Measurements of the Intrinsic Quantum Efficiency and Visible Reemission Spectrum of Tetraphenyl Butadiene Thin Films for Incident Vacuum Ultraviolet Light

# Measurements of the Intrinsic Quantum Efficiency and Visible Reemission Spectrum of Tetraphenyl Butadiene Thin Films for Incident Vacuum Ultraviolet Light

Christopher Benson University of California, Berkeley, CA 94720 Lawerance Berkeley National Laboratory, CA 94720    Gabriel Orebi Gann University of California, Berkeley, CA 94720 Lawerance Berkeley National Laboratory, CA 94720    Victor Gehman Lawerance Berkeley National Laboratory, CA 94720
July 14, 2019
###### Abstract

A key enabling technology for many liquid noble gas (LNG) detectors is the use of the common wavelength shifting medium Tetraphenyl Butadiene (TPB). TPB thin films are used to shift ultraviolet scintillation light into the visible spectrum for detection and event reconstruction. Understanding the wavelength shifting efficiency (WLSE) and emission spectrum are critical aspects in detector performance and modeling and hence in the ultimate physics sensitivity of such experiments. This article presents results for the WLSE and emission spectrum in the range 50 â- 250 nm, more precise and across a broader spectrum of wavelengths than previous results. The low-wavelength sensitivity would allow construction of LNG scintillator detectors with lighter elements (Ne, He) to target light mass WIMPs. This article also presents the first ever extraction of the true underlying quantum efficiency of TPB, a result that is independent of film-specific properties.

thanks: Corresponding Author: christopher.benson@berkeley.edu

## I Introduction and motivation

Noble-gas detectors are becoming important to numerous experimental efforts involving: dark matter searches; neutrino and other particle detectors; searches for the neutron’s electric dipole moment; and measurements of the neutron lifetime liquidNobleDetectorReview (); ICARUS (); WARP (); ArDM (); DarkSide (); DEAP3600 (); MiniCLEAN_2015 (); ZEPLIN (); XENON100 (); LUX (); LZ (); XMASS (); DARWIN (). The properties of these elements, particularly in the liquid phase, are very attractive. They have exceptionally high scintillation yield (20,000–40,000 photons/MeV), which results in excellent energy resolution and low threshold. Their high density makes them more self-shielding than water or organic liquid scintillators. Tracking detectors can be constructed by applying an electric field across the bulk and collecting the ionization signal. The specifics of the scintillation process in noble gasses means they are almost transparent to their own scintillation light. Additionally, the time structure of that light is dependent on the incident particle type, allowing for pulse shape analysis to distinguish nuclear from electron recoils.

Detection of the vacuum ultraviolet (VUV) scintillation light produced by noble gas targets is a critical challenge common to this class of detectors. As shown in Fig. 1, the scintillation wavelengths can range from 175 nm for Xenon down to near 80 nm for Helium and Neon. Light of these wavelengths is strongly absorbed by most materials, including those commonly used for optical windows. Many experiments sidestep the issue of directly detecting VUV light though the use of wavelength shifting (WLS) films which absorb the VUV light and re-emit photons, typically in the visible spectrum. The visible photons can then easily be detected using photomultiplier tubes (PMTs).

One such commonly used WLS is Tetraphenyl butadiene (TPB). TPB thin films have seen wide application for many experimental programs due to their relatively high efficiency. TPB may also be easily applied to surfaces using standard techniques, such as vacuum deposition in a thermal evaporator. A paper in 2011 gehmanVUV () measured the film-dependent TPB wavelength shifting efficiency, without reference to other materials, in the range of 120–250 nm. For the purposes of this paper we will refer to this as the wavelength shifting efficiency (WLSE), acknowledging that it folds in certain optical properties of the TPB and substrate and is sample dependent.

As experimental programs look toward lower energies, the use of helium and neon as a detecting medium is attractive. The scintillation wavelengths of these noble gases are around 80 nm, deep into the VUV. This has provided a primary motivation to extend measurements of the absolute WLSE below that which was presented in gehmanVUV ().

In this article, we present three major results: the reemission spectrum of TPB and its dependence on incident wavelength, the WLSE dependence on sample thickness and incident wavelength, and the intrinsic quantum efficiency (QE) of TPB and its dependence on incident wavelength. These results cover the spectral range studied by gehmanVUV () with improved precision, while extending the measurements down to 50 nm. It should be noted that the literature contains measurements of the reemission spectrum and absolute and relative measurements of the WLSE. This work improves precision and extends previous measurements to shorter wavelengths, and, to the best of our knowledge, is the first to unfold setup- and sample-dependent optical effects to determine the intrinsic QE of TPB.

Sec. II provides an overview of the hardware components of the experimental apparatus. Sec. III describes the various apparatus configurations used to cover the full wavelength region of interest (ROI). Sec. IV describes the sample fabrication. Sec. V describes the data acquisition methods. Sec. VI contains descriptions of the analysis methods used to calculate the absolute WLS efficiency, the detailed Monte Carlo model used to simulate the setup, and the techniques to extract TPB’s QE. Sec. VII presents results. Sec. VIII provides a comparison of this work to previous studies and discusses the impact of various improvements to the measurements. Conclusions are presented in Sec. IX.

## Ii Experimental apparatus

The primary objectives of this work are to measure the reemission spectrum of TPB and its dependence on incident wavelength, the WLSE dependence on sample thickness and incident wavelength, and the dependence of TPB’s intrinsic QE on a photon’s incident wavelength. These measurements are performed by exposing TPB thin film samples to UV light of a known wavelength and intensity and measuring the amount and spectrum of light reemitted from fluorescence.

A cartoon representation of the experimental apparatus is shown in Fig. 2. The setup consists of a broad spectrum UV light source, filters, optical elements, a monochromator, a sample mounting assembly and photon detectors. All of the apparatus components are installed within a windowless vacuum chamber and held at vacuum. The setup is designed to produce and project monochromatic UV light onto thin film WLS samples in a repeatable fashion. A photodiode is used to separately measure the flux of photons incident on and reemitted by the samples. A spectrometer is used to measure the reemission spectrum of the samples.

