Gate-induced ionization of single dopant atoms

Smit, G.D.J.; Rogge, Sven; Caro, J.; Klapwijk, T. M.

doi:10.1103/physrevb.68.193302

Cited by 37 publications

(49 citation statements)

References 15 publications

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“…[16][17][18][19] Much attention has been devoted to modeling the hyperfine and exchange interactions in these devices. [11][12][13][14][15][20][21][22][23][24] Intervalley interference between degenerate conduction band minima in Si has been shown to lead to oscillations in the exchange coupling as a function of the donor pair positioning in the lattice. [12][13][14][15] This poses serious problems for the fabrication of these devices, and leads to an extreme sensitivity of the exchange energy on the relative orientation of the P atoms.…”

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confidence: 99%

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

2006

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We theoretically study the Hilbert space structure of two neighboring P-donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position, and interdonor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, while the magnitude of the double occupancy probability can affect the error rate.

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Section: Introductionmentioning

confidence: 99%

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

2006

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“…For example, there is no theory to determine how the weight of a donor wavefunction will redistribute among the six conduction valleys in the presence of a generic (i.e., low symmetry) potential. Since the envelope functions in different valleys have different energies (due to anisotropy of the effective mass), this is an important question.In the context of quantum computing, several recent papers obtain tractible results for donor ionization, by ignoring valley-orbit interactions [4,5,6]. This singlevalley approach provides a useful picture of the distorted envelopes in the individual valleys.…”

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“…In the context of quantum computing, several recent papers obtain tractible results for donor ionization, by ignoring valley-orbit interactions [4,5,6]. This singlevalley approach provides a useful picture of the distorted envelopes in the individual valleys.…”

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Theory of the Stark Effect for P Donors in Si

Friesen

2005

Phys. Rev. Lett.

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We develop an effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is included perturbatively. We specifically consider the Stark effect in Si:P. In this case, the theory becomes more accurate at high fields, while it is designed to give correct experimental binding energies at zero field. Unexpectedly, the ground state energy for the donor electron is found to increase with electric field as a consequence of spectrum narrowing of the 1s manifold. Our results are of particular importance for the Kane quantum computer.Phosphorus doped silicon is one of the most wellstudied semiconducting systems [1], owing to its importance in the electronics industry. A more recent and exotic application is quantum computing, in which the Kane proposal posits nuclear spin qubits on Si:P, with interactions mediated by donor-bound electrons [2]. By tuning the potentials on aligned electrodes, the electrons are brought to the point of ionization, in order to control nuclear hyperfine interactions and the overlap between neighboring qubits. Spin dependent ionization also provides a means for electrical detection of the qubit state. The precise control of donor-bound electrons in such a complex environment remains an experimental challenge [3], requiring detailed theoretical input [4,5,6].The theory of isolated donors in silicon remains one of the crowning achievements of solid-state physics. One of the most effective treatments for shallow donors is the effective mass approximation (EMA) [7], in which the donor potential is assumed to vary slowly compared to the crystal potential. As a result, the long and shortwavelength physics decouple. An excess electron on the donor can be described by an envelope equation -a Schrödinger equation with an effective mass and a dielectric constant. The theory highlights the most essential feature of silicon's bulk band structure: the six-fold degeneracy of the conduction valleys. Near the impurity core, the assumption of slowly varying potential breaks down, causing valley-orbit interactions to couple envelope functions in different valleys. A careful treatment of the potential very near the impurity (the 'central cell' region) enables estimates for the energy splitting of the six valley states, which are in good agreement with experiments [8].In a more general, inhomogeneous environment, silicon donors can be studied by tight-binding techniques [9]. However, existing EMA theories introduce severe approximations that limit their scope. Many important questions therefore remain open. For example, there is no theory to determine how the weight of a donor wavefunction will redistribute among the six conduction valleys in the presence of a generic (i.e., low symmetry) potential. Since the envelope functions in different valleys have different energies (due to anisotropy of the effective mass), this is an important question.In the context of quantum computing, several recent papers obtain tractible results for donor ionization, by ignoring va...

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“…By contrast, this charge noise was not measurable in the nominally intrinsic sample (n = 1×10 14 cm −3 ). We therefore infer that its origin is electrons tunneling from their phosphorus donors [8,9]. While this ionization effect can occur for both substrates, in the intentionally doped material a larger and more easily measurable charge redistribution is present due to the higher doping density.…”

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confidence: 99%

Electric-field-induced charge noise in doped silicon: Ionization of phosphorus donors

Ferguson

Chan

Hamilton

et al. 2006

Applied Physics Letters

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We report low frequency charge noise measurement on silicon substrates with different phosphorus doping densities. The measurements are performed with aluminum single electron transistors (SETs) at millikelvin temperatures where the substrates are in the insulating regime. By measuring the SET Coulomb oscillations, we find a gate voltage dependent charge noise on the more heavily doped substrate. This charge noise, which is seen to have a 1/f spectrum, is attributed to the electric field induced tunneling of electrons from their phosphorus donor potentials.With their high charge sensitivity single electron transistors (SETs) provide a valuable tool for investigating charge transport at the single electron level. These sensitive electrometers have been employed to directly observe electron traps in Al 2 O 3 [1], and electron tunneling through GaAs quantum dots [2] amongst other systems. With particular relevance to this work, SETs have been used to study both time and frequency domain charge noise [3,4,5,6] in semiconductor substrates. Charge noise in semiconductors has long been of interest [7], and recently has become an important issue for solid-state quantum computation where it is crucial that such noise is minimized to extend quantum coherence times.We study the effect of electric fields on the charge noise in Si substrates with different doping levels. At millkelvin temperature the substrates are in the insulating regime (n < n MIT = 3.45 × 10 18 cm −3 ). For the intentionally doped substrate (n = 8 × 1016 cm −3 ) we find an additional 1/f charge noise on application of an electric field. By contrast, this charge noise was not measurable in the nominally intrinsic sample (n = 1×10 14 cm −3 ). We therefore infer that its origin is electrons tunneling from their phosphorus donors [8,9]. While this ionization effect can occur for both substrates, in the intentionally doped material a larger and more easily measurable charge redistribution is present due to the higher doping density. Dopant ionization has previously been measured by transient currents due to the build-up of depletion regions in p-n junctions [10,11], the slow formation of accumulation layers in MOS capacitors [12] and hysteretic effects in MOSFETs [13]. These experiments were mostly performed at an intermediate temperature range (T = 4K − 20K) where ionization can be thermally activated by the Poole-Frenkel effect [14]. At our experimental temperatures (T ∼ 100mK), electric field assisted ionization is no longer dominated by thermal activation but is expected to be purely field assisted tunneling.We fabricate the SETs using a standard bilayer resist and a shadow evaporation process. The electrostatic gate structure is evaporated Ti/Au and patterned in a separate electron beam lithography step (see fig. 1b inset). Both silicon substrates are terminated by 5nm of SiO 2 grown by thermal oxidization.The SET conductance was measured using standard lock-in techniques at an excitation frequency of 1kHz and an amplitude of 20µV . For the noise measure...

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Gate-induced ionization of single dopant atoms

Cited by 37 publications

References 15 publications

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

Theory of the Stark Effect for P Donors in Si

Electric-field-induced charge noise in doped silicon: Ionization of phosphorus donors

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