Co-sputtered MoRe thin ﬁlms for carbon nanotube growth-compatible

superconducting coplanar resonators

K. J. G. G¨otz,

∗

S. Blien, P. L. Stiller, O. Vavra, T. Mayer, T. Huber,

T. N. G. Meier, M. Kronseder, Ch. Strunk, and A. K. H¨uttel

†

Institute for Experimental and Applied Physics, University of Regensburg,

Universit¨atsstr. 31, D-93053 Regensburg, Germany

Molybdenum rhenium alloy thin ﬁlms can exhibit superconductivity up to critical temperatures of

= 15 K. At the same time, the ﬁlms are highly stable in the high-temperature methane / hydrogen

atmosphere typically required to grow single wall carbon nanotubes. We characterize molybdenum

rhenium alloy ﬁlms deposited via simultaneous sputtering from two sources, with respect to their

composition as function of sputter parameters and their electronic dc as well as GHz properties at

low temperature. Speciﬁc emphasis is placed on the eﬀect of the carbon nanotube growth condi-

tions on the ﬁlm. Superconducting coplanar waveguide resonators are deﬁned lithographically; we

demonstrate that the resonators remain functional when undergoing nanotube growth conditions,

and characterize their properties as function of temperature. This paves the way for ultra-clean

nanotube devices grown in situ onto superconducting coplanar waveguide circuit elements.

PACS numbers: 85.25.Am, 74.25.N-, 74.70.Ad

I. INTRODUCTION

The discovery of single-walled carbon nanotubes [1, 2]

opened the door for a wide range of both fundamental re-

search and technical applications in such electronic and

nano-electromechanical systems. These macromolecules

exhibit particular properties as, e.g., high mechanical,

chemical and thermal stability as well as excellent elec-

tronic and thermal conductance. They can carry high

currents, display outstanding room temperature transis-

tor characteristics, and may compete in the future with or

even replace conventional silicon-based logic devices [3–

5]. From a fundamental point of view carbon nanotubes

provide a highly promising material for quantum infor-

mation and computation. The macromolecules act as

quasi one-dimensional conductors because of their large

aspect ratio; the electrostatic deﬁnition of localized po-

tential wells can trap electrons in a nuclear spin free en-

vironment with well-deﬁned quantum levels [6–10].

One way to ensure that the carbon nanotubes re-

main clean and defect-free is to grow them directly on

pre-fabricated contact electrodes, such that subsequently

no further lithography and / or wet chemistry takes

place. This technique has led to a multitude of strik-

ing measurement results, from single quantum dot spec-

troscopy [9, 11] to the characterization of high-Q vibra-

tional modes [12, 13]. Performing high-frequency mea-

surements on single wall carbon nanotube structures is

a logical extension. Many techniques applied for such

measurements on mesoscopic structures require the use

of on-chip radiofrequency electronics, in particular su-

perconducting coplanar waveguides and microwave res-

onators formed by these [15, 16]. An example for such

∗

karl.goetz@ur.de

†

andreas.huettel@ur.de

RF-generator

DC source

ReMo

sample

29° 29°

gate

prospective device

sc coplanar waveguide

source

drain

sc ground

plane

CNT

FIG. 1. (Color online) (a) Schematic sketch of a carbon nan-

otube quantum dot device capacitively coupled to a coplanar

λ/2 resonator. For similar devices using diﬀerent material

systems, see Refs. 14 and 15. (b) Sketch of the Orion dual-

source sputtering setup used during fabrication of our metal

thin ﬁlms. The molybdenum target is driven by a radiofre-

quency source with impedance matching, the rhenium target

using a dc source. A mass ﬂow controller sets the argon ﬂow

into chamber.

a possible combined device structure is sketched in Fig.

1(a) – a carbon nanotube is capacitively coupled to the

coplanar λ/2 resonator. In combination with the over-

growth process, this poses extensive diﬃculties, since the

carbon nanotube growth process — typically 10-15 min in

a methane–hydrogen athmosphere [17] — is highly detri-

mental to superconducting thin ﬁlms.

Several solutions for this problem have been proposed,

including transfer of the nanotube from a growth chip

to a second structure [8, 15, 16, 18, 19] or capping the

superconductor with a protection layer [14]. If the metal

ﬁlm is to survive the CVD conditions, a high melting

point, as provided by e.g. rhenium and molybdenum,

becomes an important requirement.

Alloys of rhenium and molybdenum have been shown

to exhibit superconducting transition temperatures up

to 15 K [20–22]. Rhenium and molybdenum rhenium

alloy thin ﬁlms remain stable under carbon nanotube

CVD growth conditions and subsequently still exhibit

superconducting behavior [23]. In addition, after in-situ

growth they provide transparent electronic contacts to

carbon nanotubes [9, 23, 24].

In the following, we characterize molybdenum rhenium

alloy ﬁlms deposited via simultaneous sputtering from

two sources, i.e., cosputtering, with respect to their com-

position as function of sputter parameters and their dc

as well as GHz properties at low temperature. Speciﬁc

emphasis is placed on the eﬀect of the carbon nanotube

growth conditions on the ﬁlm. Coplanar waveguide λ/4

resonators are deﬁned lithographically and characterized

at dilution refrigerator temperatures; even after undergo-

ing the growth conditions internal quality factors of up to

≃ 5000 can be found. The temperature dependence of

the resonance frequency and the internal quality factor is

evaluated and found consistent with theoretical models.

