Towards carbon nanotube growth

into superconducting microwave

resonator geometr ies

S. Blien

, K. J. G. G

otz

, P. L. Stiller

, T. Mayer

, T. Huber

, O. Vavra

, and A. K. H ¨uttel

*,1

Institute for Experimental and Applied Physics, University of Regensburg, Universit

atsstr. 31, 93053 Regensburg, Germany

Key words: MoRe, superconducting resonators, carbon nanotubes.

∗

Corresponding author: e-mail andreas.huettel@ur.de, Phone: +49 941 943 1618, Fax: +49 941 943 3196

The in-place growth of suspended carbon nanotubes fa-

cilitates the observation of both unperturbed electronic

transport spectra and high-Q vibrational modes. For

complex structures integrating, e.g., superconducting rf

elements on-chip, selection of a chemically and physi-

cally resistant material that survives the chemical vapor

deposition (CVD) process provides a challenge.

We demonstrate the implementation of molybdenum-

rhenium coplanar waveguide resonators that exhibit clear

resonant behaviour at cryogenic temperatures even after

having been exposed to nanotube growth conditions. The

properties of the MoRe devices before and after CVD are

compared to a reference niobium device.

850°C

H , CH

2 4

3.28 3.30

- 31.0

- 30.0

- 28.0

|S | (dB)

f (GHz)

Q = 5000

Q = 14000

a) b)

(a) Schematic of the CVD growth environment; a metal thin

ﬁlm is exposed to a CH

/ H

atmosphere at 850

◦

C. (b) MoRe

coplanar waveguides still display superconductivity after this

treatment, with clear resonant behaviour of a λ/4 structure.

1 Introduction The integration of different types of

mesoscopic systems into hybrid device geometries has led

to a multitude of experimental insights. One recent devel-

opment is the application of coplanar waveguide resonator

technology in hybrid quantum systems, see e.g. [1] for a

detailed review of performed and possible experiments.

Recently signiﬁcant advances were made combining su-

perconducting rf systems with with semiconductor quan-

tum dots [2–4], and also in particular carbon nanotubes.

Carbon nanotube quantum dots have been coupled into

superconducting rf hybrid systems, targetting, e.g., non-

equilibrium charge dynamics [5], noise spectroscopy [6,

7], and manipulation of spin states towards quantum infor-

mation processing [8].

On their own, clean carbon nanotubes, as quasi-one

dimensional carbon macromolecules, excel in their elec-

tronic [6,9–14] as well as nanomechanical properties [15–

20]. This emerges in particular clearly if fabrication steps

after nanotube growth, as, e.g., wet chemistry or lithogra-

phy, are kept to a minimum. Several strategies to that ef-

fect are possible. A well established method is to grow the

carbon nanotubes via chemical vapor deposition (CVD) in

situ across pre-deﬁned electrodes [9]. This generally leads

to low contact resistance as well as devices resilient to me-

chanical vibrations or temperature changes. At the same

time, the choice of materials is strongly restricted; contacts

and other chip structures as, e.g., gates or isolation oxides,

have to survive the CVD process, where the devices are ex-

posed to hot and chemically aggressive gas mixtures. Metal

thin ﬁlms melt or deform strongly, or incorporate carbon

or hydrogen. In particular, superconductors may display a

strong decrease of their critical temperature. In addition the

carbon nanotubes grow at random orientation and length,

lowering the device yield.

This has recently led to the development of alter-

native strategies for the implementation of defect- and

contamination-free suspended nanotube devices, and to

ﬁrst corresponding superconductor–nanotube hybrid ex-

periments [6]. Typically the nanotubes are grown on a

separate substrate and then transferred onto the readily

2 S. Blien et al.: Nanotube growth into superconducting microwave resonators

structured device at last instance [20–24, 6,7]. The separa-

tion of growth and measurement onto different substrates

allows a wider choice in device materials and targetted

placement of the nanotubes, but may come at other costs.

Surface oxidation or contamination of the metallic elec-

trodes may require an additional annealing step to obtain

transparent contacts; even cleaning the metal surfaces in

situ using argon ion-etching and then keeping them in

vacuum during transfer and measurement [23] has been

performed. Conversely, the nanotube transfer process can

be repeated while monitoring device performance, which

for complex device geometries may lead to a higher yield

of functioning structures [23,6,7].

