Theory of individual dopants in semiconductors

Michael E. FlattéOptical Science and Technology CenterDepartment of Physics and Astronomy

Department of Electrical and Computer EngineeringUniversity of Iowa

supported by AFOSR and ARO

Theory of individual dopants in semiconductors

review of “solotronics”: Nature Materials 10, 91 (2011)

V. R. Kortan, C. E. Pryor, C. Şahin, J. M. Tang (U. Iowa)P. M. Koenraad, A. Silov, J. Bocquel, J. K. Garleff, J. van Bree, W. Van Roy,

C. Celebi, A. P. Wijnheimer, A. Yakunin (TU/e)R. Wiesendanger, J. Wiebe, F. Marczinowski, F. Meier, M. Morgenstern (Hamburg)

introduction to dopantsshallow levelsionization and effect of dopants on transportpositioning of dopants, length scalesenvelope function theory and tight-binding theorydeep levels and lattice symmetry (radial, angular)

control of confinement and changes in angular momentummagnetic deep levels (Mn and Fe in GaAs)effect of lattice symmetry, even within effective mass modelsstrain and electric field effects on magnetic deep levels

Outline

local bonding symmetry remains the sameideally, if the dopant is on the same row, it behaves as an extra proton and electron

+-

a simple change to the materialsubstitutional dopants with different valence

GaAs As

As

As

As As

As

As

Si

“hydrogenic" impurities in semiconductors

Group III: Al,Ga,InGroup IV: C,Si,GeGroup V: P,As,Sb

+-+-

theory of hydrogenic dopants

built from general effective mass theory PR 97, 869 (1955) EConduction

EValence

m becomes m*ε becomes εrelative

ERydberg becomes (m*/ε2relative)ERydberg

+-

donor states

theory of hydrogenic dopants

built from general effective mass theory PR 97, 869 (1955) EConduction

EValence

m becomes m*ε becomes εrelative

ERydberg becomes (m*/ε2relative)ERydberg

+-

donor states

ionization

ionization energies ~ meV central cell correction

Length scales of defect statesMetalInsulator

electronic states localizedon the atomic scale

electronic states extendedthrough the entire solid

short length scales = a ~ aB

a

short length scales = kF

-1 ~ aB

E

k kF

E

disorder

Semiconductor

dopant

localized electronic statesare “big”, R>> a

B

E

k

extended electronic statesvary slowly, k

F-1 >> a

B

Large distances characteristic of electronic states in semiconductors imply

Long-distance interactions and perturbations (e.g. Thomas-Fermi length)Interactions very sensitive to external perturbations (E, B fields)

using dopants in transistors

emitter base collectoron

off

Sze

, Se

mic

on

du

cto

r Ph

ysic

s

junction FET+- +-+- +-

+- +-+- +-

+ ++ +

on

off

trapping/detrapping in MOSFETs Tsai et al.,

APL 61, 1691 (1992)

+- +-using dopants in transistors

emitter base collectoron

off+ +-

Asenov et al, IEEE Trans. Elec. Dev. 50, 1837 (2003)

Shinada, Nature 437, 1128 (2005)

charge device reproducibility and dopants

Transport through a few dopants

towards asingle-dopant transistor

Tan et al.,Nano Lett. 10, 11 (2010)

electronic levelsassociated with

individual dopantspermit resonant

transport

conductance

gate voltage

sour

ce-d

rain

vol

tage

single-dopant transistor

electronic levelsassociated with a

single dopantpermit resonant

transport

conductance

gate voltage

sour

ce-d

rain

vol

tage

Fueschsle et al., Nature Nanotechnology 2012

Nature 442, 436 (2006)

Positioning Mn in the surface layer

valence edge andacceptor state

LDOS

positioning a single dopant spin

http://chemwiki.ucdavis.edu/

point-group symmetries and dopants

s

p

d

f

schematic wave functions of different symmetry

breaking degeneracy (radial potential)

Coulomb potential: energy only depends on shell #, not on which spherical harmonicgeneral central potential: energy only depends on shell # and total angular momentum l