II. THIN FILM DEPOSITION

Figure 1(b) sketches the setup used for the ﬁlm fabri-

cation. The UHV-chamber with typical pressures in the

range of 10

−8

to 10

−7

mbar contains two sputter targets.

The sample holder is placed approximately 13.5 cm above

and in the middle of both targets which are mounted at

a distance of circa 15 cm to each other. Argon gas is in-

jected via a mass ﬂow controller close to the molybdenum

target, and a plasma is ignited using a radiofrequency

drive at a chamber pressure of 10

−1

mbar.

Subsequently the chamber pressure is reduced to 7 ⋅

−3

mbar and the argon plasma at the rhenium elec-

trode is ignited using a dc power supply; at the same

time the rf-output is adjusted such that the plasma close

to the molybdenum electrode and target remains stable.

As soon as both targets are sputtered, the shutters are

opened and the deposition of the MoRe alloy starts. By

keeping the chamber pressure constant over the whole

process time, the deposition rate of both materials is kept

approximately constant. In the following the alloy com-

position of the ﬁlms is varied only by tuning one param-

eter, namely the output power P

of the rf-generator at

the molybdenum target.

III. RESULTING ALLOY

In order to obtain the alloy composition, X-ray photo-

electron spectroscopy (XPS) is performed on the cosput-

tered ﬁlms [25, 26]. Within a predeﬁned area of four to

ten square millimeters the samples are irradiated by a

monochromatic X-ray source, and the resulting emitted

photoelectrons are collected and spectroscopically ana-

lyzed with respect to energy and intensity. The chemical

sensitivity is given by the element-speciﬁc distribution of

binding energies E

of the electronic core levels.

Characteristic XPS data of a cosputtered ﬁlm are plot-

ted in Fig. 2(a). The signal peaks corresponding to

O 1s

Re 4p Mo 3p

C 1s

Re 4d

Mo 3d

Re 4f

(eV)

100200300400 0

intensity (·10

a.u.)

surface spectrum

bulk spectrum

0.5

1.0

225230235240

(eV)

normalized intensity (1)

etch

surface

bulk

0.5

1.0

normalized intensity (1)

35404550

(eV)

etch

surface

bulk

atomic percent

bulk

surface

etching steps

RF-power at Mo-target (W)

at. perc. Mo in the alloy (%)

50 100 150 200

Mo proportion

Mo(P) = -28 + 77·10

-2

P - 17·10

-3

FIG. 2. (Color online) (a) Example X-ray photoelectron spec-

troscopy (XPS) spectrum of a deposited, unstructured ﬁlm

on a p

-Si/SiO

substrate. A power setting of P

= 75 W

at the molybdenum source was used. The black line repre-

sents the chemical composition of the as-grown sample sur-

face, the red line was recorded after removing approximately

5 nm of the ﬁlm by in-situ argon-ion sputtering beam sputter-

ing within the XPS chamber. Normalized detail spectra close

to the Mo 3d-peaks (b) and the Re 4f-peaks (c) (see text).

The energetic step size is set to 0.2 eV. (d) Depth proﬁle

of the atomic composition, calculated from XPS spectra as

in (a), from surface to ∼ 5 nm depth (subsequently named

bulk). The resulting MoRe-alloy composition after each step

is stated above. (e) Relative molybdenum atomic percent-

age in the bulk ﬁlm for diﬀerent power settings P

at the

molybdenum target (see text).

atomic and molecular core levels have been identiﬁed fol-

lowing Ref. 27. The black curve in Fig. 2(a) reveals the

chemical composition of the topmost surface layers. This

is due to the small mean free path of the photoexcited

electrons within the ﬁlm material of few nanometers. In

addition to characteristic peaks originating from molyb-

denum and rhenium core levels, also signiﬁcant oxygen

and carbon peaks are observed. This is likely due to the

fact that all samples have been exposed to air during

transfer from the sputtering device into the UHV cham-

ber of the XPS setup.

Adsorbates and the ﬁlm itself can be etched by in situ

Ar-sputtering for obtaining spectra from lower layers. An

etching step lasts several minutes at a chamber pressure

of less than 3 ⋅ 10

−8

mbar in which the base pressure is

of 5 ⋅ 10

−10

mbar. Etching steps are repeated until the

oxygen 1s-peak only negligibly contributes to the whole

spectrum (at most about 10%). The red (gray) line in

Fig. 2(a) displays the corresponding spectrum. Note that

also the carbon peak is now strongly suppressed. Subse-

quent tests using a proﬁlometer show that approximately

5 nm of the ﬁlms were removed. All spectra obtained

after such a corresponding etching step are henceforth

denoted as “bulk” spectra.

Figure 2(b) and 2(c) display details of the spectrum

close to the Mo 3d- and Re 4f- peaks, referenced to the

C 1s-peak.[26] The additional structure in the Mo 3d sur-

face spectrum originates from MoO

and MoO

forming

at the alloy surface [25, 28]. It decreases subsequently un-

til disappearing in the bulk where only the two Mo 3d

5/2

and Mo 3d

3/2

-peaks are part of the spectrum. In con-

trast, at the Re 4f-peak neither changes in the line shape

nor peak shifts are observed in the surface compared to

the bulk spectrum, indicating the absence of rhenium

oxides at the surface and in the bulk layers. All ﬁlms

examined in this work exhibit the same behavior for the

rhenium peaks [25, 26].

