Detection of elementary particles using silicon crystal acoustic detectors with titanium transition edge phonon sensors

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Nuclear Instruments and Methods in Physics Research A311 (1992) 195-216 North-Holland

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INSTRUMENTE & METÜ0OS

IN PHYSM RESEARCH twon A

Detection of elementary particles using silicon crystal acoustic detectors with titanium transition edge phonon sensors B.A. Young, B. Cabrera, A.T. Lee and B.L. Dougherty Physics Department, Stanford University, Stanford, California 94305, USA

Received 16 July 1991

We are developing silicon crystal acoustic detectors (SiCADs), which operate at cryogenic temperatures and use thin-films of superconducting titanium (Tc = 435 mK) to sense phonons generated when an incident particle scatters off a nucleus or electron in pure and cold ( < 1 K) silicon. Our motivation for developing SiCADs includes their many direct applications to neutrino physics (e.g. to perform neutrino oscillation experiments), particle astrophysics (e.g. to measure the solar neutrino spectrum or search for the hypothetical dark matter in the universe) and solid state physics (e.g. to study phonon dynamics and focusing effects). We have fabricated and characterized multi-channel SiCADs with phonon sensors instrumented on both sides of a Si wafer substrate, and have used these devices to detect radioactive sources of gamma and X-rays, alpha particles and neutrons with incident energies of < 6 keV to 10 MeV. We discuss our results in terms of ballistic and quasi-diffusive phonon propagation, and show evidence for ballistic phonon focusing effects in [1001 silicon . 1. Background Over the past few years, significant progress has been made by many groups in the development of cryogenic particle detectors . A common goal of these efforts is to design and construct an array of robust, reliable and well-characterized detectors for use in a large scale neutrino or dark matter experiment. In addition, many of these devices have potential applications in more conventional areas of physics, including high resolution X-ray spectroscopy (e.g. for astrophysical or atomic and nuclear sources) and solid state physics (e.g. to study phonon dynamics) . The devices are operated at cryogenic temperatures in order to maximize energy sensitivity and obtain (for some designs) spatial and temporal information. Rather than collect the ` " 1 e'v' electron-hole pairs like a standard semiconductor diode detector, these new devices use the characteristically much lower energy ( = 1 meV) phonons to generate a signal . In principle then, phonon detectors are sensitive to energy depositions at least an order of magnitude smaller than conventional (i.e. ionization) detectors, while simultaneously providing better resolution . In addition to the intrinsic limitations on energetics (from the band gap), ionization devices (excluding those of very special design, such as microstrip detectors [1]), provide no spa-

tial resolution or information on event directionality . Furthermore, although the partitioning of recoil energy into phonons, electron-hole pairs and less-available channels (such as sub-gap photons and the creation of lattice defects) differs for nuclear and electronic scattering events, experiments and calculations suggest that in both instances = 70% or more of the recoil energy :., C; appears as nhnnnnc phonons for recoil. PT1PT01PC several keV [2-4] . Thus more event energy is readily available for detection in phonon detectors than in ionization devices . For example, a 10 keV nuclear recoil event in silicon produces = 90% of its energy in the form of phonons. Many groups have reported excellent results using phonon detectors of various designs [5]. Mosley and McCammon et al., are working with small (= 10-5 g) 1 .. .- ..et ... . . L. .. . .., rcccntl d4 silicor, 13û1V111 21a and' laavG lirwucly van energy resolution of = 7.5 eV (FWHM) for 6 keV X-rays [6], Sadoulet et al., are investigating possibilities for simultaneous detection of phonon and ionization signals using neutron transmutation doped (NTD) Ge thermistors [7] . Zehnder et al., using (50 p,m x 50 tim) Sn-SnOxide-Sn tunnel junctions, have demonstrated an energy resolution of = 47 eV (FWHM) for 6 keV X-rays [8] . And Von Feilitzsch et al., have performed an interesting series of experiments with Sri, Al, and Pb heterojunctions, and in a separate experiment with In

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B.A . Young et al. / Detection of elementary particles

Sn junctions have achieved a detector energy resolution (FWHM) of < 60 eV [9] . This group has also exposed Al tunnel junctions to alpha particles, and analyzed the data in terms of ballistic and quasi-diffusive phonon propagation [101. We note that an energy threshold of - I keV and energy resolution of -100 eV is important for our primary interest in developing a detector for neutrino experiments, however these experiments also require large detector masses in order to provide reasonable event rates [11]. Unfortunately, although the experimental results mentioned above are exemplary, the devices used were all of necessarily small fiducial volume and therefore are currently of limited use as part of a large scale experiment . (We note that preliminary results have been obtained using a 60 g Ge detector (Sadoulet) and a 280 g sapphire detector (Von Feilitzsch), however the energy resolution and overall performance of these massive bolometers are significantly poorer than those achieved with the smaller devices .) Our approach at Stanford is to develop silicon crystal acoustic detectors (SiCADs), which use superconductors on the surface(s) of a single crystal of Si to directly sense the non-thermal phonons generated when an incident particle (such as a neutrino) scatters off a nucleus or electron within the Si substrate. We have considered various candidates for the SiCAD phonon sensors, including superconducting tunnel junctions . Our current detector design, however, simply incorporates the use of single thin films of superconducting Ti as the phonon sensors . This design allows for significantly larger detector masses to be instrumented, while not sacrificing excessively on energy resolution . For example, we have already demonstrated both a detector energy threshold and resolution of = 800 eV (at 6 keV) using a = 37 mg, 1 mm thick SiCAD and a 0.2 nCi source of 55 Fe. We are confident that detectors with thresholds below = 1 keV can be built in the near future which will sense non-thermal phonons through at least 1 cm of Si . If constructed using 15.24 cm diameter Si wafer substrates (an industry standard), a 1 cm thick SiCAD would have a sensitive mass of up to 300 g, and could be readily incorporated into a detector array of significant total mass (e.g. = 10 kg). In addition, these detectors would provide x and y position resolutions at the detector surface of bettor than 1 mm, and (from timing measurements) a resolution in z (depth) of < 50 ~Lm . In the following sections of this article, we first give an overview of the phonon processes relevant to SiCAD operation, and then describe SiCAD design and construction in detail . Finally, we describe a series of experiments performed using SiCADs to detect radioactive sources of alpha particles, gamma and X-rays, and neutrons spanning an energy range of = 6 keV to = 10 MeV .

2. Phonon physics The development of a sensitive cryogenic phonon detector requires a thorough understanding of the fundamental phonon processes involved . Typically . these processes are best studied using an experimental system which does not include the new detector itself. Laser irradiation experiments have shown that the initial spectral distribution of acoustic phonons produced by nonradiative transitions in crystals contains a significant high frequency component [12]. This distribution results within the first - 10 ps from the decay into phonons of electrically excited states, the decay of electron-hole pairs to the band edge, and the decay of primary optical phonons to high frequency acoustic phonons. In Si, these processes result in a relative excess of 5-10 THz acoustic phonons, which quickly scatter and decay to lower frequencies (< 1 THz). Within tens of ns, the number density of lower energy phonons significantly increases, the high energy tail of the phonon spectrum essentially disappears, and the overall shape of the distribution becomes relatively symmetric. The approximate symmetrization of the strictly nonthermal initial phonon distribution has been confirmed in Monte Carlo calculations [13] for silicon crystals . These calculations suggest that, to first order, a typical recoil energy of = few keV in Si produces a Planck-like phonon distribution with a characteristic temperature of = 10-20 K. Perhaps more importantly, the calculations show that the frequency distribution of acoustic phonons observed after = 1 ws is essentially independent of the details of the ini', lal phonon spectrum. The rate for the anharmonic decay process is given by TA - To x (1 THz/v)5, where To - 8 p,s, 160 Ws, or 1 ms for = 1 THz longitudinal (L), fast transverse (FT) or slow transverse (ST) acoustic phonons, respectively [14]. In sufficiently pure silicon, the phonon dynamics at frequencies below = 1 THz are dominated by isotope scattering, which occurs at a rate T I = (0.4 ws) x (1 THz/v )° [14]. The anharmonic decay channels L --> L + T and L - T + T dominate the energy down-conversion processes, and isotope scattering is primarily responsible for phonon mode mixing . Because of the high rate of mode mixing, the relative number of L, FT X1'1[1 CT phnTl(1t1Ç 1'PT11a;nc essentially voiiûiani . and is ., approximately given by the ratio of their phase space populations . For Si this is L : FT : ST = 9.4 : 37.5 : 53.1 [14]. Some amount of energy down-conversion and decay into slow and fast transverse modes is necessary for detecting non-thermal phonons over large distances (i.e. ~ 1 cm). In (100) silicon, for example, most of the spatial and temporal information about an event originates from ST and FT phonons with frequencies < l THz. Nevertheless, with an excess number of scattering sites in the crystal the phonon wavefront becomes