Central

l = 0l = 1l = 2l = 3

Coulomb

all l

breaking degeneracy (angular potential)

crystalisotropicpotential

all m

As As

As

As

Si

lattice: split among the m statesalso called “crystal field”

non-magnetic: equal amount of +m and -m

breaking degeneracy (tetrahedral group)s

As As

As

As

Si

p

d

f

A1

T2

T2

E

?

deep levels - how do they form?As As

As

As

SiZunger: they are atomic levels, set relative to the vacuum

s

p

A1

T2

related observation: symmetry of tetrahedral bonds below is A1+T2

Hjalmarson et al: PRL 44, 810 (1980)

deep level is a host-like antibonding state

accessible atomic features in solids“Shallow states” - meV rather than eV

due to small effective mass and large dielectric screening

responsive to external fields

“Core states” ~1 eV - d-states, spin, spin-orbit

Nuclei (hyperfine)very long spin coherence times

Dots have hyperfine, shallow states

- missing the core, lower symmetry

Fe2+ to Fe3+

transition in GaAs

change in d-shell occupancy

S=2 to S=5/2

PRB 87, 075421 (2013)

Si in GaAsGarleff et al., PRB 84, 075459 (2011)

STM-driven electronic transitions of dopant core states

produces HUGE (x100) spin-orbit interactions EPL 98, 17013 (2012)

structural changes

Michael E. FlattéOptical Science and Technology CenterDepartment of Physics and Astronomy

Department of Electrical and Computer EngineeringUniversity of Iowa

supported by AFOSR and ARO

Spin-orbit correlations of dopants in semiconductors

review of “solotronics”: Nature Materials 10, 91 (2011)

V. R. Kortan, C. E. Pryor, C. Şahin, J. M. Tang (U. Iowa)P. M. Koenraad, A. Silov, J. Bocquel, J. K. Garleff, J. van Bree, W. Van Roy,

C. Celebi, A. P. Wijnheimer, A. Yakunin (TU/e)R. Wiesendanger, J. Wiebe, F. Marczinowski, F. Meier, M. Morgenstern (Hamburg)



Outline

breaking degeneracy (tetrahedral group)s

As As

As

As

Si

p

d

f

A1

T2

T2

E

?

deep levels - how do they form?As As

As

As

SiZunger: they are atomic levels, set relative to the vacuum

s

p

A1

T2

related observation: symmetry of tetrahedral bonds below is A1+T2

Hjalmarson et al: PRL 44, 810 (1980)


p-d hybridized deep levelsAs As

As

As


Sn

p-d hybridized deep levelsAs As

As

As

p


d

T2

E

Vogl and Baranowski, Acta Phys. Pol. A 67, 133 (1985)

Mn

Mn dopant in GaAscrystalfield

d

T2

E

d-exchange

T2

E

T2

E106

43

3

2

2

p-d interactionwith As

dangling bonds

AB-T2

E

AB-T2

EB-T2

B-T2

conduction band

valence band

S=5/2

1 heavyhole

j=3/2

sL

groundstateJ = 1

R0

R1

Ga

As

Mn

Mn in GaAs: single-ion p-d hybridization

p-d hybridization well establishede.g. for GaMnAs TcDietl et al., Science 287, 1019 (2000)

single ion: mean field theory cannot be usedwe want the spatial structure

PRL 92, 047201 (2004)

[1-gV] [G] = [g] x

x''

x''

x'

x

x'

[G] = [1-gV] [g] -1

G(x,x';ω) = g(x,x';ω) + g(x,x'';ω)V(x'')G(x'',x';ω)Σx''

sp3 tight-binding Hamiltonian with single-ion p-d exchange

R0

R1

Ga

As

Mn

Mn in GaAs: single-ion p-d hybridization

p-d hybridization well establishede.g. for GaMnAs TcDietl et al., Science 287, 1019 (2000)

single ion: mean field theory cannot be usedwe want the spatial structure

L=1

PRL 92, 047201 (2004)

sp3 tight-binding Hamiltonian with single-ion p-d exchange

experiment/theory comparison for Mn/GaAs

theoretical prediction

PRL 92, 047201 (2004)


PRL 92, 216806 (2004)

calculations

STM experiment Nature 442, 436 (2006)

theoretical prediction

PRL 92, 047201 (2004)


Mn: InAs spectra - spin-orbit-split states

PRL 99, 157202 (2007)

hybridization of Mn states

R0

R1

Ga

As

Mn

core d states split in tetrahedral crystal field into t2 states - do hybridize via pdσ hoppinge states - do not hybridize via pdσ hopping

69

by the Hamiltonian 4.3.3 the total d-like component is spherically symmetric [see

figure 4.4(Total)]. In order to obtain the anisotropy, the problem has to be solved in

the cubic approximation.

