Planar hyperblack absolute radiometer

The absolute responsivity of a planar cryogenic radiometer fabricated from micromachined silicon and having carbon nanotubes, as the absorber and thermistor were measured in the visible and far infrared (free-field terahertz) wavelength range by means of detector-based radiometry. The temperature coefficient of the thermistor near 4.8 K and noise equivalent power were evaluated along with independent characterization of the window transmittance and specular reflectance of the nanotube absorber. Measurements of absolute power by means of electrical substitution are compared to the German national standard and the uncertainty of the radiometer responsivity as a function of wavelength is summarized. © 2016 The manuscript is a contribution of the US Government and is not subject to copyright. OCIS codes: (040.0040) Detectors; (040.2235) Far infrared or terahertz; (120.5630) Radiometry; (230.4000) Microstructure fabrication. References and links 1. S. Langley, “The Bolometer and Radiant Energy,” Proc. Nat. Acad. Arts Sci. 166, 352–358 (1881). 2. F. Kurlbaum, “Notiz über eine Methode zur quantitativen Bestimmung der stahlenden Wärme,” Ann. Phys. 287, 591 (1894). 3. T. J. Quinn and J. E. Martin, “A radiometric determination of the Stefan-Boltzmann constant and thermodynamic temperatures, between −40'C and +1001C,” Philos. Trans. R. Soc. Lond. A 316(1536), 85–189 (1985). 4. N. A. Tomlin, M. White, I. Vayshenker, S. I. Woods, and J. H. Lehman, “Planar electrical-substitution carbon nanotube cryogenic radiometer,” Metrologia 52(2), 376–383 (2015). 5. M. Kehrt, C. Monte, J. Beyer, and J. Hollandt, “A highly linear superconducting bolometer for quantitative THz Fourier transform spectroscopy,” Opt. Express 23(9), 11170–11182 (2015). 6. K. Mizuno, J. Ishii, H. Kishida, Y. Hayamizu, S. Yasuda, D. N. Futaba, M. Yumura, and K. Hata, “A black body absorber from vertically aligned single-walled carbon nanotubes,” Proc. Natl. Acad. Sci. U.S.A. 106(15), 6044– 6047 (2009). 7. C. J. Chunnilall, J. H. Lehman, E. Theocharous, and A. Sanders, “Infrared hemispherical reflectance of carbon nanotube mats and arrays in the 5 50 mm wavelength region,” Carbon 50(14), 5348–5350 (2012). 8. A. Steiger, R. Müller, A. Remesal Oliva, Y. Deng, Q. Sun, M. White, and J. Lehman, “Terahertz Laser Power Measurement Comparison,” IEEE Trans. Terahertz Sci. Technol. 6(5), 664–669 (2016). 9. J. H. Lehman, B. Lee, and E. N. Grossman, “Far infrared thermal detectors for laser radiometry using a carbon nanotube array,” Appl. Opt. 50(21), 4099–4104 (2011). 10. A. Steiger, M. Kehrt, C. Monte, and R. Müller, “Traceable terahertz power measurement from 1 THz to 5 THz,” Opt. Express 21(12), 14466–14473 (2013). 11. I. Müller, C. Kwong Tang, J. Gran, and L. Werner, “Experimental validation of the predictabilty of a predictable quantum efficent detector by a direct intercomparision,” in 12th International Conference on New Developments and Applications in Optical Radiometry (2014), pp. 197 – 198. 12. B. N. Taylor and C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” NIST Technical Note 1297, 1994 Edition, p.2, (National Institute of Standards and Technology, USA).


