A generally applicable model is presented to describe the potential barrier shape in ultrasmall Schottky diodes. It is shown that for diodes smaller than a characteristic length l c ͑associated with the semiconductor doping level͒ the conventional description no longer holds. For such small diodes the Schottky barrier thickness decreases with decreasing diode size. As a consequence, the resistance of the diode is strongly reduced, due to enhanced tunneling. Without the necessity of assuming a reduced ͑non-bulk͒ Schottky barrier height, this effect provides an explanation for several experimental observations of enhanced conduction in small Schottky diodes. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1521251͔The effect of downscaling the dimensions of a device on its electrical transport properties is an important topic today. Extremely small diodes have been experimentally realized and characterized in various systems, for example, carbon nanotube heterojunctions, 1 junctions between p-type and n-type Si nanowires, 2 or junctions between the metallic tip of a scanning tunneling microscope and a semiconductor surface. 3,4 These experiments showed several deviations from conventional diode behavior. Despite some modeling in truly one-dimensional systems, 5,6 little work has been done on modeling the effects of downscaling a conventional diode, in the regime where quantum confinement does not play a role.In this letter we present a simple model ͑based on the Poisson equation͒ describing the barrier shape in a diode, that is readily applicable to arbitrarily shaped small junctions. It is related to descriptions of inhomogeneities in the Schottky barrier height ͑SBH͒ in large diodes, 7 barrier shapes in small semiconducting grains, 8 and charge transfer to supported metal particles. 9 Although we restrict ourselves to metal-semiconductor junctions, the model can easily be adapted, for example, to p -n junctions. The main result is that if the size of the metal-semiconductor interface is smaller than a characteristic length l c , the thickness of the barrier is no longer determined by the doping level or the free carrier concentration, but instead by the size and shape of the diode. The resulting thin barrier in small diodes will give rise to enhanced tunneling, qualitatively explaining measurements of enhanced conduction, 3,4,10 without the necessity of assuming a reduced SBH. Moreover, experimentally observed scaling behavior and deviating IV curve shapes 10 can be explained.The transport properties of a Schottky diode are governed by the potential landscape that has to be traversed by the charge carriers. First, we study an easily scalable and highly symmetrical model system, namely a metallic sphere embedded in semiconductor ͑see Fig. 1, upper left inset͒. The radius a of the metallic sphere is a measure for the interface size: for large a, we expect to find the well-known results for a conventional diode, while decreasing a gives the opportunity to study finite size effects.We only model the barrier sha...

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We have measured electrical transport across epitaxial, nanometer-sized metal-semiconductor interfaces by contacting CoSi 2 islands grown on Si͑111͒ with the tip of a scanning tunneling microscope. The conductance per unit area was found to increase with decreasing diode area. Indeed, the zero-bias conductance was found to be ϳ10 4 times larger than expected from downscaling a conventional diode. These observations are explained by a model, which predicts a narrower barrier for small diodes and, therefore, a greatly increased contribution of tunneling to the electrical transport. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1467980͔Electrical transport through metal-semiconductor interfaces has received tremendous interest in the past decades, both experimentally and theoretically. Nevertheless, an important shortcoming of existing models is the restriction to infinitely extending interfaces, so that all parameters vary only in the direction perpendicular to the surface. When the interface size enters the nanoscale regime, many of these models cease to apply. Only a few experiments addressing this topic have been reported. In none of them epitaxial interfaces were used. Scanning tunneling spectroscopy ͑STS͒ of metallic clusters on a semiconductor surface has been used to study small metal-semiconductor contacts. 1 In addition, experiments have been carried out in which the tip of a scanning tunneling microscope ͑STM͒ was used to contact a semiconductor surface 2,3 or a metallic cluster on a semiconductor surface 4 to form a small Schottky contact. Various deviations from the large-diode models were revealed, e.g., enhanced conductance, which was interpreted as a lower effective barrier. Besides the work that addresses a single small diode directly, measurements have been carried out on many small diodes in parallel. 5,6 In this letter, we present measurements of electrical transport through an epitaxial, nanometer-sized metalsemiconductor interface. We argue that the observations can be explained by a simple model for the Schottky barrier thickness in metal-semiconductor interfaces smaller than the free-carrier screening length ͑Debye length, L D ͒. Our model predicts an interface-size-dependent barrier thickness, leading to greatly enhanced tunneling in small Schottky diodes. The CoSi 2 /Si(111) interface used in our experiments is among the few metal-semiconductor interfaces of which reliable Schottky barrier height ͑SBH͒ values exist, mainly because it can be grown as a virtually perfect, abrupt, epitaxial interface. 7 The SBH in this system is 0.67 eV ͑for n-type Si͒ and has been measured with various techniques. 7-9 It is, therefore, a nearly ideal system to study electrical properties of metal-semiconductor interfaces and has been intensely used for that purpose. Both in our model and in the analysis of the measurements, the SBH will be considered as a given quantity, because of the well-determined character of the CoSi 2 /Si (111) interface. We do not expect that ultra-small-size effects as repor...

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...

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.