††thanks: Present address: Department of Applied Physics, Yale University, New
Haven, CT 06520

# Reducing quantum-regime dielectric loss of silicon nitride for
superconducting quantum circuits

Hanhee Paik<EMAIL_ADDRESS>Kevin D. Osborn  Laboratory for Physical
Sciences
College Park, MD 20740

###### Abstract

The loss of amorphous hydrogenated silicon nitride (a-SiNx:H) is measured at
30 mK and 5 GHz using a superconducting LC resonator down to energies where a
single-photon is stored, and analyzed with an independent two-level system
(TLS) defect model. Each a-SiNx:H film was deposited with different
concentrations of hydrogen impurities. We find that quantum-regime dielectric
loss tangent $\tan\delta_{0}$ in a-SiNx:H is strongly correlated with N-H
impurities, including NH2. By slightly reducing $x$ we are able to reduce
$\tan\delta_{0}$ by approximately a factor of 50, where the best films show
$\tan\delta_{0}$ $\simeq$ 3 $\times$ 10-5.

###### pacs:

77.84.Bw, 84.40.Dc, 85.25.-j

††preprint: APS/123-QED

Superconducting quantum circuits use amorphous dielectric films for wiring
crossovers and capacitors Siddiqi05a ; Steffen06b ; Sillanpaa07a , but these
films often cause loss at low temperatures in the quantum-regime where the
resonator is occupied by a single photon. These defects can be described by a
tunneling two-level system (TLS) model Schickfus77a . There has been recent
interest in the low-temperature properties of dielectrics in superconducting
devices OConnell ; Barends ; Gao08a  because they can increase the decoherence
rate $1/T_{1}$ in a superconducting phase qubits Martinis05a  and the phase
noise in microwave kinetic inductance detectors Gao07 .

While both films are common in microelectronics, amorphous hydrogenated
silicon nitride (a-SiNx:H) is found to exhibit less dielectric loss than
silicon dioxide (SiO2) in the quantum regime Martinis05a . Close to the
stoichiometric point $x\simeq 4/3$, the electronic and optical properties of
this film are determined by the dominant hydrogen impurity which can be
changed by deposition conditions Martinu00a .

In this paper we first show the composition of five films grown under the
condition where there is a strong variation in relative hydrogen impurity
type. Then we present low-temperature loss measurements of the a-SiNx:H films
using superconducting resonators. The loss in the quantum-regime of the films
varied dramatically as the relative amount of N-H and Si-H impurities was
changed, and in particular we discovered that the NH2 concentration is
proportional to the TLS density indicating that NH2 may be responsible for the
microscopic loss. This research demonstrates the low temperature dielectric
loss in a-SiNx:H can be reduced by reducing nitrogen impurities.

Table 1:  a-SiNx:H film and resonator sample properties: precursor gas ratio $f_{\textrm{N}_{2}/\textrm{SiH}_{4}}$, refractive index $n$ measured at 633 nm, compressive stress $\sigma_{c}$ (MPa), ratio of N-H bond concentration to total N-H and Si-H concentration $c{}_{N-H}/c_{H}$, and five resonator fit parameters. samples | $f_{\textrm{N}_{2}/\textrm{SiH}_{4}}$ | $n$ |  $\sigma_{c}$ (MPa) | $c{}_{N-H}/c_{H}$ | tan$\delta_{0}\times 10^{6}$ |  $V{}_{c}$ ($\mu$V) | $\Delta$ |  $f{}_{R}$ (GHz)
---|---|---|---|---|---|---|---|---
A (Si rich) | 1 | 2.159 | 886 | 31 | 25 | 3.8 | 0.35 | 4.970
B (Si rich) | 1.1 | 2.094 | 1178 | 40 | 25 | 2.0 | 0.35 | 4.987
C (Si rich) | 1.12 | 2.065 | 1000 | 38 | 25 | 2.0 | 0.35 | 5.170
D (N rich) | 1.2 | 1.922 | 82 | 72 | 500 | 0.65 | 0.28 | 5.196
E (N rich) | 1.21 | 1.916 | 100 | 83 | 1200 | 0.12 | 0.28 | 5.350

The a-SiNx:H films were deposited using inductively-coupled plasma chemical
vapor deposition (ICP CVD) in an Oxford Plasmalab 100, using nitrogen (N2) and
100% silane (SiH4) precursor gases. The films were deposited at T = 300 ∘C at
a pressure of 5 mTorr, with an ICP power of 500 W, and a nominal rf power of 4
W. Table 1 summarizes the device parameters and loss tangent fit results in
terms of the precursor gas flow rate ratio of N2 to SiH4,
$f_{\textrm{N}_{2}/\textrm{SiH}_{4}}$. The SiH4 flow rate was set to 10 sccm
for all films except for E (9 sccm) while N2 flow rate was varied.