B.A . Young et al. / Detection of elementary particles

increasingly diffuse, and much of the event information can be lost. It is therefore important to construct detectors out of sufficiently pure and perfect crystals . Naturally occurring Si contains 92.2°% 2"Si, 4.7Ph 21 Si and 3.1% -""Si. Silicon of approximately this isotopic composition is currently being used to build cryogenic silicon phonon detectors, and we believe it is sufficient for use in future large scale, low threshold experiments as well. Nevertheless, it is possible that isotopically enriched Si will become available (and affordable) for detector construction, since isotopically pure devices might allow determination of event directionality . Recently, a Japanese group developed an optical-chemical technique (which uses laser excitation of Si 2 F6 ) to isotopically separate Si [15]. Using this method, the following single isotope concentrations of Si have been obtained: 99.7% 28Si, = 20% 29Si, = 30% 30Si . In addition to isotopic contamination, the presence of radionuclides and other impurities in silicon could render it useless for low energy threshold and low event rate particle detection experiments. During the purification and processing of silicon, many elements appear, primarily carbon, oxygen, boron, phosphorous and some amounts of radioactive '4C and 32Si. In addition, cosmic ray spallation of silicon directly produces 3H, 22 Na, 7Be and other light radionuclides . Nevertheless, calculations by Martoff [16] show that with sufficient care it is possible to construct intrinsically low background silicon detectors for use in neutrino and dark matter experiments . For these applications, it will probably be important to use Si from underground sources (e.g. mines) rather than sources near the surface of the Earth. When the mean free path for isotope scattering is considerably shorter than the crystal dimensions, one refers to "quasi-diffusive" phonon propagation, whereas when the phonons travel through the crystal with little scattering or dispersion, the propagation is termed "ballistic" . Due to the anisotropy of silicon, whereby the group velocity is not parallel to the wavevector for each of the three phonon polarizations (L, FT and ST), the ballistic phonons become focussed into distinctive -atterns as they r .~ . the mare and cold Z... .7 propagate Y " . ..1. . a-- ._ through have been directly vericrystal [17,18] . These patterns experiments by Northrop and fied in laser heat pulse using indirectly in recent experiments Wolfe [19], and alpha particles and SiCADs [20]. Collection of the focussed energy allows single event imaging with SiCADs, which in turn provides significant background suppression capabilities . This is an important improvement over traditional bolometers, which sense the time-integrated thermalized phonons, and therefore provide no intrinsic vetoing capability.

3. Detector and setup 3.1 . Detector constri,-tion

The experiments described below were performed using 1 mm thick, double-sided silicon crystal acoustic detectors (SiCADs). Each detector contains four independent channels (two on either side of the Si wafer substrate), although only two channels were instrumented at a time. Each channel (sensor) consists of a a 400 A thick film of superconducting titanium laid down in a labyrinth pattern on the (100) surface of the single crystal Si wafer substrate (see fig . 1). Each labyrinth pattern contains 400 parallel lines (2 wm wide, 5 gm pitch) and is aligned with the [1 10] axes of the wafer . Each of the four rectangular sensors covers an area of 4 mm x 2 mm, for a total active area of 4 mm x 4 mm when two immediately adjacent detector channels are instrumented . We have developed a technique for aligning these patterns on both the front and back sides of the wafer so that the two pair of sensors coincide when viewed along the [100] axis. On both sides of the detector a single 5 Wm wide line of Ti (also 400 A thick) lies around the perimeter of the combined 4 mm x 4 mm sensor area, and is used during a run to directly monitor the detector operating temperature . The devices are fabricated in a "class 100" facility at The Center for Integrated Systems (CIS) at Stanford University using photolithographic techniques . High purity, doubly polished, intrinsic Si wafer substrates [211 with p > 1500 S? cm are first cleaned, but not stripped of the = 20-25 A thick native oxide layer. Next, in two steps. both sides of the wafers are metalized with 400 A of titanium using a Balzers 450 sputtering system under high vacuum (= 10-8 Ton). Our first attempt at this procedure produced front and back side films which differed on average by < 10% in thickness . This variation resulted in a difference in superconducting transition temperature on the two sides of only

0

E F

Fig. 1 . Meander patterns of two adjacent Ti transition edge sensors on the surface of a SiCAD.

198

B.A . Young et al. / Detection of elementan, particles

7 mK (r+ 1.6%a), which was sufficient for using the films as double-sided detectors. A modified Canon FPA-141F step and repeat projection aligner is used to expose the Ti films, using a procedure which both ensures proper mutual alignment of the front and back side patterns and protects the metalizcd wafer surface% from sustaining mechanical damage. Positive photoresist is used, and the films are etched using a solution of deionized water, hydrogen peroxide and ammonium hydroxide (5 :1 :1) - a process which also serves as an initial differential thickness monitor for the two Ti films. By properly covering the thinner of the two films after the initial etch, one can continue to etch the thicker film until the difference between them is minimized, thereby constructing very well-matched front and back side detector channels. The nine 4-channel SiCADs on a processed wafer are separated using a Kullick and Soffa dicing saw which accommodates substrate thicknesses greater than 1 cm and, when carefully used in conjunction with a porous chuck and protective tape, causes no damage to either surface of the patterned wafer. Each SiCAD is mounted in a specially designed nonmagnetic holder, and electrical contact is provided with an ultrasonic wedge bonder using 0.001 in. diameter Al(1% Si) wire. We note that, in principle, the fabrication processes discussed above can be extended in a rather straightforward manner to produce multi-channel SiCADs of significantly larger active areas and masses. Furthermore, with the advent of new fabrication technologies, including improved machine capabilities, the processing of SiCADs will only become easier. 3.2. Cryogenic apparatus The SiCADs are run in a sealed 3He refrigerator which utilizes = 5 liters (STP) of 3He and was designed by Neuhauser [22]. The heart of the probe is an activated-charcoal sorb, which is located about 3 of the way up from the bottom of the probe and is weakly coupled to the pumped liquid 4He bath. In order to initially cool the probe from 1.6 K (pumped liquid 4He) to our operating temperatures, the sorb is first heated using a resistive coil until it reaches a temperature of 25 K (= 5 min). During this time, any 3He which had been adsorbed in the charcoal is driven off and begins to condense into a small copper pot which is thermally anchored to the sample and located at the bottom of the probe . After about 10 min the condensation is complete and approximately 3 cm3 of liquid 3 He has dripped into the pot . Soon thereafter, the sorb begins to cryopump the liquid 3He, and further cools the sample to a base temperature of = 250 mK. A SiCAD can be mounted at room temperature and cooled to 250 mK in less than five hours . Under normal operating conditions, the probe can accommo-

5m 4cß

3

Û 2a

O 380

a .

400

dßJ-i e

420

440

460

Î 480

Temperature (mK)

Fig. 2. (a) Resistive transition for a titanium transition edge sensor . (b) Expanded view, to show the "dc foot" of the transition.

date a total heat load of - 100 mW while providing = 11 wW of cooling power at 260 mK. It can be used for up to = 20 hours before requiring additional liquid 4He, and can be thermally recycled in less than one hour simply by transferring = 3 liters of liquid 4 He and reheating the sorb. In a typical run we use two cryogenic preamplifiers with a combined power dissipation of = 24 mW. This raises the base operating temperature to = 272 mK and decreases the hold time, but still allows for = 12 hours of continuous operation at = 400 mK. 3.3. Operating parameters /device characteristics The devices are operated over an appropriate temperature range just below the superconducting-to-normal transition (0.90Tc _< T<_ 0.97T,,), and each active channel of the detector is independently current biased such that self-heating effects are small (Ib = 100 nA) . The thermodynamic transition temperature of the Ti films is typically = 435 mK (measured at = 90% of the normal-state resistance) Î23l, as seen in fig . 2a. The, narrow 10%-90% width of = 5 mK is evidence for high uniformity across the full 4 mm x 4 mm patterned sensor area and the "dc foot" seen in the resistance curve at temperatures between = 410 and 425 mK (fig. 2b) likely results from the S-I-S tunnel junctions formed between the AIM) bonding wires and the Ti contact pads. Based on the results of crystallographic analysis of our Ti films [24], we conclude that the Ti transition edge (TE) films are predominantly in the form of a highly ordered crystal and contain little

/ Detection ofelementary particles

B.A. Young et ai.

