29  May  2015  

Carbon  Nanotube  Based  Detectors  for  THz  Radiometry    

J.H.  Lehman  Na#onal  Ins#tute  of  Standards  and  Technology    325  Broadway,  Boulder,  Colorado  80305-­‐3228  

lehman@boulder.nist.gov    

Where and Who

Physical  Measurement  Laboratory  Quantum  Electronics  and  Photonics  Division  

Gaithersburg, MD

Boulder, CO

 Nathan  Tomlin,  Malcolm  White,  Solomon  Woods  

Andreas  Steiger,  ChrisFan  Monte,  Jörg  Hollandt  Physikalisch-­‐Technische  Bundesanstalt,  Berlin,  Germany      Free  field,  FTIR  &  far  infrared/THz    

Future

PTB - Berlin, Germany

Photo: A. Steiger

Single-wall Carbon Nanotubes

Multi-wall Carbon Nanotubes

Single sheet of graphene wrapped into a tube: microns in length, ~1-2 nm diameter, capped (Iijima, 1993).

Concentric cylinders of graphite with a hollow center, capped (Iijima, 1991)

Carbon Nanotubes

Not spectrally uniform

Very spectrally uniform

Nanotube topologies

mats

arrays

composite

R.J.C.  Brown,  P.J.  Brewer  and  M.J.T.  Milton,  J.  Mater.  Chem.,  2002,  12,  2749–2754  A.  Brenner  and  G.  E.  Riddell,  J.  Res.  Natl.  Bur.  Stand.  (U.  S.),  1946,  37,  1991.  

Nickel phosphorous Gold black “nano fractal gold”

1 µm

Lehman,  J.H.,  Theocharous,  E.,  Eppeldauer,  G.,  Pannell,  C.,  Meas.  Sci.  Technol.  14,  916-­‐922,  (2003).  

1 µm

1 µm

Bulk carbon nanotubes

Absorber Morphology, Black Coatings

Silicon

1 µm

J.  E.  Carey,  C.  H.  Crouch,  E.  Mazur,  Opt.  &  Phot.  News,  Feb  (2003)  

Black silicon

Absorber Properties

1. index ~ air (or vacuum)

α =kρc

3. Thermal diffusivity large

k ~ 400 W/mK (big!) ρ ~ 7 kg/m3 (small!) c ~ 400 J/kgK

2. “Optically thick”

Lehman et al., Applied Optics, 50, 4099-4104, (2011)

~ 10 µm

r ~ 5 nm

s  >  10  nm  

* García-Vidal, et al., Phys. Rev. Lett., 78, 4289-4292 (1997)

s polarization, E directed along tube (optical response depends only on ε┴ for graphite)

p polarization, E perpendicular to tube (optical response depends on ε║ and ε┴ for graphite)

EMA for Aligned Cylinders

310 410 510 610 710Wavelength (nm)

70

75

80

85

90

95

100

Rel

ativ

e R

espo

nsiv

ity (%

)

low fill, large spacing

high fill, small spacing

spacing = 30 nm spacing = 17 nm

spacing = 14 nm

Based on index calculated from composite dielectric function; 60 µm thick, LiTaO3, with nickel electrodes

EMA, Calculated Results

Theocharous,  et  al.,  45,  APPL.  OPT.  1093-­‐1097  (2006)  

Author's personal copy

unexposed to serve as the control and the other samples wereexposed to an oxygen plasma using a commercial plasmasystem. The settings used for the oxygen plasma treatmentwere a flow rate of 50 sccm O2, pressure of 32 Pa (0.24 T), RFpower of 50–200 W at 30 kHz, and duration of 15–300 s.

2.1. Specular reflectance

To measure the specular reflectance of the samples, we used

a commercial spectrophotometer with an accessory for mea-suring absolute specular reflectance. The incident light spotsize on the sample was 4 mm by 4 mm and an integrationtime of 1 s was used for each data point. A reference scan thatdid not reflect off the sample was used to convert the rawdetector data to absolute reflectance. Since the specularreflectance of the samples is so small, the signal is very smalland noisy, and only becomes appreciable at large incidenceangles. We have not fully evaluated the uncertainty of themeasurements, but believe it is roughly 0.005 (k = 2) due toinstrument drift and uncertainties in gains. Specular reflec-

tance at an incident angle of 65! from normal is shown inFig. 1. The plasma-treated samples all show lower specularreflectance over the whole measured wavelength range, withup to 5 times lower reflectance at long wavelengths.