Introduction 1.1 A brief history of the cryogenic radiometer
In the late 1800s, Samuel Langley demonstrated the first bolometer for infrared measurements [1].This bolometer consisted of a metal strip blackened with soot in a resistance bridge.Separately and around the same time, Ferdinand Kurlbaum demonstrated the first absolute radiometer at what is now the Physikalisch-Technische Bundesanstalt (PTB) [2].Kurlbaum's radiometer was made for experimental investigation of the so-called fourth power law for blackbody emitters and the Stefan-Boltzmann constant.Nearly one hundred years later, the electrical substitution radiometer demonstrated by Martin et al., of the National Physical Laboratory (NPL) in the United Kingdom became the definitive standard for absolute optical power measurements [3].Tomlin et al., at the National Institute of Standards and Technology (NIST) more recently demonstrated that it is possible to achieve all of the essential elements of an absolute radiometer, consisting of a carbon nanotube absorber, thermistor, heater and weak thermal link; all on a microfabricated chip for optical fiber power measurements [4].In the present work, we extend the work of Tomlin to freefield far infrared (FIR) or terahertz (THz) radiometry.We fabricated a planar hyperblack absolute radiometer with micromachined silicon as a weak thermal link and vertically-aligned carbon nanotube arrays (VANTAs) as the absorber and thermistor.We use the term hyperblack to distinguish the fact that, rather than being hyperspectral, with multiple channels to cover a broad range of wavelengths; the nanotube-based radiometer is one detector that is nearly 100% efficient and broadly uniform over the range of 0.4 µm to 400 µm.

Special challenges for far infrared
There are particular challenges to measuring free-field FIR radiation.A detector having large area is not merely a convenience, but a necessity to accommodate possible beam diffraction, even when the beam apparently underfills the detector.Broad and uniform absorption efficiency is convenient for applications such as Fourier transform spectroscopy (FTS) that require management of back reflections and unwanted interference.Also, to accommodate FTS systems, detector response time on the order of milliseconds or less is desirable.Millisecond time response is difficult to achieve with a cavity-based radiometer having broad and uniform absorption with no back reflections, because the cavity is inherently massive and slow.Dispersive systems such as a monochromator with a blackbody source provide low irradiance, so an absolute radiometer that is sensitive enough for microwatt power levels and lower is desirable.In this manuscript, we refer to FIR and THz interchangeably, but in either case we are referring to the range of approximately 50 µm to 400 µm or 6 THz to 0.75 THz.

Fabrication
Twenty independent radiometers were fabricated on a silicon wafer, 76.2 mm in diameter and 375 µm thick, along with a witness sample measuring 9.4 mm by 11.2 mm in area for investigating the VANTA reflectance.The wafer fabrication can be described as follows.Silicon dioxide (SiO 2 ) was grown on the silicon wafer by chemical vapor deposition (CVD) to have a thickness of 355 nm.On top of that, a layer of low stress silicon nitride (SiNx), 52 nm thick was deposited by plasma-enhanced chemical vapor deposition (PECVD).Several metal films were deposited and patterned by photoresist liftoff, including 75 nm-thick vanadium wiring by electron beam deposition and a 54 nm-thick tungsten heater by sputter deposition with argon.The wafer was then passivated by 100 nm of low stress SiNx that was deposited by PECVD.Reactive ion etching (RIE) was used to remove the SiNx and SiO 2 in select areas in order to make contact to the vanadium for wire-bonding, to expose the SiO 2 for VANTA growth, and to expose the Si for micromachining.Carbon nanotube catalyst layers were deposited as 2 nm Al 2 O 3 and 2 nm Fe by electron beam deposition, and patterned by photoresist liftoff.The radiometer geometry was micromachined by a Bosch-process deep reactive ion etch (DRIE).The VANTA were grown on individual radiometer chips and the witness chip by atmospheric pressure CVD in a 70 mm inner diameter quartz tube.The growth parameters are described by the following.The furnace tube is heated to 600 °C and a N 2 flow of 1225 standard cubic centimeter per minute (sccm) is introduced.Next, the furnace temperature is increased to 750 °C for 15 min while adding 490 sccm H 2 .The carbon for nanotube growth is then added by 370 sccm C 2 H 4 along with 300 sccm N 2 flowing through a water bubbler for 23 min.After this, the N 2 flow through the bubbler is stopped, the N 2 flow is reduced to 1000 sccm and the furnace is cooled to 300 °C.Then the H 2 flow is stopped and the furnace cools to 200 °C.and photo (right).