0.8 0.6 E

1-1

0

0.4 0.2 0 0

5

t0

1.5

20

gsec

Time Fig. 3. Typical pulses (obtained under constant operating conditions) for 60 keV gamma rays incident on the back surface of the detector.

amorphous structure . This result is consistent with our measured value of the electrical resistivity of the Ti films (p = 30 Wl cm). During runs, temperature stabilization to better than 0.3 mK is routinely achieved using a feedback resistor located on the detector mount. The temperature is continuously monitored using both a calibrated germanium resistor located on the sample mount and by measuring the resistance of a superconducting thin film reference line photo]ithographically deposited on the detector . The thermal cyclability of the SiCADs is excellent . At least five detectors have each been cycled

more than 20 times from room temperature to < 300 mK, and not one detector has failed as a result . Typical pulses (from a 60 keV X-ray experiment) are shown in fig . 3. The pulses occur because sufficient phonon energy density reaches the surface of the dctcctor to drive portions of the superconducting titanium film normal. We note that titanium provides a good acoustical match for silicon (p' v differs by = 15%, where p' is the mass density and l', the velocity of sound), which helps minimize the amount of phonon energy lost at the interface [25]. The pulse risetimcs are electronics limited to r, ;-> 140 ns, however, this risctimc does not adversely affect the timing resolution in our coincidence experiments. The pulse height is given by V= I x Reff, where 1 is the bias current and Rerr is the effective normal resistance of the Ti sensor. Ideally, the pulse height is simply proportional to the area of sensor driven normal . In practice, however, the pulse height is limited by a 60 kfl/p,s slew rate determined by the total capacitance in parallel with the detector. At these frequencies, the preamp has an effective input impedance of Zo = 300 kf1 which, for large amplitude signals (when the film resistance R is comparable to Zo), results in a pulse height suppression given by Reff = R Zo/(R + Zo). An "equivalent circuit" model of the SiCAD and front-end electronics is shown in fig . 4. We have included contributions from the transition edge sensor do and phonon signal resistances, the sensor magnetic and kinetic induetances, and the relevant electrical parameters of the coupling electronics. The pulse length is related to

RLoad

Vo = 9V R' = 2 kn r,,+ R = Ti Sensor Resistance

RLoad =15MQ RAmp = 1 Mn

CAm p 15 pF (incl. stay Cap.) Lo + LK = L K= 290 nH

Fig. 4. Equivalent circuit model of the SiCAD and front-end electronics.

B.A. Young et al. / Detection of elementary particles

20 0

the thermal relaxation rate of the sensor at the Ti/Si interface, which is -, 2 p.s. As later discussed in the X-ray section, a measurement of the pulse length provides important information about the event location (depth into crystal). To estimate the threshold energy density ( .EE,) necessary for the superconducting to normal state transition, we integrate the heat capacity of the superconductor from the bias temperature to T, :

calculation (tabulated result from external sources for bulk samples) and the actual value of N(0) for our films . Such variations of N(0) for titanium have been observed . For example, independently measured values of T, and the thermodynamic critical field HJT) for "pure" titanium samples [271, combined with the following two equations :

Ep =

H,,(0) = 03T,,( - dH~/dT )T_T,,

JTTsC,,Q(T) dT,

where C,.s is the electronic heat capacity below Tc as given by the BCS theory . We assume that the time constants are sufficient to allow quasi-thermal equilibrium. The asymptotic form near Tc is: EP = 5.14N(0) ,12(l - T/TC), where AO is the gap at T = 0 and N(0) is the density of states at the Fermi surface in the normal metal . For our Ti films, N(0) - 4 x 10 22 cm -3 eV-1 and D o - 47 peV, yielding EP = 22 eV/wm3 at T/Tc = 0.95 . In terms of the energy density per unit area of film, E,, we get EQ -- (22 eV/p,m3) x (40 nm) = 0.88 eV/wm2. At a slightly higher operating temperature of TIT, _ 0.97 (a very common operating condition), we get Ea 0.53 eV/p,m2. This sensitivity is nearly 10 times better than that achieved with our earliest SiCADs, which used superconducting aluminum for the phonon sensors (= 400 A thick films, Tc = 1 .35 K). Experiments performed with the aluminum TE sensors (and less sophisticated electronics) have been described elsewhere [26]. We can estimate the minimum detectable energy deposited in the Ti sensor as follows : In our current experimental setup we have an amplifier noise level of AVrms = 1.1 nV/ Hz at 1 MHz. At T/T,, = 0.95 and a bias current (I) of 160 nA we can detect a minimum sensor resistance of ARrms = 4~Vrms,IMHz/I = 6.9 l. At T >_ T, the resistance of our sensor is = 17 kiZ per 2 p,m wide line, or 8.5 l per 2 gm. x 2 pm square of the Ti film. Therefore the area of film which corresponds to a normal area resistance of ARrms = 6.9 fl is (6.9 11/8.5 fl) x (2 p,m x 2 p.m) = 2 pm x 1.6 gm. The minimum detectable energy deposited in the Ti sensor is then A Erms < EQ X Area ,m, = (0.88 eV/ gm2) x (3.2 Lm`) = 2.8 eV. This energy corresponds to = 550 phonons of frequency 1 THz. The inequalit,., holds because Joule heating contributes to the actual area driven normal . In addition, we note that our recent data indicate that EQ may be nearly a factor of three smaller than this approximate heat capacity calculation suggests. It is likely that this apparent (experimental) enhancement of the energy sensitivity EQ is in part due to a discrepancy between the value of N(0) used in the

N(0) = 0.701 H,,-'(0)/8, r(kT,, )2

and yield N(0) = 0.62

x 1022 cm -3 eV- x [27a]

and

N(0) = 4 .16 x 10 22 cm-3 eV- x [27b]. 3.4. Electronics We use cryogenic GaAs MESFET (Plessy P35-1101) voltage-sensitive preamplifiers [28] which have a bandpass from = 1 kHz to 10 MHz and AV., -1.1 nV/ Iili (at 1 MHz). These devices have an input capacitance of = 2.5 pF and provide a voltage gain of up to = 3.5 dB into 50 11. The preamps are mounted below the sorb and are thermally coupled to the pumped liquid 4He bath at = 1 .6 K. When operated at maximum gain, each preamp dissipates = 12 mW into the bath. Although this relatively high level of power dissipation limits the number of preamplifiers which can be simultaneously operated during an experimental run, it is quite straightforward to use two . (Most recently, we have used preamplifiers of a modified design . When operated in a single-stage configuration, each preamp has a power dissipation of only 1-2 mW while maintaining a similar noise level and bandwidth .) The output of each preamp is fed into a Trontech amplifier (model W50-ATC or W40C-6) at room temperature. After further amplifying the signals using an Ortec 474 shaping amplifier, a Tracor Northern 7200 multichannel analyzer is used to obtain pulse height spectra for each individual channel. All data is processed and stored using a Macintosh SE computer which contains an IEEE-GPIB interface board manufactured by National instalments inc . When running time-coincidence experiments, the outputs from the Trontechs are fed through additional electronics which provides us with a trigger for pulse pairs occurring within an 800 ns window . These time-coincident signals are then fed into a Philips 3320A digital storage oscilloscope, which can be used to directly measure various time and amplitude characteristics of the incoming traces, and greatly aids our online analysis. In addition, we typically record = 104 pair of the fully digitized

B.A. Young et al. / Detection of elementary particles

as an alpha source. The alphas have a range of -= 25 Wm in silicon, with increasing dE/dx towards the end of the track, and provide well-localized and relatively high energy events near the surface of the 1 mm thick detector. Three different source-dctcc¬or geometries were used : F/F, B/B, and F/B, where the labels F for frontside and B for backside refer to the location of the detector channels relative to the position of the source.

