High-yield thermalized positronium at room temperature emitted by morphologically tuned nanochanneled silicon targets

Positron/positronium converters were synthetized starting from substrates of silicon p-type (111) with resistivity 0.1–1.5 Ω cm. Nanochannels were produced via electrochemical etching. The etching solution was realized by adding absolute ethanol to a commercial aqueous solution at 48% of HF with a volume ratio of 1:3 = HF: ethanol. An etching current of 10 mA cm⁻² was used. After the electrochemical etching, the samples were cleaned in absolute ethanol ⩾99.8% and oxidized in air at 100 °C for 2 h. As shown in reference [15], a fine tuning of the nanochannel diameter can be obtained by different number of etchings in HF etching solution for 1 min and re-oxidation in air at 100 °C for 2 h. In the present work, we produced two targets subject to a single cycle of re-etching and re-oxidation (named #1 in reference [15]). The nanochannel length is determined by the anodization duration [31]. A first target was synthetized with an anodization time of 10 min (hereafter labelled #1a) and a second one with a time of 4 min (#1b in the following).

The diameter of the nanochannels and the thickness of the nanochanneled region were evaluated by scanning electron microscopy (SEM) carried out by a high resolution JEOL JSM-7001F thermal field emission SEM. Accelerating voltage ranges from 0.5 to 30 kV and its resolution is 1.2 nm at 30 kV. SEM pictures of the surface of the two targets are reported in figures 1(a) and (b) while the pictures of their sections are reported in figures 1(c) and (d).

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According to the SEM pictures of the surfaces of the converters, the nanochannel diameter ranges between 7 and 10 nm in both targets. The percentage of the surface not covered by nanochannels amounts to ∼80% of the overall while ∼20% of the surface is etched. This allows us to estimate the density of the nanochanneled region to be around 1.9 g cm⁻³ (=2.33 g cm⁻³ (density of silicon) × 0.8, see also reference [15]) in both the targets. The SEM pictures of the sections of the converters indicate that the thickness of the nanochanneled region is ∼3.89 μm for sample #1a and ∼1.13 μm for #1b. By comparison with converters synthetized from silicon p-type (100) with resistivity of 0.15–0.21 Ω cm, the nanochanneled region in the present converters is about two times deeper for a comparable anodization time [15]. Several characteristics of the substrate (among them crystal orientation, range of resistivity, feature of the wafer surface, sample size) could be at the origin of the observed difference in the etch rate [42].

The efficiencies of e⁺/Ps conversion and emission into the vacuum of the two converters were estimated via 2γ–3γ annihilation ratio measurements. Measurements were performed with the Trento positron beam [43] by scanning the fraction of implanted e⁺ annihilating into 3γ, F_3γ (E), as a function of the positron implantation energy, E. The term E is related to the mean positron implantation depth, ⟨z⟩, through the equation , where ρ is the material density [33]. The scan was carried out changing the positron implantation energy from 1 to 21 keV. The gamma rays generated by direct e⁺ annihilations and Ps annihilations were detected by a high purity germanium detector (HPGe) at a distance of about 3.5 cm from the samples. The HPGe detector had 45% efficiency and 1.4 keV energy resolution at 511 keV [41, 44]. The term F_3γ (E) was calculated as the ratio of the 2γ annihilations in the 511 keV annihilation peak and the 3γ annihilations in the region between 410 and 500 keV [41] after calibration with a Ge crystal held at 1000 K to have 0% and 100% Ps formation in the present experimental conditions [41, 45]. The error on F_3γ (E), both due to 0% and 100% evaluation, was estimated to be less than 3.5% [15, 45]. Further details about the measurement system and the technique are given elsewhere [15].

In order to guarantee a constant Ps production, the converters were thermally treated in situ, in ultra-high vacuum at 100 °C for 30' to remove eventual contaminants before the measurements [38, 46].