All rhenium peaks of the ﬁlm are shifted by 1.3 eV

to higher E

-values, compared to the literature values

of pure rhenium. Similar values have been identiﬁed in

Ref. 26 as chemical shift due to the Mo-Re compound

formation.

Using the method of area sensitivity factors and eval-

uating the Mo 3d-, Re 4f-, C 1s-, and O 1s-peaks, the

atomic concentrations of the sample have been estimated

[27]. Fig. 2(d) displays the atomic concentrations as a

function of depth. While the exposure to air leads to sig-

niﬁcant carbon and oxygen percentages at the surfaces,

these both decrease strongly; for the “bulk” spectrum

about 10% of carbon remains.

Subsequently the molybdenum-rhenium alloy ratio is

obtained by normalizing to the sum of both sputtered

metals. As can be clearly seen in Fig. 2(e), where the

resulting alloy ratio in the bulk ﬁlm is plotted as a func-

tion of rf power P

applied to the molybdenum sputter

source, the resulting molybdenum contribution in the al-

loy can be controlled over a wide range. The solid line in

Fig. 2(e) is a quadratic ﬁt to the data points.

IV. INFLUENCE OF THE NANOTUBE

GROWTH ENVIRONMENT

Simulating the carbon nanotube chemical vapor de-

position (CVD) growth process typically used to locally

(eV)

100200300400 0

intensity (·10

a.u.)

O 1s

Re 4p

Mo 3p

Re 4d

Mo 3d

Re 4f

surface spectrum

bulk spectrum

C 1s

0.5

1.0

surface

bulk

225230235240

(eV)

normalized intensity (1)

atomic percent

bulk

surface

FIG. 3. (Color online) (a) XPS spectrum of a molybdenum

rhenium ﬁlm sputtered at P

= 75 W, after subsequent

30 min in the carbon nanotube CVD growth environment.

The energy step size is set to 0.2 eV. (b) Detailed zoom of the

Mo 3d peak. (c) Composition of the ﬁlm at the surface and

at ∼ 5 nm depth (atomic percentage); note the large carbon

contribution.

grow few clean single-wall carbon nanotubes [17], the chip

including the MoRe thin ﬁlm is heated up in an argon and

hydrogen gas ﬂow, then exposed to a methane-hydrogen

atmosphere at about 900

◦

C for several minutes and sub-

sequently cooled down under argon and hydrogen ﬂow.

The XPS of a molybdenum rhenium alloy sputtered

with P

= 75 W after exposure to the CVD environment

is shown in Fig. 3(a), and a normalized detail plot of the

Mo 3d peak in Fig. 3(b). A strong carbon peak is visible

even in the bulk. Furthermore in both surface and bulk

molybdenum spectra oxide peaks are not observed, as

visible in Fig. 2(b).

Having in mind that molybdenum oxides exhibit dras-

tically lower melting points of 795

◦

C for MoO

, and

1100

◦

C for MoO

[29] than pure molybdenum with

2610

◦

C [30], the data indicates that reduction of the ox-

ide to atomic molybdenum takes place during CVD.

An additionally possible process is the formation of

molybdenum carbides. The expected XPS peak of Mo

= 227.75 eV) is very close to that of Mo 3d

5/2

= 228 eV), which makes detection challenging with

our experimental resolution. Interestingly, molybdenum

carbides display superconductivity with critical tempera-

tures 6 K ≲ T

≲ 9 K [31]. However, typically the growth

of molybdenum carbide out of pure molybdenum, for ex-

ample in a nitrogen-xylene atmosphere, takes place at

temperatures higher than 900

◦

C, see [31].

T (K)

2 4

6 8

(mA)

Hall bar type B

10 min CVD

100 μm

0 10 20 30

growth time (min)

(K)

B (T)

=7.29 T

=8.30 K

30 min CVD

=3.60 T

=3.92 K

(K)

2 4

6 8

FIG. 4. (Color online) (a) Exemplary SEM micrograph of

a test Hall bar structure, type A. Dimensions are for type A

width W

= 28 µm and ﬁlm thickness d

≈ 150 nm, for type B

= 5 µm and d

≈ 60 nm. (b) Measured critical current I

through a Hall bar device (type B), Mo

, as a function

of temperature. (c) Critical temperature T

of Mo

ﬁlms

as a function of applied magnetic ﬁeld B, with and without

CVD growth exposure. (d) Measured critical temperature T

as a function of CH

ﬂow time during the CVD process.

Straight lines are guides to the eye.

The area sensitivity factor analyzing method results

in a bulk composition of 26% carbon, 22% molybdenum,

and 49% rhenium plus neglectable oxygen residues. Since

the etching time for the bulk spectra has been kept con-

stant, it is obvious that the high carbon contribution does

not have its origin in atmospheric adsorbates but in dif-

fusion of carbon into the alloy during CVD. The relative

atomic ratio of the sputtered metals is Mo

, indi-

cating structural changes during CVD.

Spectroscopy on a second sample using twice the gas

ﬂow of methane results in a composition of 12% molyb-

denum, 23% rhenium, and even 58% carbon in the bulk.

From this we conclude that the penetration of carbon into

the alloy also increases. However, the resulting sputtered

metal ratio of Mo

still remains close to the previ-

ous sample.