Individual elements used in the experimental apparatus are described in this section. Because this work covers a wide range of wavelengths (50 – 250 nm), several distinct hardware configurations are used. Each of these configurations are constructed from elements described in this section. The distinct apparatus configurations are described in Sec. III.

### ii.1 UV light source

This work uses two distinct light sources. Each light source is specialized to a subset of the entire 50 – 250 nm wavelength ROI. Only one light source may be attached to the setup at a time.

#### ii.1.1 Deuterium light source

The McPherson Model 623 light source, referred to as the Deuterium Light Source (DLS), produces light for measurements in the range of 125 – 250 nm. The DLS contains a sealed deuterium gas volume which is ionized to produce broad spectrum light with a bright UV component. The output light passes through a circular 1” diameter MgF exit window. The MgF window has a transmission cutoff wavelength of 115 nm which drives the lower limit of emission for this source McPhersonOldLamp (). The DLS is powered using a McPherson Model 732 power supply.

#### ii.1.2 Windowless light source

The McPherson Model 629 Hollow Cathode Gas Discharge Source, referred to as the windowless light source, produces light for measurements in the range of 45 – 150 nm. Unlike the DLS, the windowless light source does not have a window at its output. A feed gas is supplied to the lamp at a constant pressure and is ionized using high voltage. The spectrum of light output by the lamp depends on the choice of the feed gas. Because there is no sealing window between the light source and the rest of the setup, a differential pumping port near the lamp output is used to reduce the gas load on the vacuum from the feed gas flowing out of the light source’s output.

### ii.2 Optical chain

This section describes the elements that make up the optical chain. These are the filter wheel, focusing mirror and monochromator.

#### ii.2.1 Filter wheel

An Action Research Corporation Model 52 filter wheel is coupled directly downstream of the light source. The filter wheel is used to apply optical filters to the broad spectrum light output from the light source for certain classes of measurements (Sec. V). The filter wheel has four slots which can each hold a 1.90-cm diameter disk. Changing the selected filter slot is done using an exterior nob and is possible while the setup is under vacuum. When a slot is selected, the filter is placed concentrically in the light output from the light source. All light must pass through the selected filter wheel slot to continue along the optical chain.

Three of the four slots in the filter wheel are used. The first slot is empty, which allows for a no-filter condition. The second slot contains a 0.48-cm thick, uncoated fused quartz silica filter which has a 155 nm cutoff. The third slot holds a 0.48-cm thick, uncoated MgF with a 115 nm cutoff. The fused quartz silica and MgF filters are used as high-pass optical filters which allow measurements of background levels (Sec. V.1.4).

#### ii.2.2 Focusing mirror

A McPherson Model 615 focusing elbow sits between the filter wheel and monochromator entrance slit. The focusing elbow contains a curved Al+MgF focusing mirror which focuses the light passing through the filter wheel onto the monochromator entrance slit. The focus of the mirror is adjusted using three set screws and is configured to maximize the light output at the monochromator’s exit for wavelengths in the ROI.

#### ii.2.3 Monochromator

A McPherson Model 234/302 Vacuum Ultraviolet Monochromator is used to output monochromatic light of a selected wavelength from a broad spectrum input. The light entering the monochromator passes through an entrance slit which is 1.78-mm wide and 4.88-mm high. The entrance slit projects incoming light onto a rotatable holographic diffraction grating positioned near the center of the monochromator. The angle between the diffraction grating and the incoming light determines the wavelength of light projected from the grating onto the monochromator’s exit slit. The diffraction grating’s angular position is adjusted and set using a servo motor which is controlled using the McPherson Model 789A-3 Scan Controller. The exit slit of the monochromator has the same dimensions as the entrance slit. Fig. 3 shows a comparison of monochromator wavelength setting and the measured spectrum of the output light. The peak of the output light spectrum is in good agreement with the monochromator setting.

This work uses two types of diffraction gratings. The monochromator only holds one grating at a time. Similar to the light sources, each diffraction grating is specialized to a subset of wavelengths in the ROI. The two diffraction gratings are an Al+MgF coating grating with 1200 gratings per mm, and a Platinum (Pt) coated grating with 2400 gratings per mm. As shown in Fig. 4, the Al+MgF coated grating outperforms the Pt coated grating for wavelengths greater than 105 nm.

### ii.3 Sample holder

The monochromator’s outlet attaches to a McPherson Model 648 Vacuum Filter Wheel, referred to as the sample wheel. The sample wheel contains five 2.54-cm diameter slots for sample disks. The sample disks are installed in the wheel and fixed in place using snap rings. The selected slot in the sample wheel is changed using an external knob and may be adjusted when the setup is under vacuum. The adjustment knob allows the cycling of multiple samples in and out of the UV beam during a data acquisition run. When a slot is selected, the sample slot is placed concentrically in the monochromatic UV beam exiting the monochromator. The sample slots are labeled 1 to 5. Slot 1 contains a thick aluminum disk, used to perform a dark current measurement. Slot 2 is left empty to allow for a measurement of the total VUV flux incident on the samples from the monochromator’s output. Slots 3 through 5 hold WLS samples to be studied.

### ii.4 Photon detection

This work uses two types of photon detectors: a photodiode and a spectrometer. The setup uses one of these detectors at a time. As shown in Fig. 2, photon detection occurs downstream of the sample wheel.

#### ii.4.1 Photodiode

An Opto Diode AXUV100G photodiode is used to measure the flux of VUV light incident on samples as well as the flux of reemitted light from WLS samples in the sample wheel. The device is a passive, windowless photodiode cell with an active area of 1 cm by 1 cm. A vacuum electrical feedthrough and coaxial cable (outside of the vacuum space) electrically couple the photodiode to an external Keithley 485 picoammeter for photocurrent readout. A data acquisition computer connected to the picoammeter queries real-time current readings using a LabVIEW graphical user interface (GUI) and stores the values for offline analysis. The absolute response of the photodiode was calibrated by National Institute of Standards and Technology (NIST) in February of 2016 in the range of 50 – 1100 nm. The absolute response as a function of wavelength is shown in Fig. 5.

#### ii.4.2 Spectrometer

An Ocean Optics QE65000 spectrometer is used to measure the reemission spectrum of WLS samples. A vacuum feedthrough assembly consisting of a collimating lens and fiber optic allows light to be collected and routed out of the vacuum space for analysis. A 200-m diameter quartz fiber couples the vacuum feedthrough assembly output to an input port on the spectrometer.

