Elastic Stress Relaxation in the AlN/SiC Heterostructures: Modeling

by Utilizing the Molecular Dynamics Method

E. A. Panyutin

Ioffe Institute, Polytechnicheskaya 29, St-Petersburg, Russia

Keywords: Hydrothermal Systems, Volcano Research, AlN/SiC Heterostructures, High Temperature Functional

Electronics, Molecular Dynamics, Elastic Stress Relaxation.

Abstract: A computer study of crystallographic features of lattices detected near their heterogeneous boundaries was

performed within the general direction of research on the AlN/SiC heterostructures considered as a promising

platform for functional electronics intended to operate under extreme temperature conditions (including

volcano research, geyser monitoring, ultradeep drilling, etc.). Modeling by means of the molecular dynamics

method utilizing the Tersoff potentials (for SiC) and the potential proposed by Vashishta (for AlN) allowed

researchers to obtain a 3D description of the energy landscape and locations of its characteristic points

(minima, saddle points). Minimizing the total crystallite energy as the lattice configuration varies with

changes in the distance from the interface makes it possible to directly calculate the characteristic relaxation

length in the elastic stress field posing a direct interest for the technology of low-defect nanolayers.

1 INTRODUCTION

Giant hydrothermal systems formed in the areas of

magmatic activation of the earth's crust are of interest

not only from their huge geothermal potential point

of view, but also as convenient objects for seismic

activity monitoring. The significance of such

fractured-porous geological structures, formed at

depths up to 10kM and filled with hot mineral

solutions and superheated dry steam at a high

pressure, is not least due to their relatively high

prevalence. Suffice it to mention such hydrothermal

formations as Geysers (USA, California), which go to

a depth of ~8kM and have a temperature of up to

700ºC

(Walters, et al., 1992)

; Larderello (Italy) has

temperatures up to 420ºC and is characterized by high

temperature gradients

(Bellani, et al., 2004);

systems

Wayang Windu (Indonesia) with a significant reserve

of geothermal energy

(Bogie, et al., 2008);

Hohi and

Sengan, Japan

(Tamanyu, et al., 1991)

or Ebeko

volcano, Russia

(Rychagov, et al., 2010).

Since the local parameters of such geothermal

systems largely characterize the seismological state

of the region and allow to make the necessary

forecasts or contribute, for example, to the

development of sound recommendations for the

https://orcid.org/0000-0002-6414-2927

construction of geothermal power plants, it seems

timely to carry out work aimed at creating a

distributed monitoring system based on deep high-

temperature sensors of the environment

thermodynamic and chemical state.

2 PROBLEM STATEMENT

The creation of reliable and thermally stable sensors

capable of operating for a long time in a high-

temperature and aggressive environment is possible

only when using wide-band semiconductor or

functional materials such as silicon carbide (SiC) and

aluminum nitride (AlN), which, among other

attractive properties, are distinguished by exceptional

chemical resistance, mechanical strength and thermal

stability of parameters

(Fraga, et al., 2014)

. Currently,

SiC is the main candidate for creating the element

base of high-temperature electronics, and

microcircuits have already been created for operation

in the range of up to 500ºС

(Tian, et al., 2017;

Kargarrazi, et al., 2018; Spry, et al., 2018)

, while AlN is

a functional material, on the basis of which it is

possible to create pyrosensors, strain gauges and

chemical sensors

(Gavrilov, et al., 2018; Umeda, et al.,

2013; Jiang, et al., 2014).

268

Panyutin, E.

Elastic Stress Relaxation in the AlN/SiC Heterostructures: Modeling by Utilizing the Molecular Dynamics Method.

DOI: 10.5220/0012008600003536

In Proceedings of the 3rd International Symposium on Water, Ecology and Environment (ISWEE 2022), pages 268-271

ISBN: 978-989-758-639-2; ISSN: 2975-9439

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

. In addition, advances in modern epitaxial

technologies make it possible to obtain SiC/AlN

heterostructures

(Panyutin, et al., 2020), which opens

the way to single-chip integration of an AlN sensor

with a high-temperature SiC microcircuit capable of

performing primary processing of an analog signal

and representing it in digital form.

However, the absence of an exact match between

the crystallographic parameters of these materials

leads to the appearance of an elastically stress, which

is usually maximum at the heterointerface and

gradually decreases as it moves away. The purpose of

this study is to determine the nature of the relaxation

of this elastic stress within the framework of the

molecular dynamics method, which is of practical

importance for the technology of nanolayered

heterostructure.

3 MODELING

Classical molecular dynamics method is one of the

effective computational approaches, within which

many of the topical problems of this kind can be

solved.

The main idea of this method is to describe a

spatially ordered set of N atoms with coordinates r

each of which interacts with all the others through a

certain type of potential U(r

-r

), depending on the

pairwise distances between these atoms or ions and

representing curves with a minimum that determines

their thermodynamically stable configuration. With

regard to crystalline structures, only the total (multi-

particle) potential, which is a superposition of partial

potentials corresponding to the interaction of

arbitrary pairs of atoms, has real physical meaning.

