# Identification of different silicon vacancy centers in 6$H$-SiC

Harpreet Singh1, Andrei N. Anisimov1,2, Pavel G. Baranov2 and Dieter Suter1
1Fakultät Physik, Technische Universität Dortmund,
D-44221 Dortmund, Germany. 2Ioffe Institute, St. Petersburg 194021, Russia

###### Abstract

Silicon vacancies in silicon carbide (SiC) have been proposed as interesting
candidates for quantum technology applications such as quantum sensing and
quantum repeaters. SiC exists in many polytypes with different plane stacking
sequences, and in each polytype, the vacancies can occupy a variety of
different lattice sites. In this work, we characterize and identify the three
most important charged silicon vacancies in the 6$H$-SiC polytype. We record
the photoluminescence and continuous-wave optically detected magnetic
resonance spectra at different radio-frequency power levels and different
temperatures. We individually select the zero-phonon lines of the different
silicon vacancies at low temperatures and record the corresponding optically
detected magnetic resonance (ODMR) spectra. ODMR allows us to correlate
optical and magnetic resonance spectra and thereby resolve a controversy from
earlier work.

##  I Introduction

Silicon carbide (SiC) is an interesting material for a range of applications
that rely on its wide bandgap and established manufacturing processes Wang
_et al._ (2017); Rabkowski  _et al._ (2012); Izhevskyi  _et al._ (2000);
Gonzalez Szwacki (2017); Tarasenko  _et al._ (2018); Pavunny  _et al._ (2021).
It contains different types of silicon vacancies, carbon vacancies and
silicon-carbon divacancies, which show remarkable spin properties that make
them promising candidates for new quantum technologies. Silicon vacancies, as
a specific example, are negatively charged and have spin 3/2 Riedel  _et al._
(2012). Irradiation with visible or near-infrared light results in nonthermal
population of the spin states. Two characteristic parameters of $V_{Si}^{-}$
centers are the emission wavelength and the zero field splitting.

In the low temperature photoluminescence (PL) spectra, different centers can
be identified by their emission wavelengths. In sequence of increasing
wavelengths, they are therefore labeled $V_{1},$ $V_{2}$ and $V_{3}$. In terms
of the local structure, they are associated with different lattice sites where
the environment has cubic ($k$) or hexagonal ($h$) symmetry. The
correspondence between emission wavelength and lattice sites is a matter of
ongoing controversy Baranov  _et al._ (2011); Ivády  _et al._ (2017); Sörman
_et al._ (2000); Biktagirov  _et al._ (2018); Davidsson  _et al._ (2019).

In an earlier paper, we characterized silicon vacancies in $6H$-SiC Breev  _et
al._ (2022) in terms of their photoemission as well as their spin Hamiltonian,
using optically detected magnetic resonance (ODMR). Since ODMR correlates
optical properties with energy differences between spin states, it provides a
useful approach for associating the zero-field splittings with the emission
wavelengths. The goal of this work is to identify the different types of
$V_{Si}^{-}$ centers in $6H$-SiC. For this purpose, we combine
photoluminescence (PL) measurements at different wavelengths and different
polarizations with radio-frequency excitation of the spin transitions to
record ODMR spectra under a range of different conditions, including its
temperature dependence.

This work is structured as follows: Section II introduces the spin system of
the sample, as well as its photoluminescence as a function of the direction
and orientation of the emission, and separates it into the contributions of
the 3 types of vacancies. Section III shows the temperature-dependent ODMR
spectra for emission parallel and perpendicular to the $c$-axis. To
distinguish the contributions from the different types of centers, we record
signals at different wavelengths separately. Section IV contains the spin-
lattice and spin-spin relaxation times obtained by time-resolved ODMR. Section
V contains a brief discussion and concluding remarks.

##  II System

For creating silicon vacancies homogeneously, the sample can be irradiated
with neutrons or electrons Hain  _et al._ (2014); Fuchs  _et al._ (2015).
Neutron irradiation leads to more lattice damage than electron irradiation and
creates many other unwanted detects, resulting in faster relaxation rates of
the vacancy spins Kasper (2021). For this work, we therefore used electron
irradiation of a 6$H$-SiC sample Singh  _et al._ (2022). More details of the
sample preparation are given in Appendix A.

At the silicon vacancy site, four dangling $sp^{3}$ orbitals contribute four
electrons. In addition, the silicon vacancy can capture one or two electrons,
depending on the Fermi level, and become a negatively charged silicon vacancy
($V_{Si}^{-}$). Here, we only consider centers with a single negative charge,
which have a spin of 3/2 Riedel  _et al._ (2012). The energy levels of these
vacancies can be determined from a PL spectrum.

###  II.1 Photoluminescence

We start the characterisation of the sample with the photoluminescence
spectra. Depending on the transition dipole, whose orientation varies with the
different types of vacancies Breev  _et al._ (2022); Zhou  _et al._ (2021),
the PL emission shows an orientation dependence. We therefore recorded PL
spectra for emission parallel and perpendicular to the c-axis. The detailed
description of the PL setup is given in Appendix B.

Figure 1: Photoluminescence (PL) recorded with different optical filters at 5K
(a) for photons emitted $\bot$ to the $c$-axis and (b) $\|$ to the $c$-axis.
PL spectra obtained by filtering the PL with 860 nm, 890 nm and 905 nm
bandpass filters of 10 nm bandwidth to select the zero-phonon line of $V_{1}$,
$V_{2}$, and $V_{3}$ type $V_{Si}^{-}$.

Figures 1 (a) and (b) show the PL spectra recorded for emission parallel and
perpendicular to the $c$-axis at 5 K. In addition to the full spectra, where
we used an 850 nm long-pass (LP) filter to suppress scattered laser light, we
also recorded spectra with 860 nm, 890 nm and 905 nm bandpass (BP) filters.
The zero phonon lines (ZPL) of the different $V_{Si}^{-}$ are clearly visible
in the spectra at 865 nm (V1), 887 nm (V2), and 908 nm ($V_{3}$) Sörman  _et
al._ (2000); Baranov  _et al._ (2011). Comparison of the two sets of spectra
shows that $V_{1}$ and $V_{3}$ emit more PL parallel to the c-axis, while
$V_{2}$ emits more perpendicular to the $c$-axis Janzén  _et al._ (2009);
Breev  _et al._ (2022); Singh  _et al._ (2020).

Figure 2: Energy level diagram of $V_{Si}^{-}$ and optical pumping scheme.
$|G_{i}\rangle$ are the spin states of the electronic ground state
$|E_{i}\rangle$, correspond to the electronically excited state and
$|S\rangle$ is the shelving state.

The assignment of the emission lines to specific lattice sites was debated in
the literature. An early study of $6H$-SiC Sörman  _et al._ (2000), indicated
that $V_{1}$ and $V_{3}$ correspond to $V_{Si}^{-}$ at the cubic lattice sites
$k_{1}$ and $k_{2}$ and $V_{2}$ corresponds to the hexagonal lattice site $h$.
However, more detailed studies indicate that $V_{1}$ corresponds to the
hexagonal lattice site $h$ and $V_{2}$ and $V_{3}$ to the cubic lattice sites
$k_{2}$ and $k_{1}$ respectively Davidsson  _et al._ (2019); Biktagirov  _et
al._ (2018). We adopt the latter assignment here.

###  II.2 Spin

We consider the $S=3/2$ spin of a of $V_{Si}^{-}$ center in the absence of an
external magnetic field. Figure 2 shows the relevant part of the energy level
diagram. The states $|G_{1}\rangle$ and $|G_{2}\rangle$ are doubly degenerate
spin substates of the electronic ground state with $m_{s}=\pm 1/2$ and $\pm
3/2$ in the case of $V_{1}$ and $V_{2}$ Baranov  _et al._ (2011); Davidsson
_et al._ (2019). In the case of $V_{3}$, the zero field splitting is negative
and the the lowest energy state is therefore $m_{s}=\pm 3/2$ Soltamov  _et
al._ (2019); Davidsson  _et al._ (2019). Similarly, the states $|E_{1}\rangle$
and $|E_{2}\rangle$ are spin states of the electronically excited state. The
state $|S\rangle$ represents the shelving state, which has spin $S$=1/2 and
plays an essential role for generating spin polarization by optical pumping
Baranov  _et al._ (2011); Singh  _et al._ (2021). Laser illumination excites
transitions from the ground states $|G_{1}\rangle$ and $|G_{2}\rangle$ to the
excited states $|E_{1}\rangle$ and $|E_{2}\rangle$. From the excited states
$|E_{i}\rangle$, most of the population falls back to the ground states
$|G_{i}\rangle$ due to spontaneous emission. A smaller fraction undergoes
intersystem crossing (ISC) to the shelving state $|S\rangle$, and from there,
preferentially populates the ground state $|G_{2}\rangle$, as shown in Fig. 2.

In the absence of an external magnetic field, the effective spin Hamiltonian
is

$\mathcal{H}=D(S_{z}^{2}-5/4),$ (1)

where $D$ is the zero-field splitting constant whose value depends on
environment of the center. $S_{z}$ is the electron spin operator along the $z$
axis ($||$ $c$ axis). In the magnetic resonance spectra, we therefore expect a
single resonance line at frequency $2D$ for every type of vacancy. Figure 3
shows, as an example, an ODMR spectrum of a 6$H$-SiC sample that contains
three different types of vacancies. It consists of two resonance lines close
to 28 MHz and 130 MHz. The assignment of these resonance lines to the
different types of $V_{Si}^{-}$ in $6H$-SiC has been somewhat contentious, in
particular with respect to $V_{1}$. Table 1 provides a summary of data. While
Davidsson _et al._ Davidsson  _et al._ (2019) assume that $V_{1}$ contributes
to the resonance near 28 MHz, Biktagirov _et al._ Biktagirov  _et al._ (2018)
suggest that it is close to zero and therefore not observable. In the
following section, we attempt to resolve this issue by measuring ODMR spectra
at low temperatures and separating the PL from the ZPLs of the 3 different
vacancies using suitable optical bandpass filters.

Center | Sorman _et al._ Sörman  _et al._ (2000) | Davidsson _et al._ Davidsson  _et al._ (2019) | Biktagirov _et al._ Biktagirov  _et al._ (2018) | Astakhov _et al._ Astakhov  _et al._ (2016)
---|---|---|---|---
Exp | Exp | Exp | Exp
$2D^{g}$ (Site) |  $2D^{g}$ (Site) |  $|$$2D^{g}|$ (Site) |  $|$$2D^{e}|$ (MHz)
$V_{1}$ | 27.6 MHz ($k_{1}$) | 26.6 MHz ($h$) | 0 ($h$) | 367
$V_{2}$ | 128.4 MHz ($h$) | 128 MHz ($k_{2}$) | 128 MHz ($k_{2}$) | 1030
$V_{3}$ | 27.6 MHz ($k_{2}$) | 27.8 MHz ($k_{1}$) | 28 MHz ($k_{1}$) | 367
Table 1: Experimental values for the zero field splittings (ZFS) splittings
$2D$ for the 3 types of different $V_{Si}^{-}$ in 6$H$-SiC. The upper indices
$g$ and $e$ refer to the electronic ground and excited states. The values and
the proposed assignments to the different types of centers are taken from 4
earlier publications.

