Bandgap Engineering Superlattice Simulation Tool (BESST)—package for
simulation of optoelectronic devices based on
group-III nitride superlattices.
Short-period superlattices (SPSLs) serve as important elements
of a device heterostructure design, aimed at solving either technological
or some design problems. In the case of III-nitrides, the SPSLs are
used either for reduction of dislocation density in epitaxial materials,
enhancement of Mg acceptor activation, increase of hole injection efficiency
or even as n- and p-emitters and active regions in light emitting diodes
and laser diodes. To employ the advantages of SPSLs, it is necessary to
know their electric and optical properties as a function of SPSL
parameters—thicknesses and compositions of the constituent layers.
The BESST package allows calculating of individual SPSL properties as
well as modeling of band diagram and carrier transport in a device
structure consisted of a sequence of different p- and n-doped SPSL
regions. The light emission spectra from such a device are also predicted.
2. BESST 2.0 options
The BESST package provides the following options:
Calculation of key electrical properties of individual
SLs involved in the structure
- Electronic structure: energy levels and wave
functions of localized carrier states, parameters
- Carrier concentration and impurity ionization.
- Electric field distribution
- Conductivity of SL
Simulation of the whole device at given bias by
self-consistent solution of Poisson and Schrodinger
equations coupled with carrier transport equations.
- Band diagram.
- Energy levels and wave functions of carrier
states in each QW.
- Carrier concentrations and impurity ionization.
- Carrier fluxes and recombination rates.
- Emission spectrum.
- Current-voltage (I-V) characteristic can be
calculated by series of computations.
The above information forms a good basis for
deeper insight in operation of SL based devices and
helps to optimize the parameters of individual SLs
as well as their interconnection.
3. Brief description of physical model
The developed approach is a self-consistent solution
of the Poisson and Schrodinger equations modified
for the case of SL based heterostructure coupled
with carrier transport equations.
Band diagram is calculated by the Poisson equation:
- Spontaneous polarization and piezoeffect
are taken into account.
- Carrier density is calculated with account
for the quantum nature of the carriers.
- Electroneutrality of SL period is used as
a boundary condition at the ends of the structure.
Quantum description of carrier density:
- Even at short SL periods the effective mass
approach is used to describe electrons and heavy,
light, and split-off holes.
- Localized carrier states in individual quantum
wells are found numerically by the Schrodinger equation.
- Coupling between the quantum wells and miniband
formation is treated within the tight-binding
Carrier transport and recombination:
- Discrete drift-diffusion model is used
to describe the carrier transport in SL based
- Band-to-band radiative recombination is calculated
in each quantum well with account for overlap of electron
and hole wave functions.
4. Examples of
4.1. Acceptor ionization efficiency
Fig. 2. Blue line—calculations,
red squares—experimental data (P. Kozodoy et al, Appl. Phys. Lett., 74, 3681
acceptor ionization energy in AlGaN alloys and,
therefore, low conductivity of p-type layers is well known
problem of nitride devices. Mg-doped GaN/AlxGa1-xN SLs were
shown to have higher hole concentrations than AlGaN layers
of the same average composition due to valence band modulation.
However, the hole concentration is strongly dependent on
the structural parameters of SLs. Calculations made within
the BESST package shows excellent agreement with the experimental
4.2. SPSL based UV LED
Recently, UV LEDs of various designs employing
p-n junctions between different SPSLs have been demonstrated.
In particular, it has been shown that the use of an
i-SPSL active region with a wider quantum wells between
the n- and p-doped SPSL claddings increases the emission
intensity compared to an LED consisting of the n- and
p-SPSLs only. Actually, such a p-i-n LED operates
like a conventional double heterostructure (DHS) device.
Indeed, the bandgap of the SPSL with wider quantum wells is
lower than those of the claddings, producing better
carrier localization inside the active region and, hence,
a higher internal emission efficiency.
The band diagram and carrier concentration distributions
in the p-n and p-i-n Al0.1Ga0.9N/AlN SPSL LEDs are
shown below. The barrier widths in all the SPSLs
are 1 nm, while the QW width is 1 nm in the DHS active
region and 0.5 nm in the n- and p-claddings. The impurity
concentration of 1x1019 cm-3 is taken in both n- and p-regions.
Band diagrams show a close similarity
in operation of SPSL based devices and their bulk prototypes.
Fig. 3. Band diagrams and concentrations of electrons
and heavy holes in p-n SPSL LED (left) and p-i-n
DHS SPSL LED (right) at the bias of 4 V. Effective bandgaps
are marked by thick black lines.
Band diagrams illustrate a close similarity between
the SPSL based devices and their bulk prototypes.
The effective surface charges are formed at the
interfaces of the DHS active region where the mean
electric field is directed opposite to the built-in
field of the p-n junction. Such a behavior is typical
to conventional single-quantum well (SQW) InGaN LED
heterostructures with polarization charges on the SQW
interfaces. In the case of p-n SPSL junction, no
effective surface charges are observed due to the equal
macroscopic polarizations in both n- and p-SPSLs. Thus,
the p-n SPSL LED is quite similar to ordinary p-n
To conclude, these results clearly demonstrate the
potentiality of the bandgap engineering in such SPSL-LED
heterostructures and the BESST package will help to
optimize your structure!
5. User interface
Friendly user interface allows one to
- Specify all input data: heterostructure, materials properties,
- Interactively control the computations.
- View results by internal vizualizer giving excellent
representation of the device operation.
The results also can be stored in a number of output files.
The BESST 2.0 supports export either in format of commercial
Tecplot graphical package (© Copyright 2004
Tecplot, Inc.) or plain-text data file.
Fig. 4. SL heterostructure can be easily inputted as
a sequence of SL regions.
Fig. 5. Electronic structure of SL. Wavefunctions
of each miniband can be turned on/off by the respective checkbox.
The key parameters of minibands are collected in the table below.
6. Database of material properties
The code is provided with an internal database of materials
properties of group-III nitrides necessary for simulations.
The database can be modified by user.
7. System requirements
- Operation System—Windows 98/2000/ME/XP
- RAM—256 Mb
- Disk Space—2 Mb for the BESST program files
and about 1Mb per typical simulation to save results.
- Display and video card with the
support of 1024x768 resolution in the High Color