Characterization of low-loss hydrogenated amorphous silicon films for superconducting resonators

Bruno T. Buijtendorp; Juan Bueno; David J. Thoen; Vignesh Murugesan; Paolo M. Sberna; Jochem J. A. Baselmans; Sten Vollebregt; Akira Endo

doi:10.1117/1.JATIS.8.2.028006

10 June 2022 Characterization of low-loss hydrogenated amorphous silicon films for superconducting resonators

Bruno T. Buijtendorp, Juan Bueno, David J. Thoen, Vignesh Murugesan, Paolo M. Sberna, Jochem J. A. Baselmans, Sten Vollebregt, Akira Endo

Author Affiliations +

Journal of Astronomical Telescopes, Instruments, and Systems, Vol. 8, Issue 2, 028006 (June 2022). https://doi.org/10.1117/1.JATIS.8.2.028006

Abstract

Superconducting circuit elements used in millimeter-submillimeter (mm-submm) astronomy would greatly benefit from deposited dielectrics with small dielectric loss and noise. This will enable the use of multilayer circuit elements and thereby increase the efficiency of mm-submm filters and allow for a miniaturization of microwave kinetic inductance detectors (MKIDs). Amorphous dielectrics introduce excess loss and noise compared with their crystalline counterparts, due to two-level system defects of unknown microscopic origin. We deposited hydrogenated amorphous silicon films using plasma-enhanced chemical vapor deposition, at substrate temperatures of 100°C, 250°C, and 350°C. The measured void volume fraction, hydrogen content, microstructure parameter, and bond-angle disorder are negatively correlated with the substrate temperature. All three films have a loss tangent below ^{10 − 5} for a resonator energy of 10⁵ photons, at 120 mK and 4 to 7 GHz. This makes these films promising for MKIDs and on-chip mm-submm filters.

1. Introduction

The integrated superconducting spectrometer (ISS)¹^–³ is a novel astronomical instrument that promises ultra-wideband, high-sensitivity, and three-dimensional imaging spectrometry in the millimeter-submillimeter (mm-submm) band. ISSs enable large arrays of spectroscopic pixels because they are intrinsically scalable due to the compact on-chip filterbank for signal dispersion and because they allow for frequency-domain multiplexed readout of the microwave kinetic inductance detectors (MKIDs).⁴

Currently, the DESHIMA³ ISS has a planar design using coplanar waveguide (CPW) circuit elements. The advantage of this planar design is that it can be fabricated directly on top of a crystalline substrate, in contrast to multilayer circuit elements, which generally make use of a deposited dielectric. Deposited amorphous dielectrics contain two-level system (TLS) defects that introduce dielectric loss and frequency noise.⁵^–⁷ However, multilayer circuit elements offer various benefits over planar circuit elements. The size of an MKID could be drastically reduced with a multilayer design, and microstrip filters suffer negligible radiation loss compared to planar filters.⁸^,⁹

The peak transmission ${| S_{31} |}^{2}$ through a single isolated mm-submm filter¹⁰^,¹¹ is

Eq. (1)

{| S_{31} |}^{2} = \frac{1}{2} {(1 - \frac{R}{Q_{i}})}^{2},

where

R = F / Δ F

is the resolving power and

Q_{i}

is the internal quality factor. The

1 / Q_{i}

is roughly equal to the dielectric loss tangent in the case of a superconducting microstrip filter.¹¹^–¹³ An increase in

Q_{i}

will enable a proportional increase in

R

at a particular filter transmission value.

A mm-submm $Q_{i}$ of 1440 has been achieved with amorphous silicon nitride ( ${SiN}_{x}$ ).¹¹ Recently, $Q_{i}$ values of 4800 and 8300 were reported for hydrogenated amorphous silicon (a-Si:H)¹² and hydrogenated amorphous silicon carbide (a-SiC:H),¹³ respectively. Further improvement in $Q_{i}$ is desired to enable filters with higher $R$ .

