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Stark Tuning of Electronic Properties of Impurities for Quantum Computing Applications

Stark Tuning of Electronic Properties of Impurities for Quantum Computing Applications. Rajib Rahman Advisors: Gerhard Klimeck Lloyd Hollenberg . Single Donors in Semiconductors. Motivation Shrinking device size Quantum mechanics of donors

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Stark Tuning of Electronic Properties of Impurities for Quantum Computing Applications

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  1. Stark Tuning of Electronic Properties of Impurities for Quantum Computing Applications Rajib Rahman Advisors: Gerhard Klimeck Lloyd Hollenberg

  2. Single Donors in Semiconductors • Motivation • Shrinking device size • Quantum mechanics of donors • Donors provide 3D confinement to electrons • Analogous to Quantum Dots • Can we control quantum properties of single donors ? Devices with few impurities Lansbergen, Delft Kane Qubit Andresen, UNSW

  3. Quantum Computing • Idea: • Encode information in quantum states. • Manipulate information by controlled perturbation of states. • Classical Computing: |0> or |1> • Quantum Computing: a|0> + b|1> Bloch Sphere • Advantages: • Quantum parallelism (speed) • Algorithms: Quantum search, Fourier Transform • Applications: cryptography, simulations, factoring, database search, etc. • Design criteria (DiVincenzo): • Isolation of the qubit Hilbert Space • Decoherence times • Ease of measurement • Scalability (Hollenberg, PRB 74) • Fault-tolerant designs

  4. Quantum Computing Implementations NMR 5 qubit (IBM) Ion Traps Quantum Optics http://www.uni-ulm.de/qiv/ forschung/ControlAndMeasurementE.html Gasparani et al., PRL 93, No. 2 (2004) Vandersypen et al., July 2000 PRL SQUID Oliver etal., Sceince 310, 1653 (2005) Cavity QED Mckeever, Science Express Reports (Feb 26, 2004)

  5. Solid State Qubits Electron Spin (Vrijen) Nuclear spin qubit (Kane) Scalability ? Solid State (QDs, Donors, Si QW) Ion Trap, eg. (http://www.uni-ulm.de/qiv/) • Donor Qubits • Benefits: • Industry experience in Si:P • Long coherence • Scalability • Problems: • Precise donor placement (1 nm) • Control is sensitive Si – SiGe Quantum Wells (Friesen) Donor Charge Qubit (Hollenberg)

  6. P Donor Qubits in Si Spin Qubits (Kane, Vrijen, Hill) • Spin Qubit • Single Qubit: Hyperfine (A ) + Zeeman (g) • Two-qubit: Exchange J(V) • Tunable by gates Charge Qubit (Hollenberg) • Charge Qubit • Molecular states of P2+ • Control electron localization by S & B gates • Information transport - CTAP

  7. Quantum Picture Conventional Picture Si Si Si CB CB e- ED Si P+ Si ED Donor Si Si Si ED(P) = -45.6 meV ED(As) = -54 meV Donor Physics 101 Donor QD • Simple Model • Coulomb potential screened by Si • Hydrogen analogy: 1s, 2s, 2p … • Si Band Structure: Bloch Functions, valley degeneracy • Valley-orbit interaction – binding energy varies from donor to donor EMT: Kohn-Luttinger, Das Sarma, Koiller, Hollenberg, Friesen, …

  8. Central Issues • Single Donor Spin Control • A. Hyperfine Interaction • B. g-factor control • 2. Control of Charge States • A. Orbital Stark Effect • B. CTAP • Two Electron Interactions • A. D- Modeling • B. Exchange Interaction

  9. Central Issues • 1. Single Donor Spin Control • A. Hyperfine Interaction • Can we engineer the donor hyperfine interaction? • Can we resolve discrepancies between theory and exp.? • Is it possible to generate an experimentally detectable spatial map of a wf? • B. g-factor control • How does an E-field modify the Zeeman interaction in donors? • How does multi-valley structure affect g-factor? • Can we verify ESR measurements? • 2. Control of Charge States • A. Orbital Stark Effect • B. CTAP • Two Electron Interactions • A. D- Modeling • B. Exchange Interaction

  10. Stark Shift of Hyperfine Interaction e Contact HF: ET A(ε) |(ε, r0)|2 n ES => Nuclear spin site => Impurity site oxide Donor D BMB TB ∆A(ε)/A(0) = (2ε2 + 1ε) (interface) ∆A(ε)/A(0) = 2ε2 (bulk) Exp: Bradbury et al., PRL 97, 176404 (2006) Theory: Rahman et al. PRL. 99, 036403 (2007)

  11. Stark Shift of Hyperfine Interaction How good are the theories? Quadratic Stark Coefficients EMT: Friesen, PRL 94, 186403 (2005) Why linear Stark Effect near interfaces? Asymmetry in wf Large Depth: 1st order PT: Even symmetry broken Small Depth: Oxide-Si-impurity Rahman et al. PRL. 99, 036403 (2007)