The transverse kinetic energy of the Ps emitted by the converters was probed by exploiting the Doppler broadening of the Lyman-α resonance. The measurement was performed as follows. Bursts containing ∼10⁷ e⁺ were prepared using the AEgIS e⁺-system at CERN and implanted into the converters with an energy of 3.3 keV. Briefly, e⁺ were produced by a ²²Na source, slowed by a solid Ne moderator [47] to a kinetic energy of a few eV, trapped and cooled in a Surko-style trap through the use of buffer gas [48]. Subsequently, e⁺ were moved to a second trap (accumulator) where the positron plasma containing ∼10⁷ e⁺ was stored and then extracted by fast pulsing the electric potential on the trap electrodes in the form of 20 ns bunches. The positron cloud was then magnetically transported in the direction of a chamber dedicated to Ps experiments. Here positrons were further compressed to about 7 ns in time (FWHM) using a 24-electrode buncher [49, 50] and implanted onto the converter with the final kinetic energy of 3.3 keV (see references [34, 35, 50] for details). The positron spot was of ∼3 mm in diameter [50]. In the present measurements, the target was kept at RT.

The time distribution of γ rays emitted by e⁺ and Ps annihilations (SSPALS-spectrum [39, 40]), was acquired with the same procedure used in references [34, 35]. A 20 × 25 × 25 mm PbWO₄ scintillator, coupled to a Hamamatsu R11265-100 photomultiplier tube and digitized by an HD4096 Teledyne LeCroy oscilloscope, was placed 40 mm above the target.

An example of two SSPALS spectra, one measured in the absence of Ps formation (by implantation of e⁺ on the surface of a microchannel plate, MCP, placed in the experimental chamber [50]) and one in the presence of Ps formation (by implantation of e⁺ into the converter #1a), is shown in the inset of figure 2. In the absence of Ps formation, SSPALS spectra present a prompt peak, given by the fast 2γ annihilations of e⁺ implanted in the target. On the right side of the peak, the signal quickly decreases and reaches the noise level in less than 100 ns. The small structures in the spectrum at longer times are photomultiplier ion after pulses [39, 40]. In the presence of Ps formation, SSPALS spectra show a long tail on the right side of the prompt peak. Such a tail is dominated by the 3γ decays of Ps emitted into vacuum. The Ps signal is the difference between the two spectra normalized to the peak height (see main panel in figure 2).

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Vacuum-emitted Ps atoms were probed by photo-excitation and photo-ionization, by introducing two laser pulses: an ultra-violet (UV) at 243 nm and a visible (VIS) at 532 nm. The UV drives the 1³S → 2³P transition and the VIS immediately photo-ionizes the excited fraction. The broadband 243 nm pulse was produced by frequency doubling a broadband 486 nm pulse in a barium borate crystal, produced by a commercial Continuum ND4600 amplified dye laser. The dye oscillator cavity and amplifier were operated with a mixture of Coumarin 480 and Coumarin 500 dissolved in ethanol in optimal proportions (50 ml of Coumarin 500 (2 g l⁻¹) + 150 ml of Coumarin 480 (1 g l⁻¹) + 300 ml ethanol for the oscillator, 20 ml Coumarin 500 (2 g l⁻¹) + 80 ml Coumarin 480 (1 g l⁻¹) + 450 ml ethanol for the amplifier), as described in details in reference [51]. The dye system was pumped by a frequency-tripled commercial 1064 nm CNI Model LPS-L-532 Q-switched ND:YAG pump, routinely producing 355 nm laser pulses of 10 ns temporal FWHM and 100 mJ energy, pumping the dye laser. The 243 nm peak energy was ∼900 μJ with fresh dye solutions and maximum pump power. The UV beam, with an astigmatic Gaussian spatial profile of 1.0 × 2.0 mm FWHM (∼1.8 × 3.7 mm full width at tenth of maximum, FWTM) in the horizontal and vertical directions respectively and with a Gaussian temporal profile of 8 ns FWHM. The bandwidth of the 243 nm pulses was 50 GHz. The intense 532 nm pulses were produced by frequency doubling the first harmonic of an EKSPLA NL303-HT laser pump in a KDP crystal, producing up to 65 mJ of 532 nm in a circular, top-hat spatial profile beam of ∼12 mm FWHM with a Gaussian temporal profile of 4 ns FWHM. The use of two independent laser pumps allowed the pulses to be independently triggered and tuned with a 1 ns resolution. The mutual jittering between the two laser pulses was measured to be <2 ns in a typical experimental run. Both laser beams were aligned grazing the surface of the e⁺/Ps converter.