1000 c 800 0 U ô 600

z

400

4.1. Front/ bac k alphas

200 0

0

10

20

30

40

Energy (keV)

so

60

Fig. 5. Reference spectrum of the encapsulated -'4'Am source used in these experiments . The spectrum was obtained using a Si(Li) detector operated at 77 K.

coincident traces at many operating temperatures for later use in offline analyses. 4. Alpha particle experiments The series of experiments described below (also see ref. [20]) were performed using a 24 WCi source of 24'Am. The decay spectrum of 24'Am includes several alpha lines around = 5.5 MeV, a nuclear gamma at 60 keV, and atomic X-rays at 18 and 14 keV (fig. 5). In these experiments, however, the 24'Am was used only

(FB)

In the F/B runs, the alpha particle source was collimated using a 150 l,m diameter hole cut through 250 Wm thick Mylar. The hole was aligned with the centers of the F and B sensors (fig. 6a). In one series of experiments, we digitally recorded the leading edges of signals simultaneously detected on the front and back sides of the detector for several operating temperatures . These time-coincidence runs utilized an 800 ns timing gate, which was the fastest gate our electronics could provide and was sufficient for avoiding pulse pile-up . An expanded view of the time coincident alpha pulses is shown in fig 7a. The sharp and relatively small step preceding the onset of the primary (transverse phonon) signal is consistent with the earlier arrival of longitudinal phonons at the detector surface, and the ramp which extends from the baseline to the leading edge of the signal may provide useful information on the ionization produced by the scattering event. Initially, these secondary features introduced sizable systematic errors into our time-delay analysis. However, by differentiating the digitized traces offline (see (F/F), (B/B)

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m l~,

t[

tttttttttt Source

1001

3

Source

Fig. 6. SiCAD source/detector geometry showing (a) "hole" geometry for the F/B experiments and (b) "slit" geometry for the F/F and B/B experiments.

2

B.A . Young et al. / Detection

of elementary particles For each signal, the differentiation was performed by replotting the n digitized voltage pulse points P(n) as a sequence of differences P'(n):

P(n) -P'(n) =P(n +x) - P(n -x) .

t

The original pulses contained it = 512 digitization points, and the differentiation parameter x was typically chosen equal to 2. This simple point-for-point transformation effectively sharpened the leading edge of the primary signal and de-accentuated the secondary features, allowing for an unambiguous determination of the time delay between coincident transverse phonon pulses. In addition, the validity of this analysis technique is supported by the fact that the measured (differentiated) time delays are essentially independent of the value chosen for x. The time delays for at least 200 pairs of (differentiated) F/B traces were separately histogrammed for each operating temperature, and the mean of each distribution was used to plot the graph shown in fig . 8. The point size is an estimate of the timing uncertainty due to the finite energy spread of the collimated alpha source (= 15% FWHM), as well as the systematic errors which enter into the analysis as a result of the slightly different operating characteristics of the F and B sensors. By comparison, the statistical errors of _< 1 ns are small . The dotted lines represent the time delay expected for ballistic propagation, as given by the speed of sound for transverse phonons in our detector. (The faster, longitudinal phonons contribute negligibly to the signals .) The separation of these lines results from our non-ideal alpha source, which provides a distribution of event locations (depths into crystal), and therefore introduces an uncertainty in time delay between coincident signals for even purely ballistic propagation . As shown, the observed time delays decrease with

Time (4 nsec / pixel)

Time (4 nsec / pixel)

Fig. 7. (a) Leading edges of a typical F/B time-coincident alpha pulse pair . (b) Expanded view, to show structure on the leading edges.

fig . 7b), we minimized these errors and increased the precision with which we could determine the time delay between coincident F/B signals. 0.98

Ballistic Time

0.97

E~'

w

0.96

0 0

0.95

0

0.94 0.93 0.92

0

0

40

80

120

160

200

240

280

Time Delay (nsec) Fig. 8. Temperature variation of time delays for coincident F/B alpha signals. The vertical dotted lines correspond to ballistic phonon propagation in the detector .

B.A. Young et al. / Detection of elementaq partic cc

increasing operating temperature, varying from At 263 ns at 0.92T, to At - 166 ns at 0.96T, (a typical operating temperature). At operating temperatures above = 0.96Tc , the measured F/B time delays are consistent v%ith ballistic phonon time-of-flight . At lower temperatures, however, the energy density contained in the ballistic component alone is no longer sufficient to drive the requisite portion of superconducting Ti film normal, and diffusive phonons which arrive later begin to strongly influence the timing spectra . We can use the temperature dependence of coincident F/B timing data to better understand the contribution of ballistic phonons to the backside signals. To do this, we calculate the ratio R: R = ®Thallistic/OTmin

=

(Tc -

R = 19 mK/50 mK - 0.38. However, this calculation assumes a linear dependence of the detector energy sensitivity EP on (T - Td, which is strictly valid (near Tc) only below = 0.90 Tc (i.e. below = 392 mK for this film). At 0.96Tc (i.e. 416 mK), the correction to EP from terms of higher order in (T- Tc) is = 10%, yielding: =

(1-1) (19 mK) /50 mK = 0.42.

Our value for Rcorrected suggests that ballistic phonons alone are sufficient to produce a phonon signal for the warmest (lowest) = 42% of the detector operating temperatures (thresholds), and that for over = 58% of the operating range the arrival of slower quasi-diffusive phonons is required before a signal will be detected. Thus, to first order, R provides an estimate of the height of the ballistic phonon "spires" relative to the quasi-diffusive phonon "hill" in the admixed 3-dimensional phonon energy density distribution (described below, and shown in fig. 10) most appropriate for our alpha particle experiments . It is important to note that R does not directly indicate the partitioning of energy between the ballistic and quasi-diffusive components. tV /T2 r ., ...,~, L dat can also 1"..~ be displayed ;., Drl H ~,.5 DLT H plots, 1 such as those shown in fig . 9 for the case of F/B signals detected over a range of operating temperatures (or, equivalently, detector energy thresholds) . In each plot, the dark spot corresponding to maximum signal size in the F and B sensors appears as a result of the localized energy loss mechanism for alpha particles in silicon . The size of this spot is proportional to the finite width of the source energy spectrum, and the long and fairly dense "tail" which extends to zero pulse l

T=401)mK

r .r.;' .

T = 395 mK

Thallistic)/(Tc - Turin )

where Tin is the minimum temperature at which F/B coincidences can be detected, and Tballictic is the temperature at which the time delay between F/B signals is consistent with ballistic propagation in the detector. Using Tc = 435 mK, Turin = 385 mK, and Tthallistic = 416 mK (see fig. 8), we get

R corrected

2tî3

111

1

1

T=390mK

T = 385 mK

Pulse Height Front Channel Fig. 9. Pulse height vs pulse height distributions as a function of detector operating temperature for time-coincident F/B alpha signals. height results from events which fully penetrate the edges of the collimator . Preliminary calculations suggest that the "shadow" line, which accounts for = 2% of the count rate and also merges with the dense spot, may be consistent with alpha particles which have channeled along the crystalline axes of the detector. In general, although the probability for channeling in crystals is relatively low, its effect can be significant . In silicon, for example, a 5 .5 MeV alpha which channels along the [ 100] axis can have a range of = 50 Wm [29]. We note that the signals detected by the frontside sensor are larger than those observed on the backside at every operating temperature . This effect results from the relatively high density of scattered phonons which exceed film threshold (at every temperature) and strike the front surface . And finally, there exists a minimum temperature of = 0.89Tc ( = 385 mK for this film), below which the Ti file, is. not sufficiently sensitive to "see" alpha events through the 1 mm thick crystal . Although F/B timing experiments are quite useful for studying the responsivity of sensors and many aspects of the phonon dynamics, phonon focussing effects are better studied in F/F or B/B coincidence experiments . These experiments, in which we instrument both channels on the same side of the detector and record the pulse heights of (F/F or B/B) timecoincident signals, allow for a direct mapping of the

B.A . Young et al. / Detection of elementary particles

204

-.