2.2. Total hemispherical reflectance

To measure the total hemispherical reflectance of the samples,we used the same commercial spectrophotometer with a

150 mm diameter integrating sphere accessory. Samples wereheld at the back of the sphere against a 18 mm diameter port,tilted at 8! from normal incidence. The incident light spot sizeon the samples was 7.5 mm by 15 mm, the slit width was5 mm, each data point was integrated for 1 s, and three separatescans were averaged together. Background scans were used to

account for any stray light in the sphere and a calibrated stan-dard black reference material1 was used to convert the rawdetector data to absolute reflectance. The total hemisphericalreflectance is shown in Fig. 2. The plasma-treated samples showlower total reflectance over the whole measured wavelengthrange, with up to 8 times lower reflectance at short wavelengths.

2.3. Etch rate

We observed a linear decrease in height of the VACNT withplasma exposure. Using a commercial digital contact sensor

attached to the vertical axis of an optical microscope, wemeasured an etch rate of " 20 lm/min with an uncertaintyof 50 lm (k = 2) for a RF power of 200 W. The large uncertaintyis attributed to variation in VACNT height with position anddifficulty measuring the same spatial position with succes-sive plasma treatments.

2.4. Imaging

Three samples were imaged with a helium ion microscope(HIM) using a current of 0.2 pA to 0.4 pA and an accelerating

Fig. 2 – (Top) Total hemispherical reflectance withuncertainty (k ¼ 2) shown by shaded regions. (Bottom) Ratioof total reflectance between plasma-treated samples andcontrol sample. (A colour version of this figure can beviewed online.)

Fig. 1 – (Top) Specular reflectance at an incidence angle of 65!

from normal. (Bottom) Ratio of specular reflectance betweenplasma-treated samples and control sample. (A colourversion of this figure can be viewed online.)

1 NIST standard reference material 2052-01-20 certified in 2002. Calibration was updated in 2013 by personal communication with theoptical radiation group at NIST Gaithersburg.

330 C A R B O N 7 4 ( 2 0 1 4 ) 3 2 9 – 3 3 2

Vis/NIR reflectance

0.1  %  reflectance  

400                                               1000                                                1600                                            2200  nm              

Tomlin et al., CARBON 74 (2014) 329–332

_  2  µm  

_  5  µm  

*  *   *  

Low density, ‘rough’ and low non-nt content

“water assisted” CVD

rough ⇒ varying length ⇒ varying angle

Mizuno  et  al.,  PNAS,  106  6044–6047  2009.  Chunnilall  et  al.,  Carbon,  50,  5340-­‐5350,  2012.  

FIR reflectance

Detectors  

Pyroelectric Detectors

1  cm  

Theocharous,  et  al.,  Appl.  Opt.,  52,  2013      

forest  

100  µm  silicon  pelFer  

Thermopile

Thermopile

Radiometer Design

α

wavelength (µm)

optical absorption (1-loss)

“tie points”

absolute response (from heater)

[V/W]

[V/W]

1.

2.

3. ∆T ⇒ ∆V

∆T    thermometer  

absorber  

weak  thermal  link  

heatsink  

heater  

blackened cavity and absorber

weak thermal link

heater

thermometer

Cryogenic Radiometer Design

photo:  courtesy  Malcolm  White  

Martin, et al., , Metrologia, 21, 1985

Carbon nanotube electrical substitution bolometer radiometer

heater absorber thermistor link

Tomlin, et al., Metrologia 52 (2015) 376–383

Material  DeposiFon  

Silicon Wafer (Ø75 mm) 1.  Engineer and micromachine “G” (w, t, and l) 2.  Grow SiO2 3.  Deposit Mo (all) 4.  Wet etch to define Mo pattern (heater/electrodes)

Pattern Photoresist 1.  Deposit Al2O3 2.  Deposit Fe 3.  Lift off Photoresist (acetone) 4.  Grow CNTs