V. DC CHARACTERIZATION

To characterize the electronic properties of the co-

sputtered ﬁlms at room temperature as well as at cryo-

genic temperatures, the fabricated thin ﬁlms on top of

SiO

or Al

substrates are patterned into Hall bars

by means of optical lithography and SF

/Ar reactive ion

etching (see Fig. 4(a)). Afterwards, selected structures

are placed into the CVD furnace and exposed to the

nanotube growth environment for several minutes. All

measurements have been performed on ﬁlms either ex-

amined by XPS (see last two sections) or deposited si-

multaneously to these in the same deposition step. De-

vices using two diﬀerent alloy compositions have been ex-

amined, namely Mo

and Mo

obtained with

= 75 W and P

= 200 W, respectively.

At room temperature, compared to Mo

both

resistivity and sheet resistance of the Mo

sam-

ples are higher by a factor 3–5: before CVD we obtain

ρ ≃ 3.0 ⋅ 10

−7

Ωm for Mo

and ρ ≃ 9.0 ⋅ 10

−7

Ωm

for Mo

. Resistances slightly increase during ex-

position to the CVD environment, to ρ ≃ 4.0 ⋅ 10

−7

Ωm

for Mo

and 13 ⋅ 10

−7

Ωm ≲ ρ ≲ 15 ⋅ 10

−7

Ωm for

Results of low-temperature measurements performed

on Mo

devices are plotted in Fig. 4(b) and

Fig. 4(c). Independent from CVD-exposure, the residual-

rest-resistance values RRR for all Mo

devices are

in the range 0.8 ≲ RRR ≲ 1.0. Fig. 4(b) displays the

critical current of a Mo

ﬁlm (Hall bar geometry B,

with T

= 9.2 K) after 10 min CVD exposure. It carries a

supercurrent up to I

≳ 80 mA, corresponding to a crit-

ical current density of j

≳ 2.7 ⋅ 10

A/mm

over a wide

temperature range up to ca. 5 K before the transition

to a normal conductor takes place above 8 K. This very

high value for j

is well in accordance with the results of

[32], where after high-temperature annealing critical cur-

rent densities of up to 1.8⋅10

A/mm

through suspended

-nanostructures were reported.

A second Mo

Hall bar device (type A, T

8.3 K), not exposed to CVD, exhibits a critical current

≈ 114 mA at T = 4.2 K, corresponding to a lower cur-

rent density j

= 2.8 ⋅ 10

A/mm

. Also much longer ex-

posure to the CVD environment again lowers the reach-

able critical current density.

Figure 4(c) displays data on the magnetic ﬁeld depen-

dence of the critical temperature. Fitting the empiri-

cal relation B

(T ) = B

⋅ 1 − (T /T

)

 [33] results in

high characteristic values B

= 7.3 T and T

= 8.3 K

expected for molybdenum rhenium alloys, where T

de-

notes the zero ﬁeld critical temperature and B

the ex-

trapolated critical ﬁeld at zero temperature. Again, as

observed for critical currents, prolonged (30 min) CVD

exposure results in a strong decrease of both values to

here B

= 3.6 T and T

= 3.9 K [32, 34]. This eﬀect

is also visible in Figure 4(d), displaying the critical tem-

perature for two diﬀerent alloy compositions. Even for

only 10 minutes growth time, T

of the Mo

ﬁlm

decreases to the half, well in accordance with the results

of Ref. 34. Interestingly, in contrast the Mo

alloy

keeps its critical temperature range of 8 K ≤ T

≤ 9 K for

growth times up to 20 minutes, only reaching < 4 K after

30 minutes of exposure to the CH

ﬂow.

a) b)

3.596 3.598 3.6

f (GHz)

(dB)

= 23589

= 10761

Θ = -0.04

= 3.59759 GHz

-27

-30

-33

f (GHz)

(dB)

= 4985 Q

= 2666

= 4121

3.25

1mm

FIG. 5. (Color online) (a) SEM image of a test structure with

three MoRe coplanar λ/4 resonators coupled to a feed line.

(b) Detail of the transmission S

(f)

at T = 100 mK of a

device as depicted in (a); the background value of S

(f)

has been subtracted. 150 nm pristine Mo

; see the text

for a description of the ﬁt. (c) Uncalibrated transmission

spectrum S

(f)

at T = 15 mK (dilution refrigerator mix-

ing chamber temperature) of a second 150 nm Mo

de-

vice over a wider frequency range, now after 30 min exposure

to the CVD CH

ﬂow. Resonances corresponding to the

three λ/4 structures coupled to the feedline can still be clearly

identiﬁed.

VI. COPLANAR RESONATOR DEVICES

Coplanar waveguide λ/4 resonators were fabricated to

investigate the high frequency behavior of the alloy ma-

terial and its suitability for cavity quantum electrody-

namics and optomechanics experiments. After sputter-

ing of 150 nm Mo

on SiO

or Al

substrates, the

structures were patterned using optical lithography and

reactive ion etching with SF

/Ar. A micrograph of a de-

vice coupling three λ/4 resonators to a common feed line

is shown in Fig. 5(a). The devices are glued on a printed

circuit board, bonded with aluminum bond wires and

subsequently characterized in a dilution refrigerator. On

the signal input side the experimental wiring of super-

conducting UTF85 semirigid NbTi cables includes atten-

uators as thermal anchoring at every temperature stage.

The input signal is attenuated by approximately 53 dB,

transmitted through the device under test and then am-

pliﬁed by 29 dB by a low noise HEMT ampliﬁer[35] at

the 1 K stage.