The 1³S → 2³P laser excitation and photoionization results in a decrease of the Ps population decaying via three gammas. An example is reported in figure 3(a) where SSPALS spectra of Ps emitted into vacuum by target #1a with laser off and UV + VIS lasers on are shown. In this measurement, the UV wavelength was set on resonance at λ₀ = 243.01 nm (in vacuum) and both lasers were shot with a delay of 10 ns from the positron implantation. Each reported SSPALS spectrum is the average of 40 single shots. The change in the Ps population induced by the interaction with the two laser pulses was quantified by using the S parameter evaluated as:

where f_off and f_on are the averages of the normalized areas f_off-i and f_on-i below the ith SSPALS shot, calculated between 50 and 550 ns from the prompt peak with lasers off and on, respectively [35–37].

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The saturation laser energy of both 1³S → 2³P and 2³P → ionization transitions was studied by measuring the S parameter as a function of the UV and VIS energy, respectively (see figures 3(b) and(c)). Also these measurements were performed on sample #1a. The measurements show that 243 nm laser is in saturation for energy above ∼500 μJ while the 532 nm laser saturates above ∼15 mJ.

The Doppler broadening of the Lyman-α resonance of Ps was studied by acquiring the S parameter as a function of the UV laser wavelength [13, 52, 53]. The wavelength of the UV pulse (λ) was varied around the resonance between 242.7 and 243.2 nm. Doppler broadening experiments were conducted keeping the energy of the UV laser pulse around 700 μJ and the VIS energy around 50 mJ to guarantee the saturation of the 1³S → 2³P and 2³P → ionization transition, respectively.

The fraction F_3γ (E) of implanted positrons annihilating via 3γ vs positron implantation energy E is shown in figure 4 for both the studied converters. The corresponding mean positron implantation depth in the converters, assuming the density ρ = 1.9 g cm⁻³, is shown as the upper abscissa. In both targets, F_3γ (E) tops out at E ∼ 3–3.5 keV. The maximum value is ∼0.35 and ∼0.41, in #1a and #1b, respectively.

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The slight decrease of F_3γ (E) observed at E lower than 2–3 keV is attributable to both the presence of a lower Ps formation at low positron implantation energies [54] and Ps escaping from the nanochannels after only few collisions with walls and hence with a higher kinetic energy. These Ps atoms can annihilate far-away from the HPGe detector and be detected with a reduced efficiency (see reference [15] for a more detailed explanation).

At positron implantation energy higher than 3–3.5 keV, F_3γ (E) shows a progressive decrease that is steeper in #1b than in #1a. The observed decrease is due to the presence of two contributions: (i) at high E, the fraction of Ps able to escape from the nanochannels is reduced by the 2γ pick-off annihilations of Ps with an electron of the nanochannel walls and (ii) at high E, a fraction of implanted e⁺ annihilates in the unetched Si bulk where Ps formation does not occur. The weight of the two contributions is determined by the Ps diffusion length in the nanochannels and by the thickness of the nanochanneled region.

