Ortiz Velasquez70, T. Osako47, A. Oskarsson82, J. Otwinowski120, K. Oyama84,
Y. Pachmayer106, S. Padhan50, D. Pagano141, G. Paić70, J. Pan144, S.
Panebianco139, P. Pareek142, J. Park62, J.E. Parkkila128, S. Parmar102, S.P.
Pathak127, B. Paul23, J. Pazzini141, H. Pei7, T. Peitzmann63, X. Peng7, L.G.
Pereira71, H. Pereira Da Costa139, D. Peresunko90, G.M. Perez8, S. Perrin139,
Y. Pestov5, V. Petráček38, M. Petrovici49, R.P. Pezzi71, S. Piano61, M.
Pikna13, P. Pillot117, O. Pinazza55,35, L. Pinsky127, C. Pinto27, S. Pisano53,
M. Płoskoń81, M. Planinic101, F. Pliquett69, M.G. Poghosyan98, B.
Polichtchouk93, N. Poljak101, A. Pop49, S. Porteboeuf-Houssais136, J.
Porter81, V. Pozdniakov76, S.K. Prasad4, R. Preghenella55, F. Prino60, C.A.
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Rami138, S.A.R. Ramirez46, A.G.T. Ramos34, R. Raniwala104, S. Raniwala104,
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K. RedlichV,87, A. Rehman21, P. Reichelt69, F. Reidt35, R. Renfordt69, Z.
Rescakova39, K. Reygers106, A. Riabov100, V. Riabov100, T. Richert82,91, M.
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Ronchetti53, A. Rosano33,57, E.D. Rosas70, A. Rossi58, A. Rotondi29, A. Roy51,
P. Roy112, O.V. Rueda82, R. Rui24, B. Rumyantsev76, A. Rustamov89, E.
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## Affiliation notes

I Deceased
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Science and Technology, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 Budker Institute for Nuclear Physics, Novosibirsk, Russia
6 California Polytechnic State University, San Luis Obispo, California, United
States
7 Central China Normal University, Wuhan, China
8 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
9 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
10 Chicago State University, Chicago, Illinois, United States
11 China Institute of Atomic Energy, Beijing, China
12 Chungbuk National University, Cheongju, Republic of Korea
13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia
14 COMSATS University Islamabad, Islamabad, Pakistan
15 Creighton University, Omaha, Nebraska, United States
16 Department of Physics, Aligarh Muslim University, Aligarh, India
17 Department of Physics, Pusan National University, Pusan, Republic of Korea
18 Department of Physics, Sejong University, Seoul, Republic of Korea
19 Department of Physics, University of California, Berkeley, California,
United States
20 Department of Physics, University of Oslo, Oslo, Norway
21 Department of Physics and Technology, University of Bergen, Bergen, Norway
22 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
29 Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia and
Sezione INFN, Pavia, Italy
30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
31 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
32 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy
33 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
34 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
35 European Organization for Nuclear Research (CERN), Geneva, Switzerland
36 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
37 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
38 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
39 Faculty of Science, P.J. Šafárik University, Košice, Slovakia
40 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
41 Fudan University, Shanghai, China
42 Gangneung-Wonju National University, Gangneung, Republic of Korea
43 Gauhati University, Department of Physics, Guwahati, India
44 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
45 Helsinki Institute of Physics (HIP), Helsinki, Finland
46 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
47 Hiroshima University, Hiroshima, Japan
48 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany
49 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
50 Indian Institute of Technology Bombay (IIT), Mumbai, India
51 Indian Institute of Technology Indore, Indore, India
52 Indonesian Institute of Sciences, Jakarta, Indonesia
53 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
54 INFN, Sezione di Bari, Bari, Italy
55 INFN, Sezione di Bologna, Bologna, Italy
56 INFN, Sezione di Cagliari, Cagliari, Italy
57 INFN, Sezione di Catania, Catania, Italy
58 INFN, Sezione di Padova, Padova, Italy
59 INFN, Sezione di Roma, Rome, Italy
60 INFN, Sezione di Torino, Turin, Italy
61 INFN, Sezione di Trieste, Trieste, Italy
62 Inha University, Incheon, Republic of Korea
63 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
64 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
65 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia
66 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
67 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
68 Institute of Space Science (ISS), Bucharest, Romania
69 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
70 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
71 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
72 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
73 iThemba LABS, National Research Foundation, Somerset West, South Africa
74 Jeonbuk National University, Jeonju, Republic of Korea
75 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
76 Joint Institute for Nuclear Research (JINR), Dubna, Russia
77 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
78 KTO Karatay University, Konya, Turkey
79 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France
80 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
81 Lawrence Berkeley National Laboratory, Berkeley, California, United States
82 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
83 Moscow Institute for Physics and Technology, Moscow, Russia
84 Nagasaki Institute of Applied Science, Nagasaki, Japan
85 Nara Women’s University (NWU), Nara, Japan
86 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
87 National Centre for Nuclear Research, Warsaw, Poland
88 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
89 National Nuclear Research Center, Baku, Azerbaijan
90 National Research Centre Kurchatov Institute, Moscow, Russia
91 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
92 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
93 NRC Kurchatov Institute IHEP, Protvino, Russia
94 NRC «Kurchatov»Institute - ITEP, Moscow, Russia
95 NRNU Moscow Engineering Physics Institute, Moscow, Russia
96 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
97 Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic
98 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
99 Ohio State University, Columbus, Ohio, United States
100 Petersburg Nuclear Physics Institute, Gatchina, Russia
101 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
102 Physics Department, Panjab University, Chandigarh, India
103 Physics Department, University of Jammu, Jammu, India
104 Physics Department, University of Rajasthan, Jaipur, India
105 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
106 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany
107 Physik Department, Technische Universität München, Munich, Germany
108 Politecnico di Bari and Sezione INFN, Bari, Italy
109 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
110 Rudjer Bošković Institute, Zagreb, Croatia
111 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
112 Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India
113 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
114 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
115 St. Petersburg State University, St. Petersburg, Russia
116 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
117 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France
118 Suranaree University of Technology, Nakhon Ratchasima, Thailand
119 Technical University of Košice, Košice, Slovakia
120 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
121 The University of Texas at Austin, Austin, Texas, United States
122 Universidad Autónoma de Sinaloa, Culiacán, Mexico
123 Universidade de São Paulo (USP), São Paulo, Brazil
124 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
125 Universidade Federal do ABC, Santo Andre, Brazil
126 University of Cape Town, Cape Town, South Africa
127 University of Houston, Houston, Texas, United States
128 University of Jyväskylä, Jyväskylä, Finland
129 University of Liverpool, Liverpool, United Kingdom
130 University of Science and Technology of China, Hefei, China
131 University of South-Eastern Norway, Tonsberg, Norway
132 University of Tennessee, Knoxville, Tennessee, United States
133 University of the Witwatersrand, Johannesburg, South Africa
134 University of Tokyo, Tokyo, Japan
135 University of Tsukuba, Tsukuba, Japan
136 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
137 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon
, Lyon, France
138 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
139 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
140 Università degli Studi di Foggia, Foggia, Italy
141 Università di Brescia and Sezione INFN, Brescia, Italy
142 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
143 Warsaw University of Technology, Warsaw, Poland
144 Wayne State University, Detroit, Michigan, United States
145 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany
146 Wigner Research Centre for Physics, Budapest, Hungary
147 Yale University, New Haven, Connecticut, United States
148 Yonsei University, Seoul, Republic of Korea