The spectrometer is sensitive to wavelengths in the range 200 – 1000 nm. The Ocean Optic’s Spectra Suite software package installed on the data acquisition computer is used to configure and read out the spectrometer.

## Iii Apparatus configurations

Three apparatus configurations are used to cover the ROI (50 – 250 nm). These are the long wavelength, intermediate wavelength, and short wavelength configurations. Each configuration specializes to a subset of VUV wavelengths in the ROI and is composed of the hardware elements described in Sec. II. The long wavelength and intermediate wavelength configurations overlap in the range of 130–150 nm which allows for cross checks of configuration–dependent systematic uncertainties.

The hardware composition of each configuration maximizes the intensity of VUV light exiting the monochromator within its particular wavelength range. Maximizing VUV intensity is done to minimize statistical uncertainties in measurements.

### iii.1 Long wavelength configuration

The Long Wavelength Configuration (LWC) is used to measure the WLSE and reemission spectra of samples for incident wavelengths in the range of 125 – 250 nm. As shown in Fig. 2, this configuration uses the DLS, filter wheel, focusing mirror, monochromator with the Al+MgF diffraction grating and sample wheel.

### iii.2 Intermediate wavelength configuration

The Intermediate Wavelength Configuration (IWC) is used to measure the WLSE and reemission spectra of samples for incident wavelengths in the range of 100 – 150 nm. A cartoon representation of this configuration is shown in Fig. 6. This configuration uses the windowless light source, filter wheel, monochromator with the Al+MgF grating and sample wheel. Unlike the LWC, this configuration uses the windowless light source and does not use the focusing mirror. A high purity N or argon feed gas is used in the windowless light source in this configuration.

### iii.3 Short wavelength configuration

The Short Wavelength Configuration (SWC) is used to measure the WLSE and reemission spectra of samples for incident wavelengths in the range of 45 – 100 nm. This configuration is very similar to the IWC. The only differences are that a Pt diffraction grating is used instead of the Al+MgF grating, and the feed gas used for the windowless light source is a 90% Neon, 10% Helium mixture.

## Iv Sample fabrication

Several TPB thin-film samples were fabricated using thermal evaporators at the Molecular Foundry at Lawrence Berkeley National Laboratory and in the Dr. Daniel McKinsey Laboratory at the University of California at Berkeley. A tabulation of samples used in this work are shown in Table 1. The films were deposited on stabilized ultraviolet-transmitting (SUVT) acrylic manufactured by Polymer Plastics Company, LC. A stock acylic sheet was cut into circular disks with a 2.54-cm diameter and 0.318-cm thickness. The transmission of the SUVT acrylic, shown in Fig. 8, was measured and shown to be consistent with the manufacter’s data sheet SUVT_acrylic_ref (). The acrylic’s transmission is 90% for wavelengths longer than 300-nm and 0% for wavelengths below 250-nm, as shown in Fig. 8. This is important because the acrylic substrate should behave as a high-pass filter, being transparent to the reemitted light from the TPB but opaque to the UV light incident on the sample.

Evaporative deposition was performed at a pressure less than 5E-6 torr. The final thickness of the TPB thin films was measured using a Dektak Profilometer with a film thickness resolution of 0.1 m.

Due to evidence that ambient ultraviolet light can degrade the WLS performance of TPB thin films (McKinsey_99, ; TPBDegredation_BJones, ), after fabrication the samples were stored in a separate dark, clean vacuum chamber held at a pressure of less than 1E-1 torr using an oil-less diaphragm pump. It is known that water can strongly absorb UV light with wavelengths shorter than 160 nm, further increasing motivation to store the TPB samples under vacuum.

Additionally, no more than 3 data acquisition runs per configuration were performed on each sample to minimize the risk of performance degradation from prolonged VUV exposure.

## V Measurement procedure

This section describes the two classes of measurements performed in this work: photocurrent readout for WLSE measurements, and reemission spectra.

### v.1 Photocurrent measurements

A measurement of the photocurrent output by the photodiode is required to determine the flux of VUV light incident on the samples as well as the flux of reemitted light captured by the photodiode. These photocurrent measurements are used as inputs in the WLSE calculations, described in Sec. VI. The four types of photocurrent measurements made are Dark, Light, Sample and Background. Each of these are described in this section, and are illustrated in Fig. 7.

#### v.1.1 Dark photocurrent

The dark photocurrent measurement provides a baseline measurement of the dark current for subtraction. This is shown in the top left of Fig. 7. It is performed by selecting slot 1 in the sample wheel, which contains a 2.54-cm diameter aluminum disk with 0.635-cm thickness. The aluminum disk blocks any light from reaching the photodiode, allowing for a proper baseline measurement.

#### v.1.2 Light photocurrent

The light photocurrent measurement provides a measurement of the flux of VUV light incident on the samples. This is done by selecting slot 2 on the sample wheel, which is empty. A representation of this is shown in the top right portion of Fig. 7. The photodiode active area fully captures all of the UV light that would be absorbed by a sample placed in the beam.

#### v.1.3 Sample photocurrent

The sample photocurrent measurement provides a measurement of the reemitted light flux at the photodiode’s location. This measurement is performed on slots that contain WLS samples (slots 3 to 5). A representation of this measurement is shown in the bottom left of Fig 7. The UV beam from the exit slit of the monochromator is absorbed by the WLS thin film and the acrylic substrate. Photons are reemitted from the WLS film in the forward and backward direction according to a currently unknown angular distribution. A portion of the total number of reemitted photons are collected by the photodiode. The determination of the total amount of reemitted light from this measurement is described in Sec. VI.1.

The sample photocurrent measurements are performed less than one minute after the light photocurrent measurement. The lamp output intensity was confirmed to be stable on timescales much longer than one minute thus providing confidence that the flux of incident VUV light on the sample does not change between a light photocurrent measurement and a sample photocurrent measurement.