Electrical
A schematic of the radiometer chip is shown in Fig. 1.Twelve vanadium leads, each 5 µm wide, cross the base of the radiometer chip and along the narrow leg, 500 µm wide by 2 mm long.The narrow leg functions as the thermal weak link.Two separate leads contact opposite sides of the VANTA thermistor for a total of four.Another four leads continue up to the bottom of the circular absorber area where a tungsten heater, 32 µm wide, surrounds the perimeter of the VANTA absorber.During VANTA growth, exposure to the high temperature and process gases modifies the vanadium, elevating the superconducting critical temperature ( c T ) to 11 K.This eliminates Joule heating of the leg when the radiometer is operated below the critical temperature and the critical current.
The VANTA thermistor consists of a rectangular area, 25 µm by 110 µm, of vertically aligned carbon nanotubes grown over interdigitated tungsten strips that are 5 µm wide and spaced by 5 µm.This is shown in Fig. 2. In between the tungsten fingers, the VANTA is grown on SiO 2 .The height of the VANTA on the witness sample for evaluating reflectance measured 362 µm, 397 µm, 373 µm, and 397 µm at the corners.The array height for the absorber nanotubes was 440 µm and for the thermistor nanotubes was 240 µm.We estimate the absorber VANTA height variation across the wafer to be approximately +/−10%.
The electrical measurement of the nanotube thermistor was undertaken with a four-wire resistance measurement of the nanotube thermistor while applying heat from a current source across the detector's 1157 Ω heater.The resistance of the reference block thermometer and the nanotube thermistor were acquired by means of a commercial AC resistance bridge operating with a time constant of 300 ms.The applied power (heating of the detector's metal heater) was measured and controlled by means of a computer running a proportional-integral (PI) control algorithm sampling at approximately one second intervals.

Optical a
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Thermal
The detector's thermal conductance (G) was evaluated by calibrating the nanotube thermistor against a commercial thermistor which is calibrated to the International Temperature Scale of 1990 (ITS-90).During warm up of the cryostat to room temperature, the VANTA's resistance was measured as a function of temperature shown below.With knowledge of the thermistor calibration, the detector's heater was measured by means of a four-wire resistance measurement.The amount of power was determined by supplying current to the heater in closed-loop control mode, which was defined by the thermistor set point.

VANTA reflectance
There are examples of VANTA reflectance measurements in the literature that demonstrate that it is possible to achieve low reflectance over a broad range of THz frequencies [6][7][8][9].The reflectance is expected to be dependent on length and density of the nanotubes, which vary depending on growth conditions.Therefore, we allocate an area of the parent wafer for reflectance measurements as a witness sample that represents the reflectance of each radiometer chip.
The directional reflectance was measured by collecting specularly reflected light from the THz laser, not absorbed by the VANTA witness sample, with two off-axis parabolic (OAP) mirrors arranged as shown in Fig. 4. The output stability of the laser was continually monitored by a second detector in proximity to a gold-plated reflective chopper.Light not reflected by the chopper was passed to the sample under test.The sample under test was either the nanotube witness or a gold mirror having reflectance of 0.99 in the wavelength range 50 µm to 500 µm.One detector (M) was a monitor throughout the measurements.Additionally, two other detectors were used, PTB's standard detector S 1 and a calibrated detector S 2 of the same kind [9].Detector S 1 was used to ensure the proper functioning of the laser and the monitor.Detector S 2 collected the light from the reflectance sample.The reflectance

Far infrared laser
The experimental setup for measuring FIR laser power consisted of a continuous wave (CW) laser source, focusing optics and a spatial filter, a reflective optical chopper, a monitor detector, and a THz camera.This facility is described in greater detail elsewhere [10].The camera and the detectors were mounted upon a platform, the position of which was controlled remotely.
The THz laser is a molecular gas laser which consists of a 2 m long THz resonator with the molecular gas at low pressure (< 1 Pa) as the gain medium and a grating-tuned CO 2 laser for optically exciting the molecules.Five radiation lines were selected from exciting molecules of formic acid (0.762 THz), difluoromethane (1.04 THz, 1.40 THz, 2.55 THz), and deuterated ethanol (5.57THz).The laser beam amplitude stability was recorded by a time series of the thermopile monitor detector.
A circular, nearly Gaussian beam profile was fixed to approximately 4 mm by means of an adjustable aperture and focusing optics.The beam size was measured at each wavelength and an example of this measurement is shown in Fig. 5. Furthermore, we found that the cryostat and radiometer can be translated approximately 1 mm across the center of the aperture and still maintain the maximum response.The alignment is difficult in practice and we expect some diffraction that is not apparent on the pyroelectric camera.Therefore, there is some uncertainty in the alignment and this is accounted for in our uncertainty budget.