\ FT -

ST+F1. 1 l r

ST f. t

(b)

(c)

~

si, (d)

P~ , i'

/M-l \ (e)

Fig. 10 . (a) Calculated ballistic phonon energy density incident on the (100) surface of Si for a point source at a depth of 1 mm. (b) to (e) Slices through the distribution and perpendicular to the [100] axis . phonon focussing pattern incident on the surface of the detector . Fig. 10a shows the calculated ballistic phonon energy density spectrum as viewed along the [100] axis of Si, for a pointlike event occuring at a depth of 1 mm. By operating the detector at different temperatures, we can image successive two-dimensional slices (parallel to the (100) plane) of this distribution . Four such slices, corresponding to detector thresholds of 2 .5, 2 .0, 1 .0 and 0.5 eV/p,m 2 , are shown figs . 10b to 10e . In addition, as discussed below, we can ascertain the fraction of ballistic phonons contributing to our signals by comparing the two-dimensional slices with results of Monte Carlo calculations, in which we assume various admixtures of ballistic and diffusive phonons. . For the F/F and B/B runs described below, the alpha source was collimated using a 250 gm thick Mylar mask which contained a 125 p,m wide slit . The slit was placed perpendicular to the boundary between the two Ti sensors, and to first order irradiated the channels equally (see fig . 6b) . 4.2. Back/ back alphas Fig. 11 shows a family of PH vs PH plots for a SiCAD instrumented in the B/B geometry. Each plot is effectively a projection of the above-threshold portion of the phonon energy density distribution striking the (10 0) surface of our detector (see fig . 10) . At the lowest temperature shown (400 mK), a high density

region is clearly visible along a line corresponding to equal pulse heights in the two channels (fig . I la). This nearly equal partitioning of energy results from the almost simultaneous arrival of FT and ST phonons, which when taken together first appear in energy density space as a set of four "spires" . These spires lie perpendicular to the (100) plane, and define a square parallel to the [110] axes. As the temperature is raised, this line becomes less pronounced, and two triangular features appear, corresponding to a relatively large signal amplitude in one channel and a small one in the other (fig . I 1b) . The triangles result from energy deposited in the film by FT phonons, which when projected onto the (100) plane form a "cross" of reasonably high energy density that intersects the four spires . At yet higher operating temperatures, the triangular regions remain well defined and expand towards larger pulse heights (fig . llc). At such low thresholds, the more dilute and previously ineffective ST phonon "ramps" contribute to the signals . These ramps, when viewed in the (10 0) plane, appear between the arms of the cross, as shown in fig . 10e . The location of each feature observed in fig . 11 is independent of temperature, and reflects the temperature-invariant spatial distribution of focussed phonons incident on the detector surface . The location is temperature-independent because there exists an exact (inversely proportional) equivalence between scanning the energy of the alpha particles and scanning the film threshold by varying the temperature . Finally, in fig . 11 d, we show the superposition of B/Ii data obtained at four discreet operating temperatures (400, 411, 413, and 414 mK) . The high contrast data observed in experimental B,/B plots, coupled with Monte Carlo calculations, suggests that approximately one third of the phonons striking the back surface of the detector within the first gs arrive balli ;tically [30] . This value of = 3 was obtained by qualitatively comparing the B/B data to a family of calculated B/B PH vs PH plots, which were constructed assuming various admixtures of ballistic and quasi-diffusive phonons . Two Monte Carlo calculations were initially performed, corresponding to either 100% or 0% phonon focusing . In both cases, a pointlike interaction region was assumed, and an event energy of 5 .5 MeV was partitioned into 8 x 10 6 phonons . In the calculations, individual phonons were tracked from the location of the initial scattering interaction to a projected depth of I mm . We tracked phonons propagating into 2 ,rr and appropriately doubled the result . Because of the two-fold symmetry of our model (i .e . propagation either parallel or antiparallel to the [100] axis is equivalent), this calculation retained the statistics of a full calculation into 4 ,rr . The statistics were further improved a factor of four (uncertainty reduced a factor of 2) by utilizing the 4-fold degeneracy in the (100) plane, and another factor of

B.A. Young et al. / Detection of elementary particles

205

4

3

0

Pulse Height (mV) Pulse Height (mV) Fig. I l . Coincident pulse height distributions obtained with backside sensors (B/ B) operated at (a) 400, (b) 411 and (c) 414 rnK. (d) Superposition of data obtained at 400, 411, 413 and 414 mK.

four was gained using a weighted average (in the plane) over nearest neighbor bins (2 Wm x 2 Rm detector pixels) . For the weighted average, each bin was replaced by â of its value plus 8 the value of each of its four nearest (adjacent) neighbors plus 16 .I the value of its four diagonal neighbors . The calculation corresponding to 100% phonon focusing was performed assuming a pure crystal of (anisotropic) Si and purely ballistic transport (i .e . isotope and impurity scattering were not included) . The quasidiffusive component (i .e . 0% phonon focusing) was modeled by an isotropic distribution of phonons . In

both cases, surface effects and phonon mode conversion were neglected . Results of the two separate phonon calculations were then combined in various proportions (i .e . ballistic : quasi-diffusive components = 1 : 0, 2 : 1, 1 :1, . . . , 0 : 1) and used to construct a family of two dimensional pulse height vs pulse height distributions . As an example, we show in fig . '.2û t c calculated pulse height distribution for the B/B geom-

etry assuming purely ballistic propagation. The radial lines in fig . 12a correspond to B/B coincidence events for which the center of the projected phonon pattern is in a fixed position relative to the line separating the two sensors. The azimuthal lines correspond to equal intervals of the source energy or, equivalently, the operating temperature (and therefore energy sensitivity) of the detector. Thus, fig . 12a allows us to identify each event in fig . IId with both an alpha energy and a position in the (10 0) plane . For comparison, we show in fig . 121) the calculated B/B distribution corresponding to purely quasi-diffusive propagation, and in fig . 12c, the distribution corresponding to 75% quasi-diffusive +25% ballistic phonons . The calculated three-dimensional phonon energy density distributions corresponding to figs . 12a-12c are shown in figs. 13a-13c . We note that the ballistic phonon spires account for 0.50 of the height of the energy density distribution shown in fig . 13c, which is = 20% greater than the relative height of the spires estimated using our F/B

B.A. Young et al. / Detection ofelementary particles

206

timing data (R = 0.42). Because fig. 13c corresponds to a 25% ballistic phonon contribution, we conclude that the time-delay data imply a ballistic component can the order of = 20% . We have less confidence in this result (compared to the B/B result of = 30%) because of systematic uncertainties in the temperature measurements. However, the results from the F/B timing experiments and the B/B pulse height vs pulse height experiments are consistent with each other at this level of uncertainty . We caution that these results on the ballistic transport may be significantly affected by the proximity of the surfaces to the alpha event location [30]. We cannot blindly assume that the same proportionality of ballistic : quasi-diffusive phonons arriving at the back surface would result from events deep in the crystal . For the alpha events, the back surface of the crystal collects significantly less than half of the quasi-diffusive component but exactly half of the ballistic component, thus enhancing the ratio. In addition, the metal film nearest the event region (i.e. on the front surface) may

-800

-640

-480

reradiate lower energy phonons with sufficient intensity to further enhance the ballistic component striking the back surface of the detector . 4.3. Front /front alphas The results of a series of F/F alpha experiments are shown in fig . 14. In comparison to the B/B pulse height distributions, the absence of features in the F/F data is striking, and largely results from the close proximity of the front surface to the alpha interaction region . Although small phonon focussing patterns must exist on the front surface, they are fully obscured by scattered and reflected phonons which dominate the F/F signals at every operating temperature . The single band of high intensity seen in fig. 14a corresponds to essentially full energy alpha events, and its constant density is further evidence for excellent film homogeneity . The distribution of events down to low energies results from the finite collimation and energy spread of the encapsulated source, as was seen earlier

-320

-240

-160 -120

Position (microns) -80 0

s O U

xU

0 (a) Resistance (k-Ohms)

Fig. 12 . Calculated B/B pulse height distributions assuming (a) purely ballistic phonons, (b) purely quasi-diffusive phonons and (c) 25% ballistic + 75°k quasi-diffusive phonons.

B.A . Young et al. / Detection of elementary particles

in the F/B data (fig . 9). The small, dense region just above the electronic thresholds of the two channels is due to 60 keV X-ray events which interact within 180 I,m of the front surface (discussed below), and the gaps which open along the baselines at higher pulse heights result from alpha events for which the above-threshold portion of the phonon pattern is not fully contained within the combined 16 mm2 sensor area. The absence of phonon focussing on the front surface is confirmed in fig. 14b, which was experimentally obtained by continuously ramping over a wide range of operating temperatures. In addition, these results are in agreement with the F/F pulse height distributions predicted using Monte Carlo techniques, where (again for a simplified model) we assumed significant phonon scattering and reflection, but no focussing [30]. 5. 24'Am gamma and X-ray experiments 5.1. Single channel experiments

Our earliest (single channel) alpha detection experiments using Ti sensors were soon followed by lower

207

energy X-ray experiments [311, in order to more accurately determine the detector energy threshold and sensitivity. However, the analysis of these data was complicated by the exponential attenuation lengths of the X- and -y-rays. (For 60 keV gamma rays in Si, the 1/e attenuation length is = 30 mm. This is 30 times greater than the thickness of our detector, which implies an approximately uniform distribution of interaction depths .) And because in these early experiments the data were obtained using room temperature amplifiers (C = 200 pF), the pulses had long risetimes and provided little temporal resolution. Nevertheless, by applying thermodynamic principles we were able to directly measure the distribution of signal amplitudes as a function of distance into the crystal. In this way, a single channel SiCAD was used effectively as a position-sensitive spectrometer, as discussed below. We again used a 24 WCi source of 24'Am, however the source was now covered with a 125 R,m thick sheet of Sn. This absorber stopped the 24'Am alphas and low energy X-rays, but merely reduces the intensity of the 60 keV gammas by = 47%. Alphas and 60 keV gammas which interacted in the Sn produced 25 keV (K.) secondary radiation by atomic photoexcitation, and an

