Linear thermal expansion measurements on silicon from 6 to 340 K

Lyon, Keith G.; Salinger, G. L.; Swenson, C. A.; White, G. K.

doi:10.1063/1.323747

Cited by 301 publications

(179 citation statements)

References 10 publications

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“…Between 1.6 K and 2 K the shift in frequency is only 100 Hz (5 × 10 −13 ). Whereas the CTE of an insulating crystal at low temperatures is expected to be positive and proportional to T 3 [13], in the case of silicon its thermal expansion behaviour (expansion turns into contraction between 16.8 K and 124 K) necessarily implies that such a dependence can accurately hold only for T → 0. The value predicted from compressibility and heat capacity measurements is α Si = 4.8 × 10 −13 K −1 (T /K) 3 [13].…”

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confidence: 99%

Silicon single-crystal cryogenic optical resonator

et al. 2014

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We report on the demonstration and characterization of a silicon optical resonator for laser frequency stabilization, operating in the deep cryogenic regime at temperatures as low as 1.5 K. Robust operation was achieved, with absolute frequency drift less than 20 Hz over 1 hour. This stability allowed sensitive measurements of the resonator thermal expansion coefficient (α). We found α = 4.6 × 10 −13 K −1 at 1.6 K. At 16.8 K α vanishes, with a derivative equal to −6 × 10 −10 K −2 . The temperature of the resonator was stabilized to a level below 10 µK for averaging times longer than 20 s. The sensitivity of the resonator frequency to a variation of the laser power was also studied. The corresponding sensitivities, and the expected Brownian noise indicate that this system should enable frequency stabilization of lasers at the low-10 −17 level. c 2014 Optical Society of America OCIS codes: 120.3940, 120.4800, 140.3425, 140.4780. Optical resonators with low sensitivity to temperature and mechanical forces are of significant importance for precision measurements in the optical and microwave frequency domain. In the optical domain, they serve to stabilize the frequencies of lasers for spectroscopic applications, notably for optical atomic clocks, and for probing fundamental physics issues such as the properties of space-time. Also, by conversion of ultrastable optical frequencies to the radio-frequency domain via an optical frequency comb, radio-frequency sources with ultralow phase noise can be realized [1], leading to e.g. radar measurements with improved sensitivity.The conventional approach for ultra-stable optical resonators is the use of ULE (ultra-low expansion glass) material, operated at temperatures near room temperature, where the coefficient of thermal expansion (CTE) exhibits a zero crossing. While ULE resonators with optimized designs (long length, acceleration-insensitive shape) have reached impressive performance [2], their operating temperature near 300 K necessarily leads to a level of Brownian length fluctuations which imposes a fundamental limit to the achievable frequency stability [3], [4]. Cryogenic operation of a resonator provides one avenue towards reduction of these fluctuations. The Allan deviation of length fluctuations decreases proportional to √ T [3], if the mechanical dissipation of the resonator elements, in particular of the mirror coatings, is independent of temperature. Measurements performed thus far indicate that the dissipation of mirrors with crystalline substrates at cryogenic temperature are indeed similar to those of fused silica mirrors at room temperature [5], [6]. Nowadays, robust cryogenic solutions exist for continuous operation of even fairly large objects, such as optical resonators, at temperatures as low as 0.1 K. This offers the possibility of reduction of resonator length fluctuations by more than one order of magnitude compared to today's lowest levels realized at room temperature, with a corresponding reduction in frequency instability of the laser stabiliz...

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Silicon single-crystal cryogenic optical resonator

et al. 2014

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“…(5) was started at room temperature with literature values for the refractive index 11 n, the coefficient of thermal expansion 14 a and the measured sample length L. The iterative evaluation was applied at temperatures above 26 K. This allows a sufficiently high density of (1) is placed in the probe chamber (2) which is surrounded by vacuum in the cryostat (3) to provide a thermal insulation against room temperature. A cooling coil (4) allows the heat extraction by an adjustable liquid helium flow.…”

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Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures

et al. 2012

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“…The results are ͑2.8± 1.0͒ ϫ 10 −6 K −1 for the horizontal distance and ͑1.3± 0.4͒ ϫ 10 −6 K −1 for the vertical distance. These values are in the range of the thermal expansion coefficient of silicon, the CCD substrate material, and invar, the metallic support material for the temperatures considered: literature values are ͑0.8− 1.6͒ ϫ 10 −6 K −1 for silicon 10 and ͑1−2͒ ϫ 10 −6 K −1 for invar. 11…”

Section: Temperature Dependence Of the Pixel Distancementioning

confidence: 92%

Characterization of a charge-coupled device array for Bragg spectroscopy

Indelicato

Bigot

Trassinelli

et al. 2006

Review of Scientific Instruments

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The average pixel distance as well as the relative orientation of an array of six charge-coupled device ͑CCD͒ detectors have been measured with accuracies of about 0.5 nm and 50 rad, respectively. Such a precision satisfies the needs of modern crystal spectroscopy experiments in the field of exotic atoms and highly charged ions. Two different measurements have been performed by illuminating masks in front of the detector array by remote sources of radiation. In one case, an aluminum mask was irradiated with x rays, and in a second attempt, a nanometric quartz wafer was illuminated by a light bulb. Both methods gave consistent results with a smaller error for the optical method. In addition, the thermal expansion of the CCD detectors was characterized between −105 and −40°C.

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Linear thermal expansion measurements on silicon from 6 to 340 K

Cited by 301 publications

References 10 publications

Silicon single-crystal cryogenic optical resonator

Silicon single-crystal cryogenic optical resonator

Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures

Characterization of a charge-coupled device array for Bragg spectroscopy

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