Wurtzite GaN/AlN/GaN on Si(111)


This tutorial presents how to model wurtzite heterostructures grown on zincblende (111) substrates. Here the presented example is GaN/AlN/GaN heterostructure (see — EDU — Piezo- and Pyroelectric charges in GaN/AlN/GaN wurtzite heterostructure) with the substrate replaced by equivalence of Si(111).

As nextnano++ does not support simulations containing materials of different symmetries, it is natively not possible to define wurtzite heterostructure with zincblende substrate, and vice versa. However, one can use certain simple workaround for special cases.

Solution for a special case

Let’s consider a substrate made of any material having zincblende or diamond structure with the surface (111) being prepared for the epitaxial growth. Let’s also assume that the heterostructure deposited on that surface has wurtzite symmetry oriented respective to the substrate in a way that the [0001] being perpendicular to the substrate surface (parallel to the growth direction).

Based on basic geometrical considerations (see Figure, the last monolayer of the substrate can be modelled as the last layer of some artificial material with wurtzite symmetry of proper lattice constant, somehow related to the real material of the substrate. In other words, it can be seen that the last monoatomic layer in the plane (111) of zincblende or diamond crystals have exactly the same symmetry as a monoatomic layer in the place (0001) of wurtzite crystals.


Figure Conventional unit cell of a zincblende crystal or diamond. (a) Crystallographic directions of cubic crystals are plotted. Lattice constant of the crystal is denoted as \(a_\mathrm{zb}\) (b) The unit cell is sliced through one of (111) planes. Crystallographic directions of wurtzite crystals which can be grown on such a plane are plotted. Lattice constant experienced by potentially deposited wurtzite material is denoted by \(a\).

Distances between the atoms in that monolayer constitute a lattice constant \(a\) of the artificial wurtzite crystal that can be used to define the substrate for the simulation. It’s lattice constant \(c\) does not matter here. Based on forementioned geometrical considerations, if the lattice constant of the zincblende substrate is \(a_{zb}\), then

(\[a =\frac{a_{zb}}{\sqrt{2}}\]

for the artificial, corresponding wurtzite material.

Respective thermal expansion coefficients follow the same transformation.

Therefore, if the substrate is made of Silicon, which has lattice constant \(a_{Si} = 5.4304\;\mathring{\mathrm{A}}\) at room temperature and expansion coefficient \(a_{exp,Si} = 1.8138\times 10^{-5} \;\mathring{\mathrm{A}}/\mathrm{K}\), then the corresponding artificial wurtzite crystal will have the lattice constant

(\[a =\frac{a_{Si}}{\sqrt{2}} = \frac{5.4304\;\mathring{\mathrm{A}}}{\sqrt{2}} = 3.8399\;\mathring{\mathrm{A}}\]

at room temperature and the expansion coefficient

(\[a_{exp} = \frac{a_{exp,Si}}{\sqrt{2}} = \frac{1.8138\times 10^{-5}\;\mathring{\mathrm{A}}/\mathrm{K}}{\sqrt{2}} = 1.2826\times 10^{-5}\;\mathring{\mathrm{A}}/\mathrm{K}.\]

The other lattice constant \(c\) and the related expansion coefficient can be chosen arbitrary.


To implement this solution in the simulation one needs to do only two things:

  1. define the corresponding artificial wurtzite material,

  2. use it as a substrate.


    Presented approach is valid only when the zincblende substrate is not included in the simulation domain.

The easiest way to define the artificial material for the substrate is to follow suggestions from Defining New Materials. In the input file zb-substrate-in-wz-system_GaN-AlN-Si_1D_nnp.in we did that by - copy-pasting definition of GaN from our database (database_nnp.in) under database{} group - modifying the name, one lattice constant and one expansion coefficient


We have also removed unnecessary comments and not required definitions for simplicity. The code examples are also simplified. Compare them with the input file to this tutorial.

        name = "Si_wz_substrate_only"
            a = 3.8399
            a_expansion = 1.2826e-5

To use this material for the simulation it is used only as a substrate in the global{} group.

    substrate{ name = "Si_wz_substrate_only" }

Last update: nn/nn/nnnn