#### v.1.4 Background photocurrent

The background photocurrent measurement provides a measure of the stray light contamination in the UV beam and its contribution to the light and sample photocurrent measurements. This measurement is performed by applying a high-pass optical filter using the filter wheel located near the light source (Sec. II.2.1). The filter kills the component of the light source’s output below the cutoff wavelength of the filter. For monochromator wavelength settings below the cutoff wavelength of the selected filter, the UV light normally exiting the monochromator, which is used to drive the reemission from WLS samples, is eliminated. This leaves any background light above the filter’s cutoff incident on the sample. A sample is left in the beam during the measurement to account for the transmission of the thin film.

It should be noted that light and sample photocurrent measurements are often several orders of magnitude greater than the background photocurrent, so any background current corrections are usually negligible. The background corrections become important when the sample photocurrent is of the order of the background current.

### v.2 Spectrometer measurements

Reemission spectra are measured using the setup described in this section. These spectra are used as inputs for the efficiency calculations discussed in Sec. VI.

The spectrometer is configured to integrate for 10 seconds for each spectral measurement. Three spectral measurements are averaged online and the result is written to disk as a text file. This is repeated 20 times during the course of a data run resulting in 20 files written to disk. The files written to disk are used as inputs for an offline analysis.

Two classes of data runs are required to measure a WLS sample’s reemission spectrum: Dark and Sample. In the same way as the dark photocurrent measurement, a dark spectrum is measured by selecting the aluminum disk in slot 1 of the sample wheel to block all light from reaching the spectrometer. This provides a baseline for subtraction in an offline analysis. The sample spectrum is measured by selecting the appropriate slot on the sample wheel (slots 3–5). This is exactly analogous to the sample photocurrent measurement shown in Fig. 7, because only the spectrum of reemitted light is measured in this configuration.

An offline analysis is performed using the ROOT data analysis package ROOT () to extract the corrected reemission spectrum. The measurements from the dark spectrum run are averaged and subtracted from the average of the WLS sample reemission spectrum run. The result is then corrected by the acrylic transmission (Fig. 8) and the relative transmittance of the collimating lens/fiber assembly and quartz fiber (Fig. 9).

## Vi Analysis methods

We define the absolute WLSE of a fluorescing thin film for incident light of wavelength to be the ratio of the number of photons reemitted by the sample (film and substrate) to number of photons incident on the film. Equivalently, this can be interpreted as the probability that an incident photon of a certain wavelength will be absorbed and reemitted (at a wavelength accorrding to the reemission spectrum) and escape the WLS sample. Because a single incident photon can result in the reemission of one or more photons, this probability can be greater than one.

It should be pointed out that the WLSE defined and measured in this way is the true, microphysical quantum efficiency (QE) of the material combined with optical effects of the film and the substrate. Because reemitted photons can be reabsorbed before they escape the film, the WLSE may contain a dependence on film thickness and is a property of the specific sample, rather than a property of the material. Physically, the QE is the more interesting result because it is an intrinsic property which should not depend on film thickness.

We determine the QE of TPB by measuring the WLSE of several films of different thickness and unfolding the QE from the optical effects of the thin film by comparing to a detailed microphysical simulation. Sec. VI.1 describes the method of calculating the absolute WLSE of a sample from raw photocurrent data. Sec. VI.2 describes the details of the Monte Carlo model and Sec. VI.3 discusses the method to extract the QE from measurements using the model.

### vi.1 Absolute wavelength shifting efficiency

Because the WLSE of a fluorescing thin film is defined as a ratio of photon fluxes, the total flux of photons incident on and reemitted by a wavelength-shifting sample must be determined.

The total flux of UV photons incident on a sample is determined from the light photocurrent measurements (Sec. V.1.2). The geometry of the setup is arranged such that all of the UV light incident on the samples is captured by the photodiode which allows for a direct measurement of the total flux of UV photons incident on the sample.

The flux of reemitted photons detected at the location of the photodiode is determined from the sample photocurrent measurement (Sec. V.1.3). Because the photons reemitted by the TPB are emitted in the forward and backward directions and according to a currently unknown but usually assumed Lambertian angular distribution, only a fraction of the total reemitted photons are collected by the photodiode during a sample photocurrent measurement. We define the ratio of reemitted photons collected by the photodiode to the total number of reemitted photons leaving the sample as the geometric acceptance fraction (GAF).

The GAF is interpreted as the probability that a reemitted photon which has escaped the sample (TPB film + acrylic disk) is observed by the photodiode. The GAF is independent of incident wavelength and choice of modeled QE, but does depend on sample thickness and the specifics of the setup’s geometry. The GAF’s dependence on TPB thickness is due to re-absorption and scattering of visible photons in the bulk TPB (which is dependent therefore on the reemission spectrum but not the incident wavelength). Photons which are reemitted in the forward (downstream) direction must travel through the bulk TPB and acrylic substrate before escaping the sample while reemitted photons which leave the sample in the backwards direction (upstream) only have to traverse a thin layer of TPB. Therefore, the fraction of forward-going reemitted photons which are reabsorbed in the TPB before escaping the sample increases with thickness.

The GAF is determined from a detailed micro-physical Monte Carlo (Sec. VI.2) simulation of the setup and is used to determine the total reemitted photon flux from the measured reemitted photon flux.

The measured photocurrents are a convolution of the spectrum of light incident on the photodiode, multiplied by the photon energy, with the photodiode’s calibrated response (Fig. 5), . For light photocurrent measurements at wavelength , the incident light spectrum is given by the wavelength distribution at the monochromator’s exit, , centered around . As shown in Fig. 3, can be accurately modeled as a Gaussian with the width set by the type of diffraction grating used in the monochromator. For sample photocurrent measurements the TPB reemission spectrum, , is used. The reemission spectrum of TPB was shown to be constant for illumination wavelengths from 128–250 nm in gehmanVUV (). This has been verified in this work and has been extended down to 45 nm incident light (Sec. VII.1).

The light photocurrent, , and sample photocurrent, , measurements are corrected for dark photocurrent (Sec. V.1.1) and background photocurrent (Sec. V.1.4). The dark photocurrent measurement provides a baseline correction while the background photocurrent corrects for stray light components in . The total photocurrent correction, , is the sum of the dark photocurrent and background contributions and is defined in Eq. 1.

