Effect of the applied bias on miniband structure in dimer fibonacci GaAs/Ga1-xAlxAs
superlattices
Aziz Zoubir* , Sefir Yamina, Djelti redouan and Bentata Samir
Laboratory of material valorizations, Faculty of Sciences and Technologie, Abdelhamid Ibn Badis
Mostaganem University, BO 227, 27000 Algeria
E-mail: aziz_zdz@yahoo.fr
Summary:
The effect of a uniform electric field across multibarrier systems (GaAs/AlxGa1-xAs) is exhaustively
explored by a computational model using exact Airy function formalism and the transfer-matrix
technique. In the case of biased DFHBSL structure a strong reduction in transmission properties was
observed and the width of the miniband structure linearly decreases with the increase of the applied
bias. This is due to the confinement of the states in the miniband structure, which becomes
increasingly important (Wannier-Stark effect).
Keywords: Dimer Fibonacci Height Barrier superlattices (DFHBSL); Singular extended States, Exact
Airy function and transfer matrix formalism.
1. Introduction
In recent years, much attention has been paid to study of aperiodic systems, either quasiperiodic or
random[1-3] and a large amount of work has been devoted to the one-dimensional Fibonacci chain,
as a suitable model for quasicrystals which in addition can be physically realized in the form of
superlattices manufactured by molecular beam epitaxy (MBE). The transmission is the one important
aspect in multibarrier systems (MBS), which is extensively exploited for applications in high-speed
electronic and optoelectronic devices that encompass lasers, modulators, photodetectors, signal
processing devices and resonant tunneling diodes [4-10].
In this work, we examine numerically the effect of the applied bias on the miniband structure of dimer
Fibonacci height barrier superlattices (DFHBSLs) for 144 barriers.
2. Methodology
In this section, we study the electronic properties of the DFHBSL in the stationary case. The onedimensional time-independent Schrödinger wave equation is given by :
1 2
2
 ( z )  2 E  V ( z ) ( z )  0
2
*

m ( z ) z
(1)
Where z is the growing axis, E the incoming electron energy, ψ(z) the wave function in the growing
direction and m* the effective masse of each monolayer. We solve Eq. (1) by using the transfer matrix
formalism and exact airy function formalism. The transmission coefficient is then given by [11-12]:
 k 
4 
 k
T
2
2
k    k B Cma 



 A  D   
k   ma
k 

(2)
This expression measures the electron interaction with the structure through the elements A, B, C and
D of the difusion matrix S(0;L).
1
3. Results and Discussion
The transmission coefficients were numerically evaluated for applied tensions (Va) with DFHBSL
structures and were plotted against the incident energy (Fig.1). We observe that the fractal properties
of the transmission spectra are destroyed by the application of the electric field. The first region
unveils a fair narrowing in transmission properties. It is due to the breaking of symmetry in the
potential profile as the applied bias inclines the potential profile. Owing to the Wannier Stark effect, we
notice a confinement of the subminibands and, hence, the appearance of singular extended states.
The dependence of the miniband structure width versus the applied bias Va is plotted in Fig.2 ,
indicates that the width of the miniband structure linearly decreases with the increase of the applied
bias for the ordered structure. This is due to the confinement of the states in the miniband structure,
which
becomes
increasingly
important
(Wannier-Stark
effect).
0.12
1.0
DFHBSL
Va=0.03 Volts
Width of the miniband structure
0.11
Transmission (%)
0.8
0.6
0.4
0.2
0.10
0.09
0.08
0.07
0.06
0.0
0.00
4. Conclusion
0.05
0.10
0.15
E (eV)
0.20
0.25
0.30
Fig.2 Width of mini
Fig.1 Transmission coefficient of incident electron energy E
0.02
0.04
0.06
0.08
0.10
for the structure0.00
of DFHBSL
with
N=144
barriers,
Va (Volts)
V₁=247meV, Vd=150meV and a=b=15Å for Va=0.03 Volts;
Fig.6
The effect of the applied bias on transmission properties of DFHBSL structures (GaAs/AlxGa1-xAs) was
thoroughly investigated and the use of exact airy function formalism and transfer-matrix technique has
allowed us to obtain the corresponding transmission spectra. In the case of biased DFHBSL structure
a strong reduction in transmission properties was observed and the width of the miniband structure
linearly decreases with the increase of the applied bias. This is due to the confinement of the states in
the miniband structure, which becomes increasingly important (Wannier-Stark effect).
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