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41317-AC10
Theory and Modeling of Complex Two-Dimensional Structures Fabricated with the Aid of Bacterial S-Layer Protein Masks
This project was focused on the study of dispersion relations of carriers in complex periodic structures that be fabricated by means of an S-layer protein mask lithography. Energy dispersion relations in such objects can be of great interest because of the existence in the valence band of negative-effective-masses (NEM) regions in certain momentum interval. It is well known that the curves with NEM regions can be found in many objects such as: bulk semiconductors, quantum wells, quantum wires, as well as artificially band-engineered structures such as heterostructures obtained by the cleaved edge overgrowth technique (see [1] and references therein). The existence of such NEM regions may lead to current instabilities in ballistic diodes and transistors [2]. For submicrometer base lengths of these devices the frequency of current oscillations falls into the terahertz range. For the identification and engineering of structures with well-pronounced NEM regions in energy dispersions, the tight-binding simulations of the energy band structure is an effective tool. Therefore, an empirical sp3d5s* tight-binding model which takes into account 10 atomic orbitals: s- and excited s*-orbitals, three p-, and five d-orbitals was used. The inclusion in the model of higher energy d-orbitals and spin-orbital coupling has dramatically improved the precision of the calculated electron and hole energy dispersion relations. In our calculations we used tight-binding parameters from Ref. [3]. All other details of the exploited model can be found in Ref. [4]. The developed program can be used for calculations of band structure parameters of the quantum wells as well as of quantum wires. For the tight-binding simulations Si was chosen because it has very well developed technology and thus has better chances for practical realization of the suggested devices.
The simplest analytical model of energy dispersion relations with NEM regions is based on anticrossing of two bands that are developed by carriers with light effective mass, m, and heavy effective mass, M. The quasineutral semiconductor plasma with current carriers having above-mentioned dispersion may have self-organized oscillatory regimes only when ratio of the two effective masses, m and M, satisfies the following necessary condition: M/m > 2 [5]. Note, that large ratios of M/m are preferable for NEM-based current oscillations to be established. While this model ignores many important details, it is widely used for qualitative estimates in nonlinear carrier transport. Although, the calculated energy dispersion relations are not fully described by this simple model, nevertheless qualitatively we can introduce the two effective masses, m and M, that characterize the calculated dispersions. The ratio of the effective masses after and before the NEM region, M/m, behaves differently in QWs and QWRs. For QWs in [110] direction this ratio for wide range of well thicknesses is significantly greater than in QWRs. The energy interval of NEM region in QWRs is shifted to higher energies (or higher momenta). This may be an obstacle for maintaining of ballistic oscillatory regime of a device. In addition, the energy interval of NEM region is much smaller in the case of QWRs in comparison to QWs. The fourth parameter that characterizes NEM oscillatory regime, Δ, is the distance between the lowest and the next subbands. The larger is this parameter, the better are the conditions for achieving larger amplitudes of oscillations. And this is the only parameter that is superior in QWRs in comparison with the case of QWs. The results of numerical simulations demonstrate that Si QWs are promising candidates for NEM-based terahertz generation. The data obtained in the framework of empirical tight-binding model can be fitted by the two band anticrossing model with the ratio, M/m, changing in the range from 3 to 13. Large values of M/m result in effective current oscillations in wide energy intervals. Using the anticrossing model, one can estimate the frequencies of generation band [3]. For QW structures with the base lengths 0.1 – 0.3 μm we obtain the estimates of generation band of 0.5 – 2 THz.
1. Z.S. Gribnikov et al., “Quantum real-space transfer in a heterostucture overgrown on the cleaved edge of a superlattice,” Journal of Applied Physics 93 (1), 330 (2003).
2. Z.S. Gribnikov et al., “Negative-effective-mass ballistic field-effect transistor: Theory and modeling,” Journal of Applied Physics 87 (10), 7466 (2000).
3. T.B. Boykin et al., “Valence band effective-mass expressions in the sp3d5s* empirical tight-binding model applied to a Si and Ge parametrization,” Physical Review B 69 (11), 115201 (2004).
4. A. Rahman et al., “Atomistic approach for nanoscale devices at the scaling limit and beyond – valley splitting in Si,” Japanese Journal of Applied Physics 44 (4B), 2187 (2005).
5. Z.S. Gribnikov et al., “Terahertz ballistic current oscillations for carriers with negative effective mass,” Journal of Applied Physics 80 (10), 5799 (1996).
