1.
2.
3.
4.
5.
ð6Þ
where α and β are fitting parameters related to the impurity
scattering at low temperatures and the lattice scattering at high
temperatures, respectively. The values of μmin ; μmax and N g;i are
estimated from the carrier density dependence of the mobility in
bulk GaN, reported in ref. 63, and N is the carrier density. In our
calculations, we used μEu ð300Þ ¼ 53cm2 V1 s1 for the mobility
in Eu-doped GaN as reported in ref. 17. We also used the previously determined free carrier density was for GaN:Euhigh,
N 6 ´ 1017 cm3 . By fitting the temperature dependent THz
amplitudes in Fig. 4 with Eq. (5), we obtained
α 0:2 ± 0:2; β 5:3 ± 0:2. The value of α has a large relative
error; however, since the contribution of the impurity scattering is
significantly less in the measured temperature range, the exact
value for α should have a negligible impact on the results63.
Using these parameters for GaN:Euhigh, we can now evaluate
the impact of the superlattice structure on the carrier mobility
between the doped and undoped layers and determine the barrier
potential for the electrons within this structure by using a
mobility model that takes into account the barrier height,
reported in ref. 62. Although this model includes some transport
processes, the mobility due to the thermal emission process, μth ,
should be dominant in superlattice structure due to the 10 nm
thick barrier layers62. With these considerations, the THz
emission amplitude within the superlattice structure can be
described as:
μ ðT Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
qV
8m3D qV b exp b ;
ETHz ðT Þ / μth ðT Þ / 1 þ 3D
qL
kB T
ð7Þ
6.
7.
8.
9.
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The authors declare no competing interests.
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Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s43246-023-00428-6.
Correspondence and requests for materials should be addressed to Masayoshi Tonouchi.
Peer review information Communications Materials thanks the anonymous reviewers
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Acknowledgements
M.T. acknowledges support in part by JSPS KAKENHI Grant No. JP 23H00184, and JST,
CREST Grant Number JPMJCR22O2, Japan. F.M. acknowledges support in part by
Grant-in-Aid for JSPS Fellows, JST and Program for Leading Graduate schools: “Interactive Materials Science Cadet Program”. F.M. and A.T. acknowledge support in part by
the establishment of university fellowships towards the creation of science technology
innovation, Grant No. JPMJFS2125. B.M. and V.D. acknowledge support in part by NSF
RUI Award No. 2129183. Y.F. acknowledges support in part by JSPS KAKENHI Grant
No.JP18H05212, No.JP23H00185 and No.JP23H05449, Japan.
Author contributions
F.M. and B.M. conceived the idea and proposed the research. F.M. performed THz
emission measurements. F.M., A.T. and M.T. performed data analyses with support from
B.M., V.D. and Y.F. F.M. wrote the original draft of the manuscript, B.T., V.D. and M.T.
reviewed and edited, and all authors contributed feedback and comments. M.T. directed
and supervised the research.
10
Competing interests
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