Electron drift in a large scale solid xenon
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Electron drift in a large scale solid xenon
J. Yoo ∗ and W. F. Jaskierny Fermi National Accelerator Laboratory, Kirk and Pine St., Batavia, IL 60510, USA A BSTRACT : A study of charge drift in a large scale optically transparent solid xenon is reported.A pulsed high power xenon light source is used to liberate electrons from a photocathode. Thedrift speeds of the electrons are measured using a 8.7 cm long electrode in both the liquid and solidphase of xenon. In the liquid phase (163 K), the drift speed is 0.193 ± µ s while thedrift speed in the solid phase (157 K) is 0.397 ± µ s at 900 V/cm over 8.0 cm of uniformelectric fields. Therefore, it is demonstrated that a factor two faster electron drift speed in solidphase xenon compared to that in liquid in a large scale solid xenon.K EYWORDS : Cryogenic detectors, Charge transport and multiplication in solid media, Timeprojection chambers.. ∗ Corresponding Author: [email protected] a r X i v : . [ phy s i c s . i n s - d e t ] A ug ontents
1. Introduction 12. Experiment setup 23. Charge transport 34. Discussions 85. Conclusion 10
1. Introduction
Noble elements in both the gas and liquid phases have proven to be excellent low backgroundradiation detectors [1, 2, 3, 4, 5, 6]. In particular, xenon has drawn special attention among thenoble elements due to several distinct advantages. The liquid phase of xenon possesses a veryhigh scintillation light yield (40 ∼
60 photons/keV) and the vacuum ultraviolet (VUV) wavelength(178 nm) of the scintillation is optically transparent in xenon [7, 8]. The absence of long-lived ra-dioisotopes in xenon results in no intrinsic background radiation sources. The large atomic mass ofxenon (A=131.3 and Z=54) results in excellent self-shielding effects of radioactive backgrounds.The chemical purification of xenon is straightforward with the use of hot getter or gas distilla-tion systems. A wide range of applications has been studied on particle tracking and spectroscopyincluding γ -ray astronomy, neutrinoless double beta decay, dark matter searches and neutrino co-herent scattering experiments.The solid phase of xenon has several advantages over liquid xenon. The density of solid xenon(3.41 g/cc) is higher than that of liquid xenon (2.95 g/cc), while the solid phase is transparent to itsscintillation lights ( ∼
172 nm) [7, 9, 10, 11]. The electron drift speeds in solid xenon are measuredto be faster compared to those in the liquid phase [12], which can be understood as suppressedelectron-phonon scattering in the solid phase due to the reduced energetic phonon populations inlow temperature media. Therefore, one may imagine a compact, scintillating, and fast ionizationdetector using the solid xenon.Particle detector applications based on the solid phase of noble element have been investi-gated extensively [12, 13, 14, 15, 16, 11, 17, 18, 10, 19, 20]. Even though these studies havesuccessfully demonstrated that the solid noble elements might be excellent candidates for a particledetector, large scale detectors have yet to be realized. In a previous publication, we demonstrated ascalability of above a kilogram scale of optically transparent solid xenon [21]. The electro-negativecontaminants, microscopic defects, voids and structural deformation are the dominant componentsthat affect charge transportation. Therefore, it is non-trivial to maintain the fast charge transportproperties in a large scale solid. – 1 – ight pulseroptical fiber inductive pickup coil trigger signalanode signalcathode signal- high voltage (cathode)+ high voltage (anode)photo cathodeanodeanode gridground gridfield shaping rings R = 110 M Ω R D R D R D R D R D R D xenon R D = 50 M Ω R D Figure 1.
A schematic diagram of the charge drift electrode (left) and a photograph of the electrode insolid xenon (right). The photons emitted from the optical fiber to the photo-cathode can be viewed from theexternal window. In this particular sample, there are small opaque spots near the edges of the field shaperings. Birefringence is visible near the bottom edge of the glass wall. However, the central area of theelectrode where the electrons are drifting is optically transparent.
The goal of this study is to measure the drift speed of electrons in a large scale opticallytransparent solid xenon. The sections below describe the experiment setup, results of electron driftvelocity measurements, discussions about the results, and conclusion of the study.
