supplementary information - nature research...7graduate school of library, information and media...

SUPPLEMENTARY INFORMATION

A Silicon Carbide Room Temperature Single Photon Source

S. Castelletto,1, ∗ B. C. Johnson,2, 3 V. Ivady,4, 5 N.Stavrias,6 T. Umeda,7 A. Gali,4, 8 and T. Ohshima3

1School of Aerospace, Mechanical and Manufacturing Engineering

RMIT University, Melbourne, Victoria 3001, Australia2Centre for Quantum Computation and Communication Technology,

School of Physics, University of Melbourne, Victoria 3010, Australia3SemiConductor Analysis and Radiation Effects Group,

Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan4Institute for Solid State Physics and Optics,

Wigner Research Centre for Physics, Hungarian Academy of Sciences,

Budapest, POB 49, H-1525, Hungary5Department of Physics, Chemistry and Biology,

Linkoping University, SE-581 83 Linkoping, Sweden6School of Physics, University of Melbourne, Victoria 3010, Australia

7Graduate School of Library, Information and Media Studies,

University of Tsukuba, Tsukuba 305-8550, Japan8Department of Atomic Physics, Budapest University of Technology and Economics,

Budafoki ut 8, H-1111, Budapest, Hungary

1

A silicon carbide room-temperature single-photon source

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT3806

NATURE MATERIALS | www.nature.com/naturematerials 1

© 2013 Macmillan Publishers Limited. All rights reserved.

http://www.nature.com/doifinder/10.1038/nmat3XXX

1. PHOTOLUMINESCENCE VARIABILITY AND THREE-LEVEL SYSTEM MODEL

We have used single defect spectroscopy and single photon correlation measurements tostudy the photo-physical parameters of single defects in SiC not accessible with conventionalPL ensemble measurements. A detailed analysis of the variability of parameters that maybe unobservable in ensemble measurements is made possible. Firstly, the photoluminescence(PL) spectra of single photon sources in SiC is shown in Fig. 1. The PL of samples irradiatedwith 2 MeV electrons to a fluence of 1013 e/cm2 and annealed at 300◦C excited with either a660 nm laser or a 532 nm laser are presented in Fig. 1(a) and (b), respectively. Broad PL isobserved between 600-800 nm. Fig. 1(c) shows typical spectra from a sample irradiated toa fluence of 1017 e/cm2 followed by a similar anneal. The emission with PL band observedaround 600–800 nm is associated with the CSiVC centre and is responsible for the the singlephoton emission. There are in fact eight different zero phonon lines associated with thisdefect in 4H-SiC which contribute to the variability of the band peak position. In addition,

filter

500 600 700 800 900 1000Wavelength (nm)

500 600 700 800 900 1000

Nor

mal

ized

inte

nsity

(arb

. uni

ts)

Wavelength (nm)

500 600 700 800 900 1000Wavelength (nm)

a

b

c

FIG. 1. Variability observed in PL emission at room temperature using confocal mi-

croscopy. PL emission associated with different single photon centers excited with 660 nm (a) or

532 nm (b) in samples irradiated with 2 MeV electrons to a fluence of 1013 e/cm2. (c) PL emission

measured in the sample irradiated to a fluence of 1017 e/cm2, excited at 660 nm. These emissions

do not correspond to single defects.

∗ [email protected]

22 NATURE MATERIALS | www.nature.com/naturematerials

SUPPLEMENTARY INFORMATION DOI: 10.1038/NMAT3806



!"#$%&'(')'*+,-,./+01"21',3'1"4#5&'/+,-,4'1,$%2&1'"4'6"78'!9"#$%&'()*'+)%+#&'++%,-.'(#/0(&.'(#-1#)23%+%(1#%4&21-.'(#5'6%+7#/+'8#19%#&%(1%+#6219#:;#79'6(#2(#<2=>#?#!:"!2">#@1#79'67#-#A%+B#,'6#)%5%()%(&%#'/#19%#79%,A2(=#'/#19%#8%1-71-C,%#71-1%#6219#19%#'5.&-,#%4&21-.'(#5'6%+>#D9%#&0+A%7#-+%#792E%)#/'+#&,-+21B>#!;"#;%E#-427F#$-10+-.'(#&0+A%#'/#19%#)%/%&1#GH%)#6219#IJ>#?>?#69%+%#K#L#M>M#8N*?#!7',2)#,2(%"#-()#K#L#O#!)-79%)#,2(%"P#1'#2(/%+#19%#J0-(108#B2%,)>#Q2=91#R427F#!#A%+707#%4&21-.'(#5'6%+P#GH%)#6219#19%#K#1%+8#!7',2)"#,2(%#-()#6219#KLO#!)'H%)#,2(%"##!2"#<2S(=#'/#5-+-8%1%+7#'/#19%#=!M"!1"#/0(&.'(P#,?#-()#,M#A%+707#19%#%4&21-.'(#5'6%+#6219#19%#8')%,#6219#19%#K#1%+8#!7',2)"#,2(%#-()#6219#K#L#O#!)-79%)#,2(%">##@(#1927#&-7%#19%#8')%,#6219#K#T#O#5+'A2)%7#-#C%H%+#G1#'/#19%#)-1->###