Figure 1:  FT-IR absorbance versus wavenumber $\nu=1/\lambda$, shown with
offsets for better viewing. The nitrogen to silane ratio increases from film A
to E.

The refractive index and the compressive stress were used to determine whether
a film is N-rich or Si-rich. Parsons91a ; Martinu00a . An N$\&$K Analyzer
NKT1500 was used to measure the film refractive index at $\lambda=$633 nm and
the thickness, and a KLA Tencor P-10 profilometer was used to measure film
stress. For N-rich films, the refractive index is below 2 and the compressive
stress is significantly reduced. Only a 10 $\%$ change in
$f_{\textrm{N}_{2}/\textrm{SiH}_{4}}$ yielded a 1 GPa change in stress
implying a large change in the structure of the film when the stoichiometry
changes between N-rich and Si-rich. The refractive index and stress were also
consistent with a second set of 5 films that were measured with rf, and the
growth rate in the films also systematically depended on the stoichiometry
(not shown). Although the parameters may depend on the particular machine, a
similar procedure can be performed with another deposition system to find this
crossover stoichiometry.

To evaluate the impurity types of the a-SiNx:H films, we measured FT-IR
absorption with a Nicolet 670 attenuated total-reflection FT-IR spectrometer
with a ZnSe prism. The films for FT-IR analysis were deposited to 1 $\mu$m
thick to prevent absorption from the underlying substrate and were deposited
immediately after those of the resonators. Figure 1 shows the absorption
spectra with baseline correction of five SiNx:H films (A to E). The six
absorption bands identified include 1) the Si-N stretching mode appears at 890
cm-1, 2) the N-H bending mode at 1180 cm-1, 3) the H-N-H scissoring mode at
1545 cm-1, 4) the Si-H stretching mode at 2180 cm-1, 5) the N-H stretching
mode at 3340 cm-1 and 6) the H-N-H stretching mode at 3460 cm-1 Lucovsky86a ;
Yin90a ; Hanyaloglu98a . The relative concentration of N-H bond concentration
to the sum of the N-H and Si-H bond concentrations $c_{N-H}/c_{H}$ is
estimated from the corresponding stretching mode absorbances and the relative
absorptivity of the two modes (shown in Table I). The low value $(<40\%)$ of
$c_{N-H}/c_{H}$ for films A, B, and C and the high value $(>70\%)$ of D and E
indicates that the former films are Si-rich and the later films are N-rich. It
is interesting that NH2 absorption modes (both scissoring and stretching)
appear strongly in N-rich samples D and E, which shows a N-rich film has a
different bonding structure than a Si-rich film as reported previously Tsu86a
; Lucovsky86a .

Figure 2:  a) Photograph of notch-type aluminum LC resonator with a SiNx
parallel plate capacitor. Size of the capacitor (shown in right) is 80$\mu$m
by 80$\mu$m. The substrate is sapphire which appears black in the photograph.
b) Loss tangent curves of samples A to E measured at 30 mK (shown with
markers) with the two-level system model fit in Eq. (2) (shown with fit
curves).

We measured dielectric loss of a-SiNx:H films within fabricated Al
superconducting LC resonators (see Figure 2). The LC resonator consists of a
meandering inductor $L$ and a parallel-plate capacitor $\hat{C}$ in parallel.
Here $\hat{C}=C(1-i\tan\delta)$ where $C$ is the real part of the capacitance
and tan$\delta$ is the loss tangent from dielectric. The $L$ and $C$ couple to
a coplanar waveguide [Figure 2(a)] to form a notch-filter resonator.

