, Quebec, Canada, August 19, 2014 p540
[13] Kermish Z D, Ade P, Anthony A, Arnold K, Zahn O 2012 Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VI SPIE Amsterdam, Netherlands, September 24, 2012 p84521C
[14] Gualtieri R, Filippini J P, Ade P A R, Amiri M, Benton S J, Bergman A S, Bihary R, Bock J J, Bond J R, Bryan S A, Chiang H C, Contaldi C R, Doré O, Duivenvoorden A J, Eriksen H K, Farhang M, Fissel L M, Fraisse A A, Freese K, Galloway M 2018 J. Low Temp. Phys. 193 1112
Google Scholar
[15] Thornton R J, Ade P A R, Aiola S, Angilè F E, Amiri M, Beall J A, Becker D T, Cho H M, Choi S K, Corlies P, Coughlin K P, Datta R, Devlin M J, Dicker S R, Dünner R, Fowler J W, Fox A E, Gallardo P A, Gao J, Grace E 2016 Astrophys. J. Suppl. Ser. 227 21
Google Scholar
[16] Henderson S W, Allison R, Austermann J, Baildon T, Battaglia N, Beall J A, Becker D, De Bernardis F, Bond J R, Calabrese E, Choi S K, Coughlin K P, Crowley K T, Datta R, Devlin M J, Duff S M, Dunkley J, Dünner R, Engelen A V, Gallardo P A 2016 J. Low Temp. Phys. 184 772
Google Scholar
[17] Koopman B J, Cothard N F, Choi S K, Crowley K T, Duff S M, Henderson S W, Ho S P, Hubmayr J, Gallardo P A, Nati F, Niemack M D, Simon S M, Staggs S T, Stevens J R, Vavagiakis E M, Wollack E J 2018 J. Low Temp. Phys. 193 1103
Google Scholar
[18] Ding J J, Ade P A R, Anderson A J, Avva J, Ahmed Z, Arnold K, Austermann J E, Bender A N, Benson B A, Bleem L E, Byrum K, Carlstrom J E, Carter F W, Chang C L, Cho H M, Cliche J F, Cukierman A, Czaplewski D, Divan R, Haan T D 2017 IEEE Trans. Appl. Supercond. 27 1
[19] Mather J C 1982 Appl. Opt. 21 1125
Google Scholar
[20] Ullom J N, Bennett D A 2015 Supercond. Sci. Technol. 28 084003
Google Scholar
[21] Suen J Y, Fang M T, Lubin P M 2014 EEE Trans. Terahertz Sci. Technol. 4 86
Google Scholar
[22] Feshchenko A V, Saira O P, Peltonen J T, Pekola J P 2017 Sci. Rep. 7 1
Google Scholar
[23] Wang G, Yefremenko V, Novosad V, Datesman A, Pearson J, Divan R, Chang C L, Bleem L, Crites A T, Mehl J, Natoli T, McMahon J, Sayre J, Ruhl J, Meyer S S, Carlstrom J E 2010 IEEE Trans. Appl. Supercond. 21 232
[24] Watson S K, Pohl R O 2003 Phys. Rev. B 68 104203
Google Scholar
[25] Bruls R J, Hintzen H T, De With G, Metselaar R 2001 J. Eur. Ceram. Soc. 21 263
Google Scholar
[26] Stephens R B 1973 Phys. Rev. B 8 2896
Google Scholar
[27] 华钰超, 曹炳阳 2015 物理学报 64 146501
Google Scholar
Hua Y C, Cao B Y 2015 Acta Phys. Sin. 64 146501
Google Scholar
[28] Sultan R, Avery A D, Underwood J M, Mason S J, Bassett D, Zink B L 2013 Phys. Rev. B 87 214305
Google Scholar
[29] Johnson B R, Flanigan D, Abitbol M H, Ade P A R, Bryan S, Cho H M, Datta R, Day P, Doyle S, Irwin K, Jones G, Li D, Mauskopf P, McCarrick H, McMahon J, Miller A, Pisano G, Song Y, Surdi H, Tucker C 2018 J. Low Temp. Phys. 193 103
Google Scholar
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