氏名　BANH QUOC TUAN
学位の種類　博士（工学）
学位記番号　博甲第591号
学位授与の日付　平成23年8月31日
学位論文題目　Active suppression of air refractive index fluctuation using Fabry-Perot cavity and piezoele ctric volume actuator　（ファブリ・ペロー共振器と圧電素子容積アクチュエータを用いた空気屈折率変動の能動的抑制）
論文審査委員
　主査　教授　明田川　正人
　副査　教授　柳　和久
　副査　教授　田辺　郁男
　副査　准教授　山田　昇
　副査　准教授　平田　研二

• 論文目次
• 論文要旨
• 論文審査の結果の要旨

［平成23（2011）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

Contents　Page
Abstruct　p.i
Acknowledgements　p.iv
Contents　p.v
List of abbreviations　p.vii
List of nomenclatures　p.viii
List of figures　p.ix
List of tables　p.xi
Chapter1　Introductions
　1.1　Research background　p.1
　1.2　Research objective and outline　p.8
Chapter2　Measurement of air-refractive-index fluctuation using phase modulation homodyne interferometer and frequency tunable laser
　2.1　Introduction　p.10
　2.2　Measurement principle　p.10
　2.2.1　Phase modulation homodyne interferometer　p.10
　2.2.2　Air refractive index fluctuation measurement　p.15
　2.3　Instrumentations　p.17
　2.4　Experimental results　p.24
　2.5　Conclusions　p.29
Chapter3　Improvement of air-refractive-index fluctuation measurement using a Fabry-Perot cavity and frequency tunale laser
　3.1　Introduction　p.30
　3.2　Measurement principle　p.30
　3.2.1　Fabry-Perot cavity　p.30
　3.2.2　Air refractive index fluctuation measurement　p.36
　3.3　Instrumentations　p.38
　3.4　Experimental results　p.41
　3.5　Conclusions　p.47
Chapter4　Construction of constant air-refractive-index chamber
　4.1　Introduction　p.48
　4.2　Operation principle　p.49
　4.2.1　Sealed air-environment chamber　p.49
　4.2.2　Suppression of air refractive index fluctuation　p.51
　4.3　Instrumentations and experimental rusults　p.54
　4.3.1　Response of air refractive index to the motion of the piezoelectric volume actuator　p.54
　4.3.2　Active suppresion of air refractive index fluctuation　p.59
　4.3.3　Uncertainty estimation　p.66
　4.4　Conclusions　p.68
Chapter5　Discussions and overall conclusions
　5.1　Summary of the research results　p.70
　5.2　Uncertainty improvement for the experimental system　p.72
　5.3　Overall conclusions　p.73
AppendixA　Conventional methods of air-refractive index fluctuation measurement　p.74
　A.1　The Ciddor method　p.74
　A.2　The Agilent wavelength tracker　p.78
　A.3　The Zygo compact wavelength compensator　p.80
AppendixB　The Pound-Drever-Hall method　p.82
AppendixC　Future work：improvement of the active supression of air refractive index fluctuation　p.87
References　p.90
List of papers　p.101

Due to the rapid progress of nanotechnology and ultra-precision engineering, the displacement/length measurement with an accuracy of subnanometer or less and the measurement range of 1 meter or longer, must be achievable within this decade of the century. Since the optical interferometry has some advantages of high resolution up to subnanometer, long measurement range and the traceability to the standard meter definition, it is the only solution to satisfy the requirement of long range and high resolution for the displacement/length measurement. However, in a normal air environment, conventional interferometers suffer from significant measurement uncertainty from an air refractive index fluctuation （Δnair）. Therefore, in order to achieve subnanometer accuracy in displacement/length measurement, the suppression of Δnair must be considered for improving the performance of the optical interferometers. For the suppression of Δnair, two conditions are required.
Firstly, Δnair must be measured precisely with a relative change Δnair/nair of 10-9 order or less. Secondly, a compensating system is required to compensate the measured Δnair.

For the measurement of Δnair, many research activities have been introduced. Δnair can be measured from the measurement of temperature, pressure, humidity and CO2 concentration, respectively. This method is very flexible to setup. However, the measurement speed is relative low and the measurement resolution is depends on the resolution of the environmental sensor （Δnair ~10-8 order）. Recently, there are few commercial Δnair sensors （the Agilent wavelength tracker and the Zygo wavelength compensator）. These sensors detect the deviation of the wavelength of light owing to Δnair and adjust the wavelength of light to compensate Δnair. Even these methods can achieve resolution of 10-9 order, they can be applied for only their commercial heterodyne optical interferometers. Therefore, a new method for precise Δnair measurement is required for general interferometers.
For the suppression of Δnair, passive compensation using the commercial wavelength compensator or active suppression using vacuum chamber are effective. Because the commercial products can be applied for only their commercial optical interferometry and the vacuum chamber has problem of high cost, complex construction, difficult to setup optical components, an active suppression of Δnair for precision optical interferometer in normal air environment is required.

From the explanation of the research background, the thesis objective includes two issues:
1. Precise measurement of air refractive index fluctuation at 10-9 order.
2. Active suppression of air refractive index fluctuation - Construction of a constant air refractive index chamber.