Si SiO2

Al2O3

CNT

Mo

Fe

Material  DeposiFon  

75 mm

Carbon nanotube electrical substitution bolometer radiometer Planar electrical-substitution carbon nanotube cryogenic radiometer 6

Figure 10. (a) VACNT at 4K and (b) Mo at 3.884K temporalresponse due to chopping the optical power (⇡102 µW). Thedigitization in (a) is due to the low resolution of the oscilloscope.Shading indicates times when optical power is o↵.

optical power (dark), then 30 µW of electrical powerand 100 µW of optical power (distributed evenly over a1mm diameter circle) is applied (light). For both cases,the modeled power loss due to the eight wirebondsis ⇡ 2 µW, while the power loss due to radiation is⇡ 40 pW. The mean temperature at the thermistor is0.09mK less for the dark case (figure 9c). In order toperfectly match the temperature at the thermistor forboth cases, an additional power of 0.05 µW is neededfor the dark electrical power. We use this modeledpower di↵erence in order to get a correction for thepower inequivalence (�Pequiv).

8. Time constant

To find the time constant of the PBR, we usedthe optical switch to chop the optical power whilemonitoring the current-biased thermistor voltage onan oscilloscope. An exponential fit to the thermistorvoltage signal yielded a time constant (1/e) of 11.8msat 4K (figure 10a).

Due to the elevated Tc of the Mo, we werealso able to regulate the heatsink temperature in thesuperconducting transition, and monitor the current-biased Mo voltage. An exponential fit to the Mo voltagesignal yielded a time constant (1/e) of 7.7ms at 3.884K(figure 10b).

We attribute the slower VACNT thermistor timeconstant to an additional weak thermal link. Thethermistor behaves as if it is not well thermally coupledto the substrate, perhaps because the growth rate of theVACNT over Mo is higher than over SiO2 (figure 11).The transverse VACNT thermal conductance (nanotubeto nanotube) is orders of magnitude lower than the axial

Figure 11. Schematic sectional view of thermistor VACNTshowing VACNT pulled o↵ substrate over SiO2. Thicknesses arenot to scale.

thermal conductance (nanotube to substrate)[17], whichleads to a longer thermistor time constant.

9. Measuring optical fiber power

In order to measure the optical power leaving the fiber,the following steps are performed:(i) Optical switch to port 1 (power meter). (1 s)

(ii) Pause to stabilize power meter. (4 s)

(iii) Record power meter reading. (1 s)

(iv) Pause for temperature stabilization of PID loops.(44 s)

(v) Record dark (optical power o↵) voltages. (2 s)

(vi) Optical switch to port 2 (PBR). (1 s)

(vii) Pause for temperature stabilization of PID loops.(44 s)

(viii) Record light (optical power on) voltages. (2 s)These eight steps, which take a total time of99 s, constitute two independent and traceableoptical fiber power measurements: a PBR electrical-substitution measurement and a commercial powermeter measurement.

PPBR = (1�RTHR)

·✓

Vref,D � Vref,D,0

Rref

◆· (VD � VD,0) + �Pequiv

�✓Vref,L � Vref,L,0

Rref

◆· (VL � VL,0)

�(1)

The measurement equation for the PBR powermeasurement (PPBR) is shown in equation 1. Line 1is a correction for the non-unity VACNT absorption.Line 2 is the Joule power dissipated in the electricalheater with the optical power o↵ (dark), where Rref

is the current reference resistor, Vref,D is the voltageacross Rref with o↵set voltage Vref,D,0, and VD is thevoltage across the Mo heater with o↵set voltage VD,0.The term �Pequiv is the o↵set power correction due tononequivalence determined from the FEM. Line 3 is

Tomlin, et al., Metrologia 52 (2015) 376–383 SPEED  

Carbon nanotube electrical substitution bolometer radiometer Planar electrical-substitution carbon nanotube cryogenic radiometer 8

Table 2. Typical uncertainty budget for the opticalpower meter measurement equation (equation 2). Values(uncertainties) shown are the mean value (uncertainty) of 100measurements. For type A uncertainties, N is the number ofmeasurements. When N is not listed, the uncertainty is thecombined uncertainty (k = 1) from a separate measurement.

The last column (percent fractional uncertainty) is | @PPM

@x

·u

x

|/PPM · 100. The expanded uncertainty is k = 2.

uncertainty

variable value (x) type/N value (ux

) % frac.