Near its fundamental resonance frequency, given by the

length of the resonator l and an eﬀective permittivity ε

eﬀ



eﬀ

, (1)

each of the three resonators behaves like a parallel

lumped-element RLC circuit, coupling energy out of the

feed line and leading to a distinct resonant drop in feed-

line transmission S

. In the vicinity of the resonance,

the transmitted signal can be expressed by [36]

= 1 −

Q



⋅ e

iΘ

1 + 2iQ

⋅

f−f

, (2)

where 1/Q

= 1/Q

+ 1/Q

. Here, Q

is the material

and temperature dependent internal quality factor of the

λ/4 structure, and Q

the geometry dependent coupling

quality factor. Q

is a complex-valued parameter closely

related to the coupling quality factor Q

, whose ﬁnite

phase Θ can give rise to a line shape asymmetry due

to non-ideal circuit elements, e.g. a complex loading of

the resonator or impedance mismatches. Its real part

fulﬁls the condition Re[Q

−1

] = Q

−1

. Fig. 5(b) shows

the normalized data of the transmission S



for one

exemplary resonance of a pristine ﬁlm at T = 100 mK. It

includes a ﬁtted curve following Eq. 2; an intrinsic quality

factor of Q

≃ 23600 and a coupling quality factor of

≃ 10800 are obtained. Fig. 5(c) displays an overview

plot of the uncalibrated transmission of a similar device,

this time after an exposure of 30 min to the hot CVD

gas mixture. Still, all three resonances can be clearly

recognized, with quality factors up to Q

≃ 5000.

VII. COPLANAR RESONATOR

TEMPERATURE DEPENDENCE

Fig. 6 shows the observed temperature dependence of

the resonance frequency f

(T ) (Figs. 6(a,c)) and the in-

ternal quality factor Q

(T )(Figs. 6(b,d)) for two devices.

The device of Figs. 6(a,b) (device 1) has been character-

ized after thin ﬁlm deposition and patterning, the device

of Fig. 6(c,d) (device 2) has been additionally exposed to

the nanotube CVD growth environment.

As can be seen in the ﬁgure, the resonance frequency

clearly decreases at high temperatures (T ≳ 0.8 K for

device 1, T ≳ 0.4 K for device 2). This can be attributed

to a decrease in superﬂuid density of the superconducting

thin ﬁlm. A related rise in the quasiparticle density leads

to a higher damping of the resonator and therefore to a

reduction of the internal quality factor. Following Mattis

and Bardeen [34, 37], the temperature dependence of f

can be expressed as

δf

δσ

, (3)

with δf

(T )= f

(T )− f

the deviation of the resonance

frequency with ﬁnite temperature and f

= f

(T = 0)the

approximated resonance frequency at T = 0. In the limit

hf ≪ ∆(T = 0) and k

T ≪ ∆(T = 0) the imaginary

part σ

of the complex conductivity σ of the device can

be approximated using the temperature-dependent BCS

energy gap ∆ and the normal state conductivity σ

[38]

π∆



1 − 2e

−∆/k

−hf/2k





, (4)

(GHz)

3.56

3.57

3.58

3.55

1 2 3 4

T (K)

δf

(kHz)

T (K)

0.2 1.0

(GHz)

T (K)

4.20

4.24

1 3 5

T (K)

(·10

)

(·10

)

1 2 3 4

0.2

(K)

0.4

23.6

23.7

T (K)

(·10

)

1 2 3

4 5

2 4

4.18

4.22

4.26

δf

(kHz)

T (K)

0.2 0.8

-20

-40

(·10

)

0.1

T (K)

4.25

4.35

0.2 0.3

FIG. 6. (Color online) Temperature dependence of reso-

nance frequency f

and internal quality factor Q

for two

λ/4 resonator devices. (a), (b) Resonance frequency f

(a)

and internal quality factor Q

(b) for device 1 (no CVD

treatment); compensation-doped silicon substrate covered by

500 nm thermal SiO

, 10 nm ALD-deposited Al

and a

150 nm thick Mo

ﬁlm. The insets display detail zooms

for low temperatures. (c), (d) Corresponding plots for de-

vice 2, after undergoing 10 min CH

ﬂow in the CVD

growth oven. Compensation-doped silicon substrate covered

by 500 nm thermal SiO

and 150 nm Mo

. For a de-

scription of the ﬁt models (solid and dashed lines) see the

text.

where I

(x)is a modiﬁed Bessel function of the ﬁrst kind.

The parameter α

in Eq. 3 is the kinetic inductance frac-

tion in zero-temperature limit of the coplanar waveguide.

The solid red lines in Figs. 6(a,c) are ﬁt curves corre-

sponding to this model, using in each case α

as a free pa-

rameter. The result agrees very well with the experimen-

tal data. For device 1 (no CVD) we obtain α

= 0.199,

for device 2 (after 10 min CVD) α

= 0.249. The value of

can be calculated from the normal-state conductance

and the critical temperature T

following [39]. Us-

ing the parameters of our devices, we obtain α

= 0.243

and α

= 0.284, in reasonable agreement with the ﬁt re-

sults. The corresponding functional dependence of f

(T )

is plotted in Figs. 6(a,c) each as a green dashed line.