In the thesis, two methods for precise measurement of Δnair and the active suppression of the measured Δnair at 10-9 order are presented, respectively. The thesis is organized into 5 chapters:
Chapter 1- Introduction: this chapter introduces a research background on the current development of the lithography industry conducing to the need of the optical interferometer measuring system. The remained problems of the conventional interferometers to the motivation of the thesis are presented. The outline of the thesis will be also briefly described

Chapter 2 - The first Δnair measurement method using a phase modulation homodyne interferometerwith an ultralow thermal expansion material （ULTEM） and an external cavity laser diode （ECLD） is presented. The Michelson type interferometer is fixed on the ULTEM to reduce the optical path length deformation. The ECLD frequency is controlled to maintain the resonance of the interferometer using the null-point method. The controlled ECLD frequency, recorded via frequency counter unit, is used to derive Δnair. The first Δnair measurement method provides a direct link between light frequency and Δnair. However, the measurement uncertainty is only 10-8 order due to the relatively low signal to noise ratio of the control signal. The improvement of measurement uncertainty is shown in chapter 3.

Chapter 3 - The second method of Δnair measurement based light frequency for achieving the Δnair measurement uncertainty of 10-9 order is proposed. In the second method, a Fabry-Perot cavity, constructed on an ULTEM, is used as Δnair sensor. An ECLD is used as light source for the cavity. The Pound-Drever-Hall method, based on the phase modulation technique, is used to control the light frequency for maintaining the resonance of the cavity. Δnair will be derived from the recorded ECLD frequency. In this case, Δnair measurement uncertainty is estimated of 10-9 order. Therefore,the second method of Δnair measurement is adequate for the performance of the precision laser interferometers.

Chapter 4 - From the precise measurement of Δnair, the thesis proposes a method to suppress Δnair actively for the precision optical interferometers by constructing a constant air refractive index chamber. The volume of the chamber （also it means the inner air refractive index） can be adjusted via a piezoelectric volume actuator with bellows. From the precise observation of Δnair using a Fabry-Perot cavity with the ultralow thermal expansion material and the frequency stabilized laser （presented in chapter 3）, the volume of the chamber is adjusted by controlling the volume actuator to compensate Δnair. The evaluated stability of air refractive index inside the chamber using the proposed method is 4x10-9, and it shows a good agreement with the conventional methods for measuring air refractive index.

Chapter 5: Overall conclusions. A review of my research work and some conclusions for the next development system is discussed.

本論文は、「Active suppression of air refractive index fluctuation using Fabry-Perot cavity and piezoelectric volume actuator （ファブリ・ペロー共振器と圧電素子容積アクチュエータを用いた空気屈折率変動の能動的抑制）」と題し、5章より構成されている。
　第1章「Introduction」では、半導体露光装置などで多用される干渉測長計の問題点に関し論じている。干渉測長計の誤差の要因として、位相補間誤差、光源レーザの周波数安定性、干渉計周辺の空気屈折率変動などを挙げ、特に空気屈折率変動が、干渉計誤差に最も大きく寄与することを指摘した。従来、空気の温度・圧力・湿度などを計測し、これらの値から受動的に空気屈折率を計算・補正する方法が提案されている。しかしこの手法の限界が10-8 （ 1メートルの測定範囲で10 ナノメートルの精度）オーダであることを指摘した。これらの問題を解決するべく、高精度な能動的空気屈折率変動抑制法の開発がこの論文の目的であることを論じた。
　第2 章「Measurement of air-refractive-index fluctuation using phase modulation homodyne interferometer and frequency tunable laser diode」では、周波数計測から空気屈折率変動を捉える手法とその実験に関し論じた。極低熱膨張材（線膨張率2×10-8K-1）で構成された位相変調ホモダイン干渉計と周波数可変ダイオードレーザを用い、周波数測定から空気屈折率変動を10-8オーダの不確かさで計測した。
　第3章「Improvement of air-refractive-index fluctuation measurement using Fabry-Perot cavity and frequency tunable laser」では、2章で論じた周波数計測から空気屈折率変動を捉える手法の改善とその実験を論じている。位相変調ホモダイン干渉計を、第2 章と同じ極低熱膨張材で構成したファブリー・ペロー共振器に替え、空気屈折率変動を10-9 オーダで計測した。
　第4章「Construction of constant air-refractive-index chamber」では、第2章と第3章で論じた空気屈折率変動測定法を拡張し、空気屈折率変動を能動的に抑制する手法とその装置化に関し論じている。密閉型恒温チャンバーに、極低熱膨張材で構成したファブリー・ペロー共振器と圧電素子容積アクチュエータを組込む。周波数安定化HeNe レーザの光を共振器に導光し、共振器の共鳴点を維持するように圧電素子容積アクチュエータを可変制御する。この装置により、空気の屈折率変動を能動的に10-9 オーダまで抑止した。
　第5章「Discussion and overall conclusions」では、第1章から第4章まで得られた結果を考察している。空気屈折率変動を10-9 オーダまで能動的に抑止できたことを述べている。また、光源としてヨウ素安定化HeNe レーザなど、より周波数安定度の高い光源を用いることで、空気屈折率変動が10-11 オーダまで能動抑止できる可能性も論じている。
　本論文の研究成果は、干渉測長計のみならず、産業界で利用される光学干渉計全般の誤差低減に大きく寄与するものである。よって、本論文は工学上および工業上、貢献するところが大きく，博士（工学）の学位論文として十分な価値を有するものと認める。