P1 (µW) 96.3 A/1 0.1 0.12

Cabs 1.0058 A 0.0025 0.25

CNL (P1) 0.99999 A 0.000 65 0.065

upol 1 B 0.000 08 0.008

rswitch 1.059 A/4 0.001 0.1

uf,bend 1 B 0.000 26 0.026

nair 1.0002 B 0.000 001 0.000 02

nf,cold 1.443 10 A 0.000 01 0.0001

nf,warm 1.444 40 A 0.000 01 0.0001

PPM (µW) 101.43

combined uncertainty (µW) 0.31 0.30

expanded uncertainty (µW) 0.62 0.61

9.1. Linearity

As a check of linearity, the eight measurement stepswere performed for 100 di↵erent applied optical powersfrom 10 µW to 460 µW (figure 13). From the FEM,we fit �Pequiv = m · P1 + b where m = 3.4⇥ 10�4 andb = 6.2 nW. A linear fit to the di↵erence of PPM�PPBR

shows that PPM is consistently higher than PPBR by0.09%. While this di↵erence is within the combineduncertainties, it suggests that some of the uncertaintiesmay be biased.

For the linearity measurements, the heatsink wasregulated at 4.0776K and the PBR was regulated at4.8074K (R = 304⌦). The mean of the 99 s standarddeviation (k = 2) temperature fluctuations of theheatsink and PBR temperatures were 1mK and 4mK,respectively.

10. Discussion

The main limitation of the current PBR measurementsis the poor sensitivity of the VACNT thermistor,which leads to poor PID temperature stability. Asa performance test, we swapped the roles of theVACNT thermistor and Mo heater to be VACNTheater and Mo thermistor. Since the Mo transitionis much more sensitive than the VACNT, the PIDtemperature fluctuations of the PBR are 38 times lower.Additionally, the Mo was operated under a current

Figure 13. Results of 100 measurements of varying appliedoptical powers. (a) PPBR has been subtracted purely forfigure clarity and no error propagation was performed for thesubtraction. The expanded uncertainty (k = 2) is shown by errorbars. The solid red line is a linear fit to the P

PM

o↵set with aslope of 0.0009. (b) Fractional uncertainty percentage vs. power.

bias, which is a positive electrothermal feedback mode.The temperature fluctuations would be even lower ifoperated under a voltage bias, which is a negativeelectrothermal feedback mode[22]. However, the PBRwas not designed for operation in this swapped mode,and the poor thermalization of the VACNT heaterleads to measurements of PPBR that are low (2.3%below PPM), which we attribute to blackbody radiationfrom the hot VACNT heater coupling to the VACNTabsorber.

By using a more sensitive voltage-biased Mothermistor and a normal metal heater, the uncertaintyof future PBR measurements should be limited only bythe uncertainty in the measurement of the reflectanceof the VACNT.

In conclusion, we have demonstrated results ofa lithographic electrical-substitution carbon nanotuberadiometer. The lithographic design allows for greaterflexibility and lower time constants, compared totraditional cryogenic radiometers. In addition tobeing a primary standard for optical power, by furtherdecreasing the time constant and using high speed PIDelectronics, the PBR could find applications in Fouriertransform infrared (FTIR) spectroscopy.

Acknowledgments

SEM image was taken by Aric Sanders in the PrecisionImaging Facility at NIST Boulder.

“electrical”  “opFcal”  

Tomlin, et al., Metrologia 52 (2015) 376–383 EQUIVALENCE  

Low-Temperature Nanotube Bolometer Behavior Planar electrical-substitution carbon nanotube cryogenic radiometer 5

Figure 8. (a) Mo heater resistance as a function of temperaturewith logistic function fit R = Rn/ (1 + exp (� (T � Tc) /�T )).Since the transition is not symmetric about Tc, we fit fordi↵erent values of �T below Tc (�T = 8.4mK) and above Tc

(�T = 34.4mK). The dashed vertical line shows Tc. In order toconvert to resistivity, the formula ⇢ = R · 2.5⇥ 10�9 m can beused. (b) Thermistor sensitivity figures of merit, calculated fromfits. At Tc, the Mo TCR = 14.1K�1 and ↵ = 54.9.

shows two common thermistor sensitivity figures ofmerit, temperature coe�cient of resistance (TCR =1/R · dR/dT ) and ↵ = T/R · dR/dT .