For loss tangent measurement, we used an Anritsu 68369A microwave synthesizer,
frequency locked to an Agilent E4440A spectrum analyzer. The driving line is
attenuated with 20 dB attenuators at both 1 K and the base temperature stages
and the input line is calibrated at room temperature. The return line is
isolated by a PAMTech circulator at the 1 K stage and the transmitted signal
is amplified with a 4-12 GHz Caltech HEMT amplifier at 4K. Thermal photons
from the circulator at 1 K, can create on the order of one thermal photon in
our resonators, allowing us to measure coherent response down to the quantum-
regime. We obtained the loaded quality factor $Q$ and the internal quality
factor $Q_{i}$ by fitting the measured power transmission to our model
function $|t|^{2}$ given by

$|t|^{2}=\left|1-e^{i\phi}\frac{1-Q/Q_{i}}{1+2iQ(f-f_{0})/f_{0}}\right|^{2}.$
(1)

A loaded $Q$ and an internal $Q_{i}$ are the fitting parameters together with
a resonance frequency $f_{0}$ and a loss tangent is given as
tan$\delta=1/Q_{i}$. The coupling quality factor $Q_{e}$ is
$\left(Q^{-1}-Q_{i}^{-1}\right)^{-1}\simeq 20000$ for our resonators, and the
parameter $\phi$ accounts for small impedance mismatches for waveguides near
our resonator. The capacitor dielectric has a thickness of 250 nm, and a
nominal capacitance of 1.47 pF assuming a relative permitivity of 6.5, which
at $<V^{2}>^{1/2}\approx 3\times 10^{-7}$ corresponds to an average photon
number of $\langle n\rangle\approx$ 0.1 (not including thermal photons).
However, from the the resonant frequency in Table I, it is apparent that the
dielectric constant changes with stoichiometry.

Figure 2(b) shows the loss tangent of a-SiNx:H films at 30 mK as a function of
RMS voltage $V$ on the resonator. The error bars are from our $\chi^{2}$ fit
of the resonance peaks to the model function $|t|^{2}$. The horizontal scale
error is limited by a calibration of our input line at room temperature. We
fit the low temperature loss tangent data to a two-level system defect model
with a parallel-plate geometry which is given as

$\tan\delta=\frac{\pi\rho(er)^{2}\textrm{tanh}(\hbar\omega/2k_{B}T)}{3\epsilon\sqrt{1+(\Omega_{R})^{2}T_{1}T_{2}}}\simeq\frac{tan\delta_{0}}{\sqrt{1+(V/V_{c})^{2-\Delta}}}$
(2)

where $\rho$ is the TLS density of states, $e$ is the electron charge, $r$ is
a distance between two level sites, $\varepsilon$ is a permittivity of the
film, $\Omega_{R}=eVr/\hbar d$ is a TLS Rabi frequency, $V$ is an RMS voltage,
d is the thickness of a-SiNx:H, $\omega$ is the angular resonance frequency
and $T$ is the temperature of the resonator Martinis05a . Here the intrinsic
loss tangent tan$\delta_{0}$ which is defined as the dielectric loss in a
single photon regime is a function of TLS density of states $\rho$ and $V_{c}$
is a threshold voltage where saturation starts to occur in TLS Phillips87a .
The fitting parameters are summarized in Table I.

Surprisingly, Si-rich SiNx:H films (A, B and C) showed a 20 and 50 lower
intrinsic loss than the N-rich films (D and E). This also implies that the TLS
density of states $\rho$ is correlated with the N-H bond concentration. We
believe the results are reproducible from the fact that the samples A, B (low
loss) and D (high loss) were fabricated 8 months after the samples C (low
loss) and E (high loss) were made. We confirmed our film’s reproducibility by
making another low-loss a-SiNx:H film 4 months after these films A, B, and D,
using the same recipe as the sample A. With that new film we obtained
tan$\delta_{0}\simeq$ 3$\times$ 10-5, which agrees with the original
measurement of film A.

Figure 3:  Density of states as a function of NH2 bonding peak area in FT-IR
measurement.