# Measurement of Spin-Polarized Photoemission from Wurtzite and Zinc-Blende
Gallium Nitride Photocathodes

S.J. Levenson<EMAIL_ADDRESS>M.B. Andorf  B.D. Dickensheets  I.V.
Bazarov  Cornell Laboratory for Accelerator-Based Sciences and Education
(CLASSE), Cornell University, Ithaca, NY 14850, USA  A. Galdi  Department of
Industrial Engineering, University of Salerno, Fisciano (SA) 84084, Italy  J.
Encomendero  V.V. Protasenko  School of Electrical and Computer Engineering,
Cornell University, Ithaca, New York 14853, USA  D. Jena  H.G. Xing  School of
Electrical and Computer Engineering, Cornell University, Ithaca, New York
14853, USA  Department of Material Science and Engineering, Cornell
University, Ithaca, NY 14583, USA  Kavli Institute at Cornell for Nanoscale
Science, Cornell University, Ithaca, NY 14583, USA  J.M. Maxson  Cornell
Laboratory for Accelerator-Based Sciences and Education (CLASSE), Cornell
University, Ithaca, NY 14850, USA

###### Abstract

Spin-polarized photoemission from wurtzite and zinc-blende gallium nitride
(GaN) photocathodes has been observed and measured for the first time. The
p-doped GaN photocathodes were epitaxially grown and activated to negative
electron affinity (NEA) with a cesium monolayer deposited on their surfaces. A
field-retarding Mott polarimeter was used to measure the spin-polarization of
electrons photoemitted from the top of the valence band. A spectral scan with
a tunable optical parametric amplifier (OPA) constructed to provide low-
bandwidth light revealed peak spin polarizations of 17% and 29% in the
wurtzite and zinc-blende photocathodes, respectively. Zinc-blende GaN results
are analyzed with a spin-polarization model accounting for experimental
parameters used in the measurements, while possible mechanisms influencing the
obtained spin polarization values of wurtzite GaN are discussed.

††preprint: AIP/123-QED

Spin-polarized electron beam generation is a critical component for many
nuclear and particle physics experiments by enabling the study of spin-
dependent properties such as parity-violation and nucleon spin structure
Michizono (2019); ncp (2017, 2015, 2013). Spin-polarized electrons are also
valuable in electron microscopy for investigating magnetic structures and
material spin states Suzuki  _et al._ (2010); Kuwahara  _et al._ (2014);
Rougemaille and Schmid (2010). For these applications, photocathodes based on
Gallium Arsenide (GaAs) are currently the only viable spin-polarized source
and are employed at facilities such as the Mainz Microtron (MAMI) Heidrich
_et al._ (2019) and the Continuous Electron Beam Accelerator Facility (CEBAF)
Adderley  _et al._ (2023). Future facilities like the International Linear
Collider (ILC) Michizono (2019) and Electron-Ion Collider (EIC) Xu and et al.
(2022), which call for higher average beam currents than facilities operating
today, can benefit from a more robust spin-polarized electron source.