Here, in preparation for the in-place growth approach,

we use the CVD process environment to simulate nan-

otube growth across pre-deﬁned electrodes and investigate

metal ﬁlms with/without having undergone CVD. For

high-frequency experiments, where a suspended carbon

nanotube is to be coupled to, e.g., a coplanar microwave

resonator, a physically and chemically stable metal is re-

quired that remains superconducting even after incorpo-

ration of carbon and possible segregation processes dur-

ing the high-temperature step. We characterize coplanar

waveguide resonators fabricated from the co-sputtered

molybdenum-rhenium alloy Mo

[25]. Even after

CVD clear resonant behaviour is observed. We compare

the device parameters with a reference niobium device

and analyze the temperature dependence of resonance fre-

quency and quality factor.

2 Carbon nanotube CVD growth process Our car-

bon nanotube growth via CVD follows a well-established

process [26] that is able to produce few clean single-wall

carbon nanotubes. The nanotubes grow from well-deﬁned

positions and subsequently fall over contact structures.

A catalyst suspension consisting of iron(III) nitrate

nonahydrate Fe(NO

)

· 9H

O, molybdenum dioxydi-

acetylacetonate MoO

(acac)

, and Al

nanoparticles in

methanol is used. The catalyst deposition area is deﬁned

lithographically. Following development of the electron-

beam resist, the catalyst suspension is drop-cast onto the

chip, and the solvent is evaporated on a hot plate at 150

◦

After a lift-off step, only the catalyst in the growth area re-

mains on the chip. The devices are then placed into a 1

quartz tube, where they are heated up in an argon and hy-

drogen gas ﬂow to a temperature of 850

◦

C. As soon as

the temperature is reached, the argon ﬂow is stopped and

the devices are exposed to a hydrogen (20 sccm) / methane

(10 sccm) atmosphere for ten minutes. During this time, the

growth of the carbon nanotubes takes place. Afterwards,

the devices are cooled down again under argon and hy-

drogen ﬂow. Nanotube devices can now be electronically

tested and pre-characterized.

For the thin-ﬁlm material tests presented here, fo-

cussing on the effect of the high-temperature process on

the metal ﬁlms of the devices, both lithography and cata-

lyst deposition steps are omitted for simplicity. The high-

temperature process is performed in an identical way as

actual nanotube CVD growth.

3 Resonator device fabrication and basic proper-

ties Two types of substrate form the starting point of de-

vice fabrication, either crystalline Al

or compensation-

doped Si with a 500 nm thermally grown oxide. A metal

layer is sputter-deposited and structured via optical lithog-

raphy and reactive ion etching. Fig. 1(a) shows a result-

ing reference device, in this case made of niobium on a

Si/SiO

substrate, containing three λ/4 resonators capac-

itively coupled to a common feed line. In Fig. 1(b), in a

transmission measurement at T = 4.2 K the resonances of

the λ/4 structures can be clearly identiﬁed as distinct min-

ima of the feed line power transmission |S

The required resonator lengths for intended design fre-

quencies can be calculated following

1 − α



eff

(1)

where α is the kinetic inductance fraction of the supercon-

ductor, discussed below in more detail, l is the length of

the resonator, and 

eff

is an effective relative permittivity

resulting from the substrate below and the vacuum (or he-

lium, depending on the measurement; both with 

' 1)

above the substrate. In the simple case of a uniform sub-

strate with permittivity 

, 

eff

can be approximated as



eff

= (

+ 1)/2.

Fig. 1(c) displays a detail measurement of the reference

device from (b) in a dilution refrigerator at T = 15 mK.

The overall transmission values are setup-speciﬁc, result-

ing from an attenuation of −53 dB for thermal coupling in

the signal input line and an ampliﬁcation of +29 dB via a

HEMT ampliﬁer [27] at the 1K stage in the signal output

line. We experimentally determine a center frequency of

≈ 4.2159 GHz.

