Seung Hyun Park

Hyperfine Mapping of Donor Wave Function Deformations

in Si:P based Quantum Devices

Seung Hyun Park

Advisors: Prof. Gerhard Klimeck

Prof. Lloyd Hollenberg

Seung Hyun Park

Outline

1. Single Donor Physics

- Basic single donor physics

- Si:P based quantum device

2. Single donor wave function engineering

- Hyperfine mapping of donor electron wave function deformations

Seung Hyun Park

Basic Donor Physics

Si

Si

Si

P+

Si

Si

Si

Si

Si

e-

Quantum Picture

CB

ED

Donor QD

Conventional Picture

CB

DonorED

ED(P) = -45.6 meV

ED(As) = -54 meVDonor Physics

• Donors provide 3D confinement to electrons

• Analogous to Quantum Dots

• Hydrogen-like system : 1s, 2s, 2p, …

• Six fold degeneracy corresponding to the valley structure of the Si CB

• Valley-orbit interaction contributes the splitting of Donor GS in multi-valley Si

Seung Hyun Park

Si:P based Quantum Computing (QC) QC Idea:

• Encode information in quantum states.

• Manipulate information by controlled perturbation of states.

• Classical Computing: |0> or |1>• Quantum Computing: a|0> + b|1>

Nuclear Spin Qubit Device: • Tunable Spin Qubit

- Single Qubit: Hyperfine Interaction A(E)- Double Qubit: Exchange Interaction J(E)

B. Kane, Nature.1998.p316

Nuclear spin qubit (Kane)

Donor Charge Qubit (Hollenberg)

L. Hollenberg, PRB 69, 113301 (2003)

Donor QubitsBenefits: • Vast experience in Si:P• Long spin coherence time• Scalability

Problems:• Precise donor placement• Control is sensitive

Seung Hyun Park

Outline

1. Single Donor Physics

- Basic single donor physics

2. Single donor wave function engineering

- Hyperfine mapping of donor electron wave function deformations

- Usefulness of measurement for hyperfine coupling probing by 29Si

Seung Hyun Park

29Si (S=1/2)28Si (S=0)Si isotopes:Wavefunction (wf) distortion

by electric field

Wavefunction (wf) distortion

by electric field

Impurity WF at an interface

A: Probing the field induced distortions of the donor wavefunction by 29 Si atom using hyperfine interaction

HF application: Experimentally mapping WF deformations

Q: Possible to generate an experimentally detectable spatial map of a WF in the presence of E-field?

Recently Accepted in PRL 103, 106802 (Sept. 2009)S.H. Park, R. Rahman, G. Klimeck, and L. Hollenberg

Hyperfine Mapping of WF

Seung Hyun Park

Aij =γ IγSh2 (

8π3

Ψ(0) 2 + Ψ3rirj −r2δ ij

r5 Ψ )

A(,r0) C | Ψ(,r0) |2Hyperfine:

Fermi contact hyperfine interaction Directly proportional to WF

Hyperfine Interaction

Anisotropic hyperfine interaction (AHF) (Magnetic dipolar interaction)

Information about average WF about the 29Si site

B(,r) C Ψ | B | Ψ AHF :

Hyperfine Interaction

Usefulness of the study

=> Possible to WFObservables in QM: E H

Seung Hyun Park

Possible to measure of deformed WF

Measurement of deformed WF

29 Si atom act as a probe

|Ψ|2

E=0 MV/m

Byy

E=0 MV/m

Y (

nm

)0

15

0 10

0.12

0.02E

E-0.04

0

015

E=20 MV/m

E=20 MV/m

0 10

0.16

0.02

0.01

-0.04

X (nm)

-0.02

E=40 MV/m

E=40 MV/m

0 10

0.4

0

0.015

Coulomb Confinement Hybridization Interface Confinement

A (Coulomb Confinement) B (Hybridization) C (Interface Confinement)E-field

E=0 MV/m E=20 MV/m E=40 MV/m

R. Rahman et al. [Orbital Stark Effect Theory Paper, PRB 80 165314 (2009)]

Seung Hyun Park

Measurement of deformed WF

|Ψ|2

E=0 MV/m

Byy

E=0 MV/mY

(n

m)

015

0 10

E

E0

15

E=20 MV/m

E=20 MV/m

0 10

X (nm)

E=40 MV/m

E=40 MV/m

0 10

Coulomb Confinement Hybridization Interface Confinement

015

Mapping deformed donor electron WF

29 Si atom act as a probe

Seung Hyun Park

Outline

1. Single Donor Physics

- Basic single donor physics

2. Single donor wave function engineering

- Hyperfine mapping of donor electron wave function deformations

- Feasibility and usefulness of the technique

- Measurement of hyperfine resonance peak for experiments

Seung Hyun Park

Gat

e

SiO

2 Si

Proposed Experiments and Shell

[100] axis

Proposed experiments to measure hyperfine tensor for shells around donor

Measure hyperfine frequencies at shells near the donor site

What is shell?

* Note: a0=0.543095 nm

Donor

Seung Hyun Park

Relative change of Hyperfine coupling peak for various E-field at shells on the [100] axis

Shell 1 Shell 2

HF

AHF

• Points in shell 1 are equidistant

• Peaks are NOT distinguishable at E=0 MV/m

(Degeneracy at E=0 MV/m)

• (+/- a0,0,0) and (0,0,+/-a0) are perpendicular

to E-field -> Produce a single resonance peak

• Curves start splitting with E-filed

[100] axis E-field on [010] direction

Measure of Hyperfine Resonance Peak

Seung Hyun Park

Usefulness of the hyperfine peak curves

Shell 1 Shell 2

HF

AHF

Relative change of Hyperfine coupling for various E-field at nearest neighbors on [100] axis

Δα(Eur

) = α (0)(η 2E2 +η1E)

,where α (,ij )

Fit curves to

Provide Table of hyperfine Stark coefficients η2 and η1

Answer)Yes! Be able to expect WF deformations before measurement.

Q: Can experimentalists figure out how WF is deformed before measurement?

β at (0,0,4) β at (0,0,8)

η2 η1

-3.8 1.7

η2 η1

-4.1 1.8

Seung Hyun Park

Outline

1. Single Donor Physics

- Basic single donor physics

2. Single donor wave function engineering

- Hyperfine mapping of donor electron wave function deformations

- Feasibility and usefulness of the technique

- Measurement of hyperfine resonance peak for experiments

- Practical issues from the perspectives of an experimentalist

Seung Hyun Park

Issues for Experiments

Relative change of Hyperfine coupling for various E-field at nearest neighbors on the [100] axis

Shell 1 Shell 2HF

AHF

For practical implementation issues from the perspective of an experimentalist

1. Distinguishablity of each peak ? Yes! (Degeneracy at E=0 MV/m) A) Error bars for an uncertainty of 0.1 MV/m in the E-field

2. Inhomogeneity of field perturbation due to gates? Yes, but it can be resolved. A) Parallel plate capacitor like structure

Seung Hyun Park

Summary

1. Simple Donor Physics

- Basic single donor physics

2. Single donor wave function engineering

- Mapping donor electron wave function deformation

Usefulness of measurement for hyperfine coupling probing by 29Si

Measurement of hyperfine resonance peak at points grouped into shell

Practical implementation issues from the perspectives of an experimentalist

Recently Accepted in PRL 103, 106802 (Sept. 2009)S.H. Park, R. Rahman, G. Klimeck, and L. Hollenberg