Although TLSs are successfully modeled by the standard tunneling model (STM),⁵ their microscopic origin remains unknown. The TLSs dominate the dielectric loss in superconducting resonators at microwave frequencies.⁷^,¹²^–¹⁵ In the STM the TLS density of states is frequency independent, and this leads to the suggestion that a decreased microwave loss translates to increased performance for the mm-submm filters. Currently, the best low-power microwave loss tangents $\tan δ \sim 10^{- 5}$ have been measured for a-Si:H films⁷^,¹²^,¹⁴^,¹⁵ and a-SiC:H films.¹³

Due to an observed relation between TLS density and atomic silicon density, it has been proposed that the TLSs in electron-beam evaporated amorphous silicon (a-Si) are related to voids in the material.¹⁶ It was found that a very low void volume fraction can be achieved by depositing at elevated substrate temperatures $T_{sub}$ .¹⁶ Recently, it has been observed that although the TLS-induced internal friction in a-Si correlates with the atomic silicon density, the TLS-induced loss tangent instead correlates with the dangling bond density.¹⁷

In this work, we investigate the effect of $T_{sub}$ on the microstructural and compositional properties of a-Si:H, and we study if these properties relate to the dielectric loss at 4 to 7 GHz and at 120 mK. For this purpose, we deposited a-Si:H films using plasma-enhanced chemical vapor deposition (PECVD) at three different substrate temperatures, and we measured their void volume fraction, hydrogen content, microstructure parameter, bond-angle disorder, and infrared (IR) refractive index.

2. Film Deposition

We deposited the a-Si:H films by PECVD with an Oxford Plasmalab 80 Plus. The substrate temperatures $T_{sub}$ during the PECVD processes were 100°C, 250°C, and 350°C. The $T_{sub}$ was the only parameter that was varied. The deposition parameters are listed in Appendix A. We used crystalline silicon (c-Si) substrates with (100) crystal orientation. Further substrate details and the wafer preparation details depend on the subsequent experiment and are described in the methods of each experiment. For the dielectric loss measurements, we used high resistivity wafers.

3. Characterization at Room Temperature

3.1.

Hydrogen Content, Microstructure Parameter, and Infrared Refractive Index

The microstructure of a-Si:H is largely governed by the occurrence of SiH and ${SiH}_{2}$ configurations in the material.¹⁸^–²⁰ The $SiH$ configurations reside mostly in small vacancies, corresponding to up to three missing silicon (Si) atoms¹⁹ per vacancy. This is in contrast to the ${SiH}_{2}$ configurations that exist mostly on the surface of voids with a radius of 1 to 4 nm, corresponding from $10^{2}$ to $10^{4}$ missing Si atoms¹⁹ per void. We used Fourier-transform IR (FTIR) spectroscopy in transmission mode to measure the microstructure parameter $R^{*}$ [Eq. (4)], which quantifies the relative amount of SiH and ${SiH}_{2}$ bonds. Using this method we also obtained the total hydrogen content $C_{H}$ [Eq. (3)] of the films, and their IR refractive indices $n_{ir}$ .

For the FTIR measurements, we deposited a-Si:H films on double side polished (DSP) $p$ -type c-Si substrates with resistivity $ρ > 1 k Ω cm$ . The substrates were dipped in 1% hydrofluoric acid for 1 min prior to film deposition.

By fitting the FTIR transmission data to a transfer-matrix method calculation²¹ we obtained the $n_{ir}$ and the absorption coefficients $α$ of the a-Si:H films. In the fitting, we used a nondispersive $n_{ir}$ . We also measured the $n_{ir}$ and $α$ of the bare c-Si substrate, and used this to model the substrate in the calculation.

The measured $α$ and their Gaussian fits are plotted in Fig. 1. With increasing $T_{sub}$ , we observe a decrease in intensity of the wagging mode near $640 {cm}^{- 1}$ (referred to as 640 wag), indicating a decrease in the total hydrogen content.¹⁸^,²² We also observe an absorption peak near $500 {cm}^{- 1}$ that can be attributed to a stretching mode²³ (referred to as 500 stretch). Also with increasing $T_{sub}$ , we observe a decrease in intensity of the stretching mode near $2100 {cm}^{- 1}$ , indicating a decrease in the amount of ${SiH}_{2}$ bonds.

Fig. 1

The absorption coefficients $α$ that we measured using FTIR spectroscopy, as a function of wavenumber. Each column shows the results for a particular film that was deposited at the substrate temperature $T_{sub}$ shown on top. The top row shows the absorption near the wagging mode at $640 {cm}^{- 1}$ (referred to as 640 wag), from which we calculated the hydrogen content $C_{H}$ [Eq. (3)]. The bottom row shows the absorption near the stretching modes at 2000 and $2100 {cm}^{- 1}$ (referred to as 2000 stretch and 2100 stretch), from which we calculated the microstructure parameter $R^{*}$ [Eq. (4)].