Aside from the center frequency f

, the resonance

is characterized by the intrinsic quality factor Q

, de-

scribing energy loss within the resonator, and the cou-

pling quality factor Q

, describing energy transfer from

and to the feed line. The so-called loaded quality factor

= 1/ (1/Q

+ 1/Q

) combines both. The solid line in

Fig. 1(c) is a ﬁt following [28,29], where the transmission

(scattering matrix) parameter S

is expressed as

= 1 −

iθ

1 + 2iQ

f−f

. (2)

Here, Q

= |Q

−iθ

has been additionally introduced, a

complex-valued parameter related to the coupling quality

factor Q

as Q

−1

= Re Q

−1

, while Im Q

represents reso-

nance asymmetries. For the reference device of Fig. 1(c)

we ﬁnd at T = 15 mK values of Q

= 234000 and

= 9775, demonstrating the quality of our niobium ﬁlms

f (GHz)

|S | (dB)

4.214 4.216

- 60

- 55

- 50

- 35

Q = 234000

Q = 9775

4.00 4.25 4.75

-6

(dB)

(GHz)

b) c)a)

1.2 mm

Figure 1 (Color online) (a) SEM image of a device containing three λ/4 superconducting coplanar waveguide resonators

of different length, coupled to a common feed line, on a dielectric substrate. (b) Transmission spectrum (T = 4.2 K) of

the feed line of a device with geometry as depicted in (a); 130nm niobium sputtered onto a silicon substrate with 500nm

thermally grown SiO

cap layer. The spectrum is normalized to the high-power transmission where superconductivity

within the resonators is suppressed. (c) Exemplary detail measurement of a resonance of the device from (b) at T = 15 mK;

the solid red line is a ﬁt (see text) resulting in Q

= 234000 and Q

= 9775.

and the lithographic patterning as well as the function of

our measurement setup.

4 Molybdenum-rhenium as resonator material

While niobium is a well-established material for super-

conducting coplanar radiofrequency circuit elements, its

thin ﬁlms unfortunately do not survive the conditions of

CVD carbon nanotube growth. Platinum cap layers on nio-

bium have been used successfully in literature [30], but

turned out to be unreliable in our testing. Rhenium thin

ﬁlms are stable under CVD conditions [12,18], however

in our observation the critical temperature typically de-

creases below 1 K. A highly promising material is given

by molybdenum-rhenium alloys. Pristine ﬁlms have been

shown to exhibit critical temperatures up to 15 K [31–33].

In addition, the ﬁlms remain stable under CVD conditions

[25,34,35]. While a signiﬁcant amount of carbon is inte-

grated into the metal, the high temperature process even

leads to annealing-like processes and an initial increase in

critical temperature, current and ﬁeld [25,35,36].

Fig. 2(a) shows transmission resonances of three

lithographically identical λ/4 structures, using different

metallization layers. The rightmost resonance at high-

est frequency (black) uses niobium, the middle one (red)

pristine molybdenum-rhenium, and the left one (blue)

molybdenum-rhenium which has undergone the CVD pro-

cess used for carbon nanotube growth. The molybdenum-

rhenium 20:80 thin ﬁlms have been deposited via simulta-

neous sputtering from two sources and their composition,

identical for all devices discussed here, has been veriﬁed

via x-ray photoelectron spectroscopy [25].

The difference in resonance frequency predominantly

stems from a difference in the so-called kinetic inductance

of the waveguide: the inertia-delayed response of charge

carriers to a high-frequency ﬁeld is mathematically equiv-

alent to an increased inductance and can be described as

such. It leads to an additional contribution L

to the in-

ductance per length of the coplanar waveguide. Given the

geometric, temperature-independent inductance per length

of a waveguide, the so-called kinetic inductance frac-

tion is then deﬁned as α = L

/(L

+ L

From the data of Fig. 2(a), assuming a small kinetic

inductance fraction for niobium α

' 0 at dilution re-

frigerator base temperature T = 15 mK, we obtain using

Eq. 1 from the resonance frequency for the molybdenum-

rhenium device before CVD α

= 1−(f

)

0.131 and after CVD α

MoRe,CVD

= 0.279.

Via ﬁtting to Eq. 2 we obtain the quality factors Q

and

of the resonator structures. The coupling quality fac-

tor Q

is similar (Q

∼ 10

) for all three devices, con-

sistent with the identical geometry and thereby coupling

capacitance. For the intrinsic quality factor we here obtain

= 234000 for Nb, Q

= 20800 for MoRe without CVD

exposure, and Q

= 2700 for MoRe after 30min CVD ex-

posure. Q

differs strongly, due to the presence of quasi-

particle excitations and corresponding dissipation (see fol-

lowing section).

5 Temperature dependence of resonator prop-

erties Fig. 2(b) shows the resonance of the CVD-treated

molybdenum-rhenium device from Fig. 2(a), at differ-

ing temperature. The resonance frequency f

decreases

strongly with temperature, as does the total quality factor.