##  III Optically detected magnetic resonance

Optically detected magnetic resonance (ODMR) combines optical measurements
with electron spin resonance spectroscopy. Compared to conventional EPR, this
double resonance technique increases the sensitivity and information content
of magnetic resonance Suter (2020); Carbonera (2009). For low-temperature
ODMR, we placed the sample in a liquid helium flow cryostat and irradiated it
with 785 nm laser light. The emitted PL was collected using a convex lens and
focused with another convex lens on an avalanche photodiode (APD) via a
suitable optical filter. The photocurrent was measured with a lock-in
amplifier. A radio-frequency (RF) field was applied to the sample through a
wire (for continuous-Wave ODMR) or a coil (for pulsed experiments) ,
terminated with a 50-Ohm resistor. To reduce background signal, we modulated
the RF with a TTL signal from a digital word generator (DWG) and demodulated
the APD signal with a lock-in amplifier referenced to the TTL signal. Appendix
B provides a detailed description of the ODMR setup.

###  III.1 Dependence on RF Power

Figure 3 (a) shows ODMR spectra recorded with different RF powers at room
temperature (296 K) and at 5 K. These spectra were recorded with a 850 nm long
pass optical filter, which suppresses the scattered laser light but passes
most of the PL from $V_{si}^{-}$. At low RF power, only two ODMR peaks are
visible near 28 MHz and 130 MHz. With increasing RF power, additional
resonances appear at 14 MHz ($P_{3}^{2}$), 42 MHz ($P_{2}^{3}$), and 64 MHz
($P_{2}^{2}$). The peak $P_{3}^{2}$ is due to the absorption of 2 RF photons
by the $V_{1}/V_{3}$ vacancy Singh  _et al._ (2022), whereas the peaks
$P_{2}^{2}$ and $P_{2}^{3}$ are due to 2 and 3 photon absorption by the
$V_{2}$ vacancy Singh  _et al._ (2022). Figure 3 (b) shows the amplitudes of
the 1-photon peaks of $V_{1}/V_{3}$ and $V_{2}$ vs. the applied RF power: they
increase with the applied power but saturate for $P>0.3$ W. This behaviour can
be fitted with the function

$S(P)=S_{max}[P/(P_{0}+P)],$ (2)

where $S(P)$ is the signal amplitude at power $P$, $S_{max}$ is the asymptotic
amplitude and $P_{0}$ the saturation power. The resulting fitting parameters
are given in Table 2.

Figure 3 (c) shows the linewidths of the 1-photon peaks of $V_{1}/V_{3}$ and
$V_{2}$ vs. the RF power. The linewidth data $LW(P)$ were fitted to the
function

$LW(P)=LW_{0}+a\sqrt{P},$ (3)

where $LW_{0}$ and $a$ are the fitting parameters and their values are given
in Table 2.

$V_{si}^{-}$ | Temp |  $S_{max}$($\Delta PL/PL$) |  $P_{0}$(W) |  $LW_{0}$(MHz) |  $a$ (MHz W-1/2)
---|---|---|---|---|---
$V_{1}/V_{3}$ | 5 K | -0.014 $\pm$0.001 | 0.023$\pm$0.012 | 5.5 $\pm$ 0.8 | 2.3 $\pm$ 0.7
$V_{2}$ | 298 K | -0.069 $\pm$ 0.007 | 0.070 $\pm$ 0.043 | 8.4$\pm$0.7 | 3.7$\pm$0.6
$V_{2}$ | 5K | -0.234$\pm$0.054 | 0.097$\pm$0.097 | 7.5 $\pm$ 0.4 | 3.4 $\pm$ 0.4
$V_{1}/V_{3}$ | 298 K | 0.14 $\pm$ 0.01 | 0.05 $\pm$ 0.03 | 6.6 $\pm$ 0.4 | 3.4 $\pm$0.3
Table 2: Fitting parameters of Eqs (2) and (3). Figure 3: (a) ODMR signal vs.
frequency recorded with different RF powers in zero magnetic field at 5 K and
296 K. The horizontal axis is the frequency in MHz and the vertical axis the
relative change of the PL, recorded by the lock-in amplifier. (b) ODMR signal
vs RF power and (c) linewidth vs RF power. Figure 4: ODMR signal as a function
of temperature recorded with PL emitted (a, c) parallel and (b, d)
perpendicular to the $c$-axis. The range from 5 MHz to 50 MHz is shown on an
expanded scale in (c, d). The color scale and the $y$-axis of the 1D spectra
are in units of $\Delta$PL/PL%. Figure 5: (a) ODMR spectra recorded with
different optical filters at 28 K for PL emitted parallel to the $c$-axis. 860
nm, 890 nm and 905 nm bandpass filters were used to select the zero-phonon
lines of $V_{1}$, $V_{2}$, and $V_{3}$. (b) The range from 18 MHz to 38 MHz,
where the $V_{1}$ and $V_{3}$ resonances are located, are shown on an expanded
scale. The main peaks was fitted to a Lorentzian. With the 860 nm and 905 nm
BP filters, the center frequencies are 27 MHz and 28.08 MHz, respectively.

###  III.2 Temperature dependence

Figures 4 (a) and (b) show the ODMR spectra for the range of temperatures from
5 K to 290 K when the PL is recorded parallel and perpendicular to the
$c$-axis using an RF power of 26 dBm (0.3 W). The horizontal axis corresponds
to the RF frequency, and the vertical axis to the temperature. The color
represents the relative change of PL, as indicated by the scale bar on the
right. The ODMR signal near 130 MHz, which corresponds to $V_{2}$, increases
with decreasing temperature while the ODMR signal near 28 MHz, which is due to
$V_{1}/V_{3}$, decreases. We recorded larger ODMR signals ($\Delta$PL/PL) when
the PL is emitted parallel to the $c$-axis in the case of $V_{1}/V_{3}$,
whereas the ODMR signal of $V_{2}$ was larger for emission $\perp c$. In both
orientations, the $V_{2}$ signal increases with decreasing temperature, while
it gets smaller in the case of $V_{1}/V_{3}$. However, for PL emitted parallel
to the $c$-axis, the ODMR signal near 28 MHz changes sign. Figure 4 (c), shows
that the ODMR signal vanishes at 22 K and becomes negative at 15 K. At even
lower temperatures, the negative signal increases in magnitude.

Figures. 6 (a) and (b) show the measured frequency of the ODMR resonance lines
that correspond to the ZFS as a function of temperature. (a) corresponds to
the $V_{2}$ center while the resonance line near 28 MHz is dominated by the
signal from $V_{3}$ in the temperature range from 36 K to 295 K. The extracted
data is fitted to the function

$ZFS(T)=ZFS_{0}+b\,T^{2}.$ (4)

The best fits are obtained for the parameters $ZFS_{0}$ = 129.9 $\pm$ 0.5 MHz
and 28.64 $\pm$ 0.02 MHz , $b$ = (-1.19 $\pm$ 0.02) $\times$ 10-5 MHz K-2 and
(-1.52 $\pm$ 0.02) $\times$ 10-5 MHz K-2 for $V_{2}$ and $V_{1}/V_{3}$,
respectively. These results correspond to an improvement over earlier reports
that the ground-state ZFS does not depend on temperature Astakhov  _et al._
(2016).

Figure 6: Measured temperature dependence of the ZFS of the resonance lines
near 130 (a) and 28 MHz (b).

###  III.3 Optically selective detection

For a better identification of the different ODMR signals, we only collect PL
from specific wavelength ranges by passing it through different optical
filters. Figure 5 (a) shows the ODMR spectra recorded with different bandpass
(BP) filters at 28 K for PL emitted $\parallel$ $c$-axis. The top, middle, and
bottom spectra were recorded with 860 nm, 890 nm, and 905 nm BP (10 nm
bandwidth) filters, which predominantly select PL from the zero-phonon line
(ZPL) of the $V_{1}$, $V_{2}$, and $V_{3}$ vacancies, respectively.

The top spectrum (860 nm BP), contains only a small negative peak at 27 $\pm$
1 MHz. This differs strongly from the ODMR spectra in Fig. 3 recorded with the
850 nm LP filter, where we observed two single-photon resonances near 28 MHz
and 130 MHz. Since the 860 nm BP filter selects the ZPL of $V_{1}$, we assign
the negative peak at 27 MHz to $V_{1}$. Since the signal is quite small under
these conditions, we expanded the vertical scale of the top spectrum by a
factor of 20 to make the peak visible.

The middle ODMR spectrum was recorded with a BP filter centered at the ZPL of
$V_{2}$. It is dominated by a signal at 130 $\pm$ 0.01 MHz, which we therefore
attribute to $V_{2}$. The bottom ODMR spectrum was recorded with the 905 nm BP
filter; we observe one negative and two positive peaks. We attribute the
positive peak at 28.1 $\pm$ 0.6 MHz to the $V_{3}$ center, whose ZPL coincides
with the center of the 905 nm BP filter. The negative peak at 129.93 $\pm$0.03
MHz is due to the phonon sidebands (PSB) of $V_{2}$, which extend well into
the range of the 905 BP filter.

Figure 5 (b) shows the frequency range from 18 MHz to 38 MHz, where the
signals from $V_{1}$ and $V_{3}$ are centered, on an expanded scale. In the
top spectrum, the signal from $V_{1}$ dominates, in the bottom spectrum that
from $V_{3}$.

As an additional way to distinguish between the PL emitted by $V_{1}$ and
$V_{3}$, we also measured ODMR spectra with polarizers at different
orientations. The corresponding data are presented in appendices E and F.

###  III.4 Separating the contributions from $V_{1}$ and $V_{3}$

As discussed in the introduction, there is conflicting evidence on the ZFS of
$V_{1}$ and $V_{3}$. The experiments presented in subsections III.2 and III.3
were designed to provide data for distinguishing between them. The results can
be interpreted consistently if we assume that the ZFS splittings of $V_{1}$
and $V_{3}$ are both close to 28 MHz but have slightly different frequencies
(27 MHz and 28 MHz) and contribute to the ODMR spectrum with opposite signs :
for $V_{1},$ the ODMR signal is negative ($\Delta PL/PL$< 0), for $V_{3}$ it
is positive. Since the combined linewidth is larger than the separation
between the two resonance frequencies, only a single line is obersved and the
two signals partially cancel. Since the PL from the two centers show different
polarisation, the positive and negative signal contribution depend differently
on the orientation of the polarizer, as shown in Appendix F.

Figure 7: ODMR spectra measured with the 850 nm LP filter at different
temperatures for PL emitted parallel to the $c$-axis. Only the region of the
$V_{1}$ and $V_{3}$ resonances are shown and the spectra are fitted to a sum
of two Lorentzians.