To calculate the films’ hydrogen contents $C_{H}$ and their microstructure parameters $R^{*}$ from the $α$ spectra we numerically calculated the integrated absorptions $I_{x}$

Eq. (2)

I_{x} = \int \frac{α_{x} (\tilde{ν})}{\tilde{ν}} d \tilde{ν},

where

x

denotes the center wavenumber of the Gaussian absorption peak that is being integrated. From

I_{640}

we calculated

C_{H}

in atomic percent (at. %)¹⁸^,¹⁹^,²²^,²⁴

Eq. (3)

C_{H} = \frac{A_{640} I_{640}}{A_{640} I_{640} + N_{Si}},

where

A_{640}

is a proportionality constant that is an inverse cross-section for photon absorption at this wavenumber. We used the value

A_{640} = 2.1 \cdot 10^{19} {cm}^{- 2}

.²² For

N_{Si}

, the atomic density of silicon, we used the value

5 \cdot 10^{22} {cm}^{- 3}

. The modes near 2000 and

2100 {cm}^{- 1}

can be attributed to SiH and

{SiH}_{2}

, respectively.¹⁸ The fraction of Si atoms that are bonded as

{SiH}_{3}

is negligible below hydrogen concentrations of 40%.²⁵ The microstructure parameter

R^{*}

was defined as¹⁸

Eq. (4)

R^{*} = \frac{I_{2100}}{I_{2100} + I_{2000}} .

The results for the hydrogen content $C_{H}$ , microstructure parameter $R^{*}$ , and IR refractive index $n_{ir}$ are plotted in Fig. 2. We observe that $C_{H}$ decreases monotonically with increasing $T_{sub}$ . The microstructure parameter $R^{*}$ also decreases monotonically with increasing $T_{sub}$ , indicating that a smaller fraction of the hydrogen is bonded in ${SiH}_{2}$ configurations, which reside mostly on the surface of voids.¹⁹ Additionally, we observe that $n_{ir}$ increases monotonically with increasing $T_{sub}$ , indicative of an increase in film density.

Fig. 2.

The hydrogen contents $C_{H}$ , microstructure parameters $R^{*}$ , and IR refractive indices $n_{ir}$ of the three films, which we derived from the FTIR data. The films were deposited at the substrate temperature $T_{sub}$ . The dashed line in the right-most figure represents the literature value of the $n_{ir}$ of c-Si.²²

3.2.

Bond-Angle Disorder

Films of a-Si:H exhibit bond-angle disorder $Δ θ$ in their silicon network, defined as the root mean square deviation from the tetrahedral bond angle of 109.5 deg. We measured $Δ θ$ using Raman spectroscopy with a 514-nm laser²⁶

Eq. (5)

Δ θ = \frac{505.5 - {\tilde{ν}}_{TO}}{2.5},

where

{\tilde{ν}}_{TO}

is the center wavenumber of the transverse-optic (TO) mode near

480 {cm}^{- 1}

(TO 480).

For Raman spectroscopy, we deposited the a-Si:H films on single side polished (SSP) $n$ -type substrates with a resistivity $ρ$ of $1 - 5 Ω cm$ , and with a 101-nm thick thermal oxide layer.

In Fig. 3, we show the Raman measurement of the film deposited at 100°C, and the Gaussian fits. Apart from the TO 480 mode, we observe a transverse-acoustic (TA) mode near $170 {cm}^{- 1}$ (TA 170),²⁷ a longitudinal-acoustic mode near $300 {cm}^{- 1}$ (LA 300),²⁸ a longitudinal-optic mode near $425 {cm}^{- 1}$ (LO 425), and at $520 {cm}^{- 1}$ the TO mode of the c-Si substrate, fitted with a Lorentzian.²⁶^,²⁹ The peak near $620 {cm}^{- 1}$ can be attributed to a variety of modes.²⁸^–³⁰ In our fit, we fixed the peak position of the LA 300 mode at $300 {cm}^{- 1}$ .