A quantitative description of this is given by the so-called

Mattis-Bardeen theory [25,37]. The temperature depen-

dence of f

and Q

can be expressed as

− f

δσ

, (3)

4 S. Blien et al.: Nanotube growth into superconducting microwave resonators

3,300 3,630 4,235

-60

-50

-30

(dB)

f (GHz)

3.24 3.27

-32

-31

-28

(dB)

f (GHz)

15mK

1200mK

1500mK

1800mK

2000mK

3,564 3,960 4,2196

-57,6

-48,0

-28,8

(dB)

f (GHz)

3.586

3.916

4.2123.564

3.960

4.220

-57.6

-48.0

-28.8

(dB)

f (GHz)

(pristine)

(after 30

minutes

of CVD)

Figure 2 (Color online) (a) Power transmission resonances |S

(f) at T = 15 mK of three lithographically identical

λ/4 structures (see Fig. 1(a) for the optical mask geometry). The patterned thin ﬁlm consists of 130nm Nb (right reso-

nance), 145nm pristine Mo

(middle resonance), and 145nm Mo

after undergoing 30 min of CVD process

(left resonance). The distinct shift in the resonance frequency f

is caused by different kinetic inductance fractions α for

the different materials. (b) |S

(f) at the resonance of the CVD-treated Mo

device from (a), for temperatures

15 mK ≤ T ≤ 2 K.





= α

δσ

, (4)

with f

and α

as the zero-temperature limit of resonance

frequency and kinetic inductance fraction. σ

and σ

are

the real and imaginary part of the complex conductivity σ

of the device. We use analytical approximations for both

parts of the complex conductivity in the low temperature

limit [25,38], containing the temperature dependent BCS

energy gap and the normal state conductivity.

Figure 3 shows the extracted resonance frequency f

0.0 1.0

3.20

3.24

T (K)

f (GHz)

0.0 1.0

1000

2000

3000

4000

T (K)

a) b)

Figure 3 (a) Resonance frequency f

(T ) and (b) internal

quality factor Q

(T ) as function of temperature, for the de-

vice of Fig. 2(b) (145 nm MoRe, after 30 min CVD condi-

tions). The red lines show ﬁt curves using Mattis-Bardeen-

theory, see the main text.

(Fig. 3(a)) and internal quality factor Q

(Fig. 3(b)) as func-

tion of temperature T . The solid line in Fig. 3(a) is a ﬁt

following Eq. 3, with α

as the only free ﬁt parameter. Us-

ing a critical temperature of T

= 4 K determined via dc

measurements, the ﬁt results in α

= 0.361. This is larger

than the value we found by comparing the resonance fre-

quencies of different materials in Sec. 4, however, a smooth

drop of the resistance in dc measurements makes a precise

determination of T

difﬁcult.

In the same manner, we obtain α

= 0.176 for the pris-

tine MoRe device, and α

= 0.029 for the niobium device.

The value of α

for the MoRe device is comparable to the

one of Sec. 4, while the value for the niobium device con-

ﬁrms that α ≈ 0 was a good approximation. Generally,

we ﬁnd small kinetic inductance fractions for niobium and

intermediate ones for MoRe, with increasing values for in-

creasing CVD exposure time, corresponding to deteriora-

tion of the superconducting properties.

Regarding the intrinsic quality factor Q

in Fig. 3(b),

we use the value α

= 0.361 extracted from the ﬁt of

Fig. 3(a), and plot the theoretical result following Eq. 4

without additional free parameters. The result (solid red

line) displays acceptable agreement with the data points.

However, models more complex than the straightforward

Mattis-Bardeen description may be appropriate, see, e.g.,

[39] for the integration of a ﬁnite quasiparticle lifetime.

6 Impact of the substrate material Two different

substrate materials have been tested, on one hand crys-

talline Al

(Fig. 4(c)), on the other highly resistive sil-

icon with a thermally (dry) grown, 500nm thick SiO

cap

layer (Fig. 4(d)). The dielectric constant of the substrate 

enters the resonance frequency via Eq. 1. Fig. 4(a) displays

the transmission spectrum of two devices using the same

lithographic structure and metal ﬁlm (pristine MoRe), but

different substrates.