The signals from the two centers also have different temperature dependence.
At low temperatures, the $V_{1}$ signal at 27 MHz dominates, resulting in an
overall negative signal but at high temperatures, the $V_{3}$ signal at 28 MHz
dominates, resulting in an overall positive signal. For a more detailed
analysis, we compare the experimental signal at different temperatures to a
theoretical spectrum consisting of two Lorentzians with the frequencies of
$V_{1}$ and $V_{3}$ and opposite amplitudes

$S(f,T)=\frac{A_{1}(T)\,\sigma_{1}}{(f-ZFS_{1})^{2}+\sigma_{1}^{2}}+\frac{A_{3}(T)\,\sigma_{3}}{(f-ZFS_{3})^{2}+\sigma_{3}^{2}}.$
(5)

The frequencies $ZFS_{i=1,3}$=$2D$ were calculated from Eq. (4) for different
temperatures, using the temperature coefficient $b$ = (-1.52 $\pm$ 0.02)
$\times$ 10-5 MHz K-2 for $V_{1}$ and $V_{3}$. The values of the ZFS at $T=0$
were determined from the spectra measured with optical filters at 28 K as
$ZFS_{0}$ = 26.99 MHz and 27.99 MHz for $V_{1}$ and $V_{3}$ . The linewidths
$\sigma_{1}=5.9$ MHz and $\sigma_{3}=6.1$ MHz were also taken from the spectra
measured at 28 K.

Figure 7 shows the ODMR spectra for the frequency range 10 to 50 MHz at
different temperatures, together with a fitted signal, where only the
amplitudes $A_{i}$ were taken as fitting parameters to measure the
contributions from $V_{1}$ and $V_{3}$. Overall, the superposition of the two
resonance lines yields excellent agreement with the experimental data.

For PL emitted $\perp c$, the signal near 28 MHz decreases with temperature
but does not become negative, as shown in Fig. 4 (d). This is also consistent
with the assumption that the negative signal is associated with $V_{1}$: as
shown in appendix E, $V_{1}$ emits less PL perpendicular to the $c$-axis as
shown in Fig.1 and therefore can not dominate over the contribution from
$V_{3}$.

##  IV Relaxation measurements

In this section we focus on the evolution of the spin system towards thermal
equilibrium, which is driven by interactions with the environment Abragam
(1961). Each type of silicon vacancies has a different structure and therefore
different interactions with the environment that can be probed by relaxation
measurements.

###  IV.1 Population relaxation

The spin-lattice interaction drives the spin system towards thermal
equilibrium with its environment. Under our experimental conditions, the
thermal equilibrium spin state is completely unpolarised, i.e. the density
operator is proportional to the unit operator. The time scale on which the
system approaches this equilibrium state is characterized by the spin-lattice
relaxation time $T_{1}$. Figure 8(a) shows the pulse sequence used to measure
the $T_{1}$ relaxation time. A 300 $\mu$s laser pulse was applied to polarize
the spin system, which was then allowed to evolve for a time $\tau_{1}$. An RF
pulse with flip angle $\pi$ was applied before measuring the remaining spin
polarisation with a second laser pulse of 4 $\mu$s. The measured signal was
subtracted from the reference signal obtained without applying the RF
pulseSingh  _et al._ (2020, 2021, 2022). Figure 8(b) shows the measured signal
vs. the delay $\tau_{1}$. The recorded experimental data can be fitted by an
exponential

$S_{\pi}(\tau_{1})-S_{0}(\tau_{1})=A~{}e^{-\tau_{1}/T_{1}}.$ (6)

At room temperature, the extracted relaxation times $T_{1}$ were 145$\pm$2
$\mu$s for $V_{2}$ and 166 $\pm$ 2 $\mu$s for $V_{1}/V_{3}$.

Figure 8: (a) Pulse sequence used to measure the $T_{1}$ relaxation. The
orange and blue rectangles represent the laser and RF pulses. The duration of
the laser pulses is written above each pulse. (b) Resulting signal
(normalized) as a function of the delay $\tau_{1}$, measured at room
temperature. The experimental data (circles) for $V_{2}$ and $V_{1}$/$V_{3}$
are fitted to function Eq.6.

###  IV.2 Dephasing

Relaxation affects not only the populations, but also the coherence of the
spins. While population relaxation is dominated by fluctuations at the Larmor
frequency, coherence dephases under the influence of (quasi-) static
interactions. A free induction decay (FID) for both $V_{Si}^{-}$ was measured
using the Ramsey scheme Ramsey (1950). The dephasing time $T_{2}^{*}$ was 42
$\pm$4 ns for $V_{2}$ and 65 $\pm$ 5 ns for $V_{1}/V_{3}$ Singh  _et al._
(2022). Details of the pulse sequence used and experimental data obtained are
given in Appendix D.

Next, we focus on homogeneous dephasing, which can be measured using the spin-
echo experiment Hahn (1950). We refer to the time constant of the spin-echo
decay as $T_{2}$. Figure 9 (a) shows the pulse sequence. The system was again
polarised with a 300 $\mu$s laser pulse. The first RF pulse with flip-angle
$\pi/2$ generated coherence between the states $\pm 3/2\longleftrightarrow\pm
1/2$. The inhomogeneous dephasing was reversed with a $\pi$ pulse, which
generated a spin-echo at time $\tau_{2}$ after the initial $\pi/2$ pulse. A
second $\pi/2$ RF pulse at the time of the echo converted the remaining
coherence into population difference, which was measured by the final laser
pulse Singh  _et al._ (2020, 2021). Figure 9(b) shows the experimental signal
vs. the delay $\tau_{2}$. The recorded experimental data can again be fitted
to a single exponential and the extracted dephasing times $T_{2}$ were 4.1
$\pm$ 0.4 $\mu$s and 7.1 $\pm$1.7 $\mu$s for $V_{2}$ and $V_{1}/V_{3}$,
respectively, roughly 2 orders of magnitude longer than $T_{2}^{*}$. The spin-
echo data for $V_{1}/V_{3}$ does not fit well to the single exponential, so we
also compared it to a sum of 2 exponentials
$(A~{}e^{-\tau_{2}/T_{2}^{s}}+B~{}e^{-\tau_{2}/T_{2}^{f}}$), as shown in Fig.
9 with a yellow dashed curve ( $A$= -0.8 $\pm$0.1, $T_{2}^{s}$= 7.7 $\pm$ 0.3
$\mu$s, $B$= -0.2 $\pm$ 0.1, and $T_{2}^{f}$= 0.8 $\pm$ 0.4 $\mu$s.).

Figure 9: (a) Pulse sequence for measuring the spin coherence time with a
refocusing pulse. The red and blues rectangles represent the laser and RF
pulses, respectively. (b) Decay of the spin coherence during the echo
sequence. The experimental data (circles) for $V_{2}$ and $V_{1}/V_{3}$ are
fitted to exponential functions.

Next, we applied multiple refocusing pulses to further extend the coherence
lifetime. These refocusing pulses remove the dephasing effect of non-static
perturbations that have longer correlation times than the spacing between the
refocusing pulses. The measured dephasing time $T_{2}^{CPMG}$ for the $V_{2}$
($V_{1}$/$V_{3}$) type of $V_{Si}^{-}$ spin ensemble was 47 $\pm$ 7 $\mu$s (59
$\pm$ 3 $\mu$s) when the spacing between the refocusing pulses was 200 ns (100
ns), and the duration of each $\pi$ pulse was 38 ns (40 ns). Details of the
pulse sequence used and plots of the experimental data are given in Appendix
D.

Exp 13C (1.1$\%$) &29Si(4.7$\%$) 13C (4.7$\%$) & 29Si(0.1$\%$) Singh  _et al._
(2020) V1/V3 V2 V1/V3 V2 T1 166$\mu$s 142$\mu$s 142$\mu$s 107 $\mu$s
T${}_{2}^{*}$ 65 ns 42 ns 38 ns 31 ns T${}_{2}^{SE}$ 7.1$\mu$s 4.6$\mu$s
3.7$\mu$s 3.3$\mu$s T${}_{2}^{CPMG}$ 57$\mu$s 47$\mu$s 56$\mu$s 51$\mu$s

Table 3: Comparison of room-temperature relaxation times of two 6H-SiC
samples.

Table 3, shows the comparison of the relaxation times measured in our previous
paper where the 6H-SiC sample contained a higher concentration of 13C but
lower concentration of 29Si Singh  _et al._ (2020). In the present sample,
$T_{1}$ is slightly longer than in the sample used in Singh  _et al._ (2020),
which indicates a somewhat lower concentration of paramagnetic centers Simin
_et al._ (2017). The longer dephasing times $T_{2}^{*},$ $T_{2}$ can be
attributed to the lower concentration of 13C, which represent the nearest
neighbors (NN) of the silicon vacancy. The higher concentration of 29Si does
not have a significant effect, since the silicon atoms have a much weaker
hyperfine interaction.

##  V Discussion and Conclusion

The $V_{Si}^{-}$ center in SiC has attracted considerable interest in the
context of emerging quantum technologies, since its spin can be optically
polarized, has a sufficiently long coherence time and can be coherently
controlled. These properties make it an attractive candidate for quantum
information and quantum sensing. To develop this potential, it is essential to
more precisely characterise its properties. They depend, e.g., on the lattice
site at which the vacancy is created. In the $6H$-SiC polytype, three
different lattice sites exist, and the corresponding vacancies are referred to
as $V_{1}$, $V_{2}$ and $V_{3}$.

In this work, we have gathered new data on all three types of vacancies. In
particular, we related the properties of the PL of each center to the magnetic
resonance by performing ODMR experiments for different optical frequencies,
different optical polarizations and different directions of PL emission
(parallel and perpendicular to the $c$-axis of the sample). We found that the
$V_{1}$ and $V_{3}$ vacancies emit more PL parallel to the $c$-axis, whereas
$V_{2}$ emits more perpendicular to the $c$-axis. ODMR experiments detecting
photons that are emitted mostly by one type of center allowed us to determine
the zero-field splitting of the $V_{1}$ vacancy, for which different values
had been reported in previous works Biktagirov  _et al._ (2018); Davidsson
_et al._ (2019). Our results agree with those of Ref: Davidsson  _et al._
(2019). With the identification of the ODMR frequencies of all three
vacancies, we can explain the temperature dependence and change of sign of the
ODMR signal near 28 MHz: At the high temperature, the signal from $V_{3}$
dominates but at low temperature the signal from $V_{1}$ dominates, which is
negative. In real systems, the ZFS typically shows a small temperature
variation. We checked the ZFS variation with temperature and found that the
values increase by about 1 MHz as the temperature decreases from room
temperature to 5 K.

Further, we measured the transverse and longitudinal relaxation rates. The
relaxation rates measured here were lower than those reported earlier in a
different sample Singh  _et al._ (2020) that contained a higher concentration
of 13C. In the spin-echo decay for $V_{1}/V_{3}$, does not fit well to a
single exponential, which may indicate differences in the relaxation of
$V_{1}$ and $V_{3}$ . In future work, we will try to obtain more specific data
for the relaxation times of the different centers and determine the different
hyperfine coupling constants.