Visible laser 532 nm
The laser for the visible (532 nm) measurement was actively amplitude stabilized and monitored for power during the course of the measurement.The beam was spatially filtered and collimated to a diameter of less than 1 mm at the plane of the window, and incident on the detector.The window transmittance measurement was made with the same beamline, adjusted to a 2 mm diameter.

Description of PTB detectors/standard
The measurement comparisons were undertaken with two types of measurement systems; one for the visible wavelength and the other for FIR/THz.The PTB standard detector for the 532 nm wavelength measurement was a silicon-based photodiode trap described elsewhere [11].The PTB standard detector for FIR measurements was a modified commercial thermopile with an absorbing element with a special 0.6 mm thick NG1 glass absorber, 12 mm in diameter [10].The radiometer response was collected from the average of 100 samples spaced one second apart.

Measurement results
A plot of the VANTA resistance as a function of temperature is shown in Fig. 6, acquired at one second intervals during the period of cryostat warming from approximately 4.4 K to 75 K.The temperature coefficient near 50 kΩ was derived from interpolating 1000 evenlyspaced points and a derivative with a 10-point smoothing window.At 4.8 K, the temperature coefficient of resistance dR dT K −1 , and α, the unitless sensitivity

VANTA thermistor noise and the radiometer's thermal conductance
The detector was operated in a closed-loop feedback mode at a resistor set point of 50 kΩ (4.8 K) and near the operating point of approximately 30 µW applied power P. Making a linear approximation of P G T = ⋅Δ at the set point, 350 μW / k.G = .This value is given for reference and is not general, however, because the temperature coefficient of the thermistor is not linear.For example, 150 μW / k.G = at 52 kΩ.We estimate a time constant of approximately 30 ms based on the properties of a comparable heat capacity from Tomlin et al. [4].In the present scheme of electrical substitution, the temporal response is limited by the resistance bridge at 300 ms and 1 s sampling rate of the PI control.
With knowledge of the thermistor calibration and thermal conductance of the detector, we estimated the expected thermal fluctuation noise B k TR = nV Hz .A datum estimating the total noise can be obtained by sampling the resistance of the nanotube thermistor, which represents the combined contribution of the thermal and electrical noise within the closed-loop operation.For example, the standard deviation of 100 samples at one-second intervals is approximately 100 Ω, so the combined noise is approximately 0.2% of 30 µW or 60 nW.This value is substantially higher than we expect from knowledge of the calculated thermal fluctuation noise, but its value is also dependent on the stability of the PI control so it not solely a representation of thermal fluctuation noise.In addition, separately, we measured the noise with a dynamic signal analyzer in open-loop mode without PI control.We measured a value of approximately 20 nV/Hz 1/2 in the range of 10 to 100 Hz.This number is provided merely for comparison and the uncertainty has not been evaluated.

Absorber evaluation (specular reflectance)
A summary of the specular reflectance measurements is given in Table 1.The specular reflectance was found to be consistent with previous results for an array of nanotubes having a greater height [8].The diffuse reflectance was immeasurably small.

Relative uncertainty
The relative uncertainty is derived from statistical (Type A) and other means (Type B) as described in [12].The contributions of the radiometer comparison include the following: 1.The hyperblack radiometer as an absolute detector, which includes the window transmittance, reflectance of the VANTA, and the heater power measurement by means of electrical substitution.
2. The comparison procedure, which includes the statistical uncertainties of the measured signals of each detector.These are quantified in Table 2. "PHAR S.O.M." represents the standard deviation of the mean of the radiometer response (multiple averages of the radiometer response acquired at one second intervals)."PTB Power" is the uncertainty of the PTB reference.The uncertainty contribution of beam alignment, diameter, diffraction and amplitude stability of the laser source are grouped under "Beam".
3. The spectral power responsivity of the PTB reference detector as described by Steiger and coauthors for the PTB scale for THz power measurement as in reference [8].The uncertainty in the transmittance, reflectance and heater power could be considered a systematic offset with further investigation and modeling, but it is beyond the scope of this work.The standard deviation of the measured power of the hyperblack radiometer is attributable to mostly random noise of the detector but also includes drift from the source.The uncertainty has not been thoroughly evaluated and is subject to change with further investigation.