Spin-polarized electrons from GaAsPierce and Meier (1976) are produced with
circularly-polarized light at a photon energy tuned to the material bandgap to
photoexcite electrons occupying the top of the valence band into the
conduction band. Ordinarily, these electrons could not contribute to the
photoemission process because their energy is not sufficient to overcome the
workfunction. Fortunately, GaAs can be brought to a condition called Negative
Electron Affinity (NEA) where the conduction band minimum is at a higher
energy than the vacuum on the surface, thus enabling bandgap energy photons to
produce photoemission. Bulk GaAs is limited to a theoretical maximum spin-
polarization of 50% because of its light-hole (LH) and heavy-hole (HH)
degenerate band states Pierce  _et al._ (1980), while measured polarization is
around 35% due to various depolarization mechanismsBir, Aronov, and Pikus
(1976); D’Yakonov and Perel (1971); Elliott (1954); Chubenko  _et al._ (2021).
In strained superlattice GaAs, the degeneracy can be removed and $>$90% spin
polarizations are achievable Maruyama  _et al._ (1992).

To activate GaAs to NEA, about one cesium monolayer and an oxidant are
deposited on the surface Karkare  _et al._ (2015). This layer is highly
reactive to gas molecules and, therefore, GaAs operation requires an extreme-
high vacuum (XHV) environment, which restricts its use to DC electron guns
only. Despite XHV operation, chemical poisoning Chanlek  _et al._ (2014); Wada
_et al._ (1990) along with ion back-bombardment Grames  _et al._ (2011) and
thermal desorption Kuriki  _et al._ (2011) severely limit the operational
lifetime of NEA GaAs photocathodes. While much work has been done to improve
the lifetime Bae  _et al._ (2018); Cultrera  _et al._ (2020); Bae  _et al._
(2020, 2022); Biswas  _et al._ (2021), there is motivation to investigate
other materials as potential robust spin-polarized electron beam
sourcesCultrera (2022). A recent result indicates an alkali-antimonide
photocathode (K2NaSb) can produce spin-polarized electrons Rusetsky  _et al._
(2022). In this work we present the first ever spin-polarized electron beam
demonstration from Gallium Nitride (GaN) based photocathodes grown in both the
hexagonal wurzite (W-GaN) and cubic zinc-blende (ZB-GaN) crystal orientations
Levenson  _et al._ (2023).

GaN is a direct bandgap material widely studied for its use in light emitting
diodes (LEDs) and other opto- and micro-electronics Nakamura, Mukai, and Senoh
(1991); Nakamura  _et al._ (1995); Amano  _et al._ (1988); Mukai, Narimatsu,
and Nakamura (1998); Nagahama  _et al._ (2000); Zhang  _et al._ (2023).
W-GaNKhan  _et al._ (1993) and ZB-GaNPaisley  _et al._ (1989) have respective
bandgap energies ($E_{g}$) of 3.4 and 3.2 eV Bougrov  _et al._ (2001a). Like
GaAs, a GaN photocathode requires activation to NEA for efficient operation.
Despite its common use in the electronics industry, GaN has been far less
investigated as a photocathode material because growth techniques for high-
quality samples were developed much more recently than those of GaAs Wang  _et
al._ (2021). Nonetheless, GaN boasts many interesting photocathode properties
Bazarov  _et al._ (2009); Levenson  _et al._ (2022). P-doped W-GaN has
achieved $>$50% quantum efficiency (QE)Uchiyama  _et al._ (2005) and N-polar
GaN was used to achieve NEA without Cs Marini  _et al._ (2018). The thermal
conductivity of GaN is more than a factor of two larger than that of GaAs
Carlson, Slack, and Silverman (1965); Sichel and Pankove (1977) which may
mitigate thermal desorption effects at high operational beam currents. NEA
W-GaN has also demonstrated a 20 times longer dark lifetime at its emission
threshold energy of 365 nm compared to GaAs at 780 nm Nishitani  _et al._
(2014), indicating GaN to be a more robust photo-emitter. GaN has been
extensively studied for its applicability in spintronics and spin-polarized
devices Faria Junior  _et al._ (2017); Chang  _et al._ (2007); Yu  _et al._
(2016); Banerjee  _et al._ (2013); yu  _et al._ . Several works have reported
asymmetries between left and right circularly-polarized light emission in
W-GaN resulting from spin-polarized excitation yu  _et al._ ; Sapega  _et al._
(2005); Brimont  _et al._ (2008); Bhattacharya  _et al._ (2017).

Mg-doped (3$\times$1019 cm-3 Mg concentration) W-GaN and ZB-GaN samples were
epitaxially grown on single-crystal W-GaN and 3C-SiC substrates, respectively
(see the Supplemental Information for details on sample preparation, narrow
band UV laser and spin polarization measurements). They were activated to NEA
through Cs deposition yielding QEs of 16.5% with W-GaN and 5% with ZB-GaN at
265 nm. To characterize the photoemission, a spectral response was performed
with both UV (LEDs) and visible (monochromator with white-light Xenon lamp)
light. This data is plotted in Fig. 1, where expected bandgap energies of
around 3.2 eV and 3.4 eV, and their associated QEs of 0.1% and 3.9%
(respectively for ZB- and W-GaN) are shown.

Both the LEDs and monochromator produced light with a typical 10 nm bandwidth
(BW). The energy spread corresponding to this bandwidth far exceeds the
valence band splitting of W- and ZB-GaN. Consequently, to be able to measure
the electron spin polarization (ESP) accurately, a narrow-band (1.4 nm FWHM),
tunable UV source was developed.

Figure 1: The QE of the ZB and W-GaN photocathodes. The inset data was
measured near the spin-polarization region (shown in gray) of the
photocathodes with the 1.4 nm bandwidth UV laser.

