Atomistic description of shallow levels in semiconductors

Gate-induced wave function manipulation of a single dopant atom is a possible basis of atomic scale electronics. From this perspective, we analyzed the effect of a small nearby gate on a single dopant atom in a semiconductor up to field ionization. The dopant is modeled as a hydrogenlike impurity and the Schrödinger equation is solved by a variational method. We find that-depending on the separation of the dopant and the gate-the electron transfer is either gradual or abrupt, defining two distinctive regimes for the gate-induced ionization process. DOI: 10.1103/PhysRevB.68.193302 PACS number͑s͒: 03.67.Lx, 85.30.De, 73.21.Ϫb, 71.55.Ϫi The size regime where the discreteness of doping must be taken into account is brought within experimental reach by today's semiconductor lithography techniques. In this regime, single dopant atoms have been demonstrated to dominate the behavior of downscaled versions of conventional devices. 1 On the other hand, the promising opportunity is offered to study the physics of semiconductors on their ultimate length scale by addressing separate dopants. Putting a small gate close to a single impurity would, for example, allow for the manipulation of individual hydrogenlike wave functions. Furthermore, large electric fields ͑otherwise only achievable in astronomy͒ can be experimentally obtained in semiconductors due to the occurrence of large dielectric constants and small effective masses. Apart from the fundamental importance, an ultimate application is found in a Si-based solid state quantum computer, 2,3 in which the nuclear spins of single 31 P dopants are envisioned as qubits. In this proposal, addressing a single qubit by nuclear magnetic resonance is achieved via the hyperfine interaction of the nuclear spin and its valence electron, which can be tuned by modifying the electron wave function with a nearby gate. In a recent variation of this design, 4 the ionization of single dopants by this gate is an essential ingredient.Our aim is to quantitatively investigate the effect of the electric field generated by a local gate on a single neutral dopant atom in a semiconductor, ultimately leading to ionization. The response to small fields has been addressed before in the context of quantum computing. 5,6 In this paper, the complete ionization process is discussed. Our approach incorporates the computation of time independent ground state wave functions of the system and, subsequently, the estimation of transition probabilities. We conclude that the separation of the dopant and the gate determines the nature of the ionization process. When the dopant resides close to the gate, the electron is gradually pulled away from the dopant when the gate voltage is increased, while for a larger separation the dopant ionizes abruptly at a well-defined gate voltage.Addressing a single dopant requires a small local gate. When a dopant would be ionized by a large gate ͑e.g., an infinite strip 6 ͒, the electron would be delocalized along the gate. This would be undesirable in applications where ͑sp...

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“…We learned that similar results have been obtained independently with different methods by A.S. Martins et al 19 and L.M. Kettle et al 20 …”

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Gate-induced ionization of single dopant atoms

et al. 2003

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“…Recently, calculations of a silicon donor in an electric field in the tight binding approach have been presented 28 . This approach seems to be a useful alternative to calculations based on effective mass theory.…”

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confidence: 99%

Stark effect in shallow impurities inSi

et al. 2004

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We have theoretically studied the effect of an electric field on the energy levels of shallow donors and acceptors in silicon. An analysis of the electric field dependence of the lowest energy states in donors and acceptors is presented, taking the bandstructure into account. A description as hydrogenlike impurities was used for accurate computation of energy levels and lifetimes up to large (several MV/m) electric fields. All results are discussed in connection with atomic scale electronics and solid state quantum computation.

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“…Recent studies have demonstrated that the tight-binding (TB) approach, traditionally adopted for deep levels, 5 provides a valid description for intermediate 6,7 and shallow levels 8 in semiconductors. Impurity states are calculated from a sequence of supercell sizes and a finite-size analysis which provides extrapolation to the bulk limit.…”

Section: Introductionmentioning

confidence: 99%

Electric-field control and adiabatic evolution of shallow donor impurities in silicon

2004

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We present a tight-binding study of donor impurities in Si, demonstrating the adequacy of this approach for this problem by comparison with effective mass theory and experimental results. We consider the response of the system to an applied electric field: donors near a barrier material and in the presence of an uniform electric field may undergo two different ionization regimes according to the distance of the impurity to the Si/barrier interface. We show that for impurities ∼ 5 nm below the barrier, adiabatic ionization is possible within switching times of the order of one picosecond, while for impurities ∼ 10 nm or more below the barrier, no adiabatic ionization may be carried out by an external uniform electric field. Our results are discussed in connection with proposed Si:P quantum computer architectures.

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Atomistic description of shallow levels in semiconductors

Cited by 16 publications

References 15 publications

Gate-induced ionization of single dopant atoms

Gate-induced ionization of single dopant atoms

Stark effect in shallow impurities inSi

Electric-field control and adiabatic evolution of shallow donor impurities in silicon

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