2. Experiment setup
The solid xenon test setup is designed to maximize the visual access of the cryogenic xenon volume.The cryostat consists of a stainless steel vacuum jacketed chamber with an outermost diameter of30 cm with three 15 cm diameter glass window ports. Two concentrically placed glass chambers re-side inside allowing optical access to the xenon bulk volume. The larger of the two glass chambers,which is used as a liquid nitrogen bath for cooling and has a diameter of 23 cm, is referred to as theliquid nitrogen chamber. The smaller 10 cm diameter inner chamber houses the xenon volume andis made out of Pyrex with a 5 mm thick side wall and a 10 mm thick flat bottom, is referred to asthe xenon chamber. A commercial hot getter (PF4-C3-R-1 and Monotorr PS4-MT3-R-1 by SAES)and a circulation loop allows continuous purification of the xenon. The temperature and pressureare controlled using a programmable logic control system.The cryogenic and gas control of the system largely overlap with those of liquid-based systems,but additional fine tuning is required to solidify the xenon. Due to the density change between theliquid and the solid phase, the freezing process requires extra effort in order to not damage thedetector components. A modified
Bridgeman’s technique [22] was adopted to grow solid xenonabove a kg-scale. Details of the production of optically transparent solid xenon using this setup– 2 –an be found in reference [21]. Here we briefly explain the solid xenon growing process. First,xenon gas is condensed to liquid in the chamber at a set temperature of 163 K and pressure of14.5 ± ± ± µ m wire diameter. The geometrical transparency of the grid is 98.8%. Theanode grid and the field-shaping rings are connected to the cathode grid by an internal chain of50 M Ω resistors. The photocathode which is attached at the cathode disk is an aluminum platecoated with 50Å of titanium and 1000Å of gold. A powerful (5 Joule) xenon flash lamp witha wide ultra-violet spectrum was used as the light source. The pulsed light is guided into thexenon chamber using two 0.6 mm diameter core optical fibers. The edge of the fibers are directedto the center of the photocathode using a guide structure made by G-10 material. The distancebetween the edge of fibers to the photocathode is set at 1 mm. Owing to the geometrical spread,the effect of the reflected photons producing photoelectrons is estimated to be less than 0.1% ofthe primary photoelectrons. Therefore the contribution of those reflected photons to the chargedrift time measurement is negligible. FIG. 1 (left) shows a schematic diagram and a photograph ofthe charge drift electrode. The distances between the photocathode surface and the cathode-grid is1.8 cm, cathode-grid and anode-grid is 6.2 cm with five field shape rings, anode-grid and anode is0.7 cm. Therefore, the full drift distance of electrons from the photocathode to the anode is 8.7 cm.FIG. 1 (right) shows a photograph of the electrode in solid xenon.A trigger signal is produced using an inductive pickup coil on the power leads of the flash lamp.The photo-electrons that are liberated from the photocathode drift to the cathode grid (1.8 cm).After crossing the cathode grid, the electrons drift between the cathode grid and the anode grid(6.2 cm). An electric current is induced at the anode after the electrons pass through the anodegrid. The signals are read out using charge amplifiers which have a 5 pF integration capacitorand a 22 M Ω resistor in parallel. The capacitor provides a typical time constant of 110 µ s. ATektronix 3034C Digital Phosphor Oscilloscope is used to readout the cathode and anode traces.For each trace, a total of 10 samples are read out over a 400 µ s of time window. The oscilloscopeis connected to a PC through a GPIB communication protocol. A LabVIEW software is used torecord the traces in a text file.
3. Charge transport
The pulsed light from the high power xenon lamp propagates through a 5 m long optical fiber. Thepropagation time of the light in the optical fiber is about 25 ns. The power and the frequency of– 3 – igure 2.