## Appendix A: Sample

Synthesized SiC crystals were grown with a low content of background
impurities. We synthesized polycrystalline sources from semiconductor silicon
and spectrally pure carbon. Spectrally pure graphite in powder form and
polycrystalline silicon was chosen as sources. They were degassed using a
resistive heating growth machine over 2 hours at 2200° C and 10-3 Torr under
vacuum to prepare the crucible and internal furnace reinforcement for
synthesis. After that, a stoichiometric mixture of carbon and silicon powders
was loaded into the crucible. Manufacturing silicon carbide powder took place
in a vacuum. Graphite with a minimum of background impurities was used to make
the crucible, such as Mersen 6516PT. It should note that all parts of the
crucible should be made from the same graphite. To avoid the destruction of
parts, when the crucible is heated above the synthesis temperature of the
source (above 1600°C). We used silicon carbide crystals polytype 6$H$ as
seeds. To grow crystals, the following conditions were used: 2050 ° C, 1 to 5
Torr argon pressure, 99.9999% pure argon, a growth rate of 150 $\mu$m / h.
Crystals that grew under these conditions had no micropores more than 3 cm-2.

## Appendix B: PL setup

For measuring the photoluminescence (PL) at different temperature, the sample
was cooled down using a helium cryostat. A tunable (799-813 nm) single-mode
diode laser DL pro from Toptica Photonics modulated by a chopper was used to
excite the sample optically. With the help of two convex lenses, PL was
collected parallel to the c-axis of sample. The collected PL passed through a
monochromator (Spex 1704) via an 850 nm long-pass filter (Thorlabs). For
detecting the PL, an avalanche photodiode(APD) module with a frequency
bandwidth from dc to 100 kHz (C5460-1 series from Hamamatsu) was attached to
the monochromator. The output voltage of the APD was measured with the lock-in
amplifier. The sync signal from the chopper was used as a reference for the
lock-in amplifier Singh  _et al._ (2020).

## Appendix C: ODMR setup

Figure 10: Experimental setup for measuring ODMR at low temp.

Figure 10 shows the setup used for the cw- and time-resolved ODMR
measurements. For cooling the sample, we used a liquid helium flow cryostat
(MicrostatHe-R from Oxford instruments). We used a turbopump for creating a
vacuum in the cryostat pressure less than $10^{-6}$ mbar (from Pfeiffer
vacuum). An LD785-SE400 diode laser was used as the light source (a laser
diode controller (LDC202C series) and temperature controller (TED 200C). The
laser light pulses were generated by an acoustic-optical modulator (NEC model
OD8813A). We used three orthogonal coil pairs to apply a static magnetic field
to the sample. APD module (C12703 series from Hamamatsu) was used to record
the PL signal. APD signal was recorded with the PicoScope 2000 series USB
oscilloscope card during pulse mode ODMR experiments. For cw-ODMR, the signal
from APD was recorded with the lock-in (SRS model SR830 DSP). Analog Devices’
AD9915 direct digital synthesizer (DDS) was used as an RF source for cw-ODMR
experiments. We used a Hunter Micro DAx14000 arbitrary wave generator (AWG)
for pulsed ODMR experiments. An RF signal from the source was amplified with
an RF amplifier (LZY-22+ from mini circuits). For feeding RF power to a
sample, we used wire and coil terminated with a 50-ohm resistor for
continuous-wave and pulsed ODMR experiments, respectively. We generated TTL
(transistor transistor logic) pulses using a digital word generator (DWG;
SpinCore PulseBlaster ESR-PRO PCI card) to trigger the laser RF pulses.

## Appendix D: ZFS with temperature

## Appendix D: FID and CPMG

Figure 11: (a)Pulse sequence to measure the FID of $V_{Si}^{-}$. (b) The
experimental recorded FID signal of $V_{Si}^{-}$ at room temperature.

Figure. 11 (a) shows the pulse sequence for the FID measurement. A laser pulse
of 300 $\mu$s and a power of 100 mW was used to polarize the vacancy spin
ensemble. A delay $\tau_{f}$ was given between the two $\pi/2$ RF pulses, and
the PL signal was using the second laser pulse. The phase of the first $\pi/2$
pulse was along x. For the second $\pi/2$ pulse, it was along x+$\phi_{d}$. We
repeated the same sequence for the reference scan except for the phase of the
second $\pi/2$ pulse was $-x+\phi_{d}$. Here the $\phi_{d}=\nu_{det}\tau_{f}$
and FIDs measured with the detuning frequency $\nu_{det}$= 40 MHz. Figure. 11
(b) shows the signals recorded for the both $V_{Si}^{-}$ as a function of
dephasing time delay $\tau_{f}$. The experimental recorded signal of $V_{2}$
($V_{3}$) vacancy fitted to the function

$S_{x+\phi_{d}}-S_{-x+\phi_{d}}=A\;cos(2\pi\nu_{det}\tau_{f}+c)e^{-\tau_{f}/T_{2}^{*}},$
(7)

where $S_{\pm x+\phi_{d}}$ is the average PL signal measured with $\pi/2$ RF
detection pulse of phase $\pm x+\phi_{d}$. After fitting the experimental
signal in the Eq.7, the $T_{2}^{*}$= 42 ns (65$\pm$5 ns).

Figure 12(a) shows the pulse sequence for measuring the spin coherence time
under the CPMG sequence. We first polarized the spin ensemble with the 300
$\mu$s laser pulse, and then the coherence was created with the $\pi$/2 pulse.
The CPMG sequence was applied i.e., a train of $2N$ $\pi$ pulses applied along
the $y$-axis, which was separated by the delay $\tau_{c}$/2 from each other.
Atlast coherence was coverted into the population with the application of
second $\pi$/2 pulse along the $x$-axis and PL signal was measured with the
second laser pulse. The experiment was repeated for recording the reference
signal for which the pulse sequence was same except the second $\pi$/2 pulse
was applied along the $-x$-axis. The difference between the experimentally
measured PL signals was fitted to the function

$S_{x}-S_{-x}=A\;e^{-(\tau_{CPMG}/T_{2}^{CPMG})^{n}},$ (8)

where the time period $\tau_{CMPG}$=2N($\tau_{c}+\pi$ pulse duration), 2N is
number of $\pi$ pulses.

Figure 12: (a) Pulse sequence for measuring the spin coherence time under the
CPMG sequence. (b) The experimental recorded decay of the spin coherence of
$V_{Si}^{-}$ during the CPMG sequence at room temperature.

## Appendix E: PL Polarization

Figure 13: Polarization plots of the ZPL intensities for the different centers
at 5 K, (a) with monochromator, and (b) with bandpass filters for emission
perpendicular to the $c$-axis ; (c) with monochromator, and (d) with bandpass
filters, for emission parallel to the $c$-axis. $\theta$ is the angle
difference between the initial and final position of the polarizer’s
transmission axis and in case of $\perp$ $c$-axis orientation, $0^{\circ}$ is
$\parallel$ to $c$-axis.

Figure 13 shows the polarization plots of the $V_{1}$, $V_{2}$ and $V_{3}$ ZPL
intensities recorded perpendicular and parallel to the $c$-axis at 5K. A
polarizer was used for selecting the particular PL polarization. Before
detecting the signal, individual ZPLs of the different silicon vacancies were
selected using the monochromator or suitable bandpass filters. With the
monochromator, we can select a very narrow bandwidth and minimise the
contribution from the phonon sidebands of the other vacancies. With the
optical bandpass filters, the width of the passband is larger (10 nm), but it
has the advantage of passing more signal, which is important for the ODMR
measurements. Figure 13 (a) shows the data for PL emission perpendicular to
the c-axis using the monochromator. The emission of $V_{2}$ is linearly
polarized perpendicular to the c-axis, while that of $V_{1}$ is almost
unpolarized Breev  _et al._ (2022). In the case of $V_{3}$, a significant
signal contribution comes from the phonon side band (PSB) of $V_{1}$ and
$V_{2}$. The data in figure 13 (b) were recorded with different bandpass
filters; accordingly, they contain larger contributions from PSB other
centers, which results in lower polarization. In contrast to previous work
Breev  _et al._ (2022) we did not apply a background correction, since the
available data do not allow a reliable separation into contributions from the
different ZPLs and sidebands.

## Appendix F: ODMR Polarization

Figure 14: (a) Plot of ODMR recorded for different polarizations at 5 K. (b)
ODMR of $V_{1}/V_{3}$ for different polarizationss at 16 K. In both cases, PL
was emitted $\|$ to the $c$-axis. $\theta=0$ corresponds to vertical
polarization.

Since we were not able to separate the ODMR signal of $V_{1}$ in PL emission
$\bot$ $c$-axis we recorded ODMR spectra for different orientations of the
polarization for the PL emitted $\|$ $c$-axis. Figure 14 (a) shows several
ODMR spectra recorded at 5 K for different orientations of a polarizer in the
detection path The amplitude of the signal near 28 MHz does not change
significantly, but the signal near 130 MHz varies by $\approx$ 21 %. Figure 14
(b) shows the ODMR spectrum measured at 16 K from 0 to 60 MHz. At this
temperature, the signal appears to consist of a positive and a negative
contribution. The amplitude of the positive peak varies with the polarisation
by $\approx 31$ % while the negative peak remains constant. This appears to be
consistent with the different polarization dependence of $V_{1}$ and $V_{3}$
discussed in Appendix E.

###### Acknowledgements.

This work was supported by the Deutsche Forschungsgemeinschaft in the frame of
the ICRC TRR 160 (Project No. C7)and by RFBR, project number 19-52-12058.

## Note

All experiments were done on the sample provided by A. N. A. and P. G. B well
before the EU sanctions. H.S and D.S did experimental measurements and data
analysis. To our knowledge, these results do not have any short-term economic
or military relevance.