In the cubic approximation the symmetry of the wave-function 4.3.5 is reduced.

If the condition 4.3.2 is satisfied, the acceptor wave-function transforms according to

the same irreducible representations as the top of the valence band, Γ8 point

Γ±8 × Γ±

8 = 2Γ+15 + 2Γ+

25 + Γ+12 + Γ+

2 + Γ+1 . (4.3.14)

The wave-function that transforms according to these representations has the form

Ψ3/23/2 =

cΓ1

2R0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

Y0,0

0

0

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ25

2√

2R2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

0

−2Y2,1

Y2,2 − Y2,−2

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ12

2√

2R2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

√2Y2,0

0

Y2,2 + Y2,−2

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

, (4.3.15)

Ψ3/21/2 =

cΓ1

2R0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

0

Y0,0

0

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ25R2

2√

2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

2Y2,−1

0

0

Y2,2 − Y2,−2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ12

2√

2R2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

0

−√

2Y2,0

0

Y2,2 + Y2,−2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

. (4.3.16)

The angular dependence of the spherical functions Y (ϕ, θ) as a function of the az-

imuthal angle θ with respect to the quantization direction is shown in figure 4.4.

In the equations 4.3.15 and 4.3.16 the angular part of the d-component includes

terms that transform according to the Γ12 (dx2−y2−like) and Γ25 (dxy−like) repre-

sentations of the tetrahedral point group. Their corresponding coefficients are the

constants cΓ12 and cΓ25 , respectively, whose ratio is denoted here as

η = cΓ12/cΓ25 , 0 ≤ η ≤ 1. (4.3.17)

The coefficients cΓ12 , cΓ25 and cΓ1 in the equations 4.3.15 and 4.3.16 are usually

evaluated variationally and should allow for the normalization condition given by the

effective mass wave functions (e.g. Bir, Pikus)

69

by the Hamiltonian 4.3.3 the total d-like component is spherically symmetric [see

figure 4.4(Total)]. In order to obtain the anisotropy, the problem has to be solved in

the cubic approximation.

In the cubic approximation the symmetry of the wave-function 4.3.5 is reduced.

If the condition 4.3.2 is satisfied, the acceptor wave-function transforms according to

the same irreducible representations as the top of the valence band, Γ8 point

Γ±8 × Γ±

8 = 2Γ+15 + 2Γ+

25 + Γ+12 + Γ+

2 + Γ+1 . (4.3.14)

The wave-function that transforms according to these representations has the form

Ψ3/23/2 =

cΓ1

2R0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

Y0,0

0

0

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ25

2√

2R2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

0

−2Y2,1

Y2,2 − Y2,−2

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ12

2√

2R2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

√2Y2,0

0

Y2,2 + Y2,−2

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

, (4.3.15)

Ψ3/21/2 =

cΓ1

2R0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

0

Y0,0

0

0

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ25R2

2√

2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

2Y2,−1

0

0

Y2,2 − Y2,−2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

+cΓ12

2√

2R2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

0

−√

2Y2,0

0

Y2,2 + Y2,−2

∣∣∣∣∣∣∣∣∣∣∣

∣∣∣∣∣∣∣∣∣∣∣

. (4.3.16)

The angular dependence of the spherical functions Y (ϕ, θ) as a function of the az-

imuthal angle θ with respect to the quantization direction is shown in figure 4.4.

In the equations 4.3.15 and 4.3.16 the angular part of the d-component includes

terms that transform according to the Γ12 (dx2−y2−like) and Γ25 (dxy−like) repre-

sentations of the tetrahedral point group. Their corresponding coefficients are the

constants cΓ12 and cΓ25 , respectively, whose ratio is denoted here as

η = cΓ12/cΓ25 , 0 ≤ η ≤ 1. (4.3.17)

The coefficients cΓ12 , cΓ25 and cΓ1 in the equations 4.3.15 and 4.3.16 are usually

evaluated variationally and should allow for the normalization condition given by the

hybridization of Mn states

R0

R1

Ga

As

Mn73

8x8 nm2; ML 6th=1 =0.8

=0.6 =0.4

=0.2 =0

[001]]101[

Figure 4.6: Calculated cross-sections of the Mn acceptor wave-function in GaAs bya {110} plane for various values of the cubic parameter η. Mn is located in the 6th

subsurface layer counting the surface layer as zero. 1ML = 0.2 nm. Images havesizes of 8 × 8 nm2.