Fig. 3

The Raman spectroscopy measurement of the a-Si:H film that was deposited at a $T_{sub}$ of 100°C. The plot serves to show the modes that are fitted to the measurement data. We calculated the bond-angle disorder $Δ θ$ from the position of the TO 480 mode.

We plot the measured $Δ θ$ of the three films in Fig. 4. We observe a monotonic decrease of $Δ θ$ with increasing $T_{sub}$ .

Fig. 4

The bond-angle disorder $Δ θ$ of the three a-Si:H films that we derived from the Raman spectroscopy measurements. The films were deposited at the substrate temperature $T_{sub}$ . The error bars represent the standard deviations of $Δ θ$ that we estimated from the least-squares fit.

3.3.

Void Volume Fraction

We determined the films’ void volume fractions $f_{v}$ using variable-angle spectroscopic ellipsometry. The measured change in polarization was fitted to an optical model that includes a native oxide layer, the a-Si:H film, a thermal oxide layer, and the c-Si substrate. For this, we used the commercial software CompleteEASE.³¹

For ellipsometry, we deposited the a-Si:H films on SSP $n$ -type substrates with a $ρ$ of $1 – 5 Ω cm$ , with a 101-nm thick thermal oxide layer for increased reflection.

We obtained $f_{v}$ from the fit by using the Bruggeman effective medium approximation to model the a-Si:H film as a composite material consisting of a-Si and spherical voids.¹³^,³² The results for $f_{v}$ are plotted in Fig. 5. We observe that $f_{v}$ decreases monotonically with increasing $T_{sub}$ .

Fig. 5

The void volume fractions $f_{v}$ of the three a-Si:H films, which we derived from the ellipsometry data by modeling the a-Si:H layer as a composite material of a-Si and spherical voids using the Bruggeman effective medium approximation. The films were deposited at the substrate temperature $T_{sub}$ .

4. Cryogenic Loss Tangent Measurement

4.1.

Method

We fabricated superconducting chips with 109-nm-thick aluminum (Al) quarter-wavelength CPW resonators on top of the $\sim 250 - nm$ thick a-Si:H films. To estimate the losses other than the losses due to the a-Si:H we also fabricated a chip directly on top of a c-Si substrate. The Al layer was patterned using photolithography. We deposited the a-Si:H films on DSP intrinsic c-Si substrates with $ρ > 10 k Ω cm$ . The substrates were dipped in 1% hydrofluoric acid for 1 min prior to film deposition.

A micrograph of the chip with the 250°C a-Si:H is shown in Fig. 6(a). The chips feature a CPW readout line with a slot width $s$ of $8 μ m$ and a center line width $c$ of $20 μ m$ . The readout line is coupled to 15 resonators. The resonators are divided into three geometry groups with different $s$ and $c$ . The five resonators within each group have different coupling quality factors $Q_{c}$ .

Fig. 6

(a) Micrograph of the superconducting chip. There are three groups of five quarter-wavelength CPW resonators, each group has a different CPW geometry (listed in Table 1). Within each group, the resonators vary in the coupling quality factor $Q_{c}$ . (b) Zoomed-in micrograph of the bottom-right resonator in Fig. 6(a).

We obtained the loss tangents $\tan δ$ of the a-Si:H films at 4 to 7 GHz and at 120 mK. The cryogenic setup, which uses an adiabatic demagnetization refrigerator includes a 35-dB gain low noise (noise temperature of 3 to 4 K) high-electron-mobility transistor amplifier at the cryostat’s 3-K stage, as well as two amplifiers at room temperature. The 120-mK stage is shielded from magnetic fields using a superconducting lead-tin coated shield that is surrounded by a Cryoperm shield. Further details on the cryogenic setup are given in De Visser’s PhD thesis.³³ To derive $\tan δ$ , we measured the $S$ -parameter $S_{21} (f)$ as a function of frequency using a vector network analyzer. We then obtained $\tan δ$ from $S_{21} (f)$ by fitting the squared magnitude of the measured $S_{21} (f)$ to a Lorentzian:

Eq. (6)

{| S_{21} (f) |}^{2} = 1 - \frac{1 - S_{21, \min}^{2}}{1 + {(2 Q \frac{f - f_{r}}{f_{r}})}^{2}} .