In order to extract the Ps diffusion length in the nanochannels and the fraction of Ps emitted into the vacuum, the F_3γ (E) curve measured in #1a was fitted above E = 3.5 keV with the diffusion model described in reference [15]. The fit was performed on the converter with the thicker nanochanneled region because the model assumes nanochannels with infinite length and it does not consider the decrease of Ps formation with the implantation depth due to the effect (ii). The best fit (continuous line in figure 4) points out that the diffusion length in the nanochannels of #1a is 1200 ± 200 nm. This diffusion length is around 50% longer than the one observed in nanochannels of similar diameter but synthetized in Si p-type (100) with resistivity of 0.15–0.21 Ω cm [15]. The found diffusion length is well shorter than the thickness of the nanochanneled region in #1a, while it is longer than that in the nanochannels of #1b. This confirms the expectation that in #1a the effect (i) is predominant, while in #1b the implantation of e⁺ in the Si bulk is significant and makes the decrease of F_3γ (E) steeper than in #1a. Moreover, the fit indicates that the contribution to F_3γ given by Ps annihilating via 3γ inside the pores is negligible [15]. Thus, the observed F_3γ signal at each E is almost entirely given by Ps back diffused to the surface and emitted into the vacuum. As the nanochannels diameter is found to be identical in the two targets (figure 1) and the interconnectivity of the channel is expected to be the same due to the production procedure, also the F_3γ signal measured in #1b is expected to be dominated by Ps emitted into vacuum.

Consequently, the higher F_3γ signal observed in #1b than in #1a at E ∼ 3–3.5 keV could be ascribed to the different nanochannel length and to the reflection from the nanochannel bottom end [55] that in the thinner #1b target can result in a more abundant emission into the vacuum.

SSPALS measurements confirm that Ps production given by converter #1b is slightly larger than the one by #1a in the proximity of their F_3γ (E) maximum (the spectra were acquired at E = 3.3 keV, ⟨z⟩ ∼ 140 nm). Ps signals in each converter, estimated as difference of SSPALS curves with Ps formation and the background without Ps formation, are shown in figure 5. By comparing the areas between 0 and 1200 ns below the two curves, the Ps signal measured in #1b results ∼16% larger than the one observed in #1a. The observed difference is in agreement with the one indicated by the F_3γ (E) measurements.

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In order to find the time at which the largest fraction of Ps is laser excited, a scan of the S parameter as a function of the delay of the two synchronized lasers (UV wavelength set on resonance) with respect to the positron implantation instant was performed. The curve measured for converter #1a is reported in figure 6.

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The vertical arrows in figure 6 mark the delays at which the transverse kinetic energy of the emitted Ps was measured (10 ns and 25 ns of delay, respectively). The two delay times have been chosen to sample the velocity of emitted Ps in the proximity of the time at which the maximum Ps laser excitation occurs (around 20 ns).

The scan of S parameter as a function of the UV laser wavelength, performed following the procedure reported in section 2.3, is shown in figure 7. Each S value was calculated according to equation (1) from a set of 80 SSPALS single-shot spectra (40 with lasers on and 40 with lasers off acquired in alternated mode). The line shapes of the 1³S → 2³P transition, measured in #1a at 10 ns and 25 ns, are reported in figures 7(a) and (b), respectively. The measurements performed in #1b at 10 ns and 25 ns are shown in figures 7(c) and (d), respectively. As the width of the 1³S → 2³P transition is dominated by Doppler broadening, it can be used to obtain the Ps velocity in the direction of the UV laser. The experimental data are fitted to:

where σ_λ is the Gaussian width. The root mean square (RMS) velocity along the laser propagation axis x, , can be calculated as while the mean transverse kinetic energy is , where c is the speed of light and m_Ps the mass of Ps [53].

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The RMS Ps velocities (mean Ps energies) obtained from the Doppler profiles measured in #1a are (6.3 ± 0.5) × 10⁴ m s⁻¹ (22 ± 4 meV) for a laser delay of 10 ns and (4.4 ± 0.4) × 10⁴ m s⁻¹ (11 ± 2 meV) for a delay of 25 ns. The kinetic energy measured at 25 ns corresponds to the complete thermalization of Ps in the direction of the laser in the target kept at RT. The different velocities at different laser delays can be explained with the fact that the UV laser pulse, thanks to its brief duration and its limited spatial dimension, excites only the fraction of the emitted Ps in front of the target at the time when the laser is shot [36]. Thus, the most delayed laser pulse addresses Ps that resided longer in the nanochannels losing more energy by collision with the walls. The RMS Ps velocities (mean Ps energies) measured in #1b are higher than the ones in #1a: (7.9 ± 0.5) × 10⁴ m s⁻¹ (35 ± 5 meV) for a delay of 10 ns and (7.0 ± 0.7) × 10⁴ m s⁻¹ (28 ± 6 meV) for 25 ns. This increase of the velocities (energies) could arise from the previously mentioned Ps reflection from the nanochannel bottom end that could induce a slightly shorter permanence time of Ps inside target #1b compared to in #1a with a consequent less efficient cooling.

