Cosmogenic activation of silicon

The production of ${}^3\mathrm{H}$, ${}^7\mathrm{Be}$, and ${}^{22}\mathrm{Na}$ by interactions of cosmic-ray particles with silicon can produce radioactive backgrounds in detectors used to search for rare events. Through controlled irradiation of silicon CCDs and wafers with a neutron beam that mimics the cosmic-ray neutron spectrum, followed by direct counting, we determined that the production rate from cosmic-ray neutrons at sea level is $(112\pm 24)\mathrm{atoms}/(\mathrm{kg}\mathrm{day})$ for ${}^3\mathrm{H}$, $(8.1\pm 1.9)\mathrm{atoms}/(\mathrm{kg}\mathrm{day})$ for ${}^7\mathrm{Be}$, and $(43.0\pm 7.2)\mathrm{atoms}/(\mathrm{kg}\mathrm{day})$ for ${}^{22}\mathrm{Na}$. Complementing these results with the current best estimates of activation cross sections for cosmic-ray particles other than neutrons, we obtain a total sea-level cosmic-ray production rate of $(124\pm 25)\mathrm{atoms}/(\mathrm{kg}\mathrm{day})$ for ${}^3\mathrm{H}$, $(9.4\pm 2.0)\mathrm{atoms}/(\mathrm{kg}\mathrm{day})$ for ${}^7\mathrm{Be}$, and $(49.6\pm 7.4)\mathrm{atoms}/(\mathrm{kg}\mathrm{day})$ for ${}^{22}\mathrm{Na}$. These measurements will help constrain background estimates and determine the maximum time that silicon-based detectors can remain unshielded during detector fabrication before cosmogenic backgrounds impact the sensitivity of next-generation rare-event searches.

Figure 1

Experimental measurements (magenta error bars) [18, 19, 20] and model estimates (continuous curves) of neutron-induced tritium production in silicon. Measurements of the proton-induced cross section [21, 22] are also shown for reference (gray error bars).

Figure 2

Experimental measurements (magenta error bars) [45] and model estimates (continuous curves) of the neutron-induced ${}^7\mathrm{Be}$ production cross section in silicon. Measurements of the proton-induced cross section [46, 47] are also shown for reference (gray error bars).

Figure 3

Experimental measurements (magenta and pink error bars) [45, 58, 59, 60, 61] and model estimates (continuous curves) of the neutron-induced ${}^{22}\mathrm{Na}$ production cross section in silicon. Measurements of the proton-induced cross section [46, 47] are also shown for reference (gray error bars).

Figure 4

Photograph of the CCD package inside its aluminum storage box. Left: Package before wire bonding. Right: After wire bonding, with aluminum frame to keep the CCD package fixed in place.

Figure 5

geant4 renderings of the three setups used to position targets in the neutron beam, with the beam passing from right to left. Aluminum (Al) boxes holding the CCDs (yellow) were held in place by an Al rack (dark gray). For the initial setup (left), the Al box is made transparent to show the positioning of the CCD (red), air (gray), and other structures (light brown). The other targets include pairs of Si wafers (green), a Ge wafer (blue), and Cu plates (copper brown). The polyethylene wafer holder (purple) is simplified to a rectangle of the same thickness and height as the actual object, with the sides and bottom removed. All targets were supported on an acetal block (light gray).

Figure 6

Layout of the samples as placed in the beam during the final irradiation setup (cf. Fig. 5, right). The beam first passes through the cylindrical fission chamber (far right) and then through the samples (from right to left): three CCDs in Al boxes (with flex cables emerging at the top), three pairs of Si wafers, one Ge wafer, and two Cu plates.

Figure 7

Comparison of the LANSCE 4FP30R/ICE II neutron beam with sea-level cosmic-ray neutrons. The black data points and left vertical axis show the number of neutrons measured by the fission chamber during the entire beam exposure used for this measurement. Uncertainties shown are statistical only (see main text for discussion of systematic uncertainties). The colored markers show the simulated fluence for each of the CCDs in the setup. For comparison, the red continuous line and the right vertical axis show the reference cosmic-ray neutron flux at sea level for New York City during the midpoint of solar modulation [74].

Figure 8

Experimental measurements (circles) [67, 69, 71] and evaluations (squares) [68, 70, 72, 73] of the ${}^{238}\mathrm{U}(n,f)$ cross section. The cross section assumed by the LANSCE facility to convert the fission chamber counts to a total neutron fluence is shown by the black line, with the shaded gray band indicating the assumed uncertainty.

Figure 9

Spectral comparison of the gamma-counting results for the Si-wafer pairs. Inspection of the full energy range (top panel) reveals two peaks in the irradiated samples (1, 2, and 3) at 478 keV (bottom left) and 1275 keV (bottom right) that are not present in the unirradiated sample (0), corresponding to ${}^7\mathrm{Be}$ and ${}^{22}\mathrm{Na}$ activated by the LANSCE neutron beam, respectively.

Figure 10

Postirradiation dark-current profile for CCD 3, obtained from the median pixel values across multiple images. The elevated number of dark counts in the center of the CCD shows the effect of the neutron damage on the CCD.

Figure 11

Data spectrum and best-fit model with the spectral components stacked in different colors. The spectrum was fit from 2 to 25 keV with the shaded region around the 8 keV copper $K$-shell fluorescence line excluded from the fit. The rise in the spectrum below 18 keV from ${}^3\mathrm{H}$ decay is clearly visible above the nearly flat background and ${}^{22}\mathrm{Na}$ spectrum.

Figure 12

Schematic diagram showing triton ejection and implantation. The filled circles indicate example triton production locations, while the triton nuclei show the final implantation locations. Production rate estimates include trajectories (a) and (b), while counting the tritium decay activity in the CCD measures (a) and (c).

Figure 13

Shown are the activities (mBq) of ${}^3\mathrm{H}$ (left), ${}^7\mathrm{Be}$ (middle), and ${}^{22}\mathrm{Na}$ (right) produced and implanted in various volumes (i.e., $T_{ij}·P_j$) as predicted by the geant4 inclxx model. CCD 1, CCD 2, CCD 3 are the CCDs, with CCD 1 being closest to the fission chamber. Box 1, Box 2, and Box 3 are the aluminum boxes that contain CCD 1, CCD 2, and CCD 3, respectively. Si 1, Si 2, Si 3, and Ge are the silicon and germanium wafers downstream of the CCDs. World represents the air in the irradiation room.

Figure 14

Experimental measurements (data points) and model estimates (continuous lines) of the neutron-induced tritium production in aluminum. Measurements of the proton-induced cross section are also shown for reference. For direct comparison, we also show the corresponding model predictions for silicon (dashed lines) from Fig. 1.

Figure 15

Comparison of sea-level cosmic-ray fluxes of protons [92, 93, 94], gamma rays [96], and neutrons [74].

Figure 16

Estimated photonuclear cross-section models for production of ${}^3\mathrm{H}$, ${}^7\mathrm{Be}$, and ${}^{22}\mathrm{Na}$. The dashed lines indicate the original models from talys, while the solid lines indicate the models scaled to match yield measurements made with bremsstrahlung radiation [97, 98].