Here,

Q

is the loaded quality factor,

S_{21, \min}

is the minimum of the resonance dip, and

f_{r}

is the resonance frequency. The internal quality factor

Q_{i}

is determined from the equality³³

Eq. (7)

Q_{i} = Q / S_{21, \min} .

For each geometry group, we used the data of the resonator that was designed for the largest $Q_{c, design} = 3 \times 10^{5}$ since these have the smallest fitting errors when fitting Eq. (6). The measured $Q_{c}$ values vary between the different resonators in the range of $Q_{c} = 1.7 – 3.3 \times 10^{5}$ and the values are listed in Appendix C. The $1 / Q_{i}$ can be expressed as

Eq. (8)

\frac{1}{Q_{i}} (g) = p (g) \tan δ + b (g),

where

g

makes it explicit that these quantities are dependent on the CPW geometry. The

p (g)

is the filling fraction of the a-Si:H film (or the c-Si substrate in the case of the c-Si reference chip), which is the fraction of the resonator’s electric energy that is stored inside the dielectric.⁶ The

b (g)

term in Eq. (8) represent the sum of all loss mechanisms other than the

\tan δ

of the dielectric film. We calculated the

p (g)

using the EM-solver Sonnet,³⁴ where we used the film thicknesses

t_{f}

(listed in Appendix B), which we measured using ellipsometry, and the

ε_{mw}

listed in Table 1. The resulting

p (g)

are visible in Table 1.

Table 1

The filling fractions p of the a-Si:H films, which we calculated using the EM-solver Sonnet.34 In the case of c-Si, the p is calculated for the substrate. The εmw of the a-Si:H films were estimated from their IR values as εmw≈(nir/ncSi,ir)2εcSi,mw. In the heading, s is the CPW slot width and c is the CPW center line width.

	CPW s-c-s (μm)
Material	2-3-2	6-9-6	18-27-18
c-Si ( $ε_{mw} = 11.44$ )	0.920	0.920	0.920
a-Si:H 100°C ( $ε_{mw} \approx 9.5$ )	0.208	0.101	0.044
a-Si:H 250°C ( $ε_{mw} \approx 10.1$ )	0.197	0.095	0.042
a-Si:H 350°C ( $ε_{mw} \approx 11.2$ )	0.214	0.103	0.045

From the STM, it follows that the TLS-induced $\tan δ$ is dependent on power, frequency, and temperature⁶^,¹⁷

Eq. (9)

\tan δ = \tan δ_{0} \tanh \frac{ℏ ω}{2 k_{B} T} {(1 + \frac{N}{N_{0}})}^{- β / 2},

where

\tan δ_{0}

is the TLS-induced loss tangent at zero temperature and low internal resonator power,

N

is the average number of photons inside the resonator,

N_{0}

is the critical photon number above which the TLSs start to saturate, and

β

is equal to 1 in the STM, but has experimentally been found to range between 0.3 and 0.7.¹⁷ The frequency

ω

, the temperature

T

, and the photon number

N

are controlled by the experiment. We defined

N

as the average number of photons per quarter-wavelength, which is equal to

N = P_{int} / (2 h f^{2})

, where

P_{int}

is the internal resonator power, which can be calculated from the readout power.⁶

By equating the losses $b (g)$ from Eq. (8) to zero when deriving $\tan δ$ from $1 / Q_{i}$ we calculate an upper bound of the $\tan δ$ of the dielectric under consideration. Additionally, we estimated the $\tan δ$ of the a-Si:H films by equating $b (g)$ to the $1 / Q_{i}$ of the c-Si reference chip.

4.2.

Results

In Fig. 7(a), we plot the measured $Q_{i}$ versus $N$ of the resonators. We observe that $Q_{i}$ increases with increasing $N$ and that it is dependent on the CPW geometry, even for the c-Si where the filling fraction of the c-Si substrate does not depend on the CPW geometry. The filling fractions of the dielectrics are listed in Table 1.

Fig. 7

(a) The measured internal quality factors $Q_{i}$ of the resonators. The horizontal axis shows the average number of photons in the resonator per quarter-wavelength $N = P_{int} / (2 h f^{2})$ , where $P_{int}$ is the internal resonator power. (b) The upper bounds of $\tan δ$ , which we calculated by equating $b (g)$ in Eq. (8) to zero. The lines show the overall upper bounds of the $\tan δ$ of each material and are fits to a power law. (c) The estimates of $\tan δ$ which were calculated by equating $b (g)$ in Eq. (8) to the $1 / Q_{i}$ of the c-Si reference chip, which has resonators directly on top of the c-Si substrate.

