Biomedical Engineering Reference
In-Depth Information
This chapter is organized as follows: we begin in Sect.
6.2
by providing an
overview of the theoretical framework used here to study the electronic structure of
c
-plane InGaN/GaN QDMs, including discussion of our approach to the calculation
of strain and built-in fields in such systems. Section
6.3
reviews more general
features of the electrostatic built-in field of isolated nitride-based QDs, where we
show why the built-in electrostatic field should be significantly reduced in an
isolated QD compared to the field in a QW of the same composition and height.
In Sect.
6.4
we focus on the experimental findings regarding the shape, the size, and
the composition of isolated and stacked InGaN dots. We also discuss uncertainties
in one of the key material parameters that determines the built-in fields in nitride-
based heterostructures, namely the sign of the piezoelectric coefficient
e
15
and
show how its value affects the built-in potential both within and outside an isolated
InGaN/GaN QD with realistic dimensions and indium content. Section
6.5
considers
the electrostatic built-in field in stacked nitride-based QDs, showing how this can be
further reduced compared to the field in an isolated dot. Section
6.6
then discusses
the electronic structure of InGaN QDMs. We first deal in Sect.
6.6.1
with the
idealized situation of a QDM made up of two identical dots, while Sect.
6.6.2
then
focuses on the realistic situation of an InGaN/GaN QDM made up of two non-
identical dots. Finally, in Sect.
6.7
we summarize our results.
6.2
Theory: Electrostatic Built-In Fields and Electronic
Structure Calculations
In this section we discuss the theoretical framework used to study the electronic
structure of InGaN/GaN QDMs. For a realistic description, strain and built-in fields
have to be taken into account. Therefore, in a first step, Sect.
6.2.1
describes the
determination of the strain field and the built-in potentials in nitride-based QDs
using a surface integral method. We use this surface integral approach because it can
give very useful insight into trends in the behavior of the strain and built-in potential
as a function of dot shape and aspect ratio. In a second step, Sect.
6.2.2
describes
the method we use for the electronic structure calculations of InGaN/GaN QDMs.
These calculations are carried out in the framework of an empirical tight-binding
(TB) model, taking both strain and built-in fields into account.
6.2.1
Strain and Built-In Potentials
The growth of semiconductor heterostructures involving alloys with different lattice
constants leads inevitably to the introduction of strain into the system. This strain
field couples to charge carriers through the electronic (band) structure and the
piezoelectric effect. Therefore, to perform realistic electronic structure calculations,
strain and electrostatic built-in fields have to be taken into account. Different