9' 2';

0.1

0.2

0.3

0.4

0.58

0.6

0.72mW

−50 0 500

1

2

3

4

5

6

7

g2 (!)

! (ns)

!

!

!

!

!

! !

!!

!

!!

!

!

!

0.0 0.4 0.80

2

4

6

8

0

0.2

0.4

0.6

0.8

1

Cou

nts/

s (1

05 )

a

Excitation power (mW)

!!

!

! !

!

!

!

0.0 0.4 0.80.0

0.2

0.4

0.6

0.8

1.0

1.2

0

0.05

0.1

0.15

0.2(b)

" 1 (n

s#1 )

" 2 (n

s#1 )

Excitation power (mW)

FIG. 2. Temporal dynamics of single photon sources in SiC. a, Second-order correlation

function at different 532 nm excitation powers from the center with PL shown in Fig. 1d(i). A

weak dependence of the metastable state shelving with the optical excitation power is observed.

The curves are shifted vertically for clarity. b, Saturation curve of the defect fitted with Eq. 2

where β = 2.2 mW−1 (solid line) and β = 0 (dashed line), to infer the quantum yield (left axis).

a versus excitation power, fitted with the β term (solid) line and with β = 0 (dotted line) (right

axis). c, Decay rates, λ1 and λ2 extracted from the fits in a versus the excitation power fit with

the model with the β term (solid line) and without it (dashed line).

in the high fluence irradiated sample a broad emission in the 900 nm region was also observedindicating the presence of the silicon vacancy defect, VSi.

We studied the excitation power dependence of the photon correlation function of singledefects to deduce the decay rates. As an example Fig. 2a shows the anti-bunching behaviorof the center with PL shown in Fig 2d (i) in the main paper, for a range of excitation powersat 532 nm. Due to the presence of a photon-bunching effect (higher correlation at longerdelay times), each curve was fit with a three-level system model, where the second-ordercorrelation function is expressed as the sum of two exponentials,

g(2)(τ) = 1− (1 + a) exp[−λ1τ ] + a exp[−λ2τ ] (1)

with λ1 and λ2 as free parameters and related to the transition rates, rij, from level (i)to level (j) by the equations λ1 = r12 + r21, λ2 = r31 + r23r12/λ1 [1]. The value of a is ameasure of the photon-bunching, that prevents radiative decay to the ground state (1) fromthe excited state (2) by a metastable state (3) and can be expressed as a = r12r23/(λ1r31).Photon-bunching at longer delay times in single molecules[2] and color centers[3] in diamondhas been associated with the presence of a long-lived metastable state. Non-radiative decayto the ground-state takes place from this metastable state, inducing an overall reduction ofthe single photon emission arising from low rate electron trapping in the metastable state.

For this particular center the saturation count rate and optical saturation power areΦ∞ = 1.3 × 106 counts/s and Psat = 0.5 mW, respectively. This is obtained from fittingthe data in Fig. 2b with Φ = Φ∞Popt/(Psat + Popt). The dependence of the transition rateparameters of this model, a and λ1,2, on the excitation power are shown in Fig. 2b,c. Alinear optical power dependence of the coefficient λ1 = r021(1 + αPopt) is assumed, wherer12 = αr021Popt = σIopt/(hν), is related to the absorption cross-section of the defect, σ. Due

3NATURE MATERIALS | www.nature.com/naturematerials 3



http://www.nature.com/doifinder/10.1038/nmat3806

to the very weak dependence of the metastable state population on the excitation power,we have assumed that the shelving (r23) and de-shelving (r31) decay rates of the metastablestate are constant. Other models used to describe the population dynamics of the excitedstate and of the metastable state versus the excitation optical power[4, 5], however, may alsodescribe our data. For example, in some cases a linear dependence of r31 = r031(1 + βPopt)may be employed where β is a fitting parameter that describes the variation of the decayrate from the metastable to ground states with changes in optical excitation power. Thisparameter is important since it signifies that a power dependent effect in de-shelving themetastable level is operative. This dependence has also been observed for single molecules[6].Fits with and without the β term are shown in Fig. 2b,c.