## References

  * Wang  _et al._ (2017) J. Wang, Y. Zhou, X. Zhang, F. Liu, Y. Li, K. Li, Z. Liu, G. Wang, and W. Gao, Efficient generation of an array of single silicon-vacancy defects in silicon carbide, Phys. Rev. Applied 7, 064021 (2017).
  * Rabkowski  _et al._ (2012) J. Rabkowski, D. Peftitsis, and H. Nee, Silicon carbide power transistors: A new era in power electronics is initiated, IEEE Industrial Electronics Magazine 6, 17 (2012).
  * Izhevskyi  _et al._ (2000) V. Izhevskyi, L. Genova, J. Bressiani, and A. Bressiani, Review article: silicon carbide, Structure, properties and processing. Cerâmica 46, 4 (2000).
  * Gonzalez Szwacki (2017) N. Gonzalez Szwacki, Structural and electronic properties of silicon carbide polytypes as predicted by exact exchange calculations, Computational Condensed Matter 13, 55 (2017).
  * Tarasenko  _et al._ (2018) S. A. Tarasenko, A. V. Poshakinskiy, D. Simin, V. A. Soltamov, E. N. Mokhov, P. G. Baranov, V. Dyakonov, and G. V. Astakhov, Spin and optical properties of silicon vacancies in silicon carbide - a review (phys. status solidi b 1/2018), physica status solidi (b) 255, 1870101 (2018).
  * Pavunny  _et al._ (2021) S. P. Pavunny, A. L. Yeats, H. B. Banks, E. Bielejec, R. L. Myers-Ward, M. T. DeJarld, A. S. Bracker, D. K. Gaskill, and S. G. Carter, Arrays of si vacancies in 4 h-sic produced by focused li ion beam implantation, Scientific reports 11, 3561 (2021).
  * Riedel  _et al._ (2012) D. Riedel, F. Fuchs, H. Kraus, S. Väth, A. Sperlich, V. Dyakonov, A. A. Soltamova, P. G. Baranov, V. A. Ilyin, and G. V. Astakhov, Resonant addressing and manipulation of silicon vacancy qubits in silicon carbide, Physical review letters 109, 226402 (2012).
  * Baranov  _et al._ (2011) P. G. Baranov, A. P. Bundakova, A. A. Soltamova, S. B. Orlinskii, I. V. Borovykh, R. Zondervan, R. Verberk, and J. Schmidt, Silicon vacancy in sic as a promising quantum system for single-defect and single-photon spectroscopy, Phys. Rev. B 83, 125203 (2011).
  * Ivády  _et al._ (2017) V. Ivády, J. Davidsson, N. T. Son, T. Ohshima, I. A. Abrikosov, and A. Gali, Identification of si-vacancy related room-temperature qubits in $4h$ silicon carbide, Phys. Rev. B 96, 161114 (2017).
  * Sörman  _et al._ (2000) E. Sörman, N. T. Son, W. M. Chen, O. Kordina, C. Hallin, and E. Janzén, Silicon vacancy related defect in 4h and 6h sic, Phys. Rev. B 61, 2613 (2000).
  * Biktagirov  _et al._ (2018) T. Biktagirov, W. G. Schmidt, U. Gerstmann, B. Yavkin, S. Orlinskii, P. Baranov, V. Dyakonov, and V. Soltamov, Polytypism driven zero-field splitting of silicon vacancies in $6h$-sic, Phys. Rev. B 98, 195204 (2018).
  * Davidsson  _et al._ (2019) J. Davidsson, V. Ivády, R. Armiento, T. Ohshima, N. T. Son, A. Gali, and I. A. Abrikosov, Identification of divacancy and silicon vacancy qubits in 6h-sic, Applied Physics Letters 114, 112107 (2019), https://doi.org/10.1063/1.5083031 .
  * Breev  _et al._ (2022) I. Breev, Z. Shang, A. Poshakinskiy, H. Singh, Y. Berencén, M. Hollenbach, S. Nagalyuk, E. Mokhov, R. Babunts, P. Baranov, _et al._ , Inverted fine structure of a 6h-sic qubit enabling robust spin-photon interface, npj Quantum Information 8, 1 (2022).
  * Hain  _et al._ (2014) T. C. Hain, F. Fuchs, V. A. Soltamov, P. G. Baranov, G. V. Astakhov, T. Hertel, and V. Dyakonov, Excitation and recombination dynamics of vacancy-related spin centers in silicon carbide, Journal of Applied Physics 115, 133508 (2014), https://doi.org/10.1063/1.4870456 .
  * Fuchs  _et al._ (2015) F. Fuchs, B. Stender, M. Trupke, D. Simin, J. Pflaum, V. Dyakonov, and G. Astakhov, Engineering near-infrared single-photon emitters with optically active spins in ultrapure silicon carbide, Nature communications 6, 1 (2015).
  * Kasper (2021) C. A. Kasper,  _Engineering of Highly Coherent Silicon Vacancy Defects in Silicon Carbide_ , Ph.D. thesis, Universität Würzburg (2021).
  * Singh  _et al._ (2022) H. Singh, M. A. Hollberg, A. N. Anisimov, P. G. Baranov, and D. Suter, Multi-photon multi-quantum transitions in the spin-$\frac{3}{2}$ silicon-vacancy centers of sic, Phys. Rev. Research 4, 023022 (2022).
  * Zhou  _et al._ (2021) J.-Y. Zhou, Q. Li, Z.-Y. Hao, F.-F. Yan, M. Yang, J.-F. Wang, W.-X. Lin, Z.-H. Liu, W. Liu, H. Li, _et al._ , Experimental determination of the dipole orientation of single color centers in silicon carbide, ACS Photonics 8, 2384 (2021).
  * Janzén  _et al._ (2009) E. Janzén, A. Gali, P. Carlsson, A. Gällström, B. Magnusson, and N. T. Son, The silicon vacancy in sic, Physica B: Condensed Matter 404, 4354 (2009).
  * Singh  _et al._ (2020) H. Singh, A. N. Anisimov, S. S. Nagalyuk, E. N. Mokhov, P. G. Baranov, and D. Suter, Experimental characterization of spin-3/2 silicon vacancy centers in $6h$-sic, Phys. Rev. B 101, 134110 (2020).
  * Soltamov  _et al._ (2019) V. A. Soltamov, C. Kasper, A. V. Poshakinskiy, A. N. Anisimov, E. N. Mokhov, A. Sperlich, S. A. Tarasenko, P. G. Baranov, G. V. Astakhov, and V. Dyakonov, Excitation and coherent control of spin qudit modes in silicon carbide at room temperature, Nature Communications 10, 1678 (2019).
  * Singh  _et al._ (2021) H. Singh, A. N. Anisimov, I. D. Breev, P. G. Baranov, and D. Suter, Optical spin initialization of spin-$\frac{3}{2}$ silicon vacancy centers in $6h\text{$-$}\mathrm{SiC}$ at room temperature, Phys. Rev. B 103, 104103 (2021).
  * Astakhov  _et al._ (2016) G. Astakhov, D. Simin, V. Dyakonov, B. Yavkin, S. Orlinskii, I. Proskuryakov, A. Anisimov, V. Soltamov, and P. Baranov, Spin centres in sic for quantum technologies, Applied Magnetic Resonance 47, 793 (2016).
  * Suter (2020) D. Suter, Optical detection of magnetic resonance, Magnetic Resonance 1, 115 (2020).
  * Carbonera (2009) D. Carbonera, Optically detected magnetic resonance (odmr) of photoexcited triplet states, Photosynthesis research 102, 403 (2009).
  * Abragam (1961) A. Abragam,  _The principles of nuclear magnetism_ (Oxford University Press, UK, 1961).
  * Ramsey (1950) N. F. Ramsey, A molecular beam resonance method with separated oscillating fields, Phys. Rev. 78, 695 (1950).
  * Hahn (1950) E. L. Hahn, Spin echoes, Phys. Rev. 80, 580 (1950).
  * Simin  _et al._ (2017) D. Simin, H. Kraus, A. Sperlich, T. Ohshima, G. V. Astakhov, and V. Dyakonov, Locking of electron spin coherence above 20 ms in natural silicon carbide, Phys. Rev. B 95, 161201(R) (2017).


11institutetext: Indian Institute of Technology, Kharagpur, West Bengal, India
11email: {vahinimirididdi, jalend.bantupalli, chakra.souvic,
<EMAIL_ADDRESS>
# Decoding Demographic un-fairness
from Indian Names

Medidoddi Vahini  Jalend Bantupalli  Souvic Chakraborty  Animesh Mukherjee

###### Abstract

Demographic classification is essential in fairness assessment in recommender
systems or in measuring unintended bias in online networks and voting systems.
Important fields like education and politics, which often lay a foundation for
the future of equality in society, need scrutiny to design policies that can
better foster equality in resource distribution constrained by the unbalanced
demographic distribution of people in the country.

We collect three publicly available datasets to train state-of-the-art
classifiers in the domain of gender and caste classification. We train the
models in the Indian context, where the same name can have different styling
conventions (Jolly Abraham/Kumar Abhishikta in one state may be written as
Abraham Jolly/Abishikta Kumar in the other). Finally, we also perform cross-
testing (training and testing on different datasets) to understand the
efficacy of the above models.

We also perform an error analysis of the prediction models. Finally, we
attempt to assess the bias in the existing Indian system as case studies and
find some intriguing patterns manifesting in the complex demographic layout of
the sub-continent across the dimensions of gender and caste.

###### Keywords:

Caste Gender Fairness Demographic bias India

##  1 Introduction

The name of a person can convey various demographic features of the
individual. This demographic information plays a crucial role in multiple
studies related to racial inequality, recommendation systems, biomedical
studies, hate-speech target identification, group sentiment analysis etc. [14,
1, 4, 15, 5]. Consequently, much work has been done on demographic
classification and a variety of online web APIs and tools capable of
predicting demographics from user name [2, 3, 11]) exist. Most of this
research work, however, is focused on US demographics [14, 12], and many of
the works [2, 3, 11, 14] build classifiers that require a proper division of
the first name, middle name, and last name to work. So, we introduce caste and
gender-specific datasets on Indian demographics, which hosts one-seventh of
the world population. Indian names vary significantly over states when
compared to other countries due to high religious, ethno-demographic and
linguistic variance111https://www.britannica.com/place/India/Indo-European-
languages. Also, Indian names do not always fall under the division of
first/middle/last name, primarily because the name of a person may contain the
name of their ancestors (e.g., Avul Pakir Jainulabdeen Abdul Kalam, former
President of India - here the first name of the person is Abdul). Indian names
may also contain the name of father in the name of a woman. This can make
gender or race detection difficult in faulty name segmentation.

So, to achieve a realistic outcome for name to demography detection, we train
our classifiers as an end-to-end sequence classification task, overcoming the
need for a segmentation model. The Indian society is divided by gender and
caste, unlike the US demographics, divided by races. Thus we focus on caste
and gender prediction in this study. To summarize, the objective of this study
is to predict the gender and the caste from any complete Indian name
overcoming the need to build a segmentation model. We list down our
contributions in this paper below.

  1. 1.

Toward fulfilling the classification objective, we build large datasets
acquiring already public data of India-wide examination records and parsing
electoral rolls containing over 7.63 million unique names.

  2. 2.

We demonstrate the efficacy of our model through several case studies and make
interesting observations about caste and gender based discrimination in India
both online and on the ground.

  3. 3.

We show that there has been an upward trend of participation in competitive
exams among women and backward classes over the years. We perform a multi-
dimensional study to understand the nuance of caste and gender-based
discrimination present in Indian society to help policymakers make data-driven
choices.

  4. 4.

We perform state-wise chronological analysis to understand the efficacy of
discrimination-limiting practices/laws implemented in the Indian states.

  5. 5.

We also analyze the Indian social media ‘Koo’ to understand the degree of
representation a weaker section of the Indian society has on the web and its
improvement over time.

We have opensourced our codebase encouraging further
research222https://github.com/vahini01/IndianDemographics

##  2 Related work

Gender classification: Hu et al (2021) [8] inferred gender from user first
names (US data) using character based models. They further conclude that using
complete names results in better prediction results compared to only first
names. [16] (2011) inferred gender from Facebook data with an accuracy of
95.2% for users in the NYC area using their first names. Muller et al (2016)
[10] inferred gender from Twitter usernames with 80.4% accuracy. Tripathi and
Faruqui (2011) [18] presented a SVM based approach for gender classification
of Indian names using n-gram suffixes and features based upon morphological
analysis, obtaining a F1-score of 94.9%. We refer the reader to Kruger et al
(2019) [9] for a comprehensive survey on gender detection models based on
textual data. There are also a few commercial APIs available for gender
detection: Gender API [2], Onograph API [11], Genderize API [7]. We have used
these APIs as baselines.

