The combination of atomic force microscopy and Kelvin probe technology is a powerful tool to obtain high-resolution maps of the surface potential distribution on conducting and nonconducting samples. However, resolution and contrast transfer of this method have not been fully understood, so far. To obtain a better quantitative understanding, we introduce a model which correlates the measured potential with the actual surface potential distribution, and we compare numerical simulations of the three-dimensional tip-specimen model with experimental data from test structures. The observed potential is a locally weighted average over all potentials present on the sample surface. The model allows us to calculate these weighting factors and, furthermore, leads to the conclusion that good resolution in potential maps is obtained by long and slender but slightly blunt tips on cantilevers of minimal width and surface area.
We have investigated the cross-sectional electric field and potential distribution of a cleaved n ϩ -InP/InGaAsP/p ϩ -InP p -i -n laser diode using Kelvin probe force microscopy ͑KFM͒ with a lateral resolution reaching 50 nm. The powerful characterization capabilities of KFM were compared with two-dimensional ͑2D͒ physics-based simulations. The agreement between simulations and KFM measurements regarding the main features of the electric field and potential is very good. However, the KFM yields a voltage drop between n-and p-doped InP regions which is 0.4 times the one simulated. This discrepancy is explained in terms of surface traps due to the exposure of the sample to the air and in terms of incomplete ionization. This hypothesis is confirmed by the 2D simulations.
A tunable quantum point contact with modes occupied in both transverse directions is studied by magnetotransport experiments. We find conductance quantization that can be suppressed by degeneracies of onedimensional modes. The mode spectrum is determined as a function of the magnetic field of different orientations with respect to the quantum wire. A magnetic field applied parallel to the direction of the current flow couples the modes. This can be described by an extension of the Darwin-Fock model. Anticrossings are observed as a function of the parallel magnetic field, but not for zero field or perpendicular field directions, indicating coupling of the subbands due to nonparabolicity in the electrical confinement. ͓S0163-1829͑99͒15235-4͔Conductance quantization in quasi-one-dimensional ͑1D͒ systems 1,2 is one of the crucial discoveries in the physics of semiconductor nanostructures. 3 Usually, such 1D channels ͓quantum point contacts ͑QPC's͔͒ are realized by split-gate electrodes fabricated on Ga͓Al͔As heterostructures. In analogy to optical waveguides, 4 QPC's are also known as ''ballistic electron waveguides.'' Meanwhile, QPC's have become a key device for transport experiments in lowdimensional systems. 3 Typically, they are realized in an extreme limit where the confinement of the two-dimensional electron gas at the heterointerface is so strong that only the lowest two-dimensional ͑2D͒ subband lies below the Fermi energy. The mode spectrum of a QPC defined in such a heterostructure is dominated by the lateral confinement, which can be tuned by appropriate voltages on the split-gate electrodes. The modes, characterized by a single quantum number, are well separated in energy and do not couple to each other.Here, we present experimental results from a ballistic electron waveguide realized by a split-gate electrode on top of a wide electron system in a parabolic quantum well, in which two subbands formed due to the quantization in the growth direction are occupied. We find that the conductance quantization survives this extension to an additional dimension, provided the one-dimensional modes are not degenerate at the Fermi level.The 1D energy levels can be described by two quantum numbers for the two confining directions. A rich mode spectrum as a function of gate voltages and magnetic fields, applied in different directions with respect to the electron waveguide, is observed. While all levels move upwards in energy when a magnetic field is applied in the plane of the quantum well but perpendicular to the waveguide, one finds also levels moving downwards in energy as a function of a parallel magnetic field. The confining potential landscape inside the constriction can be studied by analyzing these measurements. We explain our data in terms of a generalization of the Darwin-Fock model, which describes the energy spectrum of a circular disk in magnetic fields perpendicular to it. 5 Thus, our experiment is closely related to those on quantum dots. 6 Level crossings and anticrossings are observed, manifesting them...
Genetic and simplex-downhill (SD) algorithms were used for the optimization of the electron-beam lithography (EBL) step in the fabrication of microwave electronic circuits. The definition of submicrometer structures involves complex exposure patterns that are cumbersome to determine experimentally and very difficult to optimize with linear search algorithms due to the high dimensionality of the search space. A SD algorithm was first used to solve the optimization problem. The large number of parameters and the complex topology of the search space proved too difficult for this algorithm, which could not yield satisfactory patterns. A hybrid approach using genetic algorithms (GAs) for global search, and a SD algorithm for further local optimization, was unable to drastically improve the structures optimized with GAs alone. A carefully studied fitness function was used. It contains mechanisms for reduced dependence on process tolerances. Several methods were studied for the selection, crossover, mutation, and reinsertion operators. The GA was used to predict scanning patterns for 100-nm T-gates and gate profiles with asymmetric recess and the structures were fabricated successfully. The simulation and optimization tool can help shorten response times to alterations of the EBL process by suppressing time-consuming experimental trial-and-error steps.
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