In Figs. 6(b,d), clearly also the internal quality factor

of the devices decreases at high temperature. Follow-

ing Mattis and Bardeen, the corresponding change of the

quality factor is





= α

δσ

(5)

with the real part of the complex conductivity [38]

4∆

−∆/k

sinh









. (6)

Here K

(x) is a modiﬁed Bessel function of the second

kind. Using the parameters extracted in Figs. 6(a,c) we

can plot the corresponding expected temperature depen-

dence Q

(T ), again as solid red and dashed green lines;

while signiﬁcant deviations exist, the overall tendency

agrees well with the data.

For T ≪ T

, the theory by Mattis and Bardeen pre-

dicts no change in the resonance frequency with tem-

perature. However, in our devices for T ≲ 0.5 K a slight

decrease in f

is observed, leading to an overall nonmono-

tonic behaviour of f

(T ), see the insets of Figs. 6(a,c).

This is consistent with the inﬂuence of two-level systems

(TLS) in the substrate contributing to both dissipation

and dispersion and can be described by [40–42]

δf

δε

(7)

F ϑ



ReΨ



2π i

(T )



− ln



2π

(T )



(8)

Here, Ψ is the digamma function, 0 < F < 1 the ﬁlling

factor, giving the ratio of the electric energy stored in the

TLS hosting material to the total electric energy stored

in the resonator, and ϑ the loss tangent of the substrate.

The insets of Figs. 6(a,c) show the measured data along

with a low-temperature ﬁt, using the product F ϑ and f

as ﬁt parameters.

In the case of device 1, Fig. 6(a), this results in

F ϑ = 3.968 ⋅ 10

−5

. This value of F ϑ is comparable to

literature values for niobium resonators on sapphire, see

e.g. [43]. The ﬁt value for F ϑ provides an approximation

for the TLS-related low-power, low-temperature internal

Q-factor Q

i,TLS

≈ 1/(F ϑ) ≈ 25000. As expected this

slightly exceeds our measured value of Q

(T = 20 mK)≈

23500. The ﬁt for device 2 provides F ϑ = 4.087 ⋅ 10

−5

This results in a quality factor Q

i,TLS

≈ 24500, compa-

rable to the value for device 1 and apparently insensitive

to the degradation of the device due to the CVD process.

Similar to f

, also the low-temperature behavior of the

quality factor Q

is governed by interactions with sub-

strate TLS. This can be modeled by [41, 42]

= F ϑ

eﬀ

tanh



(T )



other

. (9)

Here, ϑ

eﬀ

is an eﬀective, reduced loss tangent which takes

into account that at strong driving the two-level sys-

tems are partially saturated and thereby unable to ab-

sorb energy. Q

other

describes dissipative processes unre-

lated to TLS. The ﬁt for device 1 again agrees well with

the measured data (inset of Fig. 6(b)) and results in

F ϑ

eﬀ

= 5.677 ⋅ 10

−7

and Q

other

= 23800. For device 2

(inset of Fig. 6(d)) only few data points at low temper-

ature are available, and a saturation of the device tem-

perature cannot be excluded. Applying the ﬁt, we obtain

F ϑ

eﬀ

= 1.634 ⋅ 10

−6

and Q

other

= 4370, dominating the

TLS contribution.

As can be seen in Fig. 6, the combined eﬀect of two-

level systems and a temperature dependent superﬂuid

density provide a good description of our devices. Due

to the CVD process the kinetic inductance fraction in-

creases. The low temperature ﬁts tentatively display sim-

ilar inﬂuence of two-level systems before and after CVD,

however a signiﬁcant non-TLS induced dissipation term

results in the second, post-CVD device.

VIII. SUMMARY AND CONCLUSIONS

The x-ray photoelectron spectroscopy characterization

demonstrates that our co-sputtering process from two in-

dependent targets can generate MoRe thin ﬁlms of con-

trolled alloy composition. We observe traces of molyb-

denum oxides at the ﬁlm surface after ambient air ex-

posure. Exposing the thin ﬁlms to the carbon nanotube

CVD growth environment, a signiﬁcant amount of car-

bon is incorporated into the ﬁlm. No clear indications

for the formation of molybdenum carbide can be found;

the surface oxide is absent after CVD, pointing towards

its reduction in the 850

◦

C H

atmosphere.

In electrical characterization, we observe a higher re-

silience to the CVD process for Mo

ﬁlms; the crit-

ical temperature only drops below T

= 8 K for growth

times > 20 min. For shorter growth times, data indicates

that the CVD process may have eﬀects similar to the

annealing discussed in [32], i.e., enhancing the critical

temperature and critical current density. We observe up

to j

≃ 2.7 ⋅ 10

A/mm

and T

≃ 9.2 K in a Hall bar

geometry.

λ/4 coplanar waveguide resonators were deﬁned by

thin ﬁlm deposition and subsequent reactive ion etching.

After structuring, we observe internal quality factors up

to Q

= 23700 in pristine devices and up to Q

= 5000 af-

ter undergoing the CVD process. The temperature evolu-

tion of the resonance frequency f

and the internal qual-

ity factor Q

of the devices can be understood for low

temperatures T ≲ 0.4 K via interaction with substrate

two-level systems, at higher temperatures T ≳ 0.8 K via

the decreasing superﬂuid density.

clearly excels in terms of stability during

the CVD process, critical temperature and ﬁeld as well

as critical current. However, the achieved quality fac-

tors are clearly lower than those reported in literature

for similar materials [34]. Our reference niobium devices

characterized for comparison have reached Q

≃ 4 ⋅ 10

excluding the detection setup as cause. The eﬀect of the

CVD process in lowering Q

is similar to other published

observations [34]. Further improvements thus should be

targeted at the radiofrequency properties of the substrate

as well as the the pristine, as-deposited metal ﬁlm and

coplanar waveguide resonators deﬁned in it.