As a consistency check, we can compare the resonance

positions, deduce the effective permittivity of the Si/SiO

bilayer, and compare it with a calculation. Using Eq. 1 it

3.6 4.0

(a)

-3

-2

-1

|S |

(dB)

f (GHz)

12 18

Si/SiO

(GHz

)

Al O

2 3

(GHz

)

Al O

2 3

SiO

metal

SiO

Al O

2 3

metal

(b) (c)

(d)

(e)

optical

axis

Figure 4 (a) Transmitted signal |S

for two devices made of molybdenum-rhenium using the same optical mask,

but different substrate materials. The shift in resonance frequency is caused by different relative permittivities of the

substrates (red: Si/SiO

, black: Al

). (b) The ratio of the squared resonance frequencies is used to determine the relative

permittivity of Si/SiO

. (c) - (e) Different substrate structures: (c) crystalline Al

, (d) compensation-doped silicon with

500nm of SiO

on top, (e) same as in (d) with an additional layer of Al

that was grown using atomic layer deposition.

is easy to show that the effective dielectric constants of the

two devices relate to the resonance frequencies as



eff



Si/SiO

eff

Si/SiO

, (5)

with 

r,⊥

= 9 and 

eff

= 5. From the data of

Fig. 4(a,b) we obtain 

Si/SiO

eff

= 4.86. Using the geo-

metrical device dimensions and following [40] leads to

an expected value of 

eff

= 4.88 and thereby to excellent

agreement with the experimentally determined value.

For integrating carbon nanotube quantum dot struc-

tures with coplanar resonators, additional gate isolation

layers are desirable. With this in mind we have tested ad-

ditionally inserted oxide layers below the superconducting

coplanar waveguide. This is sketched in Fig. 4(e), where an

additional Al

layer has been grown using atomic layer

deposition before applying the resonator metallization. In

a ﬁnal device this layer could, e.g., separate contact elec-

trodes and nanotube from local top gate electrodes.

Table 1 shows an overview of internal quality factors

at T = 4.2 K of devices without or with additional

layer below pristine molybdenum-rhenium. While

there is a certain scatter, no clear tendency towards lower

or higher quality factor is recognizable; within the experi-

mental resolution achievable at this temperature no impact

of the layer can be seen.

7 Conclusion We demonstrate that λ/4 coplanar

waveguide resonators fabricated from a molybdenum-

rhenium alloy display resonant behaviour at millikelvin

temperatures even after being exposed to the chemical

vapor deposition conditions required for carbon nan-

thickness f

(GHz) Q

(4.2 K)

0 nm 3.510 2060

0 nm 3.777 2170

0 nm 4.265 1600

10 nm 3.560 2690

10 nm 3.840 2480

150 nm 3.576 2570

150 nm 3.842 1420

150 nm 4.350 1900

Table 1 Internal quality factors Q

at T = 4.2 K of de-

vices without or with additional Al

layer below pris-

tine molybdenum-rhenium, cf. Fig. 4(e). At this tempera-

ture within experimental scatter no impact of the Al

the quality factor can be seen.

otube growth. Compared to a reference niobium device,

the resonance frequency of lithographically identical

molybdenum-rhenium devices is lower due to a larger ki-

netic inductance fraction of the material. The temperature

dependence of resonance frequency and internal quality

factor can be well described by Mattis-Bardeen theory in

the analyzed temperature range. Both Si/SiO

and Al

substrates can be used, with the expected impact of the

permittivities on the resonance frequency. An additional

layer deposited on a Si/SiO

substrate via atomic

layer deposition, which could, e.g., be used for nanotube

top gate isolation, does not lead to any change in quality

factor detectable at T = 4.2 K.

While our thin ﬁlm deposition via co-sputtering from

two sources has the advantage of adjustable alloy compo-

sition [25], other published results using pre-alloyed sput-

6 S. Blien et al.: Nanotube growth into superconducting microwave resonators

ter targets display signiﬁcantly higher quality factors [35].

Given our excellent results using niobium, we can exclude

problems with substrate, lithography, and detection cir-

cuitry. Further work shall thus target additional optimiza-

tion of the metal thin ﬁlms regarding both nominal compo-

sition and detailed deposition parameters.

Acknowledgements We thank T. N. G. Meier and M.

Kronseder for experimental help with XPS spectroscopy of the

metal ﬁlms. The authors gratefully acknowledge funding by the

Deutsche Forschungsgemeinschaft via SFB 631, SFB 689, GRK

1570, and Emmy Noether project Hu 1808/1.

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