On fitting the three-level system model, we obtain the decay rate terms r021, r031, r23,

α and β. Extrapolation to zero excitation power gives the excited state lifetime, r021, andthe shelving decay rates, r31. While extrapolation to infinite excitation power of λ2 givesr23. For the center shown in Fig. 2 we obtain 1/r021 = (1.2 ± 0.1) ns, α = (0.3 ± 0.1), β =(2.1±0.5) mW−1, 1/r031 = (45±3) ns, 1/r023 = (7±2) ns, and for β = 0, 1/r031 = (23±2) ns,1/r023 = (8±2) ns. The absorption cross section is σ ≈ 5×10−16 cm2. Using these values thefollowing model can be used to determine the quantum efficiency, ηqe, of this single photonsource,

Φ = ηqeηcollηdetr21(1 + r21/r12 + r23/r31)−1, (2)

By fitting the count rate we obtain ηqeηcollηdet = 0.008 ± 0.001. If we assume that thedetection efficiency is only limited by the detector’s quantum efficiency (ηdet=55%) with thefilters having a transmission of 90%, and a collection efficiency of our setup determined tobe ηcoll ≈ 2%[7], ηqe ≈ 70% is estimated.

By studying over 100 centers we determine average values of the excited state lifetimeand metastable state lifetime. We observed a moderate dispersion of the excited statelifetime from 1.2–2.1 ns, yielding an average value of 1.5 ± 0.3 ns (20% variability) andα = (0.4 ± 0.3) mW−1. Concerning the metastable state, due to the very small photon-bunching effect observed with increased excitation power, the measurement of the decayrates from and to the metastable state are affected by a large variability, giving averagevalues of 1/r031 = (40 ± 20) ns and 1/r23 = (13 ± 5) ns. In addition, not all the emitterswere best fit with the β parameter. The measurement of the excited state lifetime was alsoconfirmed by a direct measurement using a pulsed laser.

2. BLINKING STATISTICS

We studied the statistical behavior of the “on” and “off” time distributions of singleemitters and identified a number of blinking categories. One common case is an unclearblinking behavior as shown in Fig. 3(a). Emitters having two on-off states are shown inFig. 3b and c, where in case (b) the “on” time dominates the “off” time. The opposite istrue in (c) where the “off” state has a non-zero intensity. Finally, Fig. 3d shows blinkingbetween 3 separate states. This last example is less common but is more likely to occurwhen 532 nm laser is used for excitation. Fig. 3(e) shows the dependence of the “on” and“off” times on the excitation power for a two state single blinking centre, both the“on” and“off” times reduce with increasing excitation power.





(e)

FIG. 3. Example of blinking statistics of single defects. a-d show examples of blinking of

single photon emitters in a 4H-SiC sample irradiated with 2 MeV electrons to a fluence of 1013

e/cm2 and annealed at 300◦C. The time constants for each state are also given. e, The on/off time

constant dependence excitation power.

3. SINGLE DEFECT CONCENTRATION VERSUS IRRADIATION FLUENCE

AND ANNEALING TEMPERATURE

Using confocal imaging, we studied the concentration of the defects in samples preparedwith different electron irradiation fluences 1013, 1014 and 1017 e/cm2 (Fig. 4). For thispurpose we used 660 nm excitation. The optically active defects observed here were similarto those observed in the PL measurements. We also imaged an unirradiated sample forcomparison (Fig. 4)e. This material contains as-grown optically active defects displayingsingle photon emission behaviour. The density of these defects can be significantly enhancedwith electron irradiation fluence and annealing. This indicates that the defect responsiblefor the single photon emission can be formed by electron irradiation.

We measured the concentration of the defects in samples prepared with the same electronirradiation fluence of 1013 e/cm2, applying different annealing temperatures (as described inMethods of the main text). We observed a remarkable increase in the number of defects forhigher temperature annealing. A summary of the total number of defects in a 100×100 µm2

scan versus temperature and fluences is shown in the Fig. 2(f) of the main text.

The increase in the number of defects with the increased annealing temperature indicates





FIG. 4. Confocal maps versus irradiation fluence and annealing temperature. a-g

Confocal maps of 4H SiC with the processing conditions indicated. The control map in e is an

unirradiated sample showing as-grown optically active defects. Note that only g is on a different

color scale since it is relatively bright and shows no isolated defect PL.

that the defects studied here are stable after high annealing temperature (up to 800◦C).In the 500◦C annealed sample bright spots appeared to consist of more than one defect(g(2)(0) ∼ 0.5), and very few defects blinked.