Radiometer comparison
The measurement results of the radiometer comparison with the PTB scale are presented in Table 3.The larger uncertainty in the far infrared is attributable to independent evaluation of the nanotube reflectance, window transmittance and detector alignment, as well as laser drift over the course of the radiometer measurements.

Discussion and summary
A summary of the radiometer characteristics is shown in Table 4.The comparison to the PTB standard is recognized as a milestone because the PTB facility is recognized as a calibration facility for THz laser power measurements.The results are useful, however, for the purposes of our research rather than a definitive comparison between national standards.The nanotubebased radiometer operation supports the idea that VANTAs have broad and uniform total absorbance at low temperature, which until now has been supported only by specular reflectance measurements at room temperature.At angles of incidence closer to normal, we expect the reflectance to be slightly smaller, but more diffuse and difficult to measure.The uncertainties for our results of measuring absolute power by electrical substitution are relatively large given the remarkable agreement between the NIST and PTB standards, but any effort to reduce these is not a priority until the radiometer design is modified to accommodate a higher critical current and larger dynamic range.The relative uncertainty is quite large compared to the apparent agreement between the PTB standard and the hyperblack radiometer.The largest contributors of the uncertainty underscore the need for better detectors in the far infrared.The dominant contributions such as the window transmittance and beam alignment can be improved with large area detectors having minimal backscatter for FTS measurements.In our next iteration of the low-temperature radiometer, in addition to optimizing the integrated heater, incorporating a superconducting transition edge sensor will be undertaken.In the future, in addition to modifying the present embodiment, we expect that a roomtemperature version of an absolute radiometer operating over a broad wavelength range is possible.This will not include, however, a nanotube thermistor but a low-noise commercially available thermistor integrated into the chip design and mechanically bonded.
Given the wide wavelength range of the radiometer, other window choices are worth considering.polymethylpentene (TPX), for example would provide visible-wavelength transparency, mid-IR filtering and FIR transmittance.TPX would be cheaper than diamond and could be fabricated in a thicker wedge to avoid interference effects that are apparent even with a wedged diamond window with a thickness on the order of 200 µm.
We have demonstrated the first FIR and THz absolute cryogenic radiometer based on the multifunctional properties of carbon nanotubes.Production of multiple radiometer chips on a single wafer is attractive for experimental variations as well as future commercial production.We operated the radiometer in closed-loop mode with PI control with commercial, off-theshelf electronics.For ease of use and the practical matters of FIR/THz measurements, the planar hyperblack absolute radiometer meets several criteria by having broad, uniform and efficient spectral sensitivity, minimal backscatter, large area, and a temporal response limited only by the PI control.In the future, we expect the low-temperature operation near 1 µW for a 5 mm diameter detector is a favorable choice for broadband Fourier transform spectroscopy and absolute measurements with a dispersing monochromator from the visible to FIR.

Fig. 1 .
Fig. 1.Thermal and electrical schematic of the radiometer (left) with a line diagram (middle) and photo (right).

Fig. 2
Fig. 2. Represe ments and mechanic measurements mond window.0.70 with an u e were three ap ctor plane.The e.The plane of e. al measuremen wedge angle a of the quartz w using was fitte hored to the 4 K stage of the cry window is show n to the optica fracted THz ra housing is mad with a layer o 60).This recipe ne behind the the aperture wa the quotient of ratios of detector signals (S 2 /M) from a sequence of measurements of VANTA and the gold reference.On this basis, the reflectance of the nanotube sample at each wavelength was calculated.

Fig. 5 .
Fig. 5. Laser beam profile at 117 um wavelength showing the beam diameter less than 4 mm.

Fig. 6 .
Fig. 6.Measured VANTA thermistor resistance as a function of temperature.The line represents the connection of individual measurement points.