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Misfit dislocations in epitaxy

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Abstract

This article on epitaxy highlights the following: the definition and some historical milestones; the introduction by Frenkel and Kontorowa (FK) of a truncated Fourier series to model the periodic interaction at crystalline interfaces; the invention by Frank and van der Merwe (FvdM)—using the FK model—of (interfacial) misfit dislocations as an important mechanism in accommodating misfit at epilayer-substrate interfaces; the generalization of the FvdM theory to multilayers; the application of the parabolic model by Jesser and van der Merwe to describe, for growing multilayers and superlattices, the impact of Fourier coefficients in the realization of epitaxial orientations and the stability of modes of misfit accommodation; the involvement of intralayer interaction in the latter—all features that impact on the attainment of perfection in crystallinity of thin films, a property that is so vital in the fabrication of useful uniformly thick epilayers (uniformity being another technological requirement), which also depends on misfit accommodation through the interfacial energy that function strongly in the criterion for growth modes, proposed by Bauer; and the ingenious application of the Volterra model by Matthews and others to describe misfit accommodation by dislocations in growing epilayers.

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Abbreviations

1-D and 2-D:

one- and two-dimensional

EAM:

embedded atom method

FK:

Frenkel-Kontorowa

FM and FvdM:

Frank-van der Merwe

MA, MD, and MS:

misfit: accomodation, dislocation, strain and vernier

ML:

monolayer

KS:

Kurdjumov-Sachs

NW:

Nishiyama-Wasserman

NW-x and NW-y :

with matching in x- and y-directions

ps:

pseudomorphic

SK:

Stranksi-Krastranov

VW:

Volmer-Weber

A and B:

crystals

A0 and B0:

constants in Eqs. [34] and [38]

a :

interfacial interaction period

b and b:

natural and deformed spring lengths

a x , ay, b x , and b y :

diagonal lengths of bcc(110) and fcc(111) rhombic surface unit cells

a n and b n :

nearest-neighbor distances, r n =b n /a n

a s and a0:

lattice parameters of substrate and overlayer

b 0 :

Burgers vector of MD

c :

wave velocity of chain

c r :

reference lattice parameter

c ii :

stiffness constant

D :

in Eq. [37]

E :

energy:E AA and E BB of crystals A and B: E A and E B of crystal halves and E AB of bicrystal AB

E ij :

computed value of linear AB stack at grid point P ij =(x ij , y ij )

E MD :

of MD

E 0 :

of static chain

E(k) and K(k):

complete elliptic integrals, second and first kinds

F :

kind (incomplete)

f :

misfit: f c and f l when critical and in limit

g :

w/W

H :

Hamiltonian

H 0 :

2 πh/p

h :

thickness

h c :

critical h

K :

number grid points, l a limiting

L :

l0(1 - v2/c2)1/2

M :

mass of moving MD

M 0 :

rest mass

N :

number of chains in stack, N c when critical

p :

MD spacing, P and P 0 number atoms in p: MD when strained and unstrained

r a , r x , and r y :

ideal values of r n in KS, NW-x, and NW-y orientations

R and r0:

outer and inner cutoff radii of MD strain field

S :

surface and interface areas

t :

spring tension

UMD and U ac :

energies of formation and activation of MD

V(x) and V hk :

periodic potential and Fourier coefficients

U :

relative displacement of atoms on either side of interface

W :

overall amplitude of V(x)

α0 and β0:

angles, as shown in Fig. 5

β :

variable defined in Eq. [32]

γ :

specific surface free energy: γ 0 and γ s of overlayer and substrate, γ i of their interface, γ AB of bicyrystal AB interface

μ :

spring force constant, μ 1=μ for single chain, and μ n for stack of n chains

μ :

shear modulus: μ i , μ 0, and μ s for interface, overlayer, and substrate

v :

Poisson’s ratio

λ a :

μ A /(1 − v A )

l/λ + :

l/λ a +l/λ B

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Authors and Affiliations

  1. the Department of Physics, University of South Africa, Pretoria, 0003, Unisa, South Africa

    Jan H. Van Der Merwe (Professor-Extraordinarius)

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  1. Jan H. Van Der Merwe
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Additional information

This article is based on a presentation in the symposium “Interfacial Dislocations: Symposium in Honor of J.H. van der Merwe on the 50th Anniversary of His Discovery,” as part of the 2000 TMS Fall Meeting, October 11–12, 2000, in St. Louis, Missouri, sponsored under the auspices of ASM International, Materials Science Critical Technology Sector, Structures.

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Van Der Merwe, J.H. Misfit dislocations in epitaxy. Metall Mater Trans A 33, 2475–2483 (2002). https://doi.org/10.1007/s11661-002-0369-x

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