Finite element analysis of valence band structures in quantum wires

Park, Seoung–Hwan; Ahn, Doyeol; Lee, Yong-Tak

doi:10.1063/1.1766092

Cited by 23 publications

(10 citation statements)

References 16 publications

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“…where N is an interpolation shape function and F is a nodal column vector with elements representing the values of the envelope function at the element nodal mesh points [16,19]. Substituting F into Equation 15, we obtain the following matrix form to be minimized:…”

Section: Finite Element Discretization Of a K • P Hamiltonianmentioning

confidence: 99%

“…The case is worse with narrow gap systems such as InAs/GaSb and type II heterostructures with a broken gap. The distribution of the eight components of the envelope function spinor F µ |F µ for the 21 eigenstates solution of Equation (19) near the effective gap is plotted in Figure 5. In this figure, the states numbered 4 and 20 have the largest components F µ |F µ among all other states.…”

Section: Parabolicmentioning

confidence: 99%

“…Despite FEM accuracy, its application or use remains limited. In FEM, a non-uniform mesh as well as high order Lagrange/Hermit basis functions can be utilized [19], hence the band structure and wavefunctions for heterostructures with layers of arbitrary thicknesses can be calculated accurately with a smoothed mesh the near heterointerface edges. In this work, we first choose the Luttinger-Kohn Hamiltonian as a case study and present its formulation using k • p theory taking into account strain effects and the coupling between conduction and valence bands.…”

Section: Introductionmentioning

confidence: 99%

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Modeling Energy Bands in Type II Superlattices

Bennecer

Sengouga

2019

Crystals

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We present a rigorous model for the overall band structure calculation using the perturbative k · p approach for arbitrary layered cubic zincblende semiconductor nanostructures. This approach, first pioneered by Kohn and Luttinger, is faster than atomistic ab initio approaches and provides sufficiently accurate information for optoelectronic processes near high symmetry points in semiconductor crystals. k · p Hamiltonians are discretized and diagonalized using a finite element method (FEM) with smoothed mesh near interface edges and different high order Lagrange/Hermite basis functions, hence enabling accurate determination of bound states and related quantities with a small number of elements. Such properties make the model more efficient than other numerical models that are usually used. Moreover, an energy-dependent effective mass non-parabolic model suitable for large gap materials is also included, which offers fast and reasonably accurate results without the need to solve the full multi-band Hamiltonian. Finally, the tools are validated on three semiconductor nanostructures: (1) the bound energies of a finite quantum well using the energy-dependent effective mass non-parabolic model; (2) the InAs bulk band structure; and (3) the electronic band structure for the absorber region of photodetectors based on a type-II InAs/GaSb superlattice at room temperature. The tools are shown to work on simple and sophisticated designs and the results show very good agreement with recently published experimental works.

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Section: Finite Element Discretization Of a K • P Hamiltonianmentioning

confidence: 99%

Section: Parabolicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modeling Energy Bands in Type II Superlattices

Bennecer

Sengouga

2019

Crystals

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“…It is well-known that the k.p theory is a well established method to describe the bandstructure. Despite its field of application should be restricted to not very small systems, the amazing correspondence between experimental and numerical results obtained by the k.p method suggests that the limits of validity of the method are beyond what it might be expected, reaching good descriptions of nanoscale systems [ 24 – 26 ]. In this work, using material parameters as listed in Table 1 , the subband structures and wave functions of the unstrained and stained silicon are first calculated by using the stress-dependent six-band k.p model under the triangular-well approximation, which is a powerful tool for quantitative evaluation of strain-induced effective mass changes.…”

Section: Theory Modelmentioning

confidence: 99%

Orientation Effects in Ballistic High-Strained P-type Si Nanowire FETs

Zhang

Huang

et al. 2009

Sensors

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In order to design and optimize high-sensitivity silicon nanowire-field-effect transistor (SiNW FET) pressure sensors, this paper investigates the effects of channel orientations and the uniaxial stress on the ballistic hole transport properties of a strongly quantized SiNW FET placed near the high stress regions of the pressure sensors. A discrete stress-dependent six-band k.p method is used for subband structure calculation, coupled to a two-dimensional Poisson solver for electrostatics. A semi-classical ballistic FET model is then used to evaluate the ballistic current-voltage characteristics of SiNW FETs with and without strain. Our results presented here indicate that [110] is the optimum orientation for the p-type SiNW FETs and sensors. For the ultra-scaled 2.2 nm square SiNW, due to the limit of strong quantum confinement, the effect of the uniaxial stress on the magnitude of ballistic drive current is too small to be considered, except for the [100] orientation. However, for larger 5 nm square SiNW transistors with various transport orientations, the uniaxial tensile stress obviously alters the ballistic performance, while the uniaxial compressive stress slightly changes the ballistic hole current. Furthermore, the competition of injection velocity and carrier density related to the effective hole masses is found to play a critical role in determining the performance of the nanotransistors.

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“…Usually either a spectral or the FD method is applied. For the FE method, several derivations for different dimensionalities exist [32][33][34]. Here, we focus on a general form that is applicable to wells, wires and dots for any k·p model.…”

Section: Envelope Equationsmentioning

confidence: 99%

Reliable k⋅p band structure calculation for nanostructures using finite elements

2008

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The k · p envelope function method is a popular tool for the study of electronic properties of III-V nanostructures. The equations are usually transferred to real-space and solved using standard numerical techniques. The powerful and flexible finite element method was seldom employed due to problems with spurious solutions. The method would be favorable for the calculation of electronic properties of large strained nanostructures as it allows a flexible representation of complex geometries. In this paper, we show our consistent implementation of the k · p envelope equations for nanostructures of any dimensionality. By including BurtForeman operator ordering and ensuring the ellipticity of the equations, we are able to calculate reliable and spurious solution free subband structures for the standard k·p 4×4, 6×6 and 8×8 models for zinc-blende and wurtzite crystals. We further show how to consistently include strain effects up to second order by means of the Pikus-Bir transformation. Finally, we analyze the performance of our implementation using benchmark examples.

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Finite element analysis of valence band structures in quantum wires

Cited by 23 publications

References 16 publications

Modeling Energy Bands in Type II Superlattices

Modeling Energy Bands in Type II Superlattices

Orientation Effects in Ballistic High-Strained P-type Si Nanowire FETs

Reliable k⋅p band structure calculation for nanostructures using finite elements

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