The fitted S value of the 1³S → 2³P peak at resonance (figure 7) is 10.4 ± 0.8 and 13.9 ± 1.0 for converter #1a at 10 and 25 ns, respectively. In #1b, it is 7.5 ± 0.4 and 7.8 ± 0.4 at 10 and 25 ns, respectively (see table 1). These values can be roughly approximated as the following product:

where d is the excitation efficiency imposed by the bandwidth coverage of the UV laser, s the saturation efficiency of the 1³S → 2³P → ionization process, η is the laser coverage of the solid angle of the Ps cloud and ɛ is the fraction of Ps within the measured velocity range.

The UV pulse, due to its bandwidth of ∼50 GHz, selectively excites only the emitted Ps with a velocity component parallel to the laser propagation axis, v_{x,BW ,} with |v_x,BW| < 1.3 × 10⁴ m s⁻¹. Thus, only Ps expanding within a spherical wedge, whose angle is determined by the Ps average velocity, is addressable (see also references [8, 35]). The wedge angles calculated as for the different experimental conditions are reported in table 1. From previous measurements, Ps emission is expected to be essentially isotropic in velocity [34, 36, 38]. A further evidence of the isotropy of the Ps velocity comes from the S scan of figure 6 where the excitation signal in #1a disappears after around 70 ns from the positron implantation. As Ps has to travel around 3–4 mm to cross the UV laser spot (see UV FWTM given in section 2.3), the velocity needed to cover this space within 70 ns is ∼4.2–5.7 × 10⁴ m s⁻¹, in good agreement with the measured transverse velocity in this target. In the light of the Ps velocity isotropy, the fractions of Ps expanding within the spherical wedges with the reported angles can be approximated as . The values of d for the two converters for both delay times are reported in table 1.

Taking into account the energy of the UV and VIS laser pulses used in the present scan and according to the observation of the saturation of both UV and VIS energies shown in figures 3(b) and (c), the term s gets closer to 1. Given the dimensions of the laser and the e⁺ beam and the alignment of the laser grazing the target, the laser coverage of the solid angle of the Ps cloud, η, is expected to be not far from unity. If one assumes s and η = 1, equation (3) can be simplified to and a lower bound for the fraction of Ps within each measured velocity range, ε, can be roughly estimated from the fitted s values and the geometrical evaluations of d (table 1). We find that the fraction of Ps with average velocity of ∼4.4 × 10⁴ m s⁻¹ (measured in #1a at 25 ns) is, at least, ɛ ∼ 0.8 of the entire emitted Ps. As the emitted Ps from this target is around 35% of the implanted e⁺ at 3.3 keV (from fit of figure 4), ∼28% (=35% × 0.8) of e⁺ implanted in the converter #1a kept at RT is emitted as completely thermalized Ps. Similarly, the fraction of Ps with average velocity of ∼6.3 × 10⁴ m s⁻¹ (measured in #1a at 10 ns) is, at least, ɛ ∼ 0.8 of the entire emitted Ps. The fact that ɛ ∼ 0.8 in the two cases means that, in the time elapsed between 10 ns and 25 ns, there is a balance between the fast Ps fraction escaping from the laser spot and the fraction, with lower velocity, that enters the laser spot after delayed emission from the target. For sample #1b, we find that at least ɛ ∼ 0.7 and ∼0.65 are emitted with an average velocity of ∼7.9 × 10⁴ m s⁻¹ and ∼7.0 × 10⁴ m s⁻¹, respectively.