We performed a focal axis (z) confocal scan on the high and low fluence irradiated samplesto locate the position of the defects in the material (Fig. 5(a,b)). A bright band was observedin the high fluence irradiated sample 1.5 µm below the crystal surface. It had a width ofabout 1.5 µm. The low fluence irradiated sample had a similar band consisting of singlephoton emitters.





5 µm

(a)

(b)

FIG. 5. Confocal z-scan maps. Confocal maps of SiC in the focal direction (z) with (a)

irradiation of 1017e/cm2 and annealing 300◦ C and (b) irradiation of 1013e/cm2 and annealing

400◦C. The surface of the material is at the top of each panel, while the bright spots or bright

areas correspond to the defect locations in the confocal plan.

4. SUMMARY OF DEFECT IDENTIFICATION

In the following subsections we summarize the arguments to identify the microscopicorigin of the single photon emitter. In this letter, we performed a study of the defectformation from the ensemble level down to the single defect level where these findings areused to set-up a microscopic model. The microscopic model are studied by means of ab-initiocalculations and group-theory analysis. This complex approach made possible to assign thesingle defect emitter to the positively charged carbon anti-site vacancy defect in 4H-SiC.

4.1. Ensemble measurements

Ensemble room temperature and low temperature measurements were performed on asample irradiated to 1017 e/cm2 at 532 nm using a Renishaw Micro-Raman spectrometer. At80 K the zero phonon lines (ZPL) of the AB lines [8] can clearly be observed (Fig. 6a,b). Atroom temperature a broad PL band is observed as observed in the single defect spectroscopy.The single photon emissions observed in this work are attributed to these particular lines.These lines are here assigned to the carbon antisite-vacancy pair defect, CSiVC.

The V1 and V2 lines[9] are also observed (Fig. 6c), corresponding to defects on inequiv-alent sites of the VSi defect (Fig. 4b,d). The spin state of the V lines can be coherentlymanipulated in ensemble [1, 9]. These two defect types, CSiVC and VSi, are the dominantdefects observed in this study. Confocal mapping revealed that the V1 and V2 lines are dom-inant and have a higher intensity than the AB lines in the high fluence irradiated samples.





650 660 670 680

Inte

nsity

(arb

. uni

ts)

Wavelength (nm)

850 900 950 1000In

tens

ity (a

rb. u

nits

)Wavelength (nm)

A1

A2

A3 A4

B1

B2

B3

B4

5x

V1 V2

a b

c

600 700 800 900 1000

!190°C!110°C!30°C20°C

Inte

nsity

(arb

. uni

ts)

Wavelength (nm)

V1’

FIG. 6. Ensemble measurements of defects in electron irradiated 4H-SiC. a, PL of

a sample irradiated with 2 MeV electrons to a fluence of 1× 1017 cm−2 measured at various

temperatures. Expanded view of the 80 K PL spectra showing the CSiVC (b) and VSi (c) defect

signatures. Since V1 (861.5 nm) and V2 (916.3 nm) have E||c polarisation, spectra in c have been

measured with the laser perpendicular to the c-axis so as to show all ZPLs associated with VSi,

while for spectra in a it is parallel. Only V1’ at 858.9 nm is observed clearly in a.

In samples irradiated with lower fluences this defect was rarely observed due to the greaterthreshold energy required for the Si sub-lattice of SiC causing a greater rate of productionduring irradiation. We did not observe anti-bunching for the VSi center.

In order to correlate this emission with the room temperature single photon source, wemeasured the lifetime of the AB lines on an ensemble of defects. We used a time-resolvedPL measurement with a pulsed 532 nm laser. The result, reported in Fig. 7, show a lifetimeof 1.8 ns, in agreement with the single photon correlation measurements.

For both the AB and V1/V2 lines the vibronic sideband is a significant feature. TheHuang-Rhys factor, S, was determined for the AB system. This factor is related to themean number of vibrational quanta involved in the optical transition and was determinedhere by dividing the integrated intensity of the ZPLs by the total integrated luminescence ofthe entire AB line system, S = ln IZPL/Itot. For temperatures below 120 K S = 1%. Abovethis temperature the value dropped to S = 0.01% at room temperature. Other defectscentres in diamond have S=3.2, 0.2, 0.4, 2.5% for NV, SiV, NE8 and an unknown greenemission defect, respectively[1]. Further studies are required to confirm this parameter foreach of the A and B lines.