To compare dark lifetimes, measurements were performed under similar vacuum
conditions at a 2$\times 10^{-10}$ Torr base pressure near each photocathodes’
bandgap energy, (365 and 385 nm respectively for W and ZB-GaN) yielding 1/e
lifetime values of 11.3 and 4.5 hours, as shown in Fig. 2. For comparison, a
GaAs photocathode (100, Zn-doped at 9 $\times$ 1018 cm-3 concentration) was
activated with Cs only and monitored with a 780 nm laser to measure a
corresponding 1/e lifetime.

Figure 2: Threshold lifetimes of the NEA W-GaN, ZB-GaN and GaAs photocathodes
compared under similar vacuum conditions.

As shown in Fig. 2, we see a lifetime of 0.3 hours, 12 times less than that of
the ZB-GaN and 38 times less than that of W-GaN. The higher robustness of NEA
GaN photocathodes over GaAs was also found in Ref. Nishitani  _et al._ , 2014.
Once spectral and lifetime characterization was complete, the photocathodes
were transferred under vacuum into a Mott scattering polarimeter for ESP
characterization. The resulting ESP values are shown in Fig 3, where ZB-GaN
produced a peak ESP of 29% at 386 nm and W-GaN achieved a peak ESP of 17% at
364 nm.

Figure 3: Measured spin polarization from W-GaN (top) and ZB-GaN (bottom)
photocathodes.

To model ZB-GaN spin polarized photoemission, we start with the model from
D’Yakonov and Perel D’Yakonov and Perel (1971) (DP model), which approximates
the spin-polarization of electrons in a ZB structure upon excitement from the
circularly-polarized light. This model has also been the foundation of a GaAs
Monte Carlo spin polarization calculation Chubenko  _et al._ (2021). ZB-GaN
possesses a valence band split between the degenerate HH/LH bands and the
split-off (SO) band separated by an energy of $\Delta_{so}$ de Carvalho  _et
al._ (2010). However, in ZB materials with a small $\Delta_{so}$, the SO band
states start blending slightly with the HH/LH band states, so this must be
considered in spin polarization calculations. Note the DP model cannot be
applied to wurtzite structures, which have a non-degenerate valence band. In
the model, where $n=1,2,3$ correspond to the HH, LH and SO bands respectively,
spin polarization is calculated as

$P_{o}=\frac{\sum_{n}P^{(n)}_{o}K_{n}}{\sum_{n}K_{n}}.$ (1)

Here, $P^{(n)}_{o}$ refers to the initial degree of spin orientation of the
electrons excited from each valence sub-band $n$, and $K_{n}$ are values
proportional to the absorption coefficients from the $n$-th valence sub-band.
Both $P^{(n)}_{o}$ and $K_{n}$ are calculated from the material properties of
$E_{g}$, $\Delta_{so}$, $m_{c}$, $m_{h}$ and $m_{l}$. The last three values
are the effective masses of conduction band electrons, heavy-holes and light-
holes, respectively. Experimental measurements and calculations typically
yield $\Delta_{so}$ in the 15-20 meV rangeFeneberg  _et al._ (2012); Ramirez-
Flores  _et al._ (1994); Renard  _et al._ (2010); de Carvalho, Schleife, and
Bechstedt (2011) (significantly less than the $\Delta_{so}$ = 340 meV of GaAs
Pierce  _et al._ (1980)). In terms of $m_{0}$, we have $m_{c}=0.15$ Fanciulli,
Lei, and Moustakas (1993), $m_{h}=1.3$ Bougrov  _et al._ (2001b) and
$m_{l}=0.19$ Bougrov  _et al._ (2001b) for ZB-GaN. $P_{o}(\lambda)$ is shown
in blue in Fig. 4. Here we see where $P_{o}(\lambda)$ decreases with
decreasing wavelength as the photon energies become large enough to excite
electrons from the SO band. The shoulder corresponds to the SO band absorption
threshold with an expected 50% ESP peak.

We can therefore calculate the theoretically expected fraction of spin-
up/spin-down electrons computed with the DP model, $N_{\pm}(\lambda)$ from

$P(\lambda)=\frac{N_{+}(\lambda)-N_{-}(\lambda)}{N_{+}(\lambda)+N_{-}(\lambda)},$
(2)

where $N_{+}(\lambda)+N_{-}(\lambda)$ is constrained to be 1. To consider an
incident light bandwidth with an associated energy spread comparable to
$\Delta_{so}$, we convolve $N_{\pm}(\lambda)$ with light intensity

$N_{\pm}(\lambda,B)=\int
I(\lambda^{\prime},\lambda,\sigma_{\lambda})N_{\pm}(\lambda^{\prime})QE(\lambda^{\prime})d\lambda^{\prime},$
(3)

where $I(\lambda^{\prime},\lambda,\sigma_{\lambda})$ is the intensity
distribution at a wavelength $\lambda$, which in our calculations is assumed
to be Gaussian, $\sigma_{\lambda}$ is the bandwidth and $\lambda^{\prime}$ is
an integration variable. In the above formula we also account for the QE
dependence on wavelength using data taken from Fig 1. Using Eqns. 2 and 3, we
compute the theoretically expected spin polarization.