 Icorr(λ)={Idark+Ibackgroundif λ≤150 nmIdarkif λ>150 nm (1)

The background photocurrent is included in for wavelengths less than or equal to 150 nm instead of the full ROI due to the filter availability. As described in Sec. V.1.4, background measurements can only be performed below the cutoff wavelength of the filter. The longest available cutoff wavelength is the fused quartz scilica filter with a cutoff wavelength of 150 nm. It should be noted that only measurements using the LWC (Sec. III.1) for wavelengths above 150 nm do not include background corrections. It was verified using the spectrometer and photocurrent measurements on uncoated acrylic disks that background levels in this range are consistent with dark current measurements i.e. below our sensitivity, thus eliminating the need for background measurements in this range.

As discussed in Sec. VI, the WLSE is computed by taking the ratio of the flux of reemitted light at the photodiode to the flux of incident light and dividing by the GAF, . For convenience, we define the ratio of the measured photon fluxes, , and the WLSE , , separately. These values are calculated for each sample where denotes the sample index. The measured photon ratio is given in Eq. 2:

 βi,exp(λ)=ITPB(λ)−Icorr(λ)Ilight(λ)−Icorr(λ)×∫dλ′hcλ′R(λ′)M(λ−λ′)∫dλ′′hcλ′′R(λ′′)P(λ′′). (2)

The WLSE of the ith sample is given in Eq. 3:

 εi(λ)=βi,exp(λ)×1Ai. (3)

### vi.2 Monte Carlo simulation

The purpose of the Monte Carlo simulation is two fold. First it is used to determine the GAF for calculation of the absolute WLSE (Sec. VI.1), and second, to unfold the QE of TPB from the optical effects (Sec. VI.3).

The simulation is performed using the Reactor Analysis Tool (RAT). RAT is a detailed GEANT4 based, microphysical simulation and analysis framework first written for the Braidwood experiment Braidwood (). Versions of RAT are currently being used by several experiments, including SNO+ SNO+ (), DEAP-3600 DEAP3600 () and MiniCLEAN MiniCLEAN_2015 (). This work uses the MiniCLEAN version of RAT, which contains the functionality to simulate photon absorption and reemission of TPB thin films.

#### vi.2.1 Model

The dimensions of the experimental apparatus were carefully measured and a model was constructed in RAT. Each dimension was measured 5 times. The average of the 5 measurements was used while the RMS provided the uncertainty. A rendering of the geometry as modeled in RAT is shown in Fig. 10. Important dimensions are provided in Table 2.

In the simulation, monochromatic photons are generated at the center of the diffraction grating surface. The photons are generated one at time and in the direction of the monochromator’s exit slit. The angular distribution of the photons leaving the source vertex uniformly fills a cone with a 2 degree opening angle.

Many of the generated VUV photons terminate on the monochromator’s exit slit. The fraction that pass through the slit propagate to the TPB surface boundary where they pass into bulk TPB or are reflected, according to Snell’s law. The index of refraction of bulk TPB is assumed to be equal to 1.67 HuberIndexOfRef (); TextBookIoR (). The TPB is modeled as a perfectly flat surface on all interfaces.

VUV photons that enter the bulk TPB are then absorbed according to wavelength–dependent absorption lengths. Photons are reemitted at the same vertex where the VUV photon was absorbed and according to the measured visible reemission distribution, which is consistent with  (gehmanVUV, ). The average number of photons reemitted when a VUV photon is absorbed is determined by a chosen value of the QE. The simulation assumes energy must be conserved, meaning the sum of reemitted photon energies is less than or equal to the absorbed VUV photon energy.

The absorption length for photons in TPB was taken from TPBAbsLengthRef () and is shown in Fig. 11. TPBAbsLengthRef () provides values for the photon absorption length in the range 225 to above 425 nm. No measurements of the photon absorption lengths in TPB below incident wavelengths of 225 nm were found in the literature. It is reasonable to assume VUV photons are strongly absorbed in TPB so a constant absorption length of 60 nm is used for incident wavelengths in the range of 50 to 225 nm. It was determined that the simulation results are not very sensitive to absorption lengths longer or shorter than this length by a factor of 2 or 3.

Diffuse scattering of visible light occurs in TPB. To account for this, the Rayleigh scattering of visible reemitted photons is modeled. A mean scattering length of 2.75 m is used for reemitted photons TPBScatteringLength (). Because the scattering length of VUV photons is not known and the VUV absorption length is very short, Rayleigh scattering of VUV photons is neglected in the simulation.

The reemitted visible photons produced in the TPB are propagated until they are reabsorbed by the TPB or absorbed on walls, the surface of the photodiode, or by the acrylic. All photons which terminate on the photodiode surface are assumed to be detected. Optical effects, such as refraction and reflections, are included in the simulation. The measured SUVT acrylic transmission (Fig. 8) and manufacturer supplied index of refraction are used in the simulation of the acrylic. The tracks of all photons are stored in a ROOT file for post simulation analysis.

A python analysis script loops over the stored photon tracks and calculates values of interest. For comparison to data, the photon ratio, , is evaluated by taking the ratio of the number reemitted photons which terminate on the photodiode surface, , to the number of VUV photons which were incident on the TPB surface, , in the simulation. As expected, depends on the choice of the QE, the sample thickness, and the optical properties of TPB and other materials which are constrained by measurements and values from the literature. is defined in Eq. 4 as:

 βi,sim(QE)=NpdNinc. (4)

### vi.3 Quantum efficiency extraction

As discussed at the beginning of Sec. VI, the QE of TPB for a given wavelength of incident VUV light is determined by comparing the thickness-dependent response of samples to a detailed microphysical Monte Carlo simulation. By comparing the photon ratio measurements to simulation, it is possible to unfold the intrinsic QE from the optical effects of the sample and experimental setup.

More specifically, the measured photon ratio, , is compared to the photon ratio from simulation, for samples of different thickness. All of the optical properties in the simulation remain fixed except for the TPB QE. For a given wavelength of incident UV light, a range of candidate QE values are simulated separately. All of the samples of different thicknesses that were measured are simulated for a given candidate QE value. Fig. 12 shows the data and simulation plotted for 130 nm incident light for several candidate values of QE in simulation.

The between simulation and measured values of the photon ratios is calculated for the set of sample thicknesses at each candidate QE. Fig. 13 shows the values for various QE candidate values for 130 nm incident light. The is defined in Eq. 5 as:

 χ2=n∑i=1(βi,exp−βi,simσi,exp)2. (5)

The QE of TPB at each incident wavelength is taken to be the value that minimizes the .