In Fig. 7(b), we show the upper bounds of the $\tan δ$ of the three a-Si:H films and of the c-Si substrate. The plotted $\tan δ$ take the filling fractions of the dielectrics into account [Eq. (8)]. We observe that the a-Si:H films have an order of magnitude higher upper bound of $\tan δ$ than the c-Si substrate. We do not observe a correlation between $T_{sub}$ and the upper bound of $\tan δ$ . The upper bounds of $\tan δ$ vary with the CPW geometry. For each material, the lowest values for the upper bound of $\tan δ$ represent the overall upper bound since $\tan δ$ is independent of geometry. We plotted the overall upper bounds as lines in Fig. 7(b). These lines are fits to a power law. From the fits, we observe that the upper bound of the $\tan δ$ of the a-Si:H film that was deposited with a $T_{sub}$ of 100°C has a steeper slope than the other two a-Si:H films.

The estimates of $\tan δ$ , which we calculated by using the $1 / Q_{i}$ of the c-Si chip as an estimate for the losses other than the a-Si:H loss are plotted in Fig. 7(c). We do not observe a correlation between $T_{sub}$ and the estimate of $\tan δ$ . The estimate of $\tan δ$ for each material varies with the CPW geometry.

5. Discussion

Increasing $T_{sub}$ results in films with less hydrogen, less voids, smaller microstructure parameter, less bond-angle disorder, and a higher IR refractive index and therefore higher film density. We have shown that changing $T_{sub}$ is an effective way to monotonically control the structural and compositional properties of the a-Si:H. Interestingly, recent literature on electron-beam evaporated amorphous silicon suggests that the dielectric loss is correlated to the dangling bond density $ρ_{DB}$ , which can be controlled by $T_{sub}$ ¹⁷ as well.

Even though the structural and compositional properties at room temperature of the a-Si:H show a clear dependence on $T_{sub}$ , we did not observe a correlation between $\tan δ$ and the room temperature properties or $T_{sub}$ . At the powers at which we measured, a variation in the low-power TLS-induced loss tangent $\tan δ_{0}$ cannot be distinguished from a variation in the critical photon number $N_{0}$ , above which the TLSs start to saturate. However, if we assume that the three a-Si:H films have identical $N_{0}$ , then the upper bounds of $\tan δ$ point to a low-power $\tan δ_{0}$ that decreases monotonically with $T_{sub}$ .

For the resonators with a-Si:H, it is expected that the $Q_{i}$ is dependent on the CPW geometry due to differences in the dielectrics’ filling fractions (Table 1). We observe that the $Q_{i}$ of the c-Si resonators is also dependent on the CPW geometry even though the filling fraction of the c-Si substrate is equal for these resonators. We suggest that this is an effect due to TLS-hosting interface layers,³⁵^–³⁸ whose filling fractions and therefore effect on the measured $\tan δ$ are dependent on the CPW geometry. Furthermore, we suggest that the same effect causes the upper bound and the estimate of $\tan δ$ to be dependent on the CPW geometry, even though here the filling fractions of the dielectrics have been taken into account. Finally, we note that in reality the c-Si chip is not a perfect reference for the $b (g)$ term in Eq. (8), which results in some estimates being higher than the overall upper bound of $\tan δ$ [the lines in Fig. 7(b)]. This discrepancy can be explained by a different metal-dielectric surface, a different dielectric-air surface, and an additional surface between the a-Si:H film and the substrate that is not present on the c-Si chip.

The power and frequency range in which we measured is directly applicable to MKIDs, which operate at relatively high powers in comparison with the mm-submm filters that operate at single photon energies. The a-Si:H films are promising for MKID detectors because all three films exhibit an excellent $\tan δ < 10^{- 5}$ at a resonator energy of $10^{5}$ photons per quarter-wavelength, or at –55-dBm internal resonator power. Since the low microwave $\tan δ$ points to a low TLS density, it is likely that the a-Si:H films also have low loss at mm-submm frequencies.¹² Finally, we note that a practical benefit of the a-Si:H film that was deposited at 250°C is that its stress $σ$ is close to zero, as listed in Appendix B.