For semiconductor crystals, which are characterized

by the predominance of the covalent contribution to

interatomic bonds, Tersoff's multiparticle potentials

(Tersoff J., 1988), which are based on the mathematical

formalism for systems with ordered bonds proposed

by Abel

(Abell, 1985), seem to be preferable.

In a somewhat simplified form, it can be

represented as follows:

(, ,) ( )

iij

iiji

Vxyz V r

≠



(1)

Here V

is the energy of an atom of the i-th lattice

site, Φ(r

) is the energy of interaction between atoms

i and j belonging to this lattice and located at distances

=(x

)

1/2

, and it is assumed that this energy

depends on the simultaneously acting attraction and

repulsion forces and is determined by the expression:

() () () ()

ij c ij rep ij ij att ij

rfr rb rφ= φ +φ









(2)

In this case, the function Φ

rep

) is a repulsive pair

potential determined by the interaction of electron

shells at short distances, as well as the interaction of

nuclei, and the function Φ

att

) is an attraction

potential, and includes the forces of covalent

attraction of outer electron shells.

( ) exp( )

rep ij ij ij ij

rA r

=−λ

(3)

( ) exp( )

att ij ij ij ij

rB r

=− −

(4)

()

[

]

()

cij

fr cos=+ π⋅

(5)

Here ψ is the angle between the directions of

bonds between the i-th and j-th atom; λ, μ are the scale

factors obtained from the values of elastic constants.

The numerical values of the parameters for SiC can

be found in

(Le, et al., 2014). The potential that is

reasonable to use for AlN was first proposed by

Vashishta

(Vashishta, et al., 2007). It combines

repulsive, charge-dipole, Coulomb with screening

and dispersion interactions and has been successfully

used for a number of A

III

semiconductors.

The potential can be represented (Henggao Xiang,

et al., 2017) as:

(2) (3)

() (, )

ij ij ik

ijk

ij ijk

VVr Vrr



(6)

(2)

()

ij i j ij

ZZ W

Vr e e

−

=+ − −

(7)

Equation (6) generally describes two-particle and

three-particle interactions, where r

are the distances

between i- and j- atoms. In equation (7) H

and η

are

the magnitude and index of the decay of repulsive

forces, Zi is the effective charge, W

and D

represent,

respectively, the constants of dipole and van der Waals

interactions. The values of the parameters for this

potential are given, for example, in

(Henggao Xiang, et

al., 2017). The calculated potential values for SiC

(hexagonal lattice, P6

/mc group) and AlN (hexagonal

lattice of the sphalerite type), corresponding to

equilibrium states, reach their minima, at lattice

constants, respectively, а

∞

SiC

=3, 07 A and а

∞

AlN

3,11A. However, at the SiC/AlN interface, in the

approximation of the absence of misfit dislocations,

we can determine а

SiC

= а

AlN

≈ 3, 09 A. The atomic

configuration of a fragment of such an elastically

stressed SiC/AlN heterostructure (a view from the YZ

and XZ planes) is shown in Figure 1.

Elastic Stress Relaxation in the AlN/SiC Heterostructures: Modeling by Utilizing the Molecular Dynamics Method

269

Figure 1: Atomic configuration of a fragment of an elastically stressed SiC/AlN heterostructure, a) – view in the Y direction

(XZ plane), b) - view in the X direction (YZ plane)

Then, assuming that the asymptotic behavior of the

lattice constants relaxation to their equilibrium values

corresponds to a power law, the change in the a

parameter along |z| coordinate can be represented as:

()

(1 )

SiC

(8)

()

(1 )

AlN

(9)

where ∆

SiC

+∆a

AlN

=|а

∞

SiC

- а

∞

AlN

|, and β are

relaxation parameters.

Obviously, the equilibrium configuration of such

a deformed (dislocation-free) lattice for the selected

types of potentials will correspond to such value of β,

for which the total crystallite energy V will

Figure 2: Dependence of the potential V of a fragment of

the AlN/SiC structure on the possible values of the

relaxation parameter β for various thicknesses W of the

crystallite.

The real values of β correspond to its value at

which the potential V reaches a minimum.

take a minimum value. The corresponding values of

the relaxation parameter β for crystallites of various

thicknesses (dimension Z direction) are shown in

Figure 2.

All calculations were made in the MATLAB.

ISWEE 2022 - International Symposium on Water, Ecology and Environment

270

4 CONCLUSION

This study of the lattice parameters deviation from

their equilibrium values is of great importance for the

development of a number of nano-devices, and, in

particular, nanolayered pyrosensors. However, taking

into account that, unlike the quantum mechanical

approach, the molecular dynamics method is less

universal and its results depend on the chosen type of

interatomic potential, they require comparison with

experiment for each specific case.

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