E O

U C U

(b) Resistance (k-Ohms) Fig. 12. (continued)

B.A. Young et al. / Detection of elementary particles

208

-80

Position (microns)

0

E0

0 U

e cC

l 20 60

5

j

240 MOM

r-

400 560

p

50

0

100

(C) Resistance (k-Ohms) Fig . 12 . (continued)

8 keV (K,,) X-ray line was produced by photoexcitation within the Cu sample mount . In fig. 15, the observed pulse length vs pulse height is plotted for each event in a Sn-absorber X-ray experiment. Three high density bands are clearly visible, corresponding to 60, 25 and 8 keV incident radiation . For each event, the pulse length is roughly inversely proportional to the depth of interaction squared, and by measuring the pulse duration we can separate out two branches for signals of identical pulse height and incident particle energy. The relative pulse lengths are determined on-line from measurements of both the maximum (PH) and mean (MEAN) voltage levels of each signal (length a MEAN/PH). In addition, length vs peak plots are generated off-line, where we use digitized trace files to directly measure each pulse height and length . There, the pulse length is the time during which the signal exceeds a set voltage threshold (typically twice the noise level on the leading edge of the signal). A relatively short pulse corresponds to an event which occurs deep into the crystal, since little excess energy is deposited into the film and the sensor quickly relaxes to

its superconducting state. By comparison, an event of equal pulse height which occurs very near the sensor produces many highly heated regions in the film, resulting in a significantly longer thermal relaxation time, and therefore a longer pulse length . This relationship between pulse length and interaction depth has been confirmed in Monte Carlo calculations, in which (at a given threshold) we determine the pulse height by integrating the projection of the above-threshold portion of the phonon focussing pattern incident on the sensor area. A similar, single channel experiment was performed using the z4'Am source and a 125 Wm thick Pb absorber. Again, the relative pulse lengths were determined online by using a digital oscilloscope to measure the peak and mean voltage levels of each signal . A 250 R.m thick layer of mylar was placed between the source and Pb absorber to avoid the (albeit improbable) alpha-initiated production of secondary 75 keV (K,,) Pb X-rays (which would primarily Compton scatter in the SiCAD). The SICAD was oriented such that its active channel was unexposed to the secondary Cu radiation .

B.A. Young et al. / Detection ofelementary particles

209

The results of this experiment are shown in fig . 16, in which the single band corresponds to 60 keV X-ray events . The relatively high event rate observed at shallow depths (long pulse lengths) and small pulse heights Gee arrow in fig . 16) results from secondary (L-shell) electrons produced within the 1 absorber . These electrons have energies up to 48 keV (E = 60 keV EBinding)- Most of the ejected electrons are reabsorbed in the Pb, but those produced in the finial = 12 p.m of the Pb can exit the absorber and strike the SiCAD, producing a phonon signal. Furthermore, because of the limited range of these electrons in Si (up to = 34 p.m), nearly all such events occur in the SiCAD at shallow depths. A 125 p.m thick sheet of mylar placed between the Pb absorber and SiCAD effectively filters out the Pb electrons, and the corresponding high-density region in fig . 16 disappears. In another set of single channel experiments, this time with a 299-line Ti TE sensor, we measured the

0

2

4

6 8 Pulse Height (mV)

10

Fig. 14. (a) Coincident alpha particle pulse height distribution obtained with adjacent front side sensors (F/F) operated at 412 mK. (b) Similar F/F data obtained by smoothly increasing the operating temperature from 390 to 414 mK.

Fig. 13 . Calculated 3-dimensional energy density distribution incident on the (100) surface of Si for a point event located at a depth of 1 mm and for (a) purely ballistic phonons, (b) purely quasi-diffusive phonons and (c) 25`( ballistic + 75% quasi-diffusive phonons.

pulse height spectra obtained when a Pb or Sn absorber was placed between the 24'Am source and SiCAD. These absorbc. s stopped the alphas and low energy 24'Am X-rays, but were essentially transparent to 60 keV gamma rays. The observed shapes and count rates for all spectra obtained (for various operating temperatures, bias currents and absorbers) were consistent with the calculated values. Fig. 17a is a pulse height spectrum obtained with a 125 wrn thick Pb absorber, and fig . 17b was obtained using a 125 p.m thick Sn absorber . In both cases, the prominent photopeak at high energy is due to 60 keV gamma rays which interact in the Si, and the sharp feature at lower energy is consistent with detection of the 8 keV secondary Cu X-rays discussed above. As expected, the positions of the 60 keV and 8 keV peaks are the same in the two spectra. The additional peak which appears in fit ;. 17b at intermediate energy corresponds to 25

B.A. Young et al. / Detection of elementary particles

210

U U O 2

0 0

Pulse Height (mV)

Fig . 15 . Plot of pulse duration vs pulse height for 60, 25 and 8 keV events observed in a single channel Sn-absorber experiment.

keV K a X-rays produced from the photoexcitation of Sn. Finally, using the multichromatic spectrum produced by the 24~Am source with a Sn absorber, we

experimentally determined that the scaling of SiCAD signal pulse height with incident X-ray energy is given approximately by E a PH' t 5 .

.7 .6

.4 .3 .2 .1 0

0

100

200

300

Pulse Height (mV)

400

500

Fig . 16 . Mean/puls e height ( (x pulse length) vs pulse height obtained with 60 keV gamma rays in a Pb-absorber experiment . The high density region marked with an arrow results from secondary electrons produced in the Pb absorber .

B.A. Young et al. / Detection of elementary particles

and Sn absorber described above. The two distinct and very uniform bands seen in this plot correspond to 60 keV 24'Am -y-rays and 25 keV Sn (K,,) X-rays, with evidence of 8 keV Cu X-rays present at very low pulse heights . These bands appear near maximum pulse heights as a result of the increased probability for simultaneously triggering both B/B sensors for large spot sizes. The distribution from each band to lower pulse heights results from the I/e attenuation length of the X-rays as well as the finite extent of the source. We can estimate the area of film driven normal for 60 keV events by triggering above the 25 keV signals, and measuring the count rates for both coincident (ChA AND ChB) and total single-channel (sum of ChA OR ChB) events. We then calculate :

ô

0 0

-

0 0 0

15 a

C

s

1

keV l

25

d = (2wN,,/Ns)/(1 +NcINS),

2

C

where N,(N.) is the rate for coincident (single-channel) events, d = "diameter" of normal region, and w = width of each sensor (2 mm). For TIT, = 0.97, we get d6o 100 wm. For comparison, a similar calculation for 5.5 MeV alpha particles gives da = 500 gm. For a gamma or X-ray of given energy, we can estimate the interaction depth D corresponding to maximum pulse height by scaling the X-ray results to data obtained using alpha particles, for which the energy deposition is well-defined in both magnitude and direction . Neglecting effects due to phonon focusing, we obtain a lower limit on this interaction depth:

s

0

U

10 Min Run

0

100

200

Channel Number Fig. 17. Single channel pulse height spectra obtained with an 24'Am source and a (a) 125 ~Lnz thick Pb absorber (b) 125 Wm thick Sn absorber. 5.2 . Double channel (coincidence) experiments

In fig. 18, we present the results of a B/B X-ray experiment, in which we again used the 241Am source 2

402 mK (3500 cts)

D.Y=D«(ExIE«) i~~(

EQaIEQx) tl2 .

Using Da = 975 ~Lm, E,a = 2.5 eV/p,m 2, E,,, = 0.78 eV/Wm - , E,, = 5.5 MeV, and x = 60, 25 and 8 keV, we get D60 = 183 ~Lm, D, = 118 Wm and Ds = 67 p,rn [321 . Unfortunately, these values for D suggest that we are currently sensitive to events occurring within only a fraction of the detector thickness (1 mm) for energies up to at least 60 keV . 5.3. Discussion ofgamma and X-ray data

0

2

)Pulse Height ChB (mV) Fig. 18. Pulse height vs pulse height data for B/B experiment with 24 'Am source and a Sn absorber . (Bias current = 100 nA.)