## Vii Results

The results are presented in this section. Sec. VII.1 presents the measured reemission spectrum for several incident wavelengths. Sec. VII.2 presents the measured absolute WLSE of TPB films of different thicknesses as a function of incident wavelength. Sec. VII.3 presents the extracted QE of TPB as a function of incident wavelength.

### vii.1 Reemission spectrum

The visible reemission spectrum was measured for each of several incident wavelengths: 45, 128, 160, 175 and 250 nm. The 45-nm measurement was taken using the SWC and is the brightest peak produced using a HeNe gas mixture. The 128-nm peak measurement was performed using the IWC while the 160-, 175- and 250-nm spectra were taken using the LWC. The 128 and 175 nm wavelengths correspond to the argon and xenon scintillation wavelengths. The area-normalized reemission spectrum for each of these incident wavelengths is presented in Fig. 14.

No dependence of reemission spectrum on incident wavelength was observed. All spectra have a peak near 420 nm and cut off below 400 nm.

In this work, the measured binned spectrum is used in the Monte Carlo model. For the purposes of non-Monte Carlo based modeling, we provide here an analytic model for this spectrum. The reemission spectrum for 160-nm incident light was fit to a weighted sum of a Gaussian and exponentially modified Gaussian:

 f(λ|A,α,σ1,μ1,σ2,μ2)=Aα2eα2(2μ1+ασ21−2λ)×erfc(μ1+ασ21−λ√2σ1)+(1−A)×1√2σ22π×e−(λ−μ2)22σ22. (6)

The fit is shown in Fig. 15. The fit was performed using the RooFit package in ROOT RooFit (). The 160 nm wavelength was chosen because it is the brightest peak of any configuration, which provides the best signal to noise. Because no significant dependence of the reemission spectrum on incident wavelength was observed (Fig. 14), a model built from this fit can be reasonably applied to other incident wavelengths. The fit has a chi-squared value of 0.626. The fit parameters and the associated uncertainties are given in Table 3.

### vii.2 Sample-dependent wavelength shifting efficiency

For comparison to the literature, we provide here the measure of sample-dependent WLSE in the form of those presented in gehmanVUV (). The WLSE measured for samples of different thickness are presented in this section.

As discussed in Sec. VI.1, the GAF is determined from simulation and used to convert the observed photon ratio of a sample to the absolute WLSE (Eq. 3). The GAF’s dependence on sample thickness is shown in Fig. 16.

Fig. 17 presents the measured absolute WLSE efficiency for a representative set of samples: B, C, D, E, and H (as defined in Table 1). In general, thinner samples have a smaller WLSE, up to approximately 2 . Samples between 2 and 3 thick exhibited the largest absolute WLSE. A slight decrease in the WLSE is observed for thickest sample (H) at a number of wavelengths.

It should be emphasized that the WLSE results are dependent on both environmental factors and the exact setup. In this work, the TPB samples were measured at room temperature and in vacuum. For typical LNG applications, the TPB surfaces are often submerged in a cryogenic liquid target. Liquid noble targets have an index of refraction closer to that of acrylic and TPB, so one could expect higher WLSE since there will be fewer reflections at the LNG/TPB and LNG/acrylic interfaces for VUV and reemitted photons. The QE result is not dependent on these effects because it was decoupled from the optics of the setup and sample, and is therefore the more interesting and useful result.

#### vii.2.1 Uncertainties

Several sources of uncertainty were considered. The total uncertainty and its components are plotted as a function of incident wavelength in Fig. 18. Each of the components were added in quadrature to evaluate the total uncertainty, which is provided in Fig. 17

The photocurrent uncertainty is the RMS in the light, dark, and sample photocurrents propagated through Eq. 2. The “UV Photons” component is the uncertainty in the number of UV photons when folding in the uncertainty in incident light spectrum and photodiode response at the incident wavelengths. Similarly, the “Vis Photons” is the uncertainty in the reemission spectrum of TPB and the corresponding uncertainty of the photodiode’s response at the reemission wavelengths.

One photodiode (PD-1) was used for the majority of the measurements. A second photodiode (PD 2) was calibrated relative to a NIST standard and used as a reference to track the calibration of PD-1 over time. The “cross cal” component is the uncertainty in the re-calibration of PD-1 to the PD-2 standard.

When comparing data taken using the LWC and MWC in the region of overlapping measurements (130–150 nm), an offset of 9.8% +/- 2% was found. This offset was found to be independent of incident wavelength and was corrected for on all data sets taken using the windowless lamp (MWC and SWC). The configuration dependent offset is likely due to the different illumination profiles on the diffraction grating for the LWC and MWC/SWC. The illumination profile of light incident on the diffraction grating was studied and optimized for the LWC by adjusting the focusing mirror and is thought to be well represented in the Monte Carlo model. This provides reasonable justification to correct the constant offset seen in the MWC/SWC to the LWC.

The uncertainty in the GAF contains two components. The first is the statistical uncertainty in the simulation, which is shown as the error bars in Fig. 16 and is approximately 0.3%. The second and dominant component is the uncertainty in dimensions of the setup, as defined in Table 2. To evaluate this systematic, each critical dimension of the setup was changed by 1 sigma, as defined in the table, to evaluate the resulting change in the GAF. The change in the GAF for each dimension was taken as the uncertainty for that element. This was performed on each critical dimension separately. The uncertainties from each test were assumed to be uncorrelated and were added in quadrature. This resulted in a total systematic uncertainty on the GAF of 3.7% which is independent of incident wavelength. The statistical component and setup systematic component were added in quadrature resulting in a total uncertainty on the GAF of 3.71%.

The authors performed an additional systematic check by varying the offset of the TPB sample relative to the photodiode position. This was performed by shimming the TPB sample’s seating position in the sample wheel with snap rings. It was found that the change in the observed photon ratio for shimmed configurations was consistent with the change in the GAF given by a simulation of a shimmed setup for 3 shimmed configurations relative to the default configuration. This provides the authors additional confidence that the Monte Carlo simulation is a good representation of the setup.

