Advanced Simulation of a Donor Spin Qubit Device Fahd A Mohiyaddin1,2, Rajib Rahman3, Rachpon Kalra1,2, Gerhard Klimeck4, Lloyd C L Hollenberg1,5, Jarryd J Pla1,2

Andrew S Dzurak1,2 & Andrea Morello1,2

Introduction and Experiment

References

[1] A. Morello et al., Nature 467, 687 (2010).

[2] A. Morello et al., Phys. Rev. B 80, 081307(R) (2009).

[3] D.N. Jamieson, et. al., Appl. Phys. Lett. 86, 202101 (2005).

[4] R. Rahman et al., Phys. Rev. Lett. 99, 036403 (2007) .

Summary and Future Work

Developed TCAD, NEMO 3D and FASTCAP models to match experimental results of spin readout/control device.

Obtained a locus of donor locations compatible with ion implantation, based on simulating experimental results.

Future work will concentrate on the device-specific modelling of

(i) Triangulation of mutual capacitances (ii) Anisotropy of the hyperfine interaction

(iii) Tunnel Rate between donor electron and SET Island (iv) Multi-donor qubit devices

1Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology, Australia 2School of Electrical Engineering & Telecommunications, University of New South Wales, Sydney NSW 2052 Australia

3Advanced Device Technologies, Sandia National Laboratories, Albuquerque, NM 87185, USA 4Network for Computational Nanotechnology, Purdue University, West Lafayette, IN 47907, USA

5School of Physics, University of Melbourne, Melbourne Victoria 3010 Australia

Donor spins in silicon are strong candidates for solid state quantum bits due to long spin coherence and relaxation times. The single-shot spin readout [1,2] and coherent spin control required for qubit operations have been recently demonstrated in a Si-MOS nanostructure. Here we discuss a suite of simulation techniques and results to understand the physics of single donor qubits in a realistic spin qubit device.

Figure 1(a) : CMOS-compatible device for spin readout and control. The device consists of implanted phosphorous donors [3] tunnel-coupled to an SET Island, and a microwave transmission line (ML) to achieve spin control of the electron and nucleus [2].

Figure 1(c) : B0 is varied and several projective measurements were made on the final spin of the electron. Two resonant peaks split by the hyperfine interaction of 4.08 mT were observed. The hyperfine is Stark shifted from the bulk value due to strong electric fields in the nanostructure.

ML

TG LB RB

PL

B0

B1

1(a)

1(c)

Stark shift of the Hyperfine

Electrostatic

Potential (V)

0.25

1.45

0.65

1.05

X Y Z

TG

LB RB

PL

Figure 2(a): TCAD model (in the absence of donor) of the nanostructure with experimental gate voltages and dimensions.

Figure 2(b) : Calibration of threshold voltage of the model with experiment, by addition of interface (Si/SiO2) charges.

2(a) 2(b)

2(c)

2(d)

Simulation of Spin Readout

Figure 3 (a): NEMO 3D calculation of the hyperfine interaction [4] between the donor (31P) electron and nucleus, as a function of electric field and depth from SiO2 interface.

Figure 3(d) : Calculation of the hyperfine splitting based on NEMO (Fig. 3(a)) and TCAD (Fig 3(b)).

3(a)

Figure 5 : 3D map of donor locations obtained by matching experimental

Location of Donors

5(a) 5(b)

5(c)

Acknowledgements

We acknowledge support from the Australian Research Council, the Australian Government, the US National Security Agency and the US Army Research Office under contract number W911NF-08-1-0527. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.

Magnetic field B0 (T)

1.610 1.612 1.614 1.616

40

80

120

160

Sp

in U

p C

ou

nts

4.08 mT

0 5

-4

10 15 20 25

-6

-8

-10

-12

-14

0.0

1.0

2.0

3.0

4.0

Electric Field, Ez (MV/m)

Do

no

r D

ep

th f

rom

Si/S

iO2 i

nte

rface (

nm

)

Hyperfine (mT)

SiO2

TG PL

SET island

-40 0 30

Y (nm)

-20

0

Z (nm)

-30

Electric Field

(MV/m)

1

3

5

7

9

SiO2

TG PL

SET island

-40 0 30

Y (nm)