4.2. Group Theory analysis of the single photon emitters and its microscopic

origin

Our experiments confirmed that the single photon emitter originates from the AB PLlines in 4H SiC. Previously, the AB PL lines were assigned to the neutral carbon antisite-vacancy pair CSiVC (see Fig.4 a) based on the properties of the AB PL lines [8]. However,we emphasize that PL measurements do not often provide direct information about thechemical composition of a defect. In particular, one cannot deduce the charge state of thePL center purely from optical data. Thus, we carried out large scale supercell calculationsto support the assignment inferred in 8. Our calculations indicate that AB PL does notoriginate from the neutral CSiVC but instead may arise from the positively charged CSiVC

defect.A complete identification of the single photon emitter requires further careful experimen-

tal and theoretical study, such as low temperature single photon identification as well asfurther modelling. However, we establish at this level of experimental verification the use ofthe positively charged CSiVC pair as a working model. The center’s optical properties arethen analyzed by group theory methods and compare the results to the known propertiesof the AB PL centers in 4H-SiC. We find that our model can describe the AB PL centerswell. The combined ab intito and group theory analysis can explain the following featuresof the AB line single-photon-emitter:

1. the dominant polarization both in excitation and radiative emission is perpendicularto the c-axis (as found in 8 for AB PL centers);

2. the occurrence of the metastable shelving state and the process of non-radiative decay

600 800 1000

PL in

tens

ity (a

rb. u

nits

)

Wavelength (nm)

●

●

●●

●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

20 25 30 35 40

● datafit

τ = (1.83 ± 0.02) ns

PL in

tens

ity (a

rb. u

nits

)

Time (ns)

FIG. 7. Lifetime measurement of the AB lines defects in the high density electron ir-

radiated 4H-SiC sample. Direct lifetime measurement and PL spectra of the room temperature

PL emission corresponding to the AB lines.





via spin-orbit coupling; the scattering from all the sub-states of the shelving statecan be very effective, thus the lifetime of this shelving state can be relatively short inagreement with our experimental findings;

3. the shelving state involves a loosely bound hole near the valance band edge which maybe responsible for the detected large dispersion of lifetimes of the shelving state, as ifthe hole temporarily leaves the defect then the lifetime of the “dark state” appearslonger;

4. the nature of the shelving state may also be responsible for the blinking properties(e.g., a nearby defect can effectively capture the loosely bound hole and hinders theluminescence. The observation that the blinking effect is reduced with a high temper-ature anneal may indicate the annihilation of the defects which hinders the PL in thisway);

5. blinking may also arise in our working model from the ionization of the center from theneutral to positive charge states. In this case the electrons are continuously pumped tothe conduction band in order to maintain the PL. The 660 nm excitation can ionize theneutral defect but is less efficient in ionizing the defect further such as to the doublypositive charge state. Thus, the 660 nm excitation shows greater photo-stability thanthe 532 nm excitation.

In the next sub-sections we provide a brief description about the atomistic simulationsand group theory analysis.

4.2.1. Atomistic simulations on the microscopic models of the single-photon-emitter

We now concentrate on the ground state properties of the defect, and the possible lu-minescence processes are discussed within group theory. The nature of the ground statecan be well described by density functional theory (DFT), while we discuss the possibleexcited states with the help of the electronic structure of the ground state as obtained inthe simulations.

The dangling bonds of the carbon antisite as well as of the Si-atoms nearest to thevacancy form three levels in the fundamental band gap. In the axial configurations thelowest level has a1 symmetry and the higher one is a doubly degenerate e symmetry inthe C3v point group symmetry. In the basal-plane configurations the degenerate e statesplits due to its lower C1h symmetry. In the neutral charge state two electrons occupy thesestates. According to HSE06 calculations these states reside in the upper half of the bandgap independent of their configuration or occupation of states. As a consequence, ≈1.5 eVis sufficient to promote an electron from these defect levels to the conduction band. Thismeans that 532-nm excitation (≈ 2.35 eV) can ionize the neutral CSiVC pair at very highenergy in the conduction band where the electron can be definitely detached from the defectcenter leaving it in the positive charge state. In the positive charge state a single electronoccupies the lower fully symmetric defect level where this defect level falls in the lower halfof the band gap while the empty defect levels are still in the upper half of the band gap.