6. Conclusion

The structural and compositional room temperature properties of a-Si:H are monotonically controlled by changing the substrate temperature $T_{sub}$ during deposition. We do not observe a correlation of the room temperature properties with $\tan δ$ . All three a-Si:H films exhibit a $\tan δ < 10^{- 5}$ at 120 mK and at an average photon number $N$ of $10^{5}$ , equivalent to –55-dBm internal resonator power. This makes these films promising for application in mm-submm on-chip filters and MKID detectors.

7. Appendix A: PECVD Deposition Parameters

This appendix provides the PECVD parameters which we used for the deposition of the a-Si:H films (Table 2).

Table 2

PECVD parameters.

Material	a-Si:H 100°C/250°C/350°C
$T_{sub}$ (°C)	100/250/350
RF power (W)	15
${SiH}_{4}$ flow (sccm)	25
Ar flow (sccm)	475
Pressure (Torr)	1
Deposition time (m′s″)	10′0″/7′9″/7′0″

8. Appendix B: Results of Characterization at Room Temperature

This appendix provides a summary of the results of the characterization at room temperature (Table 3).

Table 3

Results of the characterization at room temperature.

Film	a-Si:H 100°C	a-Si:H 250°C	a-Si:H 350°C
$T_{sub}$ (°C)	100	250	350
$C_{H}$ (at.%)	22	17	13
Microstructure parameter $R^{*}$	0.32	0.20	0.15
IR refractive index $n_{ir}$	3.13	3.21	3.39
Bond-angle disorder $Δ θ$	$11.1 \pm 0.2$	$10.9 \pm 0.1$	$10.4 \pm 0.1$
Void volume fraction $f_{v}$ (%)	16.5	5.6	2.0
Film thickness $t_{f}$ (nm)	$250.8 \pm 0.1$	$236.0 \pm 0.1$	$259.9 \pm 0.1$
Native oxide thickness $t_{n}$ (nm)	$5.8 \pm 0.1$	$4.7 \pm 0.1$	$4.2 \pm 0.1$
Stress $σ$ (MPa) (tens.)	128.7	3.0	−379.0

9. Appendix C: Measured Coupling Quality Factors

This appendix provides the measured coupling quality factors of the resonators (Table 4).

Table 4

The coupling quality factors Qc of the resonators, averaged over all readout powers. The listed uncertainties are the standard deviations in Qc. In the heading, s is the CPW slot width and c is the CPW center line width.

	CPW s-c-s (μm)
Material	2-3-2	6-9-6	18-27-18
c-Si	$2.83 \pm 0.04 \times 10^{5}$	$2.65 \pm 0.09 \times 10^{5}$	$1.96 \pm 0.03 \times 10^{5}$
a-Si:H 100°C	$1.67 \pm 0.01 \times 10^{5}$	$2.06 \pm 0.05 \times 10^{5}$	$2.00 \pm 0.06 \times 10^{5}$
a-Si:H 250°C	$1.76 \pm 0.02 \times 10^{5}$	$3.05 \pm 0.07 \times 10^{5}$	$3.13 \pm 0.11 \times 10^{5}$
a-Si:H 350°C	$3.32 \pm 0.04 \times 10^{5}$	$2.06 \pm 0.05 \times 10^{5}$	$2.98 \pm 0.10 \times 10^{5}$

Acknowledgments

The first author would like to express his gratitude toward Marco van der Krogt for helping with the deposition of the a-Si:H films. This paper was based on work that was reported in the conference proceedings of SPIE. 11453, Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy X.³² The contribution of J.J.A. Baselmans was supported by the ERC CoG 648135 MOSAIC.

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Biography

Bruno T. Buijtendorp is a PhD candidate at Delft University of Technology (TU Delft), in the Terahertz Sensing Group. He received his BSc and MSc degrees in applied physics from TU Delft. His research focuses on improving and understanding the dielectric loss and noise in superconducting resonators, mainly in the context of astronomical detectors.

Juan Bueno graduated in physics from the University of Cantabria in 2003 and received his PhD from the University of Leiden in 2007. In 2008, he was awarded with a NASA postdoctoral position, joining the Jet Propulsion Laboratory. He became an instrument scientist at SRON in 2012 working on the development of far-IR and sub-mm wave kinetic inductance detectors. He is currently a high frequency RF engineer at TU Delft since 2021.