  12. Hyperfine Map of Donor Wave-functions Usefulness of HF – an example Observables in QM: Hyperfine: ESR Experiments can measure A => Direct measure of WF Si isotopes: 28Si (S=0) 29Si (S=1/2) Application: Experimentally mapping WF deformations (idea: L. Hollenberg) Park, Rahman, Klimeck, Hollenberg (submitted)

  13. Central Issues • 1. Single Donor Spin Control • A. Hyperfine Interaction • Can we engineer the donor hyperfine interaction? • Can we resolve discrepancies between theory and exp.? • Is it possible to generate an experimentally detectable spatial map of a wf? • B. g-factor control • How does an E-field modify the Zeeman interaction in donors? • How does multi-valley structure affect g-factor? • Can we verify ESR measurements? • 2. Control of Charge States • A. Orbital Stark Effect • B. CTAP • Two Electron Interactions • A. D- Modeling • B. Exchange Interaction

  14. Gate control of donor g-factors and dimensional isotropy transition Objective: Investigate Stark Shift of the donor g-factor. g-factor shift for interface-donor system. Probes spin-orbit effects with E-fields and symmetry transition. Relative orientations of B and E field. Approach: The 20 band nearest neighbor sp3d5s* spin model captures SO interaction of the host. Same atom p-orbital SO correction g-factor obtained from L and S operators. Donor wfs with E-field are obtained from NEMO Results / Impact: Quadratic trend with E-field for bulk donors. Stark parameter larger in Ge and GaAs Anisotropic Zeeman effect – E and B field Dimensional transition- multi-valley to single valley g-factors. Exp. Quadratic coef. matches in magnitude. 1e-5 Si:P Interface: g||-g|_=8e-3 Rahman, Park, GK, LH (to be submitted)

  15. Central Issues • 1. Single Donor Spin Control • Hyperfine Interaction • B. g-factor control • 2. Control of Charge States • A. Orbital Stark Effect • Can we explain single donor tunneling expt? • Can we infer info about donor species and location in devices through atomistic modeling? • Can we indirectly observe symmetry transition of a 3D electron to 2D? • B. CTAP • Can we control tunnel barriers between donors by realistic gates? • Does there exist adiabatic pathways connecting end states for transport? • Can we develop a framework to guide expts? • Two Electron Interactions • D- Modeling • B. Exchange Interaction

  16. ε Oxide-Si-impurity Orbital Stark Shift of donor-interface states ε=0 Oxide-Si-impurity Donor-interface system Smit et al. PRB 68 (2003) Martins et al. PRB 69 (2004) Calderon et al. PRL 96 (2006) Lansbergen, Rahman, GK, LH, SR, Nature Physics, 4, 656 (2008)

  17. Orbital Stark Shift of donor-interface states Exp. Measurements Energies w.r.t. ground state (below CB) Transport through donor states • Energies different from a bulk donor (21, 23, 44) • Donor states – depth & field dependent

  18. Orbital Stark Shift of donor-interface states Si:As (Depth 7a0) Si:P (Bulk) • Features found • 3 regimes • Interface effects • anti-crossing • p-manifold • valley-orbit A B C Friesen, PRL 94 (2005) A (Coulomb bound) B (Hybridized) C (Surface bound) Rahman, Lansbergen, GK, LH, SR (Orbital Stark effect theory paper, to be submitted)

  19. Stark Effect in donor-interface well Exp data with TB simulations Where are the exp. points? • Interpretation of Exp. • Indirect observation of symmetry transition • P vs As Donor distinction Lansbergen, Rahman, GK, LH, SR, Nature Physics (2008), IEDM (2008)

  20. Central Issues • 1. Single Donor Spin Control • Hyperfine Interaction • B. g-factor control • 2. Control of Charge States • A. Orbital Stark Effect • Can we explain single donor tunneling expt? • Can we infer info about donor species and location in devices through atomistic modeling? • Can we indirectly observe symmetry transition of a 3D electron to 2D? • B. CTAP • Can we control tunnel barriers between donors by realistic gates? • Does there exist adiabatic pathways connecting end states for transport? • Can we develop a framework to guide expts? • Two Electron Interactions • D- Modeling • B. Exchange Interaction

  21. Vs1 Vb1 Vb2 Vs2 15 nm P P+ P+ 15 nm V=0 V>0 Electrostatic gating of single donors Nano-TCAD+TB E2 E2 E2 E2 E2 E1 E1 E1 E1 E1 Vs1=0.05V Vs1=0.1V Vs1=0.4V Vs1=0.0V Vs1=0.3V

  22. Coherent Tunneling Adiabatic Passage (CTAP) Objective: Investigate CTAP in realistic setting. Include Si full band-structure, TCAD gates, interfaces, excited states, cross-talk. Verify that adiabatic path exists: 3 donor device. Approach: TCAD gates coupled with a 3 donor TB. Hamiltonian: obtain molecular states in the solid state. Simulate 3-4 M atoms for a realistic device. Compute time of 4-5 hours on 40 procs. Fine tune gate voltages to explore the CTAP. regime. Results / Impact: Demonstrated that the CTAP regime exists for a 3 donor test device. Verification of results (under relaxed assumptions) CTAP despite noisy solid-state environment. Developed the framework to guide future CTAP expt. Rahman, Park, GK, LH ( to be submitted)