Ethnicity classification and demographic bias: Classifying the ethnic
category, one of the most telling demographic property of a user, provides an
essential data add-on for social science research. Other important
applications include biomedical research, population demographic studies, and
marketing toward a specific group of individuals [1], [17]. Despite numerous
applications, ethnic information of users are often not directly available.

To bridge this gap, Sood et al.(2018) [14] made use of registered voters in
Florida to infer race and ethnicity from names obtaining a F1-score of 0.83
using LSTMs. Ambedkar et al. [1] presented a model that classifies names into
13 cultural/ethnic groups with data extracted from Wikipedia. Giles et al.
[17] proposed a name-ethnicity classifier that identified ethnicity from
personal names in Wikipedia with 85% accuracy.

The present work: Studies on computational bias in Indian datasets are rare
due to unavailability of good published datasets[6]. In this work, we
specifically focus on India and attempt to quantify bias in diverse Indian
datasets across the two major dimensions Indian Society is divided along-
caste and gender. To this purpose we collected multi-year data from (i)
electoral records of different Indian states, (ii) data corresponding to the
India wide $10^{th}$ and $12^{th}$ standard examination, (iii) data
corresponding to the top Indian engineering and medical entrance examinations
and (iv) data from one of the fastest growing Indian social network. We use
pre-trained transformer models to obtain better gender and caste
classification performance and perform various case studies using the
prediction from the best models to gain insights into the underlying
demographic biases based on gender and caste in India.

##  3 Datasets

We use datasets for two purposes: training models and conducting case studies.
We collected three massive datasets333Detailed stats are available in Appendix
0.A to gather training data on diverse Indian names from the Central Board of
Secondary Education (CBSE), the All India Engineering Entrance Examination
(AIEEE), and the Electoral Rolls (ER).

To conduct case studies on the social media data, we resorted to the Koo
social network444https://www.kooapp.com/. For educational data in addition to
the multi-year CBSE (standard X and XII) and the AIEEE data mentioned earlier
we also included the All India Pre Medical Test (AIPMT) data.

CBSE dataset:

Data for training models – The Central Board of Secondary Education (CBSE)
keeps a record of all students’ grades555https://resultsarchives.nic.in. We
scraped a sample of about 100K records from their website for the 2014 and
2015 academic years. CBSE data includes information such as the student’s
name, father’s name, mother’s name, and grades. It comprises information from
students in the 12${}^{\textrm{th}}$ grade during the previous years. In this
dataset, the gender labels for students are not available. However the name of
the father and the mother of every student are present. This gives us an easy
way to get the names and the corresponding gender labels.

Data for case study – We collected CBSE grade 10 student data from 2004 to
2010 and CBSE grade 12 data from 2004 to 2012 to conduct the case studies. The
number of unique names in the CBSE grade 10 and grade 12 datasets are 70.09%
and 73.12% respectively.

AIEEE dataset:

Data for training models – The All India Engineering Entrance Examination
(AIEEE) is a national examination for admission to engineering colleges. The
AIEEE data records666maintained in the same website as CBSE used for training
corresponded to the years 2009, 2010, and 2011. It includes the students’
names, state and caste categories - general/reserved (i.e.,
OBC/SC/ST)777https://en.wikipedia.org/wiki/Scheduled_Castes_and_Scheduled_Tribes,
the fathers’ and the mothers’ names.

Data for the case study – The marksheets of students for AIEEE exams spanning
the years 2004 to 2011 are randomly sampled and gathered for the case studies.

ER dataset: Electoral roll data is gathered from the electoral roll websites
of each state government. We collected only English language data from these
rolls. We show the states considered for the gender classification in Table
4(Appendix).

AIPMT dataset: The All India Pre-Medical Test (AIPMT) is a test for admission
to medical schools in India. The AIPMT data obtained spans over the years 2004
to 2011. This dataset is solely used to conduct case studies and provides
information on 435,288 students with 327,665 (75.27%) unique names.

Social media dataset: Apart from educational data for our case studies, we
also gathered data from Koo888https://www.kooapp.com/feed which is a rapidly
growing social network in India. For our study we have used the data of all
Koo users that has been recently released by [13]. We applied our models to
this dataset and analyzed the degree of representation based on caste and
gender, as shown in section 7.

##  4 Methodology

We can determine the gender/caste from a user’s name using either the first or
full name. In India, extracting the first name from the full name is dependent
on the state, religion and local culture; for example, the first name appears
as the final word in the name in certain states for certain religions. Hence
we used a person’s full name as input for both gender and caste classification
tasks.

###  4.1 Classification models

Baselines and models:

We used the top APIs available as baselines: Gender API [2], Genderize API
[11], and Forebears API [7]. For non-DL models, we use logistic regression and
SVM. We use CharCNN and CharLSTM as neural models trained from scratch. We
used BERT, mBERT, IndicBERT, and MuRIL as pretrained neural models. Details
are added in Appendix 0.A.2.

Table 1: Performance of the models(Accuracy) for gender and caste classification.  | Gender classification | Caste classification - AIEEE Data
---|---|---
Model | CBSE | ER | AIEEE | Complete Name | Name & State
LR | 91.03 | 73.55 | 87.38 | 68.71 | 69.62
SVM | 93.82 | 46.85 | 85.31 | 61.73 | 64.82
Char-CNN | 96.18 | 89.74 | 94.13 | 71.57 | 73.21
Char-LSTM | 95.81 | 90.41 | 94.72 | 71.61 | 73.38
BERT | 96.97 | 92.56 | 96.06 | 72.62 | 74.70
MuRIL | 97.07 | 92.49 | 95.97 | 71.91 | 73.79
IndicBERT | 96.32 | 91.52 | 94.59 | 70.66 | 72.86
mBERT | 96.80 | 92.50 | 95.84 | 73.05 | 74.61

##  5 Experimental setup

Gender and Caste labels: Only binary categories – male and female – are used
for gender classification task. As for the caste, the categories that one
finds are General (upper caste people who did not face historical
discrimination and benefited from the caste system), Scheduled Caste (SC: who
were discriminated historically), Scheduled Tribe (ST: who were out castes and
faced the maximum discrimination), and Other Backward Castes (OBC). For the
purpose of this study, we divide castes into broad groups: General and
Reserved (SC/ST/OBC for whom the government guarantees reservation to ensure a
level-playing field).

Repetition of names: Many names in our datasets repeat. Thus it is possible
that test points (chosen randomly) can overlap with the training points. In
order to avoid this, we run our experiments on unique names only. The label
for this instance is the majority label of all the individual instances of the
name. For our experiments we use a train-test split of 70:30. More details
related to dataset division is included in Appendix 0.A.

##  6 Results

Main results: The main results are noted in Table 1. We observe that simple ML
models like LR and SVM do not perform well. Character based models show
greater improvement over LR, SVM for gender detection showing the benefits of
the choice of character sequences for this task. Transformer based models
perform best for both gender and caste classification with no clear winner
among them. Overall, MuRIL does well in gender classification and mBERT in
caste classification.

Table 2: Comparison with baseline APIs. All results are on a held out set of 500 data points. | Model | ER | AIEEE | CBSE
---|---|---|---|---
APIS |  Gender [2] | 53.2 | 64.0 | 81.0
Onograph [11] | 71.46 | 82.00 | 92.8
Genderize [7] | 49.79 | 63.86 | 82.38
Models | MuRIL-CBSE | 74.85 | 89.00 | 97.00
MuRIL-ER | 93.81 | 94.20 | 97.40
MuRIL-AIEEE | 77.45 | 95.40 | 97.60
BERT-CBSE | 77.05 | 86.20 | 97.20
BERT-ER | 93.81 | 94.20 | 97.00
BERT-AIEEE | 76.25 | 97.00 | 97.60

Table 3: Performance in a cross-dataset setting Model | Train | Test | Accuracy | F1-Score
---|---|---|---|---
MuRIL | ER | CBSE | 97.31 | 97.28
| ER | AIEEE | 95.40 | 95.31
| CBSE | ER | 78.03 | 77.93
| CBSE | AIEEE | 90.82 | 90.72
| AIEEE | ER | 79.47 | 79.35
| AIEEE | CBSE | 97.03 | 97.00
BERT | ER | CBSE | 97.31 | 97.28
| ER | AIEEE | 94.94 | 94.84
| CBSE | ER | 78.27 | 78.15
| CBSE | AIEEE | 89.64 | 89.50
| AIEEE | ER | 79.66 | 79.53
| AIEEE | CBSE | 96.99 | 96.96

Baseline APIs: We have used only 500 unseen instances due to API request limit
per day for each of these baselines. For a set of randomly chosen 500 data
points, we observe that the transformer based models (MuRIL and mBERT) by far
outperform all the three baselines (see Table 3). Among the baselines,
Onograph performs the best.

Cross dataset evaluation From Table 3 we see that models trained on CBSE and
AIEEE datasets (having similar pan-India demographics) perform well on each
other’s test sets. Further, the models trained on the ER dataset perform
reasonably well when tested on CBSE and AIEEE datasets but the reverse setups
perform poorly due to lesser representation of north-eastern states in
CBSE/AIEEE data.

##  7 Decoding unfairness across gender and caste lines

We use social media datasets, longitudinal educational records, and electoral
roll datasets to identify and quantify the inter-sectional bias caused by
caste and gender prejudice. We also display the results over an 8-year period
to better understand how government-sponsored social programs and
globalization are influencing Indian society and reducing unfairness in
resource distribution.

For all these studies, we have used the MuRIL-based model, which is also shown
to be one of the top-performing models.

To understand the state and evolution of discrimination in the current Indian
system, we draft the following set of research questions (RQ):

Figure 1: Distribution of women and backward castes are shown in the left most
figure. Middle figure displays the median percentile in the same. The right
most diagram shows the temporal evolution of women and backward caste people
in Koo.

  * •

RQ1: Is the representation of females (no reservation) and backward castes
(reserved) in public education increasing over time?

  * •

RQ2: Is the representation of females (no reservation) and backward castes
(reserved) in competitive engineering/medical entrance exams increasing over
time?

  * •

RQ3: Are females and backward caste people less represented in the Indian
social networks?

  * •

RQ4: How vocal are the females and backward caste voices (#followers*#posts)
in Indian social media?

###  7.1 Impact of social bias on education

RQ1 & RQ2: Is the representation of females (no reservation) and backward
castes (reserved) in public education and competitive exams increasing over
time?

Indian Government has the promise of equality embedded in its emblem, and the
reservation system was introduced as a mechanism to ensure the continuous
integration of backward caste people into the mainstream social structure.
This reservation system ensures equality of representation in government
institutes of higher education and workplaces by reserving some seats for
backward class people who have faced historic injustice.