David J. Thoen is a cleanroom engineer working at TU Delft. He received his BSc degree (Hon, 2008) in applied physics from Fontys University of Applied Sciences, Eindhoven, while he worked as a microwave engineer at FOM Institute Rijnhuizen (now DIFFER) since 2007. Since 2010, he has worked at TU Delft on the development of microwave kinetic inductance detectors (MKID) far-infrared detectors for astronomy. He has extensive experience in cleanroom processing, process development, vacuum, and cryogenic technology.

Vignesh Murugesan is a process development engineer at SRON Netherlands Institute for Space Research. He is currently responsible for the process development and microfabrication of superconducting detectors. He received his MSc degree in microsystem integration technology from the Chalmers University of Technology in 2007. He worked as a process integration engineer from 2007 to 2008 for Infineon Technologies AG. From 2010 to 2013, he worked as a MEMS process engineer for Thermo Fisher Scientific.

Paolo M. Sberna received his BSc and MSc degrees in physics (cum laude) from the University of Catania, Italy. He got the PhD from the same university with a thesis on metal oxides semiconductors for thin-film solar cells. He currently works at TU Delft (The Netherlands) as a senior researcher with main focus on: photo-detectors, theory of hetero-junctions, photo-conductive antennas for THz and MEMS.

Jochem J. A. Baselmans is a senior instrument scientist at the SRON Netherlands Institute for Space Research and full professor in the THz sensing group at TU Delft. He leads the Dutch effort on the development of MKIDs, where his main interests are ultra-sensitive devices for THz radiation detection and advanced on-chip imaging spectrometers for sub-THz imaging spectroscopy.

Sten Vollebregt received his MSc (cum laude) and PhD degrees in electrical engineering from TU Delft in 2009 and 2014, respectively. Since October 2017, he has been an assistant professor with the Microelectronics Department, TU Delft. His research focuses on the integration of emerging electronic materials into semiconductor technology for sensing applications. His research interests include (carbon-based) nanomaterials, 3D monolithic integration, wide-bandgap semiconductors, and (harsh) environmental sensors.

Akira Endo is an assistant professor at the THz Sensing Group of TU Delft. He is interested in 3D-observations of large cosmological volumes, and the required development of (sub)millimeter-wave integral field units. He is the Dutch PI of the wideband DESHIMA spectrometer on the ASTE telescope. In 2022, he received his ERC Consolidator Grant to develop integral field units with many spaxels, and to demonstrate it with astronomical observations (project TIFUUN).

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Bruno T. Buijtendorp, Juan Bueno, David J. Thoen, Vignesh Murugesan, Paolo M. Sberna, Jochem J. A. Baselmans, Sten Vollebregt, and Akira Endo "Characterization of low-loss hydrogenated amorphous silicon films for superconducting resonators," Journal of Astronomical Telescopes, Instruments, and Systems 8(2), 028006 (10 June 2022). https://doi.org/10.1117/1.JATIS.8.2.028006

Received: 26 November 2021; Accepted: 13 May 2022; Published: 10 June 2022

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KEYWORDS

Resonators

Amorphous silicon

Dielectrics

Silicon films

Hydrogen

Superconductors

Photons

1.

Introduction

Eq. (1)

2.

Film Deposition

3.

Characterization at Room Temperature

3.1.

Hydrogen Content, Microstructure Parameter, and Infrared Refractive Index

Fig. 1

Eq. (2)

Eq. (3)

Eq. (4)

Fig. 2.

3.2.

Bond-Angle Disorder

Eq. (5)

Fig. 3

Fig. 4

3.3.

Void Volume Fraction

Fig. 5

4.

Cryogenic Loss Tangent Measurement

4.1.

Method

Fig. 6

Eq. (6)

Eq. (7)

Eq. (8)

Table 1

Eq. (9)

4.2.

Results

Fig. 7

5.

Discussion

6.

Conclusion

7.

Appendix A: PECVD Deposition Parameters

Table 2

8.

Appendix B: Results of Characterization at Room Temperature

Table 3

9.

Appendix C: Measured Coupling Quality Factors

Table 4

Acknowledgments

References

Biography

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