-20

0

Z (nm)

-30

Hyperfine

(mT)

4.0

4.1

4.2

4.3

4.4

0.17 0.25 0.33 0.41

4.0

4.1

4.2

4.3

4.4

Plunger (PL) Voltage (V)

Hyp

erf

ine (

mT

)

Depth

(nm)

3.8 8.1

12.0

23.9 19.9

27.9

32.0

Figure 3(e): Tunability of the hyperfine with Plunger Gate Voltage ( VPL ) for donors at locations obtained from Fig 2(c). The tunability for donors far away from the SiO2 interface is limited by:

(i) Bulk Hyperfine of 4.2 mT

(ii) Increased vertical distance from gates

(iii) Quick ionisation with Electric Field

3(b)

3(c)

3(d)

Figure 3(b) : TCAD model of electric fields in the device which Stark shift the hyperfine from the bulk value (4.2 mT).

-75 -45

-15 15

45 75

30

0 -30

0

-20

-40

-60

20

30

40

50

60

Distance from

SET (nm)

LB RB

PL

TG

-75 -45

-15 15

45 75

30

0 -30

0

-20

-40

-60

20

30

40

50

60

Distance from

SET (nm)

LB RB

PL

TG

LB RB

PL

TG

-75 -45

-15 15

45 75

30

0 -30

0

-20

-40

-60

15

20

25

30

35

Distance from

SET (nm)

LB RB

PL

TG

-75 -45

-15 15

45 75

30

0

-30

0

-20

-40

-60

Distance from

SET (nm)

20.4

20.8

21.2

21.6

5(d)

(b) Stark shift of hyperfine (a) Spin readout criterion

(c) Charge Transfer Signal (d) Intersection of (a), (b) and (c)

0

20

40

60

80

100

Isd (pA)

0.4 0.41 0.45 0.44 0.43 0.42

1.33

1.34

1.35

1.36

1.37

Top Gate

Voltage (V)

Plunger Gate Voltage(V)

E1

E2

SiO2

TG PL

SET

island

-15

-30

0

Y(nm)

0 15 30

Z(nm)

0.3

0.4

0.5

0.6

0.7

e

q

Charge Transfer Signal

Figure 4(a) :The charge stability diagram, with transitions resulting from electron tunneling between donor and SET.

4(a) 4(b

donor

SETdonor

C

C

e

q

E

E

2

1

Figure 4(b) : The charge transfer signal calculated from mutual capacitances in the device by boundary element technique.

5 15 7 9 11 13

1

9

3

5

7

Gate Oxide Thickness (nm)

Inte

rface O

xid

e C

harg

e

den

sit

y (

10

11/c

m2)

0.34

0.50

0.70

0.90

1.10

1.30

1.50

Turn On

Voltage(V)

SiO2

TG PL

SET island

-20

-40

0

Y(nm)

Conduction Band

Energy (meV)

0

20

40

60

80

0 15 30

Z(nm)

Donor depth from Si/SiO2

interface (nm)

Fir

st

4 e

nerg

y s

tate

s

(meV

)

0 5 10 15 20 25 -2

2

6

10

14

Figure 2(c) : Conduction band profile in the nanostructure to obtain the locus of donor locations compatible with electron spin readout.

Figure 2(d) : NEMO 3D donor energy states on placing donors in the lattice, where TCAD conduction band is 45.6 meV above the Fermi level.

-5 0 5

0

-5

5

1E-6

1E -4

1E-2

y (nm)

z(nm)

-5 0 5

0

-5

5

1E-6

1E-4

1E-2

y (nm)

Figure 3(c): The wave functions for the donor in bulk and for a donor in the device. The ratio of the two wave functions is used to model the wave function distortion in the nanostructure.

3(e)

-5 0 5

0

-5

5

0.0

2.0

1.0

y (nm)

z(nm)

z(nm)

Figure 1(b) : The energy levels of the system during the spin readout phase. The Zeeman splitting between spin up/down states result in spin dependant tunneling of the donor electron to the SET. The current due to tunneling is an indication of the initial spin state of the donor electron.

reservoir &

SET island

donor

drain Ef

B0

1(b)

2

bulk

22

bulkdevice

2

device