In Figure 3, we plot $\rho$ normalized by the TLS density of states $\rho_{0}$
of the lowest loss film (from samples A, B and C) as a function of NH2
scissoring mode absorption band area A${}_{NH_{2}}$, which is proportional to
the concentration of the NH2 bond Lanford78a ; Yin90a ; Parsons91a . We find
that $\rho$ is proportional to A${}_{NH_{2}}$ and the amount of NH2 in the
three Si-rich films (samples A, B and C) is much smaller than the N-rich
samples. (Note that the NH2 stretching mode almost disappears for the Si-rich
films A, B and C.) Therefore, for the two N-rich a-SiNx:H films, NH2 is likely
responsible for the TLS dielectric loss.

The mechanism by which NH2 bonding causes low temperature loss can be
understood by comparing the film with one composed of silicon dioxide with
hydrogen impurities (SiOx:H). The N-rich a-SiNx:H is known to have a local
bonding arrangement that is usually seen in Si(NH)2 Tsu86a ; Lucovsky86a
which is isoelectric and isostructural with SiOx:H. In this case, $O$ is
substituted with $NH$ Tsu86a ; Lucovsky86a ; Martinu00a , thus the NH2
impurity in a-SiNx:H is analogous to the OH impurity in SiOx:H. The molecular
motion of the OH bond is believed to cause the low-temperature loss in a-SiO2
Schickfus77a ; Phillips87a ; and similarly, the molecular motion of NH2 may
cause the loss in a-SiNx:H.

The measured loss tangent includes the loss from the few nanometer thick
native aluminum oxide on top of the bottom Al electrode, which was not
removed. In our case with a parallel plate capacitor, the field energy that
resides in the native oxide is on the order of $10^{-2}$ of the total electric
field energy. If we assume that the observed loss is entirely from the native
oxide, then the loss tangent of the aluminum oxide is
$\tan\delta_{0,AlOx}\simeq$ 3$\times$10-3, which is similar to the previously
reported estimates Martinis05a .

In conclusion, we have measured the quantum-regime loss tangent of five
a-SiNx:H films at 30 mK. Each film was grown with a different precursor gas
flow rate ratio $f_{\textrm{N}_{2}/\textrm{SiH}_{4}}$, such that films were
rich in either Si-H or N-H impurities. We found that the NH2 bond in N-rich
a-SiNx:H is correlated with TLS-induced dielectric loss and were able to
reduce the quantum-regime loss tangent to 3 $\times$ 10-5 by making a-SiNx:H
films Si-rich.

The authors thank John Martinis, Ben Palmer, Dave Schuster, and Fred Wellstood
for useful discussions, and Dan Hinkle for his advice on amorphous silicon
nitride deposition. This work was funded by the National Security Agency.

## References

  * (1) I. Siddiqi et al., Phys. Rev. Lett. 94, 027005 (2005).
  * (2) M. Steffen et al., Phys. Rev. Lett. 97, 050502 (2006).
  * (3) M. A. Sillanpaa et al., Nature 449, 438-442 (2007).
  * (4) M. von Schickfus and S. Hucklinger, Phys. Lett. 64A, 14 (1977).
  * (5) W. A. Phillips, Rep. Prog. Phys. 50, 1657 (1987).
  * (6) Aaron D. O’Connell et al., APL 92, 112903 (2008).
  * (7) J. Gao et al., Appl. Phys. Lett. 92, 152505 (2008).
  * (8) J. Gao et al., Appl. Phys. Lett. 90, 102507 (2007).
  * (9) R. Barends et al., Appl. Phys. Lett. 92, 223502 (2008).
  * (10) J. M. Martinis et al., Phys. Rev. Lett. 95, 210503 (2005).
  * (11) L. Martinu and D. Poitras, J. Vac. Sci. Technol. A 18, 2619 (2000).
  * (12) G. Lucovsky and D. V. Tsu, J. Vac. Sci. Technol. A 4, 681 (1986).
  * (13) Z. Yin and F. W. Smith, Phys. Rev. B 42, 3666 (1990).
  * (14) B. F. Hanyaloglu and E. S. Aydil, J. Vac. Technol. A 16, 2794 (1998).
  * (15) D. V. Tsu et al., Phys. Rev. B 33, 7069 (1986).
  * (16) G. N. Parsons et al., J. Appl. Phys. 70, 1553 (1991).
  * (17) W. A. Lanford and M. J. Rand, J. Appl. Phys. 49, 2473 (1978).