The resulting curve ($P_{\text{eff}}(\lambda,\sigma_{\lambda})$) is shown in
green in Fig 4, calculated for $\sigma_{\lambda}$ = 0.59 nm (FWHM 1.4 nm).
When computing the curve, $E_{g}$, $\Delta_{so}$ were allowed to vary to best
fit the data. We additionally introduce another parameter $M$ as a
multiplicative constant to Eqn. 3 to account for the electron depolarization
that occurs between excitation and emission not accounted in the DP model and
assumed to be wavelength-independent. From this model, we obtained fit values
of $E_{g}=3.205$ eV and $\Delta_{so}=15$ meV. This $\Delta_{so}$ value agrees
with a value reported for a ZB-GaN sample grown on 3C-SiCFeneberg  _et al._
(2012).

The parameter $M$ can be used to scale the DP model curve to approximate the
theoretically obtainable ESP with monochromatic light illumination
($P_{e}(\lambda)$) as shown in red in Fig 4. Fitting to our data yielded
$M=0.66$, leading to a $33\%$ maximum obtainable ESP. This value is similar to
the 35% typically reported for bulk GaAs, where due to the much larger
$\Delta_{so}$, the light bandwidth is ordinarily not considered.

Figure 4: A model to approximate the theoretical spin polarization spectrum of
the ZB-GaN photocathode. $P_{o}(\lambda)$ is the DP D’Yakonov and Perel (1971)
excitation distribution, described in the text. $P_{e}(\lambda)$ is the
excitation distribution scaled to account for depolarization mechanisms.
$P_{\text{eff}}(\lambda,\sigma_{\lambda}=0.59\text{ nm})$ is the expected
curve given 1.4 nm BW incident light.

Although ZB-GaN demonstrates higher spin-polarizations, it is much more
difficult (with less-developed growth techniques) to grow than W-GaN. Its
heteroeptaxial growth usually produces a defect-rich surface Adachi (1999),
specifically full of anti-phase boundary (APB) defects Kemper  _et al._
(2011). APBs and stacking faults originate and propagate up from the interface
between the 3C-SiC and GaN due to a substantial lattice mismatch. To
characterize these defects, another ZB-GaN sample and another single-crystal
W-GaN were grown for atomic force microscopy (AFM) images, shown in Fig. 6.
PredictablyKemper  _et al._ (2011), the ZB-GaN sample exhibits many APBs where
the crystal grain is rotated by 90 degrees. Such defects are not typical of
homoepitaxial single-crystal W-GaN samples, reportedly possessing around
$10^{5}$ cm-2 dislocation densities Kawamura  _et al._ (2003); Wu  _et al._
(2019), whereas they have been measured around $10^{9}$ cm-2 for ZB-GaN Kemper
_et al._ (2011).

Figure 5: W-GaN and ZB-GaN photocathode AFM scans. The W-GaN photocathode,
shown in areas of $a)$ 20$\times$20 $\mu$m2 and $b)$ 2$\times$2 $\mu$m2 has a
much smoother surface (0.36 nm RMS roughness) and a consistent crystal grain.
The ZB-GaN photocathode, shown in areas of $c)$ 20$\times$20 $\mu$m2 and $d)$
2$\times$2 $\mu$m2 is characterized by APBs and a relatively rough surface
(3.52 nm RMS roughness), as detailed in the text.

The DP model applied to ZB-GaN can not be applied to a wurtzite structure,
where the HH and LH bands are nondegenerate and split from a third valence
sub-band called the crystal field (CR) band Chuang and Chang (1996); Ren, Liu,
and Blood (1999). The W-GaN HH/LH band separation can be calculated as Chuang
and Chang (1996)

$\Delta
E=\frac{\Delta_{cr}+\Delta_{so}}{2}-\frac{1}{2}\sqrt{(\Delta_{cr}+\Delta_{so})^{2}-\frac{8}{3}\Delta_{cr}\Delta_{so}},$
(4)

where $\Delta_{cr}$ is the crystal field splitting. Given it is non-
degenerate, the theoretical maximum W-GaN ESP is 100%, however, the weak spin-
orbit coupling leaves only a very small HH/LH separation. The values in Eqn. 4
have been extensively calculated and measured de Carvalho, Schleife, and
Bechstedt (2011); Chuang and Chang (1996); Gil, Briot, and Aulombard (1995);
Reynolds  _et al._ (1996); Shikanai  _et al._ (1997); Korona  _et al._ (1996);
Campo  _et al._ (1997); Julier  _et al._ (1998); Yamaguchi  _et al._ (1998);
Bouzidi  _et al._ (2015); Chichibu  _et al._ (1997), and a review article on
the topic notes experiments seeming to converge around $\Delta_{cr}$ = 10 meV
and $\Delta_{so}$ = 17 meV Vurgaftman and Meyer (2003), yielding a $\Delta E$
= 5.2 meV HH and LH band separation. For these values, a 16.6 meV separation
can also be calculated between the LH and CR bandChuang and Chang (1996).

W-GaN room temperature spin relaxation time measurements, influenced by
substrate characteristics, doping concentration, and dislocation density, span
from just under a picosecond to around 100 picoseconds Kuroda  _et al._
(2004); Kum  _et al._ (2012); Bhattacharya, Baten, and Bhattacharya (2016);
Beschoten  _et al._ (2001); Buß  _et al._ (2010a). The considerably shorter
spin relaxation time in W-GaN compared to ZB-GaNRudolph, Buß, and Hagele
(2014), which has a room temperature value of around 1 nanosecondBuß  _et al._
(2014, 2010b), is a possible explanation for lower spin-polarization measured
in W-GaN. In one experimental work, a W-GaN sample with a slightly lower
dislocation density demonstrated a longer spin relaxation timeBhattacharya,
Baten, and Bhattacharya (2016). However, a mechanism where an increased
dislocation density could lead to an increased spin relaxation time has been
investigated Jena (2004).