  23. Objective: Control & design issues: donor depths, separation, gate placement. Feasible S and B gate regimes. Effect of excited states: charge state superposition. Approach: S and B gates - TCAD potentials Empirical Donor model + TB+ TCAD: bound molecular states. Lanczos + Block Lanczos solver Results: Smooth voltage control excited states at higher bias mingle with operation. Placement of S and B gates important relative to donors. Comparison with EMT RR, SHP, GK, LH (to be submitted) Charge qubit control Molecular Spectrum + Tunnel barriers Surface gate response of tunnel barriers

  24. Central Issues • 1. Single Donor Spin Control • Hyperfine Interaction • g-factor control • Control of Charge States • A. Orbital Stark Effect • B. CTAP • 3. Two Electron Interactions • A. D- Modeling • Can we interpret the D- state probed by expts? • How does the charging energy vary with donor depth and field? • B. Exchange Interaction • Does the exchange coupling for two qubit operations suffer from controllability issues, as shown by EMT?

  25. D- Modeling for As/P Donor Objective: Obtain 2e binding energy of donors with E-fields and donor depths: important in spin-dependent tunneling and measurement. D- ground and excited states : Analyze measured Coulomb diamonds from Transport Spectroscopy measurements. Approach: 1st approximation: SCF Hartree method. Use a domain of 1.4 M atoms with 1 donor. SCF: 1. Obtain wf from NEMO 2. Calculate electron density and Coulomb repulsion potential 3. Repeat NEMO with the new potential. 4. Stop when D- energy has converged. On-going: D- from configuration interaction Results: D- energy for a bulk donor within 2 meV from measured value. D- vs. Depth & field calculations. Explains charging energy of some samples Screening likely to play a role. D-, D0 vs E D0 D7a0 -45.6 D- D- vs charging energy -4 Ec comparison Rahman, Arjan, Park, GK, LH, Rogge (in prep)

  26. Central Issues • 1. Single Donor Spin Control • Hyperfine Interaction • g-factor control • Control of Charge States • A. Orbital Stark Effect • B. CTAP • 3. Two Electron Interactions • A. D- Modeling • Can we interpret the D- state probed by expts? • How does the charging energy vary with donor depth and field? • B. Exchange Interaction • Does the exchange coupling for two qubit operations suffer from controllability issues, as shown by EMT?

  27. Objective: Investigate gate control of exchange(vs EMT) Reconfirm controllability issues (from BMB) Treatment of interfaces & strain From Heitler London to Full CI Approach: atomistic basis for exchange calculations orbital interactions for short distances Interpolate TCAD potential on atomistic lattice Heitler-London scaled and tested for 4 M atoms removing previous computational bottlenecks. FCI is still a computational challenge Results / Impact: Similar exchange trends obtained as BMB Controllability issues at some specific angular separations verified Magnitude an order less from EMT Basis functions for short range interactions? Control of exchange for adjacent qubits J(V) for various impurity separations along [100] Sensitivity of J(V) to donor placement

  28. Methods and Details Tight-binding and NEMO3D

  29. Methods & Some Details NEMO Scaling (G. Klimeck) • Tight Binding: sp3d5s* NN model (NEMO3D) • Typical Domain: 3-4 M atoms • Typical Resources: 40 processors • Compute Times: Single electron 6-8 hours • Solver – parallel Lanczos / Block Lanczos (degenerate or closely spaced states) • Electrostatic modeling – • TCAD + NEMO • Two electron integrals: STOs, Monte Carlo, off-site coulomb from Ohno formula.

  30. TB parameterization of Donor On-site energy corrections TB Shift all orbitals by U0 6 2 Ep Es 3 Orbital based shift: 1 Es* Ed Mayur, et al., PRB 48, No. 15 (1993)

  31. Conclusions • Hyperfine Interaction: • Verified ESR measurements • Characterized E-field control and interface effects • Proposed expt. to measure wf at different lattice sites • G-factor Control: • Verified ESR measurements • Characterized E-field control, interface and band-structure effects • Showed dimensional transition can probe single valley g-factors • Orbital Stark Effect: • Used atomistic modeling to interpret transport data • Performed dopant metrology through modeling • Demonstrated indirect symmetry transition and quantum control

  32. Conclusions • Coherent Tunneling: • Demonstrated Gate control of single donors with TCAD • Found adiabatic path for electron transfer • Developed framework to guide future CTAP expts • Charge Qubit Design: • Established the engineering variables for a donor charge qubit • Established the effect of excited states on performance limits • D- state Modeling: • Established the effect of field and depth on the 2nd bound donor electron • Understanding of the D- states may lead to realization of spin-dependent tunneling in donor. • Exchange Interaction: • Atomistic exchange calculation also verify the basic EMT exchange results

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