However, a similar system does not exist for women. Hence, we try to
understand the system’s effect on education for both gender and caste
divisions.

In Figure 1, we plot the ratio of women and backward castes in the sampled
dataset for each year and each exam. We observe that for AIEEE, women’s
representation has steadily increased from 2005 to 2010. Also, the engineering
exam AIEEE saw much lower participation from women when compared to the
medical entrance exam AIPMT or the board exams CBSE 10th and CBSE 12th grade.
In the medical examination AIPMT, women’s representation has increased and has
achieved the population average from 2007. In the CBSE 10th and CBSE 12th
grade, we see a stable representation of women over time.

However, the representation of backward castes in the medical entrance exam
and both the board exams has remained extremely low all over time. AIEEE, the
engineering entrance exam, stands out here with much higher representation
from backward castes, and the participation is also slightly increasing with
time.

In Figure 1 we plot the median percentile attained by women and backward
castes for each year and each exam. While the average percentile for the whole
dataset will be the 50th percentile, this metric, when applied to a specific
community, will tell us the meritocratic position of that community, i.e.,
whether that community is doing better relative to other communities or lesser
and how that position is changing over time concerning specific exams. We have
the ranks available only for AIEEE data, so we try to analyze only this data.
We see that women have achieved equality in percentile and are doing better
than men in later years. However, the same is not valid for backward caste
students. The above percentile changes show need for exam-specific policy
modifications. For women, the inequality is mostly in participation, and women
need more encouragement to participate in competitive exams, whereas backward
class students need better support to score higher in the competitive exams.

###  7.2 Impact of social bias on online media and web representation

RQ3: Are women and backward caste people less represented in the Indian social
networks?

We analyze the Indian social network ‘Koo’999https://www.kooapp.com/ to
investigate the extent of representation of women and lower caste people in
this network. We use the massive dataset with 4 million usernames and metadata
from Koo provided by [13]. Using our classifier, we predicted the caste and
the gender of these names. In Figure 1, we plot the ratio of women and
backward castes in the network for each month across Koo’s existence. We
observe that upper caste people of India mostly occupied Koo during its
inception stage; however the situation quickly changed over time with a
slightly higher representation from the lower caste people. On the other hand,
women’s distribution continuously decreased in this Indian social network.

RQ4: How vocal are the women and backward caste voices (#followers*#tweets) on
Indian social media?

We quantify the overall ‘voice’ of a group by the sum of the
#followers*#tweets for each person in that group. As we do not have the number
of followers data for each month, we only compute the aggregate statistics at
the end of the last month in the dataset. The ratio of male voice to the
female voice in the network is 3.59. Similarly the ratio of the general to the
backward class voice is 10.47. These results demonstrate a striking
inequality. Further we observe that a random message posted on the platform is
37.58 times more likely to be from a forward caste male than a backward-caste
female.

##  8 Conclusion and future work

The paper introduced various large-scale datasets of Indian names and
extensively explored the possibility of gender and caste detection from these
names. We showed that the state-of-the-art APIs do not perform well on the
task of gender detection from Indian names; in contrast, the recent
transformer based models performed extremely well in this task. Further, to
the best of our knowledge, this is the first large-scale caste classification
task undertaken to understand the existing demographic disparities in across
India. Through a series of rigorous case studies we have shown the gender and
caste based biases that exist in basic and higher education as well as in the
representation in social media. We have also opensourced our codebase for
further research and contribution. In future, we will like to consider more
caste varieties and data from all states for a nuanced evaluation.

## References

  * [1] Ambekar, A., Ward, C.B., Mohammed, J., Male, S., Skiena, S.: Name-ethnicity classification from open sources. In: KDD. p. 49–58. Association for Computing Machinery, New York, NY, USA (2009)
  * [2] API, G.: https://gender-api.com (2021)
  * [3] API, N.: https://www.nameapi.org/en/home/ (2021)
  * [4] Chakraborty, S., Dutta, P., Roychowdhury, S., Mukherjee, A.: CRUSH: Contextually regularized and user anchored self-supervised hate speech detection. In: Findings of the Association for Computational Linguistics: NAACL 2022. pp. 1874–1886. Association for Computational Linguistics, Seattle, United States (Jul 2022). https://doi.org/10.18653/v1/2022.findings-naacl.144, https://aclanthology.org/2022.findings-naacl.144
  * [5] Chakraborty, S., Goyal, P., Mukherjee, A.: Aspect-based sentiment analysis of scientific reviews. In: Proceedings of the ACM/IEEE Joint Conference on Digital Libraries in 2020. p. 207–216. JCDL ’20, Association for Computing Machinery, New York, NY, USA (2020). https://doi.org/10.1145/3383583.3398541, https://doi.org/10.1145/3383583.3398541
  * [6] Chakraborty, S., Goyal, P., Mukherjee, A.: (im) balance in the representation of news? an extensive study on a decade long dataset from india. International Conference on Social Informatics, SocInfo (2022), https://arxiv.org/abs/2110.14183
  * [7] Genderize: https://genderize.io/ (2021)
  * [8] Hu, Y., Hu, C., Tran, T., Kasturi, T., Joseph, E., Gillingham, M.: What’s in a name? – gender classification of names with character based machine learning models (2021)
  * [9] Krüger, S., Hermann, B.: Can an online service predict gender? on the state-of-the-art in gender identification from texts. In: Proceedings of the 2nd International Workshop on Gender Equality in Software Engineering. p. 13–16. GE ’19, IEEE Press, Canada (2019). https://doi.org/10.1109/GE.2019.00012, https://doi.org/10.1109/GE.2019.00012
  * [10] Mueller, J., Stumme, G.: Gender inference using statistical name characteristics in twitter. In: Proceedings of the The 3rd Multidisciplinary International Social Networks Conference on SocialInformatics 2016, Data Science 2016. MISNC, SI, DS 2016, Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2955129.2955182, https://doi.org/10.1145/2955129.2955182
  * [11] Onograph: https://forebears.io/onograph/ (2021)
  * [12] Parasurama, P.: racebert – a transformer-based model for predicting race and ethnicity from names (2021). https://doi.org/10.48550/ARXIV.2112.03807, https://arxiv.org/abs/2112.03807
  * [13] Singh, A.K., Jain, C., Jain, J., Jain, R.R., Sehgal, S., Pandey, T., Kumaraguru, P.: What’s kooking? characterizing india’s emerging social network, koo. In: Proceedings of the 2021 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining. pp. 193–200. Association for Computing Machinery, New York, NY, USA (2021)
  * [14] Sood, G., Laohaprapanon, S.: Predicting race and ethnicity from the sequence of characters in a name (2018)
  * [15] Swami, S., Khandelwal, A., Shrivastava, M., Akhtar, S.: Ltrc iiith at ibereval 2017: Stance and gender detection in tweets on catalan independence. CEUR Workshop Proceedings 1881, 199–203 (Jan 2017), 2nd Workshop on Evaluation of Human Language Technologies for Iberian Languages, IberEval 2017 ; Conference date: 19-09-2017
  * [16] Tang, C., Ross, K., Saxena, N., Chen, R.: What’s in a name: A study of names, gender inference, and gender behavior in facebook. In: Xu, J., Yu, G., Zhou, S., Unland, R. (eds.) Database Systems for Adanced Applications - 16th International Conference, DASFAA 2011, International Workshops. pp. 344–356 (2011)
  * [17] Treeratpituk, P., Giles, C.L.: Name-ethnicity classification and ethnicity-sensitive name matching. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence. p. 1141–1147. AAAI’12, AAAI Press, Canada (2012)
  * [18] Tripathi, A., Faruqui, M.: Gender prediction of indian names. In: IEEE Technology Students’ Symposium. pp. 137–141. IEEE, Kharagpur (2011). https://doi.org/10.1109/TECHSYM.2011.5783842

##  Appendix 0.A Appendix

###  0.A.1 Dataset statistics

Table 4 displays the dataset stats.

Table 4: The table below contains information on datasets that are used to
train models and conduct case studies.

Gender classification
---
Data (full) | Female | Male
CBSE | 194423 | 194413
ER | 10405236 | 11632598
AIEEE | 358522 | 358522
CBSE-breakup | Female | Male
2014 | 25779 | 31573
2015 | 51744 | 63434
ER-breakup | Female | Male
Daman | 53391 | 53605
Manipur | 580415 | 589948
Meghalaya | 748820 | 737951
Nagaland | 253274 | 295039
Arunachal | 292158 | 292544
Delhi | 966324 | 1430743
Sikkim | 76145 | 88209
Goa | 372029 | 361380
Mizoram | 134305 | 158144
AIEEE-breakup | Female | Male
2009 | 66286 | 84615
2010 | 70826 | 91687
2011 | 68965 | 89490

Caste classification
---
AIEEE | Reserved | General
2009 | 47681 | 64892
2010 | 54703 | 68163
2011 | 57262 | 65810
Case study - education data
Dataset | Total | Unique names
AIEEE | 665227 | 525631
CBSE 10 | 487080 | 341430
CBSE 12 | 378123 | 276476
AIPMT | 435288 | 327665
Case study - social media data
Dataset | Total | Valid names
Koo | 4061670 | 1761958

###  0.A.2 Baseline APIs and Models

We used a bunch of APIs available for gender classification as baselines and
compared them with the results obtained from our transformer based methods.
Gender API [2]: Gender-API.com is a simple-to-implement solution that adds
gender information to existing records. It receives input via an API and
returns the split-up name (first name, last name) and gender to the app or the
website. According to the website, it will search for the name in a database
belonging to the specific country, and if it is not found, it will perform a
global lookup. If it cannot find a name in a global lookup, it performs
several normalizations on the name to correct typos and cover all spelling
variants.
Onograph API [11]: OnoGraph is a set of services that predicts a person’s
characteristics based on their name. It can predict nationality, gender, and
location (where they live). The services are based on the world’s largest
private database of living people, which contains over 4.25 billion people (as
of July 2020). According to the documentation, “OnoGraph’s results are the
most accurate of any comparable service; and it recognizes around 40 million
more names than the nearest comparable service.”
Genderize API [7]: It is a simple API that predicts a person’s gender based on
their name. The request will generate a response with the following keys:
name, gender, likelihood, and count. The probability denotes the certainty of
the gender assigned. The count indicates the number of data rows reviewed to
calculate the response.

###  0.A.3 Model description

Logistic regression: We concatenate the different parts of the name and
compute character n-grams. Next we obtain TF-IDF scores from the character
n-grams and pass them as features to the logistic regression model.

SVM: The objective of the support vector machine algorithm is to identify a
hyperplane in N-dimensional space (N = the number of features) that
categorizes the data points clearly. Then, we accomplish classification by
locating the hyper-plane that best distinguishes the two classes. There are
several hyperplanes that might be used to split the two groups of data points.
Our goal is to discover a plane with the greatest margin or the greatest
distance between data points from both classes.

Char CNN: Character-level CNN (char-CNN) is a well-known text classification
algorithm. Each character is encoded with a fixed-length trainable embedding.
A 1-D CNN is applied to the matrix created by concatenating the above vectors.
In our model, we utilize 256 convolution filters in a single hidden layer of
1D convolution with a kernel size of 7.