As shown in Fig 1, both crystal orientations exhibit photoemission far below
the bandgap photon energy, which is common in GaN photocathodes Uchiyama  _et
al._ (2005). However, as shown in Fig. 3, the W-GaN photocathode exhibits a
long tail in its spin-polarized photoemission with below bandgap photon
energies (the top of valence band is at a 3.4 eV photon energy or 365 nm
wavelength). We focus our discussion of this unexpected behavior in W-GaN on
various defect states found in GaN and on the Franz-Keldysh (FK) effect, both
of which have been previously used to explain sub-bandgap photoemission in GaN
Pakhnevich  _et al._ (2004); Sauty (2022).

Nitrogren vacancies and Mg acceptors are common defects found in MBE-grown Mg-
doped p-GaNAlves  _et al._ (2003); Reshchikov and Morkoç (2005). Nitrogen
vacancies have been attributed to bands (seen in various photoluminescence
measurements on Mg:GaN) far below (around 0.5 eV and up) the band gap energy
Nayak  _et al._ (2019); Reshchikov  _et al._ (2014); Zeng  _et al._ (2006);
Reshchikov, Ghimire, and Demchenko (2018); Hu  _et al._ (2022) and may be
responsible for the sub-bandgap photoemission in this region. The primary
bands near the bandgap concern Mg acceptor defects Reshchikov and Morkoç
(2005); Reshchikov, Ghimire, and Demchenko (2018). The Mg acceptor ionization
energy is slightly over 200 meV in W-GaN, Reshchikov, Ghimire, and Demchenko
(2018); VanDeWalle and Neugebauer (2004); Wang and Chen (2001) but only 100
meV in ZB-GaN, Hu  _et al._ (2022); Hernández-Gutiérrez  _et al._ (2020). Mg
acceptor states may explain sub-bandgap spin-polarization as they may possess
spin-orbit and crystal-field splittings in W-GaN as some works
discussMalyshev, Merkulov, and Rodina (1998); Aliev  _et al._ (2005, 2006). In
an experimental work, the P3/2 character of the Mg acceptor states was
observed via magnetic resonance only in samples with low dislocation
densityGlaser  _et al._ (2007). Since our W-GaN is such a sample (while the
heteroepitaxial ZB-GaN sample has a significantly higher dislocation density),
a long sub-valence band spin-polarization tail in the W-GaN sample could be
explained by a split Mg acceptor level state. Furthermore, in ZB-GaN, the
acceptor level may not be as strongly polarized as in W-GaN because it is not
aided by the crystal field splitting present in W-GaN. Mn-doped GaAs may
present the same effect, where the Mn acceptor states may also produce spin-
polarized photoemission Okabayashi  _et al._ (2001); Schneider  _et al._
(1987).

Another possible mechanism is the FK effect, which could also potentially
produce spin-polarized electrons from below bandgap photon energies. The FK
effectFranz (1958); Keldysh (1958), occurring when strong electric fields (can
be externally-applied, though in our case, induced by the dopants) bring some
valence band electrons into the bandgap, has also been extensively studied in
GaN Peng  _et al._ (2003); Cavallini  _et al._ (2007); Verma  _et al._ (2020);
Maeda  _et al._ (2016); Bao and Xu (2019).

Consequently, because of the lower Mg acceptor ionization energy in ZB-GaN
discussed above, ZB-GaN typically has higher hole concentrations than W-GaN
for the same Mg concentrations. A Hall Effect measurement performed on our
W-GaN sample resulted in a $9.1\times 10^{17}$ cm-3 hole concentration,
slightly higher than other measurements indicating a $3\times 10^{19}$ cm-3 Mg
concentration corresponding with hole concentrations of 1-6 $\times 10^{17}$
cm-3 in W-GaN Alves  _et al._ (2003); Horita  _et al._ (2017); Dai  _et al._
(2021). Since the 3C-SiC substrate is conductive, parallel conduction
prohibited an accurate hole concentration measurement in the ZB-GaN sample,
however hole concentrations of $7\times 10^{18}$ cm-3 in ZB-GaNHernández-
Gutiérrez  _et al._ (2020); Compeán-García  _et al._ (2019) are to be expected
with our Mg concentration. Considering the ZB-GaN sample likely possesses a
higher hole concentration, one would expect it to have a stronger induced
electric field, and thus a stronger FK effect than W-GaN. However, as
discussed, the dislocation density of the ZB-GaN sample is likely several
orders of magnitude larger than that of the W-GaN. Crystal structure defects
common to heteroepitaxial ZB-GaN can produce a wide spectra of states around
the valence band edge that may not be spin-polarized Kemper  _et al._ (2011);
Zscherp  _et al._ (2022). It is likely the appearance of these defect states
drowns out the ability to photoemit spin-polarized electrons in this region,
either from a Mg acceptor state or the FK effect. While Mg acceptor state
splittings and the FK effect are interesting mechanisms to explain the wide
W-GaN spin-polarization curve, further work is necessary to understand the
origins of the broad tail observed in our W-GaN ESP data.