The calculated ionization energies of the positively charged CSiVC pair are 1.91 eV,1.85 eV, 1.83 eV, and 1.82 eV for hh, hk, kk and kh configurations, respectively, withrespect to the conduction band edge. While 532-nm excitation is again able to ionize thissystem but the electron will be close to the conduction band edge, so the excited electronmay stay close to the defect center and can recombine with it radiatively. This event hasa much greater probability for positively charged defect than that for the neutral defect.This makes it possible to have an effective absorption and luminescence in the visible. 660-nm excitation (≈ 1.87 eV) can only rarely photo-ionize the defect than 532-nm excitationdoes which explains the improved photo-stability of the defect with 660-nm excitation wavelength. We analyze the ground and excited states of this electronic configuration by applyinggroup theory as described in the next section.

4.2.2. Group theory on the positively charged CSiVC pair in 4H-SiC

The AB PL lines indicate four ground state configurations of the same defect in 4H-SiC with two zero-phonon line for each configuration which strongly implies a pair-complexwith hh/kk axial configurations and hk/kh basal plane configurations. The highest possiblesymmetry of the axial configurations is C3v while it is C1h for the basal plane configurations.Thus, the suggested microscopic structure CSiVC is indeed consistent with the previous ABcenter assignment, however, our calculations indicate that the neutral CSiVC pair does nothave visible PL. Thus, our working model is the positively charged CSiVC pair that mayhave visible PL.

First we analyze the electronic structure of the axial configurations in detail then wedescribe the differences for the basal plane configurations. Further information on the elec-tronic structure of the defect is provided in 1. In the ground state of the axial defects, thea1 state is mainly localized on the carbon anti-site while Si dangling bonds form the e state(see Fig. 8). In the ground state, a1 is occupied by a single electron that forms the fullysymmetric 2A1 state. From the ground state electron configuration one may assume thatthe excitation can be described as 2A1 → 2E.

For the sake of completeness, we discuss the spin state of the ground and excited states.The spinor functions can be described by double groups. The single electron can be describedas the double degenerate Γ4 in the double group of C3v symmetry, where the degeneracynaturally accounts for the Kramers-doublet (ms = ±1

2={| ↑〉, | ↓〉}). The symmetry of the

ground state full wave function is A1 × Γ4 = Γ4. The symmetry of the full wave functionsof the excited state is E × Γ4 = Γ4 ⊕ Γ56, where Γ56 = Γ5 ⊕ Γ6 is degenerate due tothe time-reversal symmetry. Apparently, 2E state (4× degenerate considering the orbitaland the spin) splits to two double generate states, Γ4 and Γ56. The splitting is due to

the axial spin-orbit interaction, λz lz sz, where lz acts on the orbital (orbital momentum),sz on the spin, and λz is the strength of the coupling. If the double degenerate orbitalsare symbolically written as E = {E+, E−} where E± transforms as l = | ± 1〉 functions,then the calculated splitting is λz where {|E+, ↓〉, |E−, ↑〉} states has −λz/2 eigenenergywhereas {|E+, ↑〉, |E−, ↓〉} has +λz/2 eigenenergy. This may be described symbolically as|j = 3/2, jz = ±1/2〉 and |j = 3/2, jz = ±3/2〉, respectively, where j = l+ s.

It is important to investigate the selection rules of the optical dipole transition thathas direct correspondence on the measured polarization dependence of the emitted photonsfrom AB PL centers. The optical dipole operator transforms as er, thus the orbital partof the wave functions (single group) should be considered so that the spin part of the wave





FIG. 8. Hexagonal-hexagonal configuration of carbon antisite-vacancy pair and its correspond-

ing highest occupied and an unoccupied defect states in the gap. This unoccupied state has an

asymmetric character (a”) split from the double degenerate e state. Isosurface of red(blue) color

represents the positive(negative) value of the wave function.

function should be conserved. In C3v symmetry the optical dipole transition transformsas A1 with polarization parallel (E||c) to the c-axis of the lattice ([0001] direction) or asE with polarization perpendicular (E ⊥ c) to the c-axis. By combining these polarizationswith the initial and final states in absorption one can conclude that only E ⊥ c is the allowedpolarization. Indeed, this can be the dominant selection rule. Taking into account the spin-orbit splitting in 2E state, one might expect two E ⊥ c polarized photons. However, in themeasurements E||c polarization could be also detected. In addition, the energy differencebetween the split ZPL lines within the same configuration is about 4 meV. In nitrogen-vacancy center in diamond, the typical spin-orbit splitting is in the order of 1-10 GHz whichis about 3 orders of magnitude smaller than the splitting found in AB center. Our analysisimplies that another effect is responsible for this splitting.

