The expansion of a misfit dislocation occurs preferentially by glide of the
threading dislocation through the epilayer, Figure 2.8. Glide is the movement of a dislocation within a plane purely by the local rearrangement of atomic bonds. Glide
of a dislocation can occur in any plane that contains both the line direction andthe
Burgers vector (Hull and Bacon 2002). The glide velocity of a dislocation is an
important quantity as will be discussed below, the thermally activated glide velocity is given by:
(2.3)
where vg is the glide velocity, is the mismatch strain, Eg is the thermal activation barrier for glide, k is
Boltzmann’s constant, T is temperature in Kelvin and B is a constant (Mooney 1996).
The activation barrier for glide has been measured for the silicon-germanium system and is given by:
(2.4)
where x is germanium content (Tuppen and Gibbings 1990).
Equations (2.3) and (2.4) indicate that the glide velocity of a dislocation is highly sensitive to both temperature and composition and that the activation energy
kT E B vg exp g/ eV 7 . 0 16 . 2 x Eg
barrier for glide is relatively low at around 2 eV - this is low compared with the activation energies for homogeneous nucleation at 40 eV (Hull and Bean 1989) and
modified Frank-Read multiplication nucleation at 4 eV (Mooney et al. 1994).
Figure 2.8 – Schematic diagram of a threading dislocation propagating through an epitaxial layer leaving an interface misfit dislocation behind.
Threading dislocations have been found to glide a factor of 5000 times more quickly in bulk germanium than bulk silicon (Kasper 1995). Glide velocity can also be strongly influenced by presence of dopants and impurities, the presence of n-type
doping >1017 cm-3 having been shown to enhance dislocation motion in silicon
(Kasper 1995).
Movement of a dislocation can occur in a manner that is none conservative, rather than by simple bond rearrangement, requiring mass transport and leading to the
production of either voids or interstitials. Such movement is called climb, as to
perform such motion requires the dislocation to have climbed out of its glide plane. Climb only becomes an important factor in dislocation motion at higher temperatures
Misfit dislocation Threading arm Interface plane (001) Epitaxial layer Substrate vg Glide plane [111]
The propagation of a dislocation occurs in order to relieve strain within the epitaxial layer. The amount of strain relieved is related to the Burgers vector of the dislocation and in particular to the component of the Burgers vector resolved perpendicular to the line direction in the layer interface plane in which the strain is
present. This is known as the effective Burgers vector, beff.
(2.5)
where b is the Burgers vector of the dislocation and is the angle between the Burgers vector and the direction within the interfacial plane which is perpendicular to the line direction (Bolkhovityanov et al.
2001).
The strain energy relieved, Er