The demonstration of GaN as a spin-polarized photocathode is a promising
result with opportunities for improvements towards the viability for GaN as a
robust spin-polarized electron source. ZB-GaN displays spin-polarization
comparable to that of bulk GaAs and already boasts a longer dark lifetime.
Further lifetime and QE enhancements may come from improved growth techniques
to yield a better crystal quality with less defects. One path towards improved
ZB-GaN films is through the use of an AlN nucleation layer by improving the
lattice mismatch between GaN and 3C-SiC, thereby reducing crystal defects
Zscherp  _et al._ (2022); Gundimeda  _et al._ (2022).

A possible path towards improving the ESP of ZB-GaN is to introduce crystal
strain to remove the HH/LH degenerancy, commonly done with GaAs. The
properties of strained W-GaN are already well-understood Chuang and Chang
(1996); Chichibu  _et al._ (1997); Majewski, Städele, and Vogl (1996); Park
and Chuang (1999), and works detail experiments done with both strained W-GaN
Ghosh  _et al._ (2002) and ZB-GaN structuresMietze  _et al._ (2011). One work
reported a nearly 100% circularly polarized photoluminescent beam produced
with such a sample Chang  _et al._ (2007).

While the ability to grow W-GaN with superb crystal quality already yields
high QEs and long dark lifetimes, it has a relatively low ESP value. Cooling
W-GaN during photoemission may improve the ESP value, as one work shows that
the spin-relaxation time in n-type GaN increases by a factor of 5 at 50 K from
that of room temperatureBuß  _et al._ (2010). Lowering the doping
concentration may also help increase the spin relaxation time, although doing
so could sacrifice QE.

W- and ZB-GaN QE may be improved with the use of Distributed Bragg Reflectors
(DBRs), as done with GaAsSaka  _et al._ (1993); Liu  _et al._ (2016). DBRs
have been grown with both W-GaN Ng  _et al._ (1999); Ng, Moustakas, and Chu
(2000); van Deurzen  _et al._ (2023) and ZB-GaNLi  _et al._ (2005). Further
photocathode robustness improvements may also be found through robust hetero-
structures used as NEA activation layers, which have been developed to improve
the operational lifetime of GaAsBae  _et al._ (2018); Cultrera  _et al._
(2020); Bae  _et al._ (2020, 2022); Biswas  _et al._ (2021), and through
enhancements in N-polar GaNNomoto  _et al._ (2022), which has demonstrated a
Cs-free NEA conditionMarini  _et al._ (2018). The GaN bandgap may be tuned
with indium incorporation (InGaN)Ulmer  _et al._ (2005); Sato  _et al._
(2022); Chaudhuri  _et al._ (2022); Yu  _et al._ (2016), which may provide a
path towards an incident-light-tunable spin-polarization source.

Spin-polarized photoemission has been measured for the first time from both
wurtzite and zinc-blende GaN photocathodes. The p-doped photocathodes were
epitaxially grown and characterized in a Mott Polarimeter. The wurtzite GaN
photocathode exhibited a higher quantum efficiency and dark lifetime at
threshold wavelengths than that of the zinc-blende photocathode. However,
using a tunable OPA, a peak spin polarization of nearly twice that of wurtzite
GaN was observed in zinc-blende GaN.

See the Supplementary Information for additional details on GaN sample growth
and the narrow-band circularly polarized UV light source.

The authors would like to thank J.K. Bae, N. Otto and M.A. Reamon for
experimental assistance and T. Arias, L. Cultrera, O. Chubenko and T. Wu for
thoughtful discussion. This work is supported by United States Department of
Energy (DOE) grant DE-SC0021002 and by the U.S. National Science Foundation
under Award PHY-1549132, the Center for Bright Beams.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## Supplemental Information

##  I Sample Preparation

GaN samples were grown in a Veeco Gen10 molecular beam epitaxy (MBE) system at
Cornell University. The chamber features effusion cells filled with elemental
sources of gallium, aluminum and magnesium. To grow W-GaN, a 2$\times$2 in2
single-crystal GaN substrate was purchased from Ammono and diced into a
7$\times$7 mm2 square. For the ZB-GaN substrate, a 4$\times$4 in2 wafer of a
10.3 $\mu$m thick silicon carbide (3C-SiC) layer on a 525 $\mu$m thick silicon
(Si 100) base purchased from NOVASiC was diced into a 1$\times$1 cm2 square.
The surface morphologies of the two substrates are shown in atomic force
microscopy (AFM) scans in Fig. 1. Prior to sample growth, the substrates were
ultrasonicated sequentially for 10 minutes each in acetone, methanol and
isoproponol before being inserted into the MBE chamber, where they were
outgassed at 200 degrees Celsius for 7 hours. Next, a 100 nm thick
unintentionally-doped (UID) GaN layer was grown on each to set the epitaxial,
atomic (W or ZB) structure of the material. This was then followed by a 1
$\mu$m thick Mg-doped GaN layer, which was grown in each respective
orientation. To optimize the QE of the photocathodes, the doping concentration
was set to 3$\times 10^{19}$ cm -3 based on work reported elsewhere Uchiyama
_et al._ (2005). Metal-rich conditions were maintained throughout the
epitaxial growth process, grown within the step-flow growth mode. Ga droplets
were desorbed in-situ at the conclusion of the growth.

Figure 6: AFM scans of the single-crystal W-GaN substrate and 3C-SiC
substrate. The single-crystal W-GaN substrate, shown in areas of $a)$
10$\times$10 $\mu$m2 and $b)$ 2$\times$2 $\mu$m2 has an RMS roughness of 0.57
nm, while the 3C-SiC substrate, shown in areas of $c)$ 10$\times$10 $\mu$m2
and $d)$ 2$\times$2 $\mu$m2 has an RMS roughness of 0.49 nm.

