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Study of the vertical transport in p-doped superlattices based on group III-V semiconductors.

Dos Santos OF, Rodrigues SC, Sipahi GM, Scolfaro LM, da Silva EF - Nanoscale Res Lett (2011)

Bottom Line: The calculations are done within a self-consistent approach to the k→⋅p→ theory by means of a full six-band Luttinger-Kohn Hamiltonian, together with the Poisson equation in a plane wave representation, including exchange correlation effects within the local density approximation.It was shown that the particular minibands structure of the p-doped SLs leads to a plateau-like behavior in the conductivity as a function of the donor concentration and/or the Fermi level energy.In addition, it is shown that the Coulomb and exchange-correlation effects play an important role in these systems, since they determine the bending potential.

View Article: PubMed Central - HTML - PubMed

Affiliation: Departamento de Física, Universidade Federal Rural de Pernambuco, R, Dom Manoel de Medeiros s/n, 52171-900 Recife, PE, Brazil. srodrigues@df.ufrpe.br.

ABSTRACT
The electrical conductivity σ has been calculated for p-doped GaAs/Al0.3Ga0.7As and cubic GaN/Al0.3Ga0.7N thin superlattices (SLs). The calculations are done within a self-consistent approach to the k→⋅p→ theory by means of a full six-band Luttinger-Kohn Hamiltonian, together with the Poisson equation in a plane wave representation, including exchange correlation effects within the local density approximation. It was also assumed that transport in the SL occurs through extended minibands states for each carrier, and the conductivity is calculated at zero temperature and in low-field ohmic limits by the quasi-chemical Boltzmann kinetic equation. It was shown that the particular minibands structure of the p-doped SLs leads to a plateau-like behavior in the conductivity as a function of the donor concentration and/or the Fermi level energy. In addition, it is shown that the Coulomb and exchange-correlation effects play an important role in these systems, since they determine the bending potential.

No MeSH data available.


Related in: MedlinePlus

Schematic representation of a SL band structure used in this study. Minibands for heavy hole levels, εhh,1 , minigaps, subbands, and Fermi level, EF, are shown. The zero of energy was considered at the top of the Coulomb potential at the barrier. Horizontal dashed lines indicate the bottom of the first miniband and the top of the second miniband, respectively.
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Figure 1: Schematic representation of a SL band structure used in this study. Minibands for heavy hole levels, εhh,1 , minigaps, subbands, and Fermi level, EF, are shown. The zero of energy was considered at the top of the Coulomb potential at the barrier. Horizontal dashed lines indicate the bottom of the first miniband and the top of the second miniband, respectively.

Mentions: The prime indicates the derivative of εq,v(kz) with respect to kz . Once the SL miniband structure is accessed, σq can be calculated, provided that the values of τq,v are known. The relaxation time for all the minibands is assumed to be the same. In order to describe qualitatively the origin of the peculiar behavior as a function of EF , Equation (5) is analyzed with the aid of the SL band structure scheme as shown in Figure 1. It is important to see that minibands are presented just for heavy hole levels, since only they are occupied. Let us assume that EF moves down through the minibands and minigaps as shown in the figure. One considers the zero in the top of the Coulomb barrier. The density is zero if EF lies up at the maximum (Max) of a particular miniband εq,v . Its value rises continuously as EF spans the interval between the bottom and the top of this miniband. For EF smaller than the minimum (Min) of this miniband, remains constant. A straightforward analysis of Equation (5) shows that σq increases as EF crosses a miniband and stays constant as EF crosses a minigap. Therefore, a plateau-like behavior is expected for σq as a function of EF. For a particular SL of period d, one moves the Fermi level position down through a minigap by increasing the acceptor-donor concentration NA, so the same behavior is expected for σq as a function of NA. This fact was reported previously for n-type delta doping SLs [4].


Study of the vertical transport in p-doped superlattices based on group III-V semiconductors.

Dos Santos OF, Rodrigues SC, Sipahi GM, Scolfaro LM, da Silva EF - Nanoscale Res Lett (2011)

Schematic representation of a SL band structure used in this study. Minibands for heavy hole levels, εhh,1 , minigaps, subbands, and Fermi level, EF, are shown. The zero of energy was considered at the top of the Coulomb potential at the barrier. Horizontal dashed lines indicate the bottom of the first miniband and the top of the second miniband, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3211228&req=5

Figure 1: Schematic representation of a SL band structure used in this study. Minibands for heavy hole levels, εhh,1 , minigaps, subbands, and Fermi level, EF, are shown. The zero of energy was considered at the top of the Coulomb potential at the barrier. Horizontal dashed lines indicate the bottom of the first miniband and the top of the second miniband, respectively.
Mentions: The prime indicates the derivative of εq,v(kz) with respect to kz . Once the SL miniband structure is accessed, σq can be calculated, provided that the values of τq,v are known. The relaxation time for all the minibands is assumed to be the same. In order to describe qualitatively the origin of the peculiar behavior as a function of EF , Equation (5) is analyzed with the aid of the SL band structure scheme as shown in Figure 1. It is important to see that minibands are presented just for heavy hole levels, since only they are occupied. Let us assume that EF moves down through the minibands and minigaps as shown in the figure. One considers the zero in the top of the Coulomb barrier. The density is zero if EF lies up at the maximum (Max) of a particular miniband εq,v . Its value rises continuously as EF spans the interval between the bottom and the top of this miniband. For EF smaller than the minimum (Min) of this miniband, remains constant. A straightforward analysis of Equation (5) shows that σq increases as EF crosses a miniband and stays constant as EF crosses a minigap. Therefore, a plateau-like behavior is expected for σq as a function of EF. For a particular SL of period d, one moves the Fermi level position down through a minigap by increasing the acceptor-donor concentration NA, so the same behavior is expected for σq as a function of NA. This fact was reported previously for n-type delta doping SLs [4].

Bottom Line: The calculations are done within a self-consistent approach to the k→⋅p→ theory by means of a full six-band Luttinger-Kohn Hamiltonian, together with the Poisson equation in a plane wave representation, including exchange correlation effects within the local density approximation.It was shown that the particular minibands structure of the p-doped SLs leads to a plateau-like behavior in the conductivity as a function of the donor concentration and/or the Fermi level energy.In addition, it is shown that the Coulomb and exchange-correlation effects play an important role in these systems, since they determine the bending potential.

View Article: PubMed Central - HTML - PubMed

Affiliation: Departamento de Física, Universidade Federal Rural de Pernambuco, R, Dom Manoel de Medeiros s/n, 52171-900 Recife, PE, Brazil. srodrigues@df.ufrpe.br.

ABSTRACT
The electrical conductivity σ has been calculated for p-doped GaAs/Al0.3Ga0.7As and cubic GaN/Al0.3Ga0.7N thin superlattices (SLs). The calculations are done within a self-consistent approach to the k→⋅p→ theory by means of a full six-band Luttinger-Kohn Hamiltonian, together with the Poisson equation in a plane wave representation, including exchange correlation effects within the local density approximation. It was also assumed that transport in the SL occurs through extended minibands states for each carrier, and the conductivity is calculated at zero temperature and in low-field ohmic limits by the quasi-chemical Boltzmann kinetic equation. It was shown that the particular minibands structure of the p-doped SLs leads to a plateau-like behavior in the conductivity as a function of the donor concentration and/or the Fermi level energy. In addition, it is shown that the Coulomb and exchange-correlation effects play an important role in these systems, since they determine the bending potential.

No MeSH data available.


Related in: MedlinePlus