IX. ACKNOWLEDGMENTS

The authors gratefully acknowledge funding by the

Deutsche Forschungsgemeinschaft via SFB 631, GRK

1570, and Emmy Noether project Hu 1808/1.

[1] S. Iijima and T. Ichihashi, “Single-shell carbon nanotubes

of 1-nm diameter,” Nature 363, 603–605 (1993).

[2] D. S. Bethune, C. H. Klang, M. S. de Vries, G. Gorman,

R. Savoy, J. Vazquez, and R. Beyers, “Cobalt-catalysed

growth of carbon nanotubes with single-atomic-layer

walls,” Nature 363, 605–607 (1993).

[3] P. Avouris, “Carbon nanotube electronics,” Chemical

Physics 281, 429–445 (2002).

[4] P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based

electronics,” Nature Nanotechnology 2, 605–615 (2007).

[5] M. M. Shulaker, G. Hills, N. Patil, H. Wei, H.-Y. Chen,

H.-S. P. Wong, and S. Mitra, “Carbon nanotube com-

puter,” Nature 501, 526–530 (2013).

[6] K. Grove-Rasmussen, H.I. Jørgensen, and P.E. Lin-

delof, “Fabry–perot interference, Kondo eﬀect and

Coulomb blockade in carbon nanotubes,” Physica E:

Low-dimensional Systems and Nanostructures 40, 92–98

(2007).

[7] G. A. Steele, G. G¨otz, and L. P. Kouwenhoven, “Tunable

few-electron double quantum dots and Klein tunnelling

in ultraclean carbon nanotubes,” Nature Nanotechnology

4, 363–367 (2009).

[8] A. Benyamini, A. Hamo, S. Viola Kusminskiy, F. von Op-

pen, and S. Ilani, “Real-space tailoring of the electron-

phonon coupling in ultraclean nanotube mechanical res-

onators,” Nature Physics 10, 151–156 (2014).

[9] D. R. Schmid, S. Smirnov, M. Marga´nska, A. Dirnaich-

ner, P. L. Stiller, M. Grifoni, A. K. H¨uttel, and

C. Strunk, “Broken SU(4) symmetry in a Kondo-

correlated carbon nanotube,” Physical Review B 91,

155435 (2015).

[10] M. Gaass, A. K. H¨uttel, K. Kang, I. Weymann, J. von

Delft, and Ch. Strunk, “Universality of the Kondo Eﬀect

in Quantum Dots with Ferromagnetic Leads,” Phys. Rev.

Lett. 107, 176808 (2011).

[11] J. Cao, Q. Wang, and H. Dai, “Electron transport in very

clean, as-grown suspended carbon nanotubes,” Nature

Materials 4, 745–749 (2005).

[12] A. K. H¨uttel, G. A. Steele, B. Witkamp, M. Poot, L. P.

Kouwenhoven, and H. S. J. van der Zant, “Carbon

Nanotubes as Ultrahigh Quality Factor Mechanical Res-

onators ,” Nano Letters 9, 2547–2552 (2009).

[13] J. Moser, A. Eichler, J. G¨uttinger, M. I. Dykman,

and A. Bachtold, “Nanotube mechanical resonators with

quality factors of up to 5 million,” Nature Nanotechnol-

ogy 9, 1007–1011 (2014).

[14] M. R. Delbecq, V. Schmitt, F. D. Parmentier, N. Roch,

J. J. Viennot, G. F`eve, B. Huard, C. Mora, A. Cottet,

and T. Kontos, “Coupling a Quantum Dot, Fermionic

Leads, and a Microwave Cavity on a Chip,” Phys. Rev.

Lett. 107, 256804 (2011).

[15] J. J. Viennot, M. R. Delbecq, M. C. Dartiailh, A. Cottet,

and T. Kontos, “Out-of-equilibrium charge dynamics in

a hybrid circuit quantum electrodynamics architecture,”

Phys. Rev. B 89, 165404 (2014).

[16] V. Ranjan, G. Puebla-Hellmann, M. Jung, T. Hasler,

A. Nunnenkamp, M. Muoth, C. Hierold, A. Wallraﬀ, and

C. Schonenberger, “Clean carbon nanotubes coupled to

superconducting impedance-matching circuits,” Nature

Communications 6, 7165 (2015).

[17] J. Kong, H. T. Soh, A. M. Cassell, C. F. Quate, and

H. Dai, “Synthesis of individual single-walled carbon nan-

otubes on patterned silicon wafers,” Nature 395, 878

(1998).

[18] C. C. Wu, C. H. Liu, and Z. Zhong, “One-Step Direct

Transfer of Pristine Single-Walled Carbon Nanotubes

for Functional Nanoelectronics,” Nano Letters 10, 1032–

1036 (2010).

[19] F. Pei, E. A. Laird, G. A. Steele, and L. P. Kouwenhoven,

“Valley-spin blockade and spin resonance in carbon nan-

otubes,” Nature Nanotechnology 7, 630–634 (2012).

[20] L. R. Testardi, J. J. Hauser, and M. H. Read, “Enhanced

Superconducting T

and structural transformation in Mo-

Re Alloys,” Solid State Communications 9, 1829–1831

(1971).