Unlike for alpha particles, no clear, geometric, evidence of phonon focussing was seen using 60 keV -y-rays in (double-channel) F/F and B/B coincidence experiments performed over a wide range of operating temperatures . This is likely a result of the broad (ap..,rn - matntal pro-; ~ate! is-r) distribution of interaction depths for the 60 keV gammas in our 1 mm thick SiCAD, as well as the fact that Compton scattering (which produces a broad distribution of event energies) accounts for approximately 50% of the interaction cross section for 60 keV gammas in Si. Other contributing factors include the strictly non-local energy deposition of the scattered primary electron (track length of = 25 p.m) and the electronic noise of our measuring system . However, it is also possible that for 60 keV gammas

212

B.A . Young et al. / Detection of elementary particles

our signals are strongly dominated by diffusive phonons either because the frac`ion of concentrated energy going into ballistic phonons is significantly smaller than for alphas, or because for 60 keV gammas the SiCAD sensitivity is not yet sufficient to detect the ballistic component alone. In general, high frequency phonons produced immediately after a scattering event must be down-converted before focusing effects will be observed, however little is known about the exact initial distribution of these phonons (i.e. how it differs for 5.5 MeV alphas vs 60 keV gammas). And although calculations suggest that within = 1 Ws nearly all (reasonable) initial distributions relax to a common distribution, these calculations assume that the event (1) occurs in the "dilute phonon" limit, (2) is pointlike, and (3) is far from surfaces (which could substantially increase the number of phonons scattered and down-converted to the ballistic regime of = 1 THz). Experimentally, these conditions were not strictly valid for either the alphas or gammas. The dilute phonon limit is merely an approximation in both cases. Diffusion cloud chamber experiments show that the energy distribution of the event profile for 60 keV gamma tracks is far less pointlike than that for alpha particles. Finally, and perhaps most importantly, nearly all of the alphas, but only - 2% of the gammas interact within = 20 p,m of the surface of our 1 mm thick SiCAD. In recent Monte Carlo calculations for the expected gamma and X-ray PH vs PH distributions by Cabrera [30], the path of the scattered primary electron from a 60 keV gamma event is modeled as a sequence of ten segments, each with equal energy deposition in the SiCAD. At each vertex, the electron is allowed to scatter at an angle chosen randomly from a Gaussian distribution . The resulting track is qualitatively similar to those observed in cloud chamber experiments, and effectively forms a distributed phonon source . The phonon signal generated by a gamma event is then calculated by superimposing the phonon signals generated at each of the 10 point-like interactions (vertices). The phonons generated at each vertex propagate through the anisotropic silicon ballistically, producing on the surface a somewhat arbitrary superposition of characteristic (yet independent) focusing patterns . The result is that for a distributed source such as this, only a hint of the ballistic phonon focussing pattern obtained for. an inud iv'ldual point source remains. Calculations were also performed for the case of single 60 keV point sources at randomly selected depths of interaction, for the cases of either purely ballistic or purely diffusive phonon propagation. Qualitatively, the most reasonable fit to our 60 keV gamma ray pulse height vs pulse height data is obtained by using the distributed phonon source produced by multiple scatters of the primary electron, and assuming some admixture (not yet determined) of bal-

listic and diffusive phonons. The model provides a particularly good fit when we include accidental coincidences and our best estimate of the experimental electronic noise. Preliminary analysis of data obtained using an 24 'Am gamma and X-ray source and 300 Wm thick double-sided SiCADs supports our model, and strongly suggests a non-zero ballistic phonon contribution to the signals of order 20%. Results from an extensive series of experiments using these new detectors in two-, three- and four-channel coincidence experiments will be presented elsewhere [33] . 6. 6 keV X-ray experiments Most recently, we used a = 0.2 nCi source of 55Fe to study the response of SiCADs to 6 keV X-rays, which have a 1 /e attenuation length in Si of only â 25 pm, and produce pointlike interactions in cloud chamber experiments. Although X-rays from the Fe source more closely resemble the 60 keV gammas in terms of event total energy, their short range (albeit exponential), monochromaticity, and point-ilke event energy profile are characteristics more typical of alphas . We can take advantage of these hybrid characteristics to better understand the dependence of phonon focussing on specific interaction parameters. The uncollimated, rectangular source (1 cm x 1 mm) was placed perpendicular to the long axis of the two sensors, and a series of experiments was performed using the two front sensors only . In fig. 19, we present 6 keV (F/F) pulse height vs pulse height data obtained for three different operating temperatures . Because the external electronic noise level was relatively high when taking these data (S/N = 5), the results here are preliminary and our interpretation is tentative . The "arms" which appear above some minimum temperature of = 402 mK and extend along the axes possibly result from phonon focussing effects . Because each X-ray event energy is = 1000 times smaller than for the alphas, we do not suffer from the high density of scattered and reflected phonons which washed out the focussing features in the F/F alpha data . Nevertheless, the analysis of this 55 Fe data is more complicated than the alpha data, as a result of the exponential distribution of X-ray event interaction depths and the lower energy of the source . For a qualitative discussion, we once again refer to the ballistic phonon energy density distribution shown in fig. l0a and, in particular, to the vicinity of the "spires" . For the 6 keV X-rays, the ballistic phonon focussing pattern has little time to spread before striking the detector surface, and normal regions produced in the Ti films by the spires Lave characteristic diameters comparable to only a few linewidths . This "finite sensor" effect manifests itself in the data as a density modulation along the arms of

B.A. Young et al. / Detection of elementary particles

213

.8

Q U

.6

.4

.2

0 1 .0

.8

.8

Q .C

.6

U

bA

.4

x

.4

CL.

.2

v

.2

0

.6

0

.2

.4

.6

.8

1 .0

Pulse Height ChB (mV)

0

0

.2

.4

.6

.8

1.0

Pulse Height ChB (mV)

Fig. 19 . Pulse height vs pulse height distributions for F/F experiment using 55 Fe X-ray source.

the PH/PH plots, as events which occur at relatively greater (lesser) depths produce normal regions which successively contain one additional (one fewer) Ti line. As the operating temperature is raised, the arms extend towards larger pulse heights, and the modulation continues as additional lines are driven normal. However, at each operating temperature, there is a maximum extent to these arms as a result of the trade-off between increasing the cross-sectional area of the phonon wavefront and decreasing its energy density . On each plot, the points appearing between the arms correspond to events for which significant energy is deposited into the film from isotropic and/or scattered or reflected phonons . In addition, those events which originate from ballistic phonons not contained in the spires can also contribute in this region . A pulse length vs pulse height plot which was obtained with the 55Fe source in an earlier run (using only one (F) channel of the SiCAD) is presented in fig . 20 . From these data it is evident that we have achieved

both an energy threshold and resolution (FWHM) of < 1 keV at 6 keV . 7. Neutron experiments As previously mentioned, our goal is to achieve a SiCAD energy threshold of = 1 keV and resolution of 100 eV. Such a detector could be used to look for neutrino oscillations at a nuclear power reactor, and ., .i r_p îR n-B tthe cha. ln~sr av .. en erov eventually to., stu~ty At " C.7 r r a neutrinos produced in the sun . For a typical reactor electron neutrino spectrum, a SiCAD threshold of 0.5 keV would provide a total event rate of = 35 kg- ' day - ' . Nuclear recoils (E,,,, ;, < 7 keV) would account for = 97% of these signals, with the remainder coming from recoiling electrons (Erecoi, < 9.6 MeV). Because a, y-, and X-rays interact almost entirely with the electrons in a SiCAD, our convenient laboratory sources of `°'Am and 55Fe could not be used for

B.A . Young et al. / Detection of elernerntarv particles

214

.7 .6

.4

.1 0

0

10

20

30

40

50

60

70

80

Pulse Height (~.V)

Fig. 20. Mean/pulse height vs pulse height obtained using one (front side) SiCAD channel and an 5-"Fe X-ray source . (Bias current =165 nA.)

studying nuclear recoils . In order to characterize the phonon signals produced by elastic scattering from nuclei, we exposed a (1 mm thick) F/B SiCAD to a 1 Ci Pu-Be neutron source. The Pu-Be source has a broad decay spectrum, and provides a flux of both neutrons and gammas with energies of = 1-10 MeV. These experiments were performed without benefit of selective shielding or direct n/y discrimination capabilities. In fig . 21a, we show pulse length vs. pulse height data obtained with the Pu-Be source in place, and fig . 21b shows the distribution due to background events (source away) . Both plots include events produced by an Am source, which was mounted near the SiCAD during the entire run. Because neutrons from the Pu-Be source have a range of = 70 mm in Si, we expected to see equal rates for the leading trigger in either the front or back channel. In practice, however, the coincidence data was strongly dominated by leading triggers in the back sensor. We believe this was due to pair production from high energy (typically 4 MeV) Pu-Be gamma rays . At these energies, the e- /e' pair is foiward-peaked in the lab frame and often has sufficient energy to escape the detector . As the electron and positron scatter through the detector towards the back sensor they generate many delta rays. The delta rays produce phonons which, for most events, need travel only a short distance before reaching the back surface . As a result, a prompt signal is detected in the back sensor before phonons originating within the initial interaction region have arrived at the front surface.

