An investigation in the laboratory reports that low-energy muon spin rotation, or LE-µSR, could be used to extract effective free-electron concentrations in n-type 4H-SiC across 2 × 10^15 to 1 × 10^19 cm−3. The measurements also produced depth-dependent signals for carrier depletion and implantation damage.
The study followed muonium charge states, the different forms of the muon signal associated with electron capture. It examined nitrogen and phosphorus donors introduced by epitaxial growth or ion implantation, combining LE-µSR with capacitance-voltage and SIMS profiles and simulations of muonium electron capture.
A probe that works by depth
The spectra were analyzed with multi-component fits. Measurements used magnetic fields of 0.7 and 10 mT and temperature scans from 10 to 310 K. At 260 K, the muon implantation energy ranged from 2 to 22 keV, corresponding to mean probing ranges of 5 to 130 nm.
This setup let the researchers compare fitted signals at different depths. The comparison included nitrogen-doped epitaxial layers and nitrogen- or phosphorus-implanted regions. The implanted samples underwent post-implantation annealing for 30 minutes at 1650 °C.
What the muon signal showed
High-field HAL-9500 measurements confirmed two neutral muonium configurations in 4H-SiC, labelled Mu1 and Mu2. At 0.7 mT, low-field LE-µSR resolved two Mu1 lines at 9.8 MHz and 11.5 MHz, indicating a small anisotropic hyperfine component of about 1.7 MHz.
In the Epi-N17 sample, the temperature scan showed conversion from Mu1 to the diamagnetic Mu− state above 50 K. The Mu1 fraction fell to zero at 50 K, while the diamagnetic fraction increased between 50 and 125 K.
Different samples produced different profiles
Fits to the temperature-dependent data produced activation energies of 61(9) meV for Epi-N17, 57(2) meV for Imp-N17, 48(5) meV for Imp-N18, 57(3) meV for Imp-P17 and 53(3) meV for Imp-P18. No value was listed for Epi-N15.
Capacitance-voltage profiles indicated donor activation close to 100% for Imp-N17 and Imp-P17. For Imp-N18 and Imp-P18, no activation value was obtained; the reported reason was leakage current during the capacitance-voltage measurements.
Depth profiles also carried warning signs
At 260 K and 10 mT, the fitted depletion widths, the ranges over which the carrier-related signal was inferred to be depleted, were 34(3) nm for Epi-N17, 31(1) nm for Imp-N17, 8(1) nm for Imp-N18, 16(1) nm for Imp-P17 and 9(2) nm for Imp-P18. No width was listed for Epi-N15. The authors said the depth patterns were likely related to fixed charge in a native oxide.
A separate sample comparison was visible at 10 K. Imp-N18 had a diamagnetic fraction of 0.178(6), compared with 0.016(5) for Imp-N17. Imp-P18 had a fraction of 0.154(5), compared with 0.0094(5) for Imp-P17. The authors interpreted the larger fractions in Imp-N18 and Imp-P18 as signs of permanent lattice damage and carbon-related defects, but the experiment did not distinguish between those contributions.
A promising measurement with stated limits
To build the carrier calibration, the researchers matched measured and simulated diamagnetic fractions and phases at 260 K to known free-electron concentrations. Using measurements at 0.7 and 10 mT, they reported that effective free-electron concentrations could be extracted from 2 × 10^15 to 1 × 10^19 cm−3. The fit gave a capture coefficient of 3.5 × 10−9 cm3 s−1 and an estimated capture cross section of about 2 × 10−16 cm2.
That calibration is simulation-based and depends on the assumed electron-capture model and the reference samples. No formal validation error was reported for the stated concentration range, and the evidence is limited to laboratory measurements and simulations on n-type 4H-SiC under the studied conditions.
The analysis therefore leaves open how accurately the simulation-based calibration performs in independent or more varied samples and how the observed implantation-related signal should be divided between permanent lattice damage and carbon-related defects.
The supplied document is identified as arXiv:2608.25702v1 and dated 26 August 2026. Its acknowledgments cite Swiss National Science Foundation Grant No. 192218 and an ETH Zürich Postdoctoral Fellowship.
Paper data and sources
Original title: Muonium dynamics as a probe for depth-resolved properties of 4H-SiC
Authors: Maria Mendes Martins, Piyush Kumar, Marianne E. Bathen et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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