Principally, 2E state is Jahn-Teller unstable. Our atomistic simulations indicate thatsuch distortion can take place in CSiVC pair. For instance, the C3v symmetry is brokenwhen the e level is occupied by an electron. The Si-Si second neighbor distance is about3.0 A which is not too far from the usual Si-Si bond length (2.35 A), thus the Si danglingbonds can effectively overlap and create long bonds of ≈2.7 A. During this reconstructionthe symmetry is reduced from C3v to C1h. The many-body 2E state will split to 2A′ and2A′′, respectively, that we label as ∆JT . Assuming that ∆JT is much larger than λz in 2Estate, then the measured double ZPL peaks can be understood as ∆JT splitting. In thisdistorted geometry, the ground state will transform as 2A1 →2 A′, thus the ground andexcited states of 2A′ can interact, and the 2A1 excited state may ”borrow” the character of





the ground state. This has important consequences on the optical properties. Principally, asthis interaction can always occur the transversal spin-orbit interaction, 1/2λxy(l

+s−+ l−s+),is able to mix the excited states of 2A′ and 2A” excited states via the ground state characterof 2A′. In conjunction, E ⊥ c selection rule can be relaxed slightly when 2A′ is the lowestexcited state since 2A′ →2 A′ is allowed by E||c in C1h symmetry. The strength of thisinteraction depends on the ground state character in the 2A′ excited state. We furthernote that 100% polarization should not occur, principally, due to the transversal spin-orbitinteraction.

In the case of the basal plane configurations, the ground state already has ab ovo low C1h

symmetry. Nevertheless, the wave functions may show C3v character. The lowest excitedstate could have either 2A′ or 2A′′ symmetry. Thus, the polarization rules are very similarto that of the axial configurations.

These results can explain our experimental data on AB center in 4H-SiC. The Jahn-Tellersplitting in the excited state is responsible for the ZPL doublet where the higher energystate may be thermally occupied. The luminescence should show at least one transitionwith strong E ⊥ c polarization while the second transition may be either polarized parallelor perpendicular to c-axis. No pure polarization should occur due to spin-orbit interaction inC1h symmetry which can weakly link A′ and A” states. According to Figs. 1a,e,f in the maintext, A2, A4, B2 have such partners that emit light dominantly in the opposite polarization,while B4 and its B3 partner always emit light dominantly perpendicular to c-axis. Neitherof these transitions are purely polarized. Our model are in line with all these features.

The accurate and correct calculation of the excited states needs method beyond DFTand very difficult for large systems such as point defect model in large supercells. Anotherchallenge, that the uncertainty in the very-well converged calculations is at the border of therequired accuracy of about 0.01 eV, that is the energy difference between AB lines, exceptfor the A2 line which is about 0.06 eV apart from A4 line. Thus, comparison between theoryand experiment cannot be definite. Nevertheless, interesting conclusions can be drawn fromthe ground state properties such as ionization energies, character of the wave functionswhereas constraint DFT shows the effect of the Jahn-Teller distortion on the character ofthe wave functions in the axial configurations that might allow tentative assignment of CSiVC

configurations to the measured AB lines. The calculated ionization energies imply that theorder of transition energies follows as hh, hk, kk, and kh. The single particle a1 level ofhh configuration lies the deepest in the band gap because the CSi atom relaxes the mostamong all the configurations. This effect is not so pronounced when CSi(h) is combinedwith VC(k) but still visible. Thus, these two defects are associated with the highest energytransitions of A2 and A4 lines. We note that the stronger relaxation of CSi at h-site thanat k-site is manifested in the measured (and calculated) hyperfine signals[1]. The B2 andB4 lines are associated with such configurations where CSi at cubic site. According to oursymmetry analysis of the character of the wave function, the lowest excited state has A′, A′

and A” symmetry for hh, hk and kk configurations, respectively. This can nicely explainthe E||c, E||c and E ⊥ c dominant polarizations of A2, A4 and B2 lines, respectively, andalso the polarization dependence of the partners of these lines. The polarization dependenceof B4 and its partner B3 may need further consideration. Here, both emits light dominantlyperpendicular to c-axis. The symmetry of the lowest excitation state shows A′ symmetry inkh configuration which may allow E||c polarization for B4, but E ⊥ c is also allowed. Here,the ground state character is much less pronounced in the A′ excited state than that in theother configurations. Based on these arguments, we tentatively assign (A2, A1), (A4, A3),





(B2, B1), and (B4, B3) lines to the (lower, higher) ZPL of hh, hk, kk, and kh configurations.