PRL 92, 216806 (2004)

effect of spin-orbit interaction on shape

Mn:GaAs Cd:GaPBinding energy

102 meVBinding energy

113 meV

crystalfield

d

d-exchange

E

E

T2

E


dangling bonds

AB-T2

AB-T2

B-T2

B-T2

conduction band

valence band

T2

T2

~ -1.5 eV

~ -1.25 eV

~ -2.0 eV

~ -4.0 eV

~ 0.35 eV

~ -2.0 eV

~ -0.5 eV

E ~ -4.0 eV

E ~ 0.35 eV

~ -3.5 eV

~ 0.75 eV

~ -1.5 eV

~ -0.5 eV

Fe dopant in GaAs

crystalfield

d

d-exchange

E

E

T2

E


dangling bonds

AB-T2

AB-T2

B-T2

B-T2

conduction band

valence band

T2

T2

~ -1.5 eV

~ -1.25 eV

~ -2.0 eV

~ -4.0 eV

~ 0.35 eV

~ -2.0 eV

~ -0.5 eV

E ~ -4.0 eV

E ~ 0.35 eV

~ -3.5 eV

~ 0.75 eV

~ -1.5 eV

~ -0.5 eV

Fe dopant in GaAs

e.g. Mahadevan and Zunger, PRB 69, 115211 (2004)

Including the d states

Energy (eV)

Loca

l Den

sity

of S

tate

s (1

/eV

)

d(t2)

total spds*

p

(a)

total sp�

(b) (c) (d) (e)

[001

]

[110]

33.9 A

Experiment sp3 sp3d5d5s*Energy (eV)

Loca

l Den

sity

of S

tate

s (1

/eV

)

d(t2)

total spds*

p

(a)

total sp�

(b) (c) (d) (e)

[001

]

[110]

33.9 A

asymmetry in [001] is similar, but more pronounced X feature

hybridization of Fe states

R0

R1

Ga

As

Fe


STS

1

24

A comprehensive study of single Fe impurities in GaAs by X-STM

Figure 1.17: Spatially resolved I-V spectroscopy experiment was performed on the sameFe impurity at 4 K. a) dI/dV cross-section taken across the Fe impurity along the [001]direction. Two peaks are resolved in the bandgap. b) dI/dV maps taken at 0.46 V and1.02 V. The spatial extent of these states is consistent with those expected for the deepFe states of e (lower energy) and t2 symmetry (higher energy).

in the bandgap. dI/dV (x,y) maps taken at 0.46 V and 1.02 V, energy positionscorresponding to the two peaks, are presented in Fig. 1.17b. The spatial extent ofthese two states is clearly different. The lower energy state is strongly localizedon the Fe impurity itself. The wave function of this state almost isotropic andextend over ≈ 0.75 nm. The spatial extent of this state is consistent with the oneexpected for the deep Fe states of e symmetry from the group theory and thetight binding calculation presented in Fig. 1.15. The higher energy state is alsomainly localized on the Fe impurity itself but presents extensions in a cross-likeshape. The wave function of this state is anisotropic and extends over ≈ 2.5 nmalong the [001] direction and 2 nm along the [110] direction. These two statesdo not exhibit the even and odd symmetry expected for states resulting from asplitting of the t2 state by the effect of the reconstructed surface. Instead, thespatial extent of this state is consistent with the one expected for the deep Festates of t2 symmetry from the group theory and the tight binding calculationpresented in Fig. 1.15.