6. Heater

Due to an unexpected elevation of the Mo superconduct-ing critical temperature (Tc) to 3.884K (figure 8a), weare limited to operating temperatures above Tc wherethe Mo is normal (Rn = 74.5⌦) and the electrical heaterdissipates heat. Since Mo usually has a Tc below 1K,we speculate that the VACNT growth modifies the Mo,possibly forming molybdenum carbide. On separatedevices, we have measured Tc values up to 7K. Theelevated Tc opens the possibility for future devices touse the Mo as an extremely sensitive thermistor (fig-ure 8b) operating as a transition-edge sensor (TES).Additionally, Mo traces could be used for thin-filmsuperconducting wiring instead of Al wirebonds.

7. Thermal modeling

By varying the applied electrical power (Pelec) from1 µW to 800 µW and monitoring the thermistortemperature, we find that the thermal conductance ofthe PBR is best fit by a cubic temperature dependenceof G = dPelec/dT = G0T

3, where G0 is a constant. Theintegrated power law is then Pelec = G0/4

�T

4 � T

4HS

�,

where THS is the temperature of the heatsink. Solvingfor G0 and using measured values of Pelec = 131.15 µW,T = 4.325K, and THS = 4.0772K gives G0 =

Figure 9. (a) Modeled 2D FEM temperature profile for 130 µWof applied power. Color legend not shown, see part (b) fortemperatures. (b) 1D temperature profile along center of 2DFEM (part (a)) for two cases (dark and light) described in text.(c) Di↵erence in temperature of two curves in part (b).

7.13 µWK�4. This gives a thermal conductance at4K of 456 µWK�1.

Using finite-element model (FEM) software, wehave modeled the two dimensional (2D) temperatureprofile of the PBR. We have assumed the Si thermalconductivity is isotropic with a temperature dependenceof Si = Si,0T

3, where Si,0 is an unknown constant.For the conductivity of the Al wirebonds, we haveassumed a linear temperature dependence of Al =Al,0T with Al,0 = 3Wm�1 K�2[15]. Therefore,the power loss due to one Al wirebond is PAl,1 =1/2 (Al/T ·AAl/LAl)

�T

2 � T

2HS

�, where AAl is the

wirebond cross sectional area and LAl is the wirebondlength. The power loss due to blackbody radiation isPrad = A�✏

�T

4 � T

4HS

�, where A is the area, � is the

Stefan-Boltzmann constant, and ✏ is the emissivity with✏VACNT = 1 and ✏Si = 0.1[5, 16]. The model required avalue of Si,0 = 0.166Wm�1 K�4 in order to match themeasured conditions of Pelec, T , and THS listed above.

Figure 9a shows the modeled 2D FEM temperatureprofile for an applied power of 130 µW. Two crosssection temperature profiles are shown in figure 9b,which simulate an electrical substitution measurement.First, 130 µW of electrical power is applied without any

SuperconducFng  TransiFon  Near  4  K  

Tomlin, et al., Metrologia 52 (2015) 376–383 SENSITIVITY  

Carbon Nanotube Base Detectors

Broad, efficient and uniform wavelength range visible to 500 micrometers (!?) (BRDF needed)

τ  ~ 1 ms

Carbon Nanotube Base Detectors

Fast (suitable for FTIR)

Broad, efficient and uniform wavelength range visible to 500 micrometers (!?) (BRDF needed)

τ  ~ 1 ms

Carbon Nanotube Base Detectors

Fast (suitable for FTIR)

Scalable, reproducible Optimize per application fiber, space, few photon (open mind required)

Broad, efficient and uniform wavelength range visible to 500 micrometers (!?) (BRDF needed)

NIST-Gaithersburg (MIR/speed)

PTB Berlin (THz/FIR)

GREYC / Univ. Caen (speed) NIST-Boulder (optical fiber)

NIST  Nanotube  Bolometer  Workshop,  July  22,  23,  24,  2015  Boulder,  Colorado,  USA  hmp://www.nist.gov/pml/div686/nanotube-­‐bolometer-­‐workshop.cfm