8. Summary and conclusions In this article, we have described the development of silicon crystal acoustic detectors, and have presented results from experiments in which these devices were used to detect particles with energies in the range of 6 keV to 10 MeV. Double-sided, four-channel SiCADs with sensitive masses up to 37 mg have been fabricated and extensively characterized . With these devices we have demonstrated both an energy resolution and threshold of = 800 eV. We have demonstrated the ease with which these detectors of nonstandard geometry can be fabricated, and we have developed the necessary processing techniques for producing SiCADs of significantly larger masses and sensing areas . We are confident that an array of massive SiCADs (= 100 grams per SiCAD) with improved energy resolution and lower threshold can be constructed in a straightforward manner. The thermal cyclability of SiCADs with AI or Ti transition edge phonon sensors is excellent, and the device performance is extremely reproducible . Using 1 mm thick, double-sided (Ti sensor) SiCADs in time coincidence experiments with alpha particles, we have measured the ballistic time-of-flight for phonons generated by electronic recoils in Si. In these (F/B) experiments, a timing resolution of = 4 ns (= 2%) was obtained . In addition, the measured temperature dependence of the F/B time delays provided semi-quantitative information about the shape of the three dimensional energy density distribution relevant to our de-

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12

8

4

0 12

U U

8

4

0 0

Pulse Height (mV)

Fig. 21. (a) Pulse length vs pulse height obtained with (a) the Pu-Be (n/y) and -1'Am sources in place and (b) the Pu-Be source away. -cte '; alp, events . In another series of experiments, we recorded time coincident (B/B) signals detected in two adjacent channels on the same side of the SiCAD and observed the ballistic phonon focusing patterns when the alpha source was mounted nearest the inactive surface of the SiCAD. When combined with the results of Monte Carlo calculations, both the F/B time delay and B/B phonon focusing data were used to estimate the ratio of ballistic to diffusive phonons in the detected alpha signals. Using the B/B data, it was determined that = 30% of the phonons which strike

the back surface of the SiCAD within the first = 1 p.s arrive ballistically, whereas the r/B timing data suggest a ballistic component on the order of = 20% . We note, however, that systematic errors from the time-delay determination of the ballistic component are larger than those from the spatial anisotropy determination . Data obtained using our new experimental setup, coupled with the results from improved calculations, should provide a better understanding of the partitioning of event energy into ballistic and quasi-diffusive phonons. Although the primary goal of this continuing work is

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to develop a sensitive detector for neutrinos and dark matter, we have demonstrated that SiCADs can also be used to directly study fundamental issues in solid state physics . Of particular interest are experiments relating to phonon focusing effects, such as those discussed above . In addition, data from our current experiments using 60 keV gamma rays and a 300 wm thick, doublesided SiCAD should provide new and extremely useful information relating to various phonon processes and the (possibly dramatic) effect of surfaces on phonon energy down-conversion . To date, most of our experiments have been performed with sources of alpha particles, gamma rays and X-rays, however we have also demonstrated the feasibility of using SiCADs to detect neutrons. Soon, we will perform a series of neutron experiments in order to more carefully characterize the response of SiCADs to nuclear (rather than electronic) recoils . Because the signature for nuclear elastic scattering of neutrinos is quite similar to that of neutrons, these experiments should prove invaluable from the standpoint o: our long-term goal of developing a high resolution and low energy threshold neutrino and dark matter detector. Acknowledgements We thank K. Irwin for assistance in the laboratory and J.P. McVittie for suggestions and comments relating to semiconductor processing techniques. One of us MY) also thanks G.A. Fisher for lively discussions about nuclear and atomic interactions . R . King provided the high-quality superconducting Ti films used in SiCAD fabrication. We acknowledge B. Neuhauser and C.J. Martoff for contributions during the earlier stages of our experimental program. This work was supported in part by DOE Contract No. DE-AT03-82 ER40076 and DOE Grant No. DE-FG03-90ER40569 . References [11 [2] [31 [41 [5]

F. Antinori et al., Nucl. Instr. and Meth. A288 (1990) 82. A.R. Sattler, Phys. Rev . A138 (1965) 1815. P. Zecher et al., Phys. Rev. A41 (1990) 4058. G. Gerrbi_er et al ., Phys. Rev . D42 (loon) 3211 . B. Sadoulet, in: Phonons 89, Vol . 2, eds. S. Hunklinger, W. Ludwig and G. Weiss (World Scientific, 1990) pp. 1383-1393 . [6] McCammon et al., PANIC XII: Particles and Nuclei, eds. J.L. Matthews, T.W. Donnelly, E.H. Farhi and L.S. Osborne (North-Holland, 1991) P . 821c.

N. Wang et al., Physica B 165 & 166 (1990) 3. [8] W. Rothmund and A. Zehnder, in: Superconducting Particle Detectors, ed. A. Barrone (World Scientific, 1988) pp. 52-65 . [9] H. Kraus et al., Low Temperature Detectors for Neutrinos and Dark Matter III, eds. L. Brogiato, D.V . Camin and E. Fiorini (Editions Frontiere, France, 1990) pp. 121-135. [10] Th. Peterreins et al., J. Appl. Phys. 69 (1991) 1791. [11] Blas Cabrera, Lawrence M. Krauss and Frank Wilczek, Phys. Rev. Lett. 55 (1985) 25. [12] R. Baumgartner et al., Phys. Lett. A94 (1983) 55. [131 B. Cabrera, in: Phonons 89, Vol. 2, eds. S. Hunklinger, W. Ludwig and G. Weiss (World Scientific, 1990) pp. 1373-1382 . [14] S. Tamura, Phys. Rev. B30 (1984) 849, and S. Tamura, Phys. Rev. B31 (1985) 2574. [151 Kamioka et al., J. Phys. Chem. 90 (1986) 5727. [16] C.J. Martoff, Science 237 (1987) 507. [17] B. Cabrera et al., Nucl. Instr. and Meth. A275 (1989) 97. [181 B. Taylor, H.T. Maris and C. Elbaum, Phys. Rev. B3 (1971) 1462. [191 G.A. Northrop and J.P. Wolfe, Phys. Rev. B22 (1980) 6196. [20] B.A. Young et al., Phys. Rev. Lett. 64 (1990) 2795. [21] The intrinsic Si wafer substrates ( > 1500 f cm resistivity) were produced at Unisil Corp . (Mountain View, CA) using the magnetic Czochralski technique. [221 B. Neuhauser, in preparation for Rev. Sci. Instr . [23] In previous publications on Ti TE sensors (e.g. ref. [21]) we took T, at =10% RN rather than at a more thermodynamically correct reference point of = 90% RN . At 435 mK, a transition width of = 5 mK corresponds to a difference in the measured value of Tc of only 1%. A shift in the definition of Tc at that level would have produced negligible effect on our results reported to date. Our most recent data, however, were obtained using an improved experimental setup which provides better accuracy and makes the 1% shift relevant. [241 B.A. Young, Ph.D. Thesis, Stanford University (1990) unpublished. [25] W.A. Little, Can. J. Phys. 37 (1959) 334. [261 B. Neuhauser et al., Jpn . J. Appl. Phys. 26 (1987) 1671. [27] (a) M.C. Steele and R.A. Hein, Phys. Rev. 92 (1953) 243 ; and (b) R.L. Falge Jr., Phys. Rev. Lett. 11 (1963) 248 . [281 A.T. Lee, Rev . Sci . Instr . 60 (1989) 3315. [291 S. Anderson (ed.), Atomic Collisions in Solids IV (1972). [30] B. Cabrera, in preparation . [311 B.A. Young et al., IEEE Trans . Mag. 25 (1989) 1347. [32] B.A. Young et al., in: Low Temperature Detectors for Neutrinos and nark Matter üt, eds. T . Brogiato, D.V. Camin and E. Fiorini (Editions Fronti6re, France, 1990) pp. 183-191 . [33] A.T. Lee et al., in preparation. [7]