To summarize, two levels related to Fe are found the bandgap of GaAs in theI-V spectroscopy data. From the relative energetic position of these Fe states aswell as their spatial extent, they are here attributed to the Fe states e and t2

15

11.25

7.5

3.75

0

Current (pA) arb. units

[0.88-1.18] V

t2 t2

a) b)

0.63 V

e

[001]

e

[110]

2

1.5

1

0.5

0

spds*theorycurrent (pA)

hybridization of Fe states

R0

R1

Ga

As

Fe

t2

e

core d states split in tetrahedral crystal field into t2 states - hybridize via pdσ hoppinge states - hybridize via pdπ hopping

Fe in GaAssp3 + d orbital on impuritynot larger pdS because would cause small amount of T2 ldos on NN E level to have some ldos at pdP=0

pdP x0.0 pdP x0.010 pdP x0.020 pdP x0.030 pdP x0.040 pdP x0.050 pdP x0.060 pdP x0.070 pdP x0.080

E : 0

.512

eV

T2 : 0

.876

eVla

yer o

f Fe

E : 0

.512

eV

T2 : 0

.876

eV

l3 a

yers

abo

ve o

f Fe

pdS x0.080

16 A

[001]

[110]

increasing pdπ hopping strength



Outline

a quantum dot locally strains the material surrounding the Mn acceptor

Manipulating the Mn wave function

Mn1

Mn2

GaAs host

[00-1]

[-110]

3.3 nm

Mn1Mn1(X(X--shape)shape)

Mn3

Mn2Mn2(S(S--shape)shape)

Mn3Mn3(Mirrored S(Mirrored S--shape)shape)

InAsInAsQD1QD1

InAsInAsQD2QD2

Nature Materials 6, 512 (2007)

Mn2

m2

m1

1.3 nmMn1 1.3 nm

m2

m1

[00-1]

[1-10]

TBM

0.0

-1.0

-5.0

-2.0

-3.0

-4.0

low-energy Hamiltonian for manipulation

magneto-elastic constants derived from this effective Hamiltonian agree withMasmanidis et al,

PRL 95, 187206 (2005)

Measured - STM

Tight-binding modelNature Materials 6, 512 (2007)

Mn: InAs spectra - spin-orbit-split states

PRL 99, 157202 (2007)

Mahieu et al., PRL 94, 026407 (2005)hybridization of impurity state with excited states?

Jancu et al., PRL 101, 196801 (2008)hybridization of impurity state with intrinsic surface states?

residual asymmetry at surface - strain?

experiment

theory (no strain)

theory (with strain)

PRL 104, 086404 (2010)

explains residual asymmetry at surfacePRL 104, 086404 (2010)

Mn:GaAs

different hosts/dopants

Cd:GaP Zn:GaP

all in 5th layer

PRL 104, 086404 (2010)

L=1

E-field control of a Mn spin in GaAsPRL 97, 106803 (2006)

1 Tesla effective field for 40 kV/cm electric field

Depth of Mn [atomic layer]PRB 82, 035303 (2010)

splitting by surface E-field

Surface field splits the J=1 state into three separate peaks

Detecting Mn spin orientation in GaAs

0 0.1 0.2 0

1

2

3

4

5

6

7

Loca

l den

sity

of s

tate

s (eV

-1 )

px + i py

0 0.1 0.2 Energy (eV)

pz

0 0.1 0.2

px − i py

Mn

As

Ga

Ga

PRL 92, 047201 (2004); PRB 72, 161315(R) (2005)

eV−1A−310−4 10−3

[ ]001

110[ ]−

1 nm

[001]

[100] [010]

PRB 72, 161315(R) (2005)

HB⊥ ¼ gμBðBxσx þ ByσyÞ

¼ gμBffiffiffi2

p B⊥e−iϕBðjþ 1ih0jþ j0ih−1jÞ þ H.c.; (2)

HE⊥ ¼ −d⊥Exðσ2x − σ2yÞ þ d⊥Eyðσxσy þ σyσxÞ

¼ −d⊥E⊥eiϕE jþ 1ih−1jþ H.c.; (3)

where jii is defined tobe jms ¼ ii,B⊥ ðE⊥Þ andϕB ðEÞ are themagnitude and phase, respectively, of the magnetic (electric)field in the plane transverse to the c axis, and H.c. denotesthe Hermitian conjugate. The main difference between HB