Char LSTM: A name is a sequence of characters. Like char-CNN, each character
of the input name is transformed into trainable embedding vectors and provided
as input. Our model employs a single LSTM layer with 64 features and a 20%
dropout layer.

Transformer models

  * •

We choose BERT for demographic categorization, using full names as inputs
because it has proven to be highly efficient in English data sequence
modeling.

  * •

mBERT is trained using a masked language modeling (MLM) objective on the top
104 languages with the largest Wikipedia.

  * •

IndicBERT is a multilingual ALBERT model that has only been trained on 12
major Indian languages101010IndicBERT supports the following 12 languages:
Assamese, Bengali, English, Gujarati, Hindi, Kannada, Malayalam, Marathi,
Oriya, Punjabi, Tamil, and Telugu.. IndicBERT has much fewer parameters than
other multilingual models.

  * •

MuRIL is pre-trained on 17 Indian languages and their transliterated
counterparts. It employs a different tokenizer from the BERT model. This model
is an appropriate candidate for categorization based on Indian names because
it is pre-trained on Indian languages.

Hyperparameters: LR: learning rate = 0.003, n-gram range = (1-6)
SVM: kernel=rbf, n-gram range = (1-6), degree = 3, gamma = scale
Char CNN: learning rate = 0.001, hidden layers = 1, filters = 256, kernel size
= 7, optimizer = adam
Char LSTM: learning rate = 0.001, dropout = 0.2, hidden layers = 1, features =
64, optimizer = adam
Transformer models: models = [bert-base-uncased, google/muril-base-cased,
ai4bharat/indic-bert, bert-base-multilingual-uncased], epochs = 3, learning
rate = 0.00005

###  0.A.4 Results

More detailed results are given in Table 5 and 6.

Handling of corner cases : As a name can be common across both genders or
caste, we use majority voting inorder to label a name with binary label for
both gender and caste classification tasks. In case of equality we considered
arbitrarily decided labels.

Table 5: Performance of the models for gender classification on each dataset.
Gender classification
---
Model | CBSE | ER | AIEEE
| F1-Score | Accuracy | F1-Score | Accuracy | F1-Score | Accuracy
LR | 90.93 | 91.03 | 73.23 | 73.55 | 87.24 | 87.38
SVM | 93.69 | 93.82 | 37.91 | 46.85 | 85.12 | 85.31
Char-CNN | 96.12 | 96.18 | 89.72 | 89.74 | 94.54 | 94.13
Char-LSTM | 95.75 | 95.81 | 90.23 | 90.41 | 94.62 | 94.72
BERT | 96.94 | 96.97 | 92.52 | 92.56 | 95.99 | 96.06
MuRIL | 97.04 | 97.07 | 92.45 | 92.49 | 95.90 | 95.97
IndicBERT | 96.28 | 96.32 | 91.48 | 91.52 | 94.48 | 94.59
mBERT | 96.76 | 96.80 | 92.46 | 92.50 | 95.76 | 95.84
Table 6: Performance of the models for caste classification on AIEEE dataset.
Caste classification - AIEEE Data
---
Model | Complete Name | Name & State
| F1-Score | Accuracy | F1-Score | Accuracy
LR | 68.64 | 68.71 | 69.58 | 69.62
SVM | 53.82 | 61.73 | 59.58 | 64.82
Char-CNN | 71.18 | 71.57 | 72.74 | 73.21
BERT | 71.80 | 72.62 | 73.99 | 74.70
MuRIL | 71.57 | 71.91 | 73.04 | 73.79
IndicBERT | 69.72 | 70.66 | 72.03 | 72.86
mBERT | 71.34 | 73.05 | 73.60 | 74.61

###  0.A.5 Error Analysis - Baseline APIs vs Our Models

Table 7 lists some of the best and worst test cases for the best performing
baselines and the best performing transformer based models. Both these types
of models perform the best when the first name (first word) is a good
representative of the gender (e.g., Karishma Chettri). Baselines usually fail
in three cases: the presence of parental name or surname (e.g., Avunuri
Aruna), longer names where gender is represented by multiple words (e.g.,
Kollipara Kodahda Rama Murthy), and core Indian names (e.g., Laishram
Priyabati, Gongkulung Kamei). The main reason for the better performance of
transformer models might be that they are trained on complete names and larger
datasets. As a result, they handle the complexity of Indian names. However,
both these types of models tend to fail in presence of unusual and highly
complicated names (e.g., Raj Blal Rawat, Pullammagari Chinna Maddileti).

Table 7: Table listing some common errors by the best performing baselines and the best performing transformer models. Here W stands for wrong and C stands for correct. And XX denotes the model, API results respectively; for e.g., WC lists names where transformer predicted wrong while API predicted correct. The letter in bracket denotes the gender (M for male and F for female). The listed names have multiple instances in the datasets. So none of the names uniquely identify any person Dataset | CC | CW
---|---|---
CBSE | Himanshu Bharatia (M) | Vijay Laxmi Soni (F)
| Sudha Chaturvedi (F) | Gang Shyam Herau (M)
ER | Karishma Chettri (F) | Chingakham Romita (F)
| Shekhar Sethi (M) | Ramesh Kasarlekar (M)
AIEEE | Suguna (F) | Indra Kumar Singh Bundela (M)
| Sudeep Agrawal (M) | Avunuri Aruna (F)
Dataset | WC | WW
CBSE | Sharmil arora (M) | Raj Blal Rawat (F)
| Ramkanwar gund (F) | Vimal Soni (M)
ER | Jmod Kyrsian (F) | Embha Lyngdoh (M)
| Esphorlin Thongnibah (M) | Basanta Thapa (F)
AIEEE | Tazeen Husain (F) | Dogin Yapyang (F)
| Zakki Khan (M) | Pullammagari Chinna Maddileti (M)

###  0.A.6 Case studies - Values of Median percentile

Table 8 displays values that are plotted in the left plot of figure 1.

Dataset | Women | Reserved
---|---|---
| All Data | Top 1% | Top 10% | All Data | Top 1% | Top 10%
AIEEE 2004 | 50.00 | 48.53 | 55.60 | 54.31 | 57.81 | 52.67
AIEEE 2005 | 47.82 | 60.38 | 56.48 | 54.87 | 43.68 | 52.43
AIEEE 2006 | 48.67 | 49.08 | 57.88 | 54.06 | 47.23 | 52.78
AIEEE 2007 | 47.90 | 47.14 | 56.35 | 54.99 | 57.38 | 53.40
AIEEE 2008 | 46.78 | 55.85 | 55.03 | 55.20 | 45.97 | 53.46
AIEEE 2009 | 48.10 | 57.56 | 54.98 | 54.35 | 49.39 | 53.98
AIEEE 2010 | 50.71 | 55.55 | 55.82 | 54.22 | 52.8 | 54.28
AIEEE 2011 | 51.04 | 48.35 | 53.83 | 53.88 | 57.14 | 54.94
Table 8: Median perctile of Women and Reserved students in AIEEE data

###  0.A.7 Case Studies - State wise Results

To understand state wise distribution of Caste and Gender, we answer following
additional research questions(ARQ).

  * •

ARQ1: Which states in India have the highest representation of females and
backward castes in higher education compared to its population?

  * •

ARQ2: Which states in India have been successful in achieving a significant
decrease in bias toward females and backward castes over time? Which states
are lacking in this aspect?

Figure 2: Population normalized distribution of women and backward caste
students in AIEEE 2011 data across Indian states. Figure 3: Rate of change of
population normalized percentage of women and backward caste students across
Indian states appearing in AIEEE exams.

ARQ1: Which states in India have the highest representation of females and
backward castes in higher education compared to its population?

The AIEEE dataset has the state information for each data point. We also
collect the state wise population record from Census
2011111111https://en.wikipedia.org/wiki/2011_Census_of_India. We compute the
population normalized fraction of women and backward caste people writing the
AIEEE 2011 exam. From the plotted results in Figure 2, we observe that the top
states with population normalized higher representation of women writing the
AIEEE exam are Jammu & Kashmir, Himachal Pradesh, Punjab, West Bengal, and
Maharashtra. Similarly, the states with population normalized higher
representation of backward castes writing the AIEEE exam are West Bengal,
Maharashtra, Punjab, Uttarakhand, and Jammu & Kashmir. We believe that the
education policies of these states could act as a suitable guidance to improve
the condition of the other Indian states.

ARQ2: Which states in India have been successful in achieving a significant
decrease in bias toward females and backward castes over time? Which states
are lacking in this aspect?

One way to measure the reduction (increase) in bias would be to check for the
increase (decrease) in the population normalized percentage of women and
backward caste over time. To this purpose, we obtained the rate of change of
population normalized women and backward class candidates taking the AIEEE
exam. For each state, the rate of change is measured as the slope of the best
fit line (linear regression) of the year versus population normalized
percentage scatter plot. The year range considered was 2004 to 2011.

From Figure 3, we observe that the most successful states in reducing the
gender inequality are Himachal Pradesh, Andhra Pradesh (Seemandhra and
Telangana), Haryana and Maharashtra. With respect to reducing caste inequality
we find West Bengal, Punjab, Uttarakhand, Maharashtra, Karnataka are the most
successful.

###  0.A.8 Distribution of Caste and Gender in Koo

Table 9: Gender and caste breakup (%) in the Koo data. | General | Reserved
---|---|---
Male | 73.26 | 12.66
Female | 12.52 | 1.56
Table 10: % users at in the oldest 1% data sorted by creation date. | General | Reserved
---|---|---
Male | 67.1 | 12.66
Female | 17.65 | 2.58
Table 11: % users at in the most recent 1% data sorted by creation date. | General | Reserved
---|---|---
Male | 73.44 | 13.84
Female | 11.22 | 1.50
Table 12: % users in the top 1% data sorted by number of followers. | General | Reserved
---|---|---
Male | 63.87 | 9.00
Female | 24.65 | 2.47
Table 13: % users in the bottom 1% data sorted by number of followers. | General | Reserved
---|---|---
Male | 74.91 | 12.08
Female | 11.74 | 1.27

In Table 9 we show the % breakup of the cross-sectional categories in the Koo
dataset. We observe that the largest representation is from the general
category males while the smallest is from the reserved category females. In
the latest time point (see Table 11) we observe higher female representation
than in the oldest time point (see Table 10). The % of females (both general
and reserved) in top 1% users sorted by followers is relatively larger than in
the bottom 1% followers (see Tables 12 and 13). This is exactly the opposite
(see Tables 12 and 13) for males (both general and reserved). We believe that
a possible reason could be that women have closed coteries of followership.

###  0.A.9 Ethical implications

Like any other classification task, it can also be potentially misused when in
the hands of malicious actors. Instead of reduction of bias, the same
technology can be used to enforce discrimination. Hence, we request the
researchers to exercise caution while using this technology as some demography
classification APIs are already publicly available. Further, to keep
personally identifiable data private, we opensource the codebase to collect
the datapoints instead of sharing the datasets, a policy ubiquitous for social
science researchers.