After growth, the samples were removed from the MBE system and placed into a
static vacuum suitcase (exposed to air for less than 10 seconds) to be
transported across campus to the Bright Beams Photocathode Laboratory Cultrera
_et al._ (2018). Once transported, the suitcase was vented and the sample was
mounted on a stainless steel puck. The sample was fixed to the puck by a cap
with a 7 or 5 mm diameter hole to expose the GaN. For good electrical and
thermal contact, a small amount of indium foil was placed on each of the 4
edges of the sample beneath the cap. During this process, the photocathode was
exposed to air for approximately five minutes before insertion into the
photocathode activation chamber.

The samples were annealed at 600 degrees Celsius for 6 hours prior to NEA
activation. Here, the photocurrent was monitored with 10 $\mu$W of 265 nm
light generated by an LED incident on the photocathode while Cs was deposited
onto the surface with a filament source. Cs deposition was stopped when the QE
peaked.

##  II Narrow band UV Source

Characterization of a GaN photocathode as a spin-polarized electron source
requires illumination with a narrow spectral bandwidth due to the relatively
small valence band splitting. Additionally, for spectral analysis of both W
and ZB-GaN, broad tunability between 360-390 nm is required. To accomplish
this, we constructed an optical parametric amplifier (OPA) with output in the
near-infrared and added a frequency-doubling stage to achieve the required UV
wavelengths. The OPA is powered by a 20W PHAROS laser system purchased from
Light Conversion which generates approximately 100 fs laser pulses at a
repetition rate of 1.1 MHz and a wavelength of 1030 nm. The beam is split
between two paths. In the first path, the light is frequency doubled to 515 nm
and used as the pump source of the OPA. In the second path, the pulses are
tightly focusing into an undoped YAG crystal to generate a (chirped) white
light supercontinuum for the OPA signal beam. The 515 nm and white light are
then recombined inside a beta barium borate (BBO) nonlinear crystal where the
OPA process occurs. A tunability range from 720–780 nm was achieved by
adjusting the crystal orientation and relative arrival times of the signal and
pump light inside the BBO crystal.

The OPA output is frequency-doubled using a bismuth triborate (BiBO) nonlinear
crystal Peltz  _et al._ (2005). Over the OPA tunability range, the frequency
doubled process typically had 5-10% conversion efficiency, nominally producing
10-20 mW of narrow-band UV light. The beam is then launched into a single-mode
UV optical fiber for transport to the Mott polarimeter. Nonlinear spectral
broadening observed in the fiber was minimized by reducing the laser intensity
prior to launching into it. At the sample, we achieved a spectral bandwidth
(full-width half-maximum) of 1.4 nm and a power level of 5 $\mu$W across the
tunable UV ranges.

Circularly polarized light is required to excite an electron beam with a net
spin polarization. Upon exiting the fiber, the light is elliptically polarized
at an arbitrary angle. Circular polarization was obtained using a linear
polarizer and a quarter-waveplate with the fast axis oriented 45 degrees off
the polarizer. To account for bias in the detection rates, count rates are
measured for both left- and right-handed light during the measurement.
Handedness was switched by rotating the waveplate 90 degrees.

Prior to measurements with the Mott polarimeter, the degree of circular
polarization was measured. A second linear polarizer was placed after the
waveplate, and transmitted optical power was monitored while rotating the
second polarizer through a full 360 degrees. The degree of circular
polarization was calculated usingPierce and Meier (1976)

$P_{cp}=\frac{2(I_{min}I_{max})^{1/2}}{I_{min}+I_{max}},$ (5)

where $I_{min}$ and $I_{max}$ are the minimum and maximum intensities achieved
during rotation. The optimal waveplate angles for the $\lambda/4$ and
$3\lambda/4$ were found such that the degree of circular polarization for each
handedness was 99.8%.

##  III Spin Polarization Measurements

The spin polarization measurements were performed in a Mott Scattering
Polarimeter with a 20-keV retarding bias on a tungsten targetMott (1929);
McCarter  _et al._ (2010). A 90 degree electrostatic bend rotates the
initially longitudinally oriented electron spin to the transverse plane as
defined by the beam direction. Additional electrostatic correctors are used to
guide the beam to the target and Einzel lenses provide beam focusing.
Scattered electrons are registered in two symmetrically placed Channeltron
detectors placed on both sides of the target. A Sherman function value of 0.18
was calibrated in an earlier work Bae  _et al._ (2020).

After circularly polarized light was produced as detailed above, it was
aligned to the photocathode and the electron optics for beam transport to the
target were tuned to optimize the count rates on the Channeltron detectors.
The ESP value was determined by measuring the count rate asymmetry, $A$,
between detectors McCarter  _et al._ (2010); Dunning (1994),

$A=\frac{\sqrt{L_{-}R_{+}}-\sqrt{L_{+}R_{-}}}{\sqrt{L_{-}R_{+}}+\sqrt{L_{+}R_{-}}},$
(6)

where $L$ and $R$ correspond to the integrated number of counts registered on
the left and right detectors, respectively, while $+$ and $-$ denote the two
handedness states of the light. The measured spin-polarization is the
asymmetry scaled by the effective Sherman function. At each wavelength, 20
measurements were taken and averaged. Background detection rates were
registered and subtracted at each step of the measurement. The reported
uncertainties are statistical and do not account systematic errors in the
instrument.

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