### vii.3 Quantum efficiency

The extracted intrinsic QE of TPB as a function of incident wavelength is presented in this section and shown in Fig. 19. The QE extraction was performed using the process described in Sec. VI.3. Because the QE extraction for a single incident wavelength is a computationally intensive process, a representative subset of the wavelengths investigated in the WLSE measurements were considered.

The QE follows the shape of the WLSE efficiency curves. The QE has local maxima near 230 nm and 150 nm incident light. There is a general trend toward lower QE for shorter wavelengths.

Recalling the definitions of the QE and WLSE, it is to be expected that the QE is larger than the WLSE. This is because the WLSE efficiency is the intrinsic QE of TPB folded in with the optics of the film, sample and setup. The intrinsic QE represents the upper limit for the WLSE, which is reduced by the absorption of reemitted photons by the TPB and acrylic.

#### vii.3.1 Uncertainty

The uncertainty was determined by fitting a parabola to the vs. QE, as shown in Fig. 13, for each incident wavelength of interest. The minimum from the parabola fit was taken to be the QE of TPB for a specific wavelength. A of 1 from the minimum value was used to determine the +/- 1 uncertainties. This is shown in Fig 13. The systematic uncertainty on the QE is between 1 and 3%.

## Viii Discussion

Three major results are presented in this work: 1) the reemission spectrum of TPB for several wavelengths of incident light, 2) the sample-dependent WLSE of several samples of different thicknesses as a function of incident wavelength, and 3) the extraction of the intrinsic QE of TPB as a function of incident wavelength.

The reemission spectrum result is consistent with the literature and has confirmed that the reemission spectrum of TPB remains constant for incident wavelengths as low as 45 nm.

The WLSE result presented in this work is in tension with those presented in gehmanVUV (). The authors believe the differences can be attributed to differences in the Monte Carlo model evaluating the GAF and unaccounted for systematic uncertaities related to photodiode calibration and the setup optics in gehmanVUV (). The details of the differences are discussed in Sec. VIII.1.

To the best of our knowledge, the extraction of the intrinsic QE of TPB as a function of incident wavelength without reference to other materials is a new result. The intrinsic QE is more interesting than the WLSE because it depends on the material and not the sample. For the purposes of modeling TPB, the intrinsic QE is a critical input to current and future liquid noble gas experiments and is now well constrained.

Previous measurements of the QE of TPB were performed relative to Sodium Salicylate McKinsey_99 (). Combining the Sodium Salicylate reference Brumer69 () with the relative measurements suggests the QE of TPB should be larger than that determined in this work. The authors believe that this difference is being driven by the optical model of the TPB, which may not be effectively represented in the Sodium Salicylate reference. This is discussed in section VIII.2.

### viii.1 Comparison with previous measurement

This work builds on much of the original work in gehmanVUV (), and several items of equipment were shared between the two efforts. The authors of this article worked closely with the authors of gehmanVUV (), one of whom is an author of this work.

Differences exist between the TPB efficiency measurements presented here and what is presented in gehmanVUV (), as shown in Fig. 21. Several factors can account for the differences in the measurements. These are described in Secs. VIII.1.1– VIII.1.4. Following many detailed systematic checks, as described, there is confidence that the differences are understood.

#### viii.1.1 Photodiode calibration

The authors believe the largest differences between this work and what is presented in gehmanVUV () arise from issues with photodiode calibrations. The photodiode used in gehmanVUV () was calibrated in 2008 by NIST and had the response given by the black curve in Fig. 20 CalibrationReport2008 (). Before the start of this work, the same photodiode was recalibrated at NIST and followed the response curve given by the red curve CalibrationReport2014 (). A large change in the photodiode’s response occurred between 2008 and 2014, especially in the range of 120–150 nm. The previous work was published in 2011 gehmanVUV ().

The photodiode’s response degradation was likely due to UV damage from prolonged exposure and the build up of an oxidation layer on the bare face of the silicon photodiode surface NIST_PD_Ref (); CalibrationReport2014 (). A build up of an oxidation layer can drastically reduce the response of the photodiode for wavelengths below 150 nm. Interesting, an oxide layer may also increasing the response at higher wavelengths the layer at these wavelengths creates an anti-reflective layer (interactions inside of the oxide film). An oxide layer effectively leaves the response at the visible wavelengths unchanged. This explanation is consistent with what is seen in Fig. 20.

Because the response of the photodiode used in the 2011 publication changed by a large amount, two new photodiodes were purchased in 2016 after the start of this work. NIST calibrated one of these photodiodes (PD 1) (Fig. 5) in February of 2016. The second photodiode (PD 2) was calibrated relative to the NIST supplied calibration of PD 1 by the authors. PD 1 was used for the bulk of our measurements in this work while PD 2 was used to track the relative response of PD 1 over time.

With access to the raw data from the 2011 publication, another analysis was performed using the 2014 calibration of the photodiode used in gehmanVUV (). Fig. 21 shows the results of this reanalysis in red, along with the published 2011 result from gehmanVUV () (black). For short wavelengths (120 – 150 nm), an unaccounted degradation in the photodiode’s response would lead to one underestimating the number of UV photons incident on the sample, thus increasing the photon ratio and WLSE at those wavelengths. The opposite is true for the longer wavelengths where an increase in the photodiode’s response was observed (150 – 250 nm).

Interestingly, the shape of the reanalyzed raw data from the 2011 result using the 2014 calibration curve agrees fairly well with the results presented in this work, though there is a normalization offset which will be explained in Sec. VIII.1.2. This suggests that the bulk of the Gehman et al. photodiode’s response degradation occurred between the 2008 calibration and the 2011 publication and that the published result does not account for changes in the photodiode’s response.

#### viii.1.2 GAF determination

The GAF, described in Sec. VI.1, determines a scale factor to evaluate the total efficiency from the photon ratio (otherwise known as the forward efficiency in gehmanVUV ()). As may be expected, the GAF is observed to have a strong dependence on the distance of the photodiode from the sample. This suggests careful measurements of the apparatus dimensions are required and careful treatment of these uncertainties is critical. This systematic uncertainty has been included in our result and is the dominant uncertainty contribution for several wavelengths.

The work presented in gehmanVUV () also used a Monte Carlo simulation to determine the GAF. Their model was less detailed than that used in this work and the systematic uncertainty on the GAF was assumed to be zero.