[21] J. R. Gavaler, M. A. Janocko, and C. K. Jones, “A-15

structure Mo-Re superconductor,” Applied Physics Let-

ters 21, 179–180 (1972).

[22] V. S. Postnikov, V. V. Postnikov, and V. S. Zheleznyi,

“Superconductivity in Mo-Re System Alloy Films Pro-

duced by Electron Beam Evaporation in High Vacuum,”

Physica Status Solidi A 39, 21–23 (1977).

[23] B. H. Schneider, S. Etaki, H. S. J. van der Zant, and

G. A. Steele, “Coupling carbon nanotube mechanics to

a superconducting circuit,” Scientiﬁc Reports 2, 599

(2012).

[24] P. L. Stiller, S. Kugler, D. R. Schmid, C. Strunk, and

A. K. H¨uttel, “Negative frequency tuning of a carbon

nanotube nano-electromechanical resonator under ten-

sion,” physica status solidi (b) 250, 2518–2522 (2013).

[25] J. Talvacchio, M. A. Janocko, and J. Greggi, “Proper-

ties of Evaporated Mo-Re Thin-Film Superconductors,”

Journal of Low Temperature Physics 64, 395–408 (1986).

[26] V. A. Seleznev, M. A. Tarkhov, B. M. Voronov, I. I.

Milostnaya, V. Y. Lyakhno, A. S. Garbuz, M. Y.

Mikhailov, O. M. Zhigalina, and G. N. Gol’tsman, “De-

position and characterization of few-nanometers-thick su-

perconducting Mo-Re ﬁlms,” Supercond. Sci. Technol.

21, 115006 (2008).

[27] J. F. Moulder, W. F. Stickle, P. E. Sobol, and K. D.

Bomben, Handbook of X-ray Photoelectron Spectroscopy,

2nd ed. (Perkin-Elmer Corporation, Physical Electronics

Division, 1992).

[28] D. O. Scanlon, G. W. Watson, D. J. Payne, G. R. Atkin-

son, R. G. Egdell, and D. S. L. Law, “Theoretical and

experimental study of the electronic structures of MoO

and MoO

,” The Journal of Physical Chemistry C 114,

4636–4645 (2010).

[29] N. Wiberg, E. Wiberg, and A. F. Hollemann, Lehrbuch

der anorganischen Chemie, 101st ed. (Gruyter, 1995).

[30] H. St¨ocker and C. Hartnack, Taschenbuch der Physik, 5th

ed. (Verlag Harri Deutsch, 2007).

[31] N. Morton, B. W. James, G. H. Wostenholm, D. G. Pom-

fret, M. R. Davies, and J. L. Dykins, “Superconductivity

of molybdenum and tungsten carbides,” Journal of the

Less Common Metals 25, 97–106 (1971).

[32] M. Aziz, D. C. Hudson, and S. Russo, “Molybdenum-

rhenium superconducting suspended nanostructures,”

Applied Physics Letters 104, 233102 (2014).

[33] M. Tinkham and G. McKay, Introduction to Supercon-

ductivity, 2nd ed. (McGraw-Hill, Inc., 1996).

[34] V. Singh, B. H. Schneider, S. J. Bosman, E. P. J. Merkx,

and G. A. Steele, “Molybdenum-rhenium alloy based

high-Q superconducting mircowave resonators,” Applied

Physics Letters 105, 222601 (2014).

[35] Caltech CITCRYO1-12A cryogenic microwave ampliﬁer,

http://www.caltechmicrowave.org/.

[36] M. S. Khalil, M. J. A. Stoutimore, F. C. Wellstood, and

K. D. Osborn, “An analysis method for asymmetric res-

onator transmission applied to superconducting devices,”

Journal of Applied Physics 111, 054510 (2012).

[37] D. C. Mattis and J. Bardeen, “Theory of the anomalous

skin eﬀect in normal and superconducting metals,” Phys.

Rev. 111, 412–417 (1958).

[38] J. Gao, J. Zmuidzinas, A. Vayonakis, P. Day, B. Mazin,

and H. Leduc, “Equivalence of the Eﬀects on the Com-

plex Conductivity of Superconductor due to Temperature

Change and External Pair Breaking,” Journal of Low

Temperature Physics 151, 557–563 (2008).

[39] R. E. Collin, Foundations for Microwave Engineering,

2nd ed. (IEEE Press).

[40] W. A. Phillips, “Two-level states in glasses,” Reports on

Progress in Physics 50, 1657 (1987).

[41] A. Bruno, G. de Lange, S. Asaad, K. L. van der Enden,

N. K. Langford, and L. DiCarlo, “Reducing intrinsic

loss in superconducting resonators by surface treatment

and deep etching of silicon substrates,” Applied Physics

Letters 106, 182601 (2015).

[42] D. P. Pappas, M. R. Vissers, D. S. Wisbey, J. S. Kline,

and J. Gao, “Two level system loss in superconducting

microwave resonators,” IEEE Transactions on Applied

Superconductivity 21, 871–874 (2011).

[43] J. Gao, M. Daal, A. Vayonakis, S. Kumar, J. Zmuidzinas,

B. Sadoulet, B. A. Mazin, P. K. Day, and H. G. Leduc,

“Experimental evidence for a surface distribution of two-

level systems in superconducting lithographed microwave

resonators,” Applied Physics Letters 92, 152505 (2008).