Next, we derive the possible non-radiative decay from the excited state that are mediatedby spin-orbit interaction. We analyze this with group theory applied first on C3v symmetry,and then we show how the selection rules are relaxed by lowering this symmetry.

In our model, only single electron occupies the defect states in the gap. In order toform a S = 3/2 shelving state, another electron must be taken from the valence band edge.Due to the spin-orbit coupling in the valence band edge the top band transforms as a1,

thus a(1)1(VB)a

(1)1 e(1) state transforms as 4E where VB refers to the valence band origin of the

state. We can consider the optically excited 2E state also as a(2)1(VB)a

(0)1 e(1). The ground

state is a(2)1(VB)a

(1)1 e(0). The e wave functions have l± character while a1 wave functions have

lz character where the spin-orbit operator may be written as λz lz sz + 1/2λxy(l+s− + l−s+)

under C3v symmetry. Apparently, the axial spin-orbit operator may link a1 orbitals whilethe transverse spin-orbit operator may link e and a1 orbitals. For this reason 2E and 4Estates can be coupled via an axial spin-orbit interaction while 4E and 2A1 states couple viaa transverse spin-orbit interaction. In exact C3v symmetry the 4E state has complicatedfine structure as both the spin-orbit and electron spin – electron spin interactions split thems = ±1/2 and ms = ±3/2 substates where the scattering from the 2E optically addressedexcited state goes to thems = ±1/2 sublevel while it scatters subsequently to the 2A1 groundstate from one of the ms = ±3/2 sublevels. However, our ab-initio calculations indicate thatC1h distortion can take place in the excited states. In C1h symmetry the ms = ±1/2 andms = 3/2 states can be mixed in the basis of C3v symmetry, thus the selection rules of C3v

is efficiently relaxed. We conclude that the spin-orbit interaction can couple all the substatesof 4E-like shelving state to the ground state even in the axial configurations of the defect.

[1] Kitson, S. C., Jonsson, P., Rarity, J. G. & Tapster, P. R. Intensity fluctuation spectroscopy

of small numbers of dye molecules in a microcavity. Phys. Rev. A 58, 620–627 (1998).

[2] Basche, T., Moerner, W. E., Orrit, M. & Talon, H. Photon antibunching in the fluorescence

of a single dye molecule trapped in a solid. Phys. Rev. Lett. 69, 1516–1519 (1992).

[3] Kurtsiefer, C., Mayer, S., Zarda, P. & Weinfurter, H. Stable solid-state source of single

photons. Phys. Rev. Lett. 85, 290–293 (2000).

[4] Aharonovich, I., Castelletto, S., Simpson, D. A., Greentree, A. D. & Prawer, S. Photophysics

of chromium-related diamond single-photon emitters. Phys. Rev. A 81, 043813 (2010).

[5] Neu, E., Agio, M. & Becher, C. Photophysics of single silicon vacancy centers in diamond:

implications for single photon emission. Opt. Express 20, 19956–19971 (2012).

[6] F. Treussart, C. G., A. Clouqueur & Roch, J. F. Photon antibunching in the fluorescence of

a single dye molecule embedded in a thin polymer film. Optics Letters 26, 1504 (2001).

[7] Castelletto, S. & Boretti, A. Radiative and nonradiative decay rates in chromium-related

centers in nanodiamonds. Optics Letters 36, 4224–4226 (2011).

[8] Steeds, J. W. Photoluminescence study of the carbon antisite-vacancy pair in 4H- and 6H-SiC.

Phys. Rev. B 80, 245202 (2009).

[9] Baranov, P. G. et al. Silicon vacancy in SiC as a promising quantum system for single-defect

and single-photon spectroscopy. Phys. Rev. B 83, 125203 (2011).

[10] Soltamov, V. A., Soltamova, A. A., Baranov, P. G. & Proskuryakov, I. I. Room temperature





coherent spin alignment of silicon vacancies in 4H- and 6H-SiC. Phys. Rev. Lett. 108, 226402

(2012).

[11] Smith, J. M. et al. Optical properties of a single-colour centre in diamond with a green

zero-phonon line. New J. Phys. 13, 045005 (2011).

[12] Umeda, T. et al. Identification of the carbon antisite-vacancy pair in 4H-SiC. Phys. Rev. Lett.

96, 145501 (2006).

[13] Umeda, T. et al. Identification of positively charged carbon antisite-vacancy pairs in 4H-SiC.

Phys. Rev. B 75, 245202 (2007).





supplementary information - nature research...7graduate school of library, information and media...

Documents