Additionally, the TPB model in gehmanVUV () was treated as an infinitesimally thin film which did not account for important TPB optical effects, such as the scattering length of visible light. The authors believe the simplified Monte Carlo model in gehmanVUV () may have underestimated the value of the GAF which led to systematically higher WLSE results.

These differences in evaluating the GAF and its uncertainty contribute to differences in the WLSE measurements (Fig. 21).

#### viii.1.3 Background subtraction and beam intensity

This work used much of the same hardware as was used in (gehmanVUV, ). It was determined that the original focusing mirror and Al+MgF diffraction grating required replacement because of discoloration on the optical surfaces likely resulting from years of use. It was observed that the level of background light was elevated and the intensity of light at short wavelengths was attenuated when using the discolored optical elements. When the damaged optical elements were replaced at the start of this work, the amount of background light visible by the spectrometer was substantially reduced and the VUV light output at wavelengths between 120 – 250 nm was improved by between 20 – 50% across the wavelength range of interest.

A brighter light source leads to smaller statistical errors in the ratio of measured dark- and background-subtracted photocurrents given in Eq. (3). This is a dominant reason why the statistical error in the WLSE measurements of this work are smaller at most wavelengths than in gehmanVUV (). Higher statistics resulting from a more intense incident UV beam also result in the cleaner, more stable reemission spectra presented in this work (Fig. 14).

It is also important to note that in this work, a background subtraction is performed in addition to a dark current subtraction for wavelengths below 150 nm (Eq. (1)). Because any measurement of reemitted light from a TPB sample is actually a sum of reemitted light plus any background light, a separate measurement is required to determine the magnitude of the background light, as described in Sec. V.1. This correction was not included in gehmanVUV () – only a dark current subtraction was performed. Background levels at short wavelengths (below 135 nm) were observed to be on the order of the reemitted signal when using the discolored optics inherited from the setup used in (gehmanVUV, ). It is possible that elevated background levels may have been unaccounted for in their TPB signal measurements.

#### viii.1.4 Overlapping measurements

This work was able to leverage two distinct light sources to make multiple measurements of the total wavelength shifting efficiency in the range of 130 – 150 nm. Referred to as the overlap region, the ability to measure the WLSE in this region using multiple configurations and gases provides a nice cross check of configuration dependent systematic uncertainties. All measurements from the various configurations in this overlap region agree well, providing confidence that there is reasonable control of configuration-dependent systematic uncertainties.

### viii.2 Previous QE reference

When comparing the absolute QE from this work to relative measurements in the literature, the QE results presented in Sec. VII.3 are lower than previous results would suggest.

In particular, McKinsey in McKinsey_99 () performed a relative measurement of the WLSE for TPB samples of various thickness relative to Brumer’s sodium salicylate reference in Brumer69 (). If one considers the simplistic approach of multiplying the relative TPB measurement in McKinsey_99 () by the absolute QE of sodium salicylate measured in Brumer69 (), the difference compared to this work is approximately a factor two for select wavelengths below 100 nm.

In Brumer’s work Brumer69 (), an analytical model was developed to model the optics of sodium salicylate thin films. Similar in nature to this work, the analytical microphysical model of sodium salicylate thin films was used to unfold the sample optics from the material’s intrinsic QE. The analytical model explicitly accounted for the absorption lengths of VUV and visible photons. However, to the best of our knowledge, the model did not account scattering of the visible photons, which turns out to be an important contribution in modeling TPB.

As a check, the authors used an analogous form of the model in Brumer69 () by turning off Rayleigh scattering in the Monte Carlo and evaluating the ratio of visible to UV absorption lengths in TPB that best fit the data of photon ratio as a function of sample thickness. Interestingly, the “best-fit” analytical model derived from  Brumer69 () led to a GAF approximately smaller by a factor of two, thus making up the difference between this work’s QE result and the simplistic scaling of the relative result in McKinsey_99 () to an absolute scale using Brumer69 (). However, given the absorption lengths required by the analytical model to fit the data are inconsistent with more recent values in the literature and the fact that Rayleigh scattering is ignored suggests that Monte Carlo model used in this work is favored over the analytical model used in Brumer69 () for TPB QE measurements.

It should be emphasized that all of the values used in the Monte Carlo simulation in this work, except for the QE, were set by measurement (remission spectrum) or values in the literature. Given the highly constrained nature of this model, the fact that the model accurately predicts the dependence of photon ratio on sample thickness (Fig. 12) suggests that the Monte Carlo model used in this work is a good representation of the setup.

## Ix Conclusions

Three major results were presented in this work for TPB films at room temperature: 1) the reemission spectrum of TPB for several choices of incident light, 2) the sample-dependent WLSE of several samples of different thicknesses as a function of incident wavelength, and 3) the extraction of the intrinsic QE of TPB as a function of incident wavelength.

The precision and scope of the measurement has been improved in comparison to previous work (gehmanVUV, ). The measured TPB reemission spectrum was shown to be consistent for incident wavelengths of 45 – 250 nm. The WLSE has been measured from 50–250 nm for several samples of different thickness. The WLSE measurements presented in this work disagree with previous results gehmanVUV () for wavelengths from – 230 nm. Possible explanations for the differences have been discussed, and the authors are confident that these new results represent improvements in accuracy and robustness.

Using these data the intrinsic QE of TPB has been extracted for the first time, for incident wavelengths in the range 50–250 nm. This result is independent of optical effects in the setup and the samples themselves, and thus is most broadly applicable to other detectors.

## X Acknowledgments

This work was supported in part by the Office of High Energy Physics of the U.S. Department of Energy under contract DE-AC02-05CH11231, and in part by the Physics Department at UC Berkeley.

Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

The Ocean Optics spectrometer, McPherson monochromator, deuterium light source, lamp power supply, monochromator motor controller, and two photodiodes are kindly on loan from Dr. K. Rielage and Los Alamos National Laboratory.

The authors thank the MiniCLEAN collaboration for their permission to use MiniCLEAN RAT and Dr. Thomas Caldwell for his input on modeling TPB in MiniCLEAN RAT.

The authors thank the Dr. Daniel McKinsey group at University of California at Berkeley for the use of their thermal evaporator and for valuable discussion.

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