⊥and HE

⊥ is that HB⊥ connects triplet pairs with Δms ¼ %1,

whereasHE⊥ connects triplet pairs withΔms ¼ %2. As such,

in the same way that applying resonant transverse magneticfields can be used to drive magnetic-dipole (Δms ¼ %1)transitions, resonant transverse electric fields can be used todrive magnetic-dipole forbidden (Δms ¼ %2) transitions.Our experiments use both ac electric and magnetic field

control, for which we use separate driving elements. Open-circuit interdigitated metal electrodes on the chip's topsurface are used to drive transverse electric fields betweenadjacent digits [Fig. 1(b)], and a short-circuited striplinebeneath the chip is used to drive transverse magnetic fields

over the electrode region. A flow cryostat cools our deviceto the temperature T ¼ 20 K and a permanent magnetprovides a static B∥. QL1 color centers were produced inour 6H-SiC substrates via a carbon implantation andannealing process designed to generate defects in a400 nm thick layer immediately below the surface (seeSupplemental Material [33]). The QL1 spins betweenadjacent electrode digits are optically addressed by non-resonantly pumping their 1.09 eV near-infrared opticaltransition with 1.27 eV laser light [see Fig. 1(c) and theSupplemental Material [33] for details]. In our experiments,we simultaneously address approximately 104 QL1 spins.Future efforts to extend optical addressability to the single-spin limit in SiC will use strategies such as materialspurification [35], high-efficiency infrared detection, andlocalized ion implantation [10].Much like the NV center in diamond [34], QL1 has a

spin-dependent optical cycle, which allows nonresonantlaser illumination to both polarize and read out its ground-state spin. Because its photoluminescence intensity (IPL)depends on whether its spin state is j0i or j% 1i, we cantrack the QL1 spin dynamics by the measuring differentialphotoluminescence (ΔIPL) between an initial state and onethat has been evolved by magnetic or electric field pulses.

0.8 1 1.2 1.4 1.6 1.8

x 109

x 10-4

frequency (GHz)

(a)

(d)

778 MHz

QL1

QL2 QL6

QL5

∆IP

L / I

PL

x 10

5

10

0

-10

10

0

-10

-20 0.8 1.0 1.2 1.4 1.6 1.8

frequency (GHz)

B|| = 0 G T = 20 K

B|| = 139 G T = 20 K

+1

0

hD

2gµBB||

∆ms = ±1 ∆ms = ±2 ∆ms = ±1

∆ms = ±2

electric ∆ms = ±2

magnetic ∆ms = ±1

QL3

−1

c

dichroic

photodiode laser

PL

10 µm

6H-SiC Au (b) (c)

FIG. 1. (a) The orbital ground-state spin structure of the QL1 defect, with Δms ¼ %1 transitions (orange arrows) and the Δms ¼ %2transition (blue arrow) indicated. (b) Scanning electron microscope image of the electrode pattern. (c) QL1 spins localized within a 400 nmthick layer immediately beneath the 6H-SiC surface are optically pumped with a 1.27 eV laser in a 1.5 μm diameter spot, addressing ∼104QL1 defects at once. Photoluminescence is filtered from the pump laser with a dichroic mirror and is measured with a photodiode. Spins aredriven electrically by the electrodes and magnetically by the stripline. The electrode pattern from part (b) maps to the greendashed parallelogram. (d) The optically detected magnetic resonance (ODMR) signal when the stripline is driven at B∥ ¼ 139 G (upper)and B∥ ¼ 0 G (lower). The two Δms ¼ %1 resonances are shaded orange, and the Δms ¼ %2 resonance (at 778 MHz, shaded blue) ismagnetic-dipole forbidden and not seen in ODMR.

PRL 112, 087601 (2014) P HY S I CA L R EV I EW LE T T ER Sweek ending

28 FEBRUARY 2014

087601-2

Klimov et al, PRL 112, 087601 (2014)

electrical drive of spin-1 single defects

elements of dopant theoriesshallow or deep? hydrogenic? sharp distinction between the twocrystal field splittings and hybridizations dominate deep level defect propertiesenvelope function/effective mass theories and tight-binding theories are closer in results and assumptions than one might expect

control of confinement and changes in angular momentumstrain and electric field control of defect spin distinguishing between different symmetry d states is possible theoretically and experimentally via wave function extent

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Theory of individual dopants in semiconductors

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