Examples of traces in the liquid (163 K, blue trace) and the solid (157 K, red trace) phase ofxenon. The applied electric field in these examples is 500 V/cm. The glitch peaks at 40 ± . µ s are inducedby the high voltage trigger of the pulsed light source unit. The anode signal in the solid xenon is faster thanthat in the liquid xenon. The amplitudes of the cathode signals are similar in liquid and solid xenon. Thefunctional form fit results are overlaid on the traces in light-blue curves. The charge drift distance betweenthe photocathode (trigger signal) to the start time of the anode signal is 8.0 cm. the xenon arc lamp light source are set to 4 Joule per pulse and 10 Hz, respectively. The lightemittance to the photocathode is visually observable through the glass window. High voltageson each electrode are applied to achieve uniform electric fields over the cathode to anode. Anegative high voltage is applied between the cathode and the cathode-grid (ground), and positivehigh voltages are applied from the cathode-grid to the anode-grid and from the anode-grid to theanode. The electrons are drifted from the cathode to the anode. The electric current is read outat the cathode disk as the cathode signal . No current can be measured between the cathode gridand the anode grid. The current between anode grid to anode is then read out as the anode signal .Therefore, the time difference between the trigger signal and the start time of the anode signal isthe measurement of the electron drift time from the photo-cathode to the anode grid (8.0 cm) The drift velocity is strongly temperature dependent within ten degrees around the meltingpoint. The electro-negative impurities in solid xenon has not been measured and can be differentfrom the value of the liquid phase. Thus a direct measurement of the impurity concentration of thesolid xenon was not possible. In order to avoid this difficulty, the electron drift time at 500 V/cmelectric field is initially measured in liquid xenon. The xenon gas is continuously circulated throughthe getter system above the liquid xenon volume. The measurements were repeated until the anodesignal amplitude did not improve over time, which normally takes about two weeks. Once the Due to the HV glitch near t=40 µ s, fitting results of cathode signals show large uncertainties in the t measurement.Since the photon delivery time from the light source to the photocathode is 25ns, we conclude that the best t values canbe obtained by the timing of the HV glitch. – 4 – igure 3. Examples of pulse shapes at different drift fields for liquid xenon (left panel) and for solid xenon(right panel). The fit results are overlaid on the traces in cyan curves. anode amplitude has stabilized (i.e. purity level of xenon is saturated), the electron drift time ismeasured in various electric fields (200 V/cm to 900 V/cm). After completion of the measurement,solid xenon was grown from the liquid phase of xenon. The solidifying process takes about a weekincluding two-days of net solid xenon growing time. Once the entire xenon volume has solidified,the electron drift times in various electric fields are measured in the solid phase. The measurementsare repeated after melting the solid xenon in order to confirm the original measurements in theliquid phase.FIG. 2 shows examples of measured traces in liquid (163 K) and solid phase (157 K) of xenon.The applied electric field is 500 V/cm. The glitch peaks at 40 µ s are induced by the high voltagetrigger of the pulsed light source unit, and they can be used as references of trigger time. A totalof 64 traces are averaged to cancel white noise. Remaining noises are from the heater powersource which periodically switches from AC to DC, and noise pickup from the high-speed vacuumturbo. There is a slight monotonic increase of charge signals immediately after the glitch peaksthat we could not completely remove. We suspect there could be a small leak of electric fieldsbetween the two grids. It is clearly visible that the start time of the anode signal in the solid xenon(red curve) is earlier than that in the liquid xenon (blue curve). Therefore, a faster electron driftoccurs in solid xenon compared to that in liquid xenon over a large distance (8.0 cm) at the same500 V/cm electric field. To find the anode start time ( t i ), a functional form fit is carried out to theanode trace, given as f ( t ; A , t i , τ ) = A / t · ( − exp ( − ( t − t i ) / τ )) , when t > t i and f ( t ) = t ≤ t i where A , τ and t i are free parameters. The baseline of the anode trace is normalized byaveraging t = − µ s of the pre-trigger region. The trigger signal as the electron creation isat t i = ± . µ s. The electron drift time is defined by t d = t − t i . The drift velocity is definedby v =8.0 cm/ t d . The signal amplitude at the anode in solid phase is 2.8 times larger than that inthe liquid phase while the cathode signal amplitudes in both phase are similar. This observeddifference of the anode amplitude can be attributed to the electron life time in the xenon. Assuming– 5 – [V/cm] v L [cm/ µ s] v S [cm/ µ s] v S / v L
200 0.148 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 1.
Mean values of the measured electron drift velocities for various electric fields in liquid ( v L ) andsolid ( v S ) xenon. The errors are from the functional form fit of t through multiple measurements. Theanode-grid to anode voltages are set to 400 V/cm at above 700 V/cm of drift fields. See text for details. the amplitude of the trace is proportional to the collected charge [24], the electron life time ( τ )can be estimated by τ = t d / log ( Q c / Q a ) , where Q a / Q c (cid:39) V a / V c . The V a ( V c ) is the maximum(minimum) voltage of anode (cathode) trace, and Q a ( Q c ) is the collected charge at the anode(cathode). The electron life time in liquid xenon is τ L = . µ s / log ( . / . ) = . µ s ,while that in solid is τ S = . µ s / log ( . / . ) = . µ s . Therefore, the electron lifetime in solid and liquid phases is differ by only 12%. As the anode signals are used to evaluatethe drift time, the absolute value of the cathode and anode amplitudes do not seriously affect theelectron drift time measurement.FIG. 3 shows examples of the anode signals in liquid (left) and solid (right) xenon at variousapplied electric fields, where the cyan curves are the fit functions. TABLE 1 summarizes thesemeasurements. We used the fit function f ( t ) in order to determine t i . The fit range of the pulsesin liquid phase is t = − µ s and that of solid phase pulses is t = − µ s. The fit resultsof t i are relatively insensitive to the choice of fit range as long as it is kept to 45 < t < µ s,which assures that the HV glitch and the pulse tail does not dominate the fitting results. Thepre-anode signal region shows undershooting traces after the HV glitch and slowly approach thebaseline at around 60 µ s. In order to understand systematic uncertainties associated with the pre-anode signal region to the t i measurements, we fit the pre-pulse region (50 µ s to t i ) using a second-order polynomial function and corrected the baseline of the trace, then repeated the f ( t ) functionalform fit process. The largest shift of the t i value is -0.27 µ s which occurs in the solid phase with900 V/cm, or +0.005 cm/ µ s difference in the drift velocity. The uncertainty of the electron drifttime is estimated through repeated measurements in the same electric field. The standard deviation– 6 – -field [V/cm]100 200 300 400 500 600 700 800 900 1000 s] µ Drift velocity [cm/
SXe [157K] (first)SXe [157K] (second)SXe [157K] (thin layer) Miller 1968LXe [163K] (before freeze)LXe [163K] (after melt)LXe [163K] (thin layer) Miller 1968Effective Shockley theory S u L u E-fields between anode-grid to anode : 400V/cm
Figure 4.
Electron drift velocity in liquid and solid xenon for various electric field strength. The measuredelectron drift velocities in liquid xenon before the solidification are in magenta squares ( (cid:4) ). The measure-ments in solid phase for the first trial of solidification are in red triangles ( (cid:115) ). The measurements in liquidphase after melting the xenon are in blue circles ( (cid:108) ), where a slight offset for the electric fields is just fordisplay purpose. The second trial of solid xenon measurements after refreezing the xenon are in magentadown-triangles ( (cid:116) ), where the electric fields are off-set just for display purpose.. The previous measurementsby Miller et al. in thin-layers (145 µ m to 228 µ m) of liquid and solid xenon are shown in stars ( (cid:72) ) and blanksquares ( (cid:3) ) respectively [12]. The red line ( u S ) indicates the sound velocity in solid xenon (0.110 cm/ µ s)at 157 K. The blue line ( u L ) indicates the sound velocity in liquid xenon (0.065 cm/ µ s) at 163 K. The reddashed curve shows the effective Shockley theory. See text for details. from the repeated t i measurements is estimated about 2.5%. The drift fields from the cathode toanode are set uniform up to 650 V/cm. However, owing to the charge breakdown at the high voltagefeedthrough above ∼ t d measurements should notbe seriously affected by these inconsistent electric fields. However, a decisive test will be possibleafter resolving the charge breakdown issue in future studies. After the first set of measurements(liquid and solid), we melted the solid xenon to liquid. The heating of the xenon chamber andconvection of xenon increased the impurity level in the xenon bulk. Therefore, after the melting,the initial liquid xenon does not show large enough cathode and anode signal amplitudes. Theliquid xenon was continuously purified until we recover the cathode and anode signal amplitudesof the first set of measurements. This re-purifying process took a few days to reach the saturationlevel of charge amplitude. Then the second set of measurements are then repeated in liquid andsolid phases.The measured drift velocity as a function of the electric field is shown in FIG. 4. The electrondrift velocities in the liquid phase are measured before and after the solidification in various electric– 7 –eld strengths. The “after melt" electric fields are offset just for the display purpose. It can be seenthat the two measurements in liquid xenon are in good agreement. The results are also comparedwith previous measurements in thin-layers (145 µ m to 228 µ m) of liquid xenon by Miller et al. [12].The data points of the thin-layer measurements are taken by reading FIG. 6 of reference [12]. Theelectron drift velocities in the liquid phase are consistent between the thin-layers of xenon and thelarge scale xenon. The drift velocities of the first and the second solidifications of the xenon arein a very good agreement. The applied electric fields for the "second" measurements are the samewith the "first" measurement, and are offset for display purpose. In the solid phase, the measuredelectron drift velocity is consistent with that of the thin-layer measurement at a higher electric field(800 V/cm). The electron drift velocity in solid xenon is a factor of 2 larger than in liquid at orabove E=800 V/cm. However, there are noticeable discrepancies in the measured drift velocities atlower electric fields. The electron drift velocities are about 30% faster in thin-layer compared tothat in the large scale solid xenon at the drift fields of 200 ∼
300 V/cm.
4. Discussions
The dynamics of electron propagation in a pure single crystalline xenon is simply determined bythe interaction with acoustic phonons. For condensed xenon, the possible occurrence of molecularimpurities must be taken into account when determining the electron drift as its presence can lead toinelastic scattering of electrons that changes the energy distribution of the electrons. Impurities thatare electro-negative would not change the energy distribution of the electrons but lead to a reductionof the total number of drifted electrons. In order to avoid contamination from the outgassing of thedetector components, the xenon glass chamber with the electrode had been baked at 40 C for twodays and then the chamber was evacuated to below 10 − Torr using a turbo system for two weeks.We used research grade xenon with 99.999% of purity. The other components reported by the gasprovider are: krypton ( < < < < < < < < <
100 ppm). No other contamination above the RGA background level has been observedin the xenon gas. We regard the impurity level of the molecular components in our condensedxenon to be low enough that they do not significantly affect the dynamics of electrons.An extensive systematic study of electron drift velocities in 1 cm thick xenon substrates forvarious electric fields and temperatures has been carried out [13]. Their measured electron driftvelocities in liquid xenon is about 15% faster and about 55% (at 200 V/cm) to 23% (at 900 V/cm)faster in solid xenon compared to our results. The method applied in reference [13] is a so-called modified Townsend pulse discharge method , where a short pulse of x-rays are irradiated to an elec-trode and electrons produced in that electrode drift to the other electrode. The electron drift velocityis essentially estimated by measuring the rise time of the voltage pulse with various corrections,such as effective penetration depth of x-ray beam into the xenon, mean electron path before cap-ture, charge amplifier time constant, extrapolation of the linear part of pulse rise time to non-linearregime. These corrections significantly affect the value of the electron drift velocity. On the otherhand, our method directly measures the drift time of electrons in a distance of 8.0 cm of by shieldingthe electric fields using grids. Therefore, our method does not rely on any significant corrections.– 8 –he element xenon forms a relatively simple liquid as the binding forces between the atomsare symmetric van der Waals force and the local atomic order is determined by the close packingof ideal spheres. However, the atoms still move freely in the liquid phase with random motionwhile they form a face-centered cubic structure in the solid phase and freeze. The thin-layer ofsolid xenon substrates that were produced in the cryostat of reference [12] would most probablyhave been a single crystal or was consisted of a few polycrystalline layers. If so, the electronsdrifting in thin-layer of crystal would not suffer too much scattering at each crystal boundary. Fora large scale solid xenon, one can produce clear, transparent solid xenon specimens which arevirtually perfect crystals. Nevertheless, in most cases, they are polycrystalline and contain a largenumber of microscopic defects [22]. The drifting electrons would scatter and slow down at eachpolycrystalline grain boundaries and the defects. In weak drift fields the electron scattering at thegrain boundaries would be significant as the probabilities of scattering of electrons would be high.However at strong drift fields where the electrons acquire significant energy above the potentialbarrier, the probabilities of electrons trans-passing the boundaries would improve [25]. Hence theobserved electron drift velocity in polycrystalline would be close to that in a single crystalline. Forexample, reference [26] demonstrated that the electron mobility is proportional to the grain size ina polycrystalline film transistor. It was also shown that the electron mobility in a single crystallineis about an order of magnitude larger than of that in polycrystalline. The overall electron mobility( µ ) can be estimated by taking a harmonic mean of electron mobility in the grain ( µ g ) and theboundary ( µ b ); 1 / µ = / µ g + / µ b . Therefore, in cases where µ g (cid:29) µ b , µ only depends on thecharge transport across boundaries. As the drift field increases, the kinetic energy of electronovercomes the barrier energy and µ b becomes comparable to µ g . The microscopic mechanismwhich is qualitatively described above would require further systematic studies using well definedcrystalline xenon substrates.We assume the hot-electron theory of Shockley [27] effectively account for the results in lowelectric fields . The theory describes the energy distribution of the hot-electrons by an effectivetemperature ( T e ) and the lattice temperature ( T ). The ratio of T e / T = γ is related to the appliedelectric field as γ − γ = ( π / ) · ( µ E / u ) , where the µ is electron mobility and u is the soundvelocity in the substrate. The drift velocity is given by v = γ − / µ E . At low drift fields, γ (cid:39) v (cid:39) µ E . In high electric fields the drift velocity becomes proportional to E / . In reference [12],the electron mobility ( µ ) for liquid xenon is measured to be 2200 cm /s/V at electric fields below100 V/cm. The saturation of the drift-velocity occurs at 4.4 times the sound velocity in liquid xenon( u L ) above 10 kV/cm of the high-field region. The thin-layer of solid xenon study sets the lowerlimit of the electron mobility at 3000 cm /s/V by effectively fitting the Shockley theory curve to themeasured drift velocities at low drift fields. The complete saturation of the drift-velocity occurs at5.0 times the sound velocity in solid xenon ( u S ) above 10 kV/cm. Therefore, assuming the Shockley The Shockley theory is limited to a smaller range of electric field and cannot explain the drift velocity saturation.A more advanced hot-electron theory by Cohen and Lekner [28] describes the electron drift velocity in liquid argonremarkably well over large electric field ranges up to 10,000 V/cm, but this theory cannot adequately describe othernoble elements. The agreements between the two theories are good in low electric fields. Therefore, we used theShockley theory to estimate the effective electron mobility in the solid phase measurements. In the case of liquid phasemeasurements, however, a saturation of the electron drift velocity was observed in the lowest electric field. Thereforethe Shockley theory is not applicable in liquid phase measurement. – 9 –heory is effectively extended to the drift fields in the range of 200 V/cm to 400 V/cm, the electronmobility is estimated at 1100 cm /s/V in the non-linear regime. The red-dashed curve in the FIG. 4shows the fit results of the Shockley theory to the measured electron drift velocity in solid xenon.
5. Conclusion
A study of electron drift in a large scale optically transparent solid xenon is reported. In the liquidphase (163 K), the drift speed is 0.193 ± µ s, while the drift speed in solid phase (157 K) is0.397 ± µ s at an electric field strength of 900 V/cm. Therefore it has been demonstratedthat the electron drift speed is faster by factor two in the solid phase compared to that in the liquidphase for large scale xenon. The results are consistent with the thin-layer measurements in theprevious study [12]. However, in lower electric fields, the measured electron drift velocities areslower than that in the thin-layer substrate. Assuming the Shockley theory is effective in the non-linear regime, the electron mobility is estimated to be about 1100 cm /s/V at 200 V/cm to 400 V/cmof electric fields in a large scale solid xenon. Acknowledgments
We are very grateful to M. Miyajima, J. White, and A. Bolozdnya for the initial discussions ofthe solid xenon particle detector and sharing their ideas. We would like to thank the Fermilabtechnical staff who aided in the design and construction of the apparatus. This work supported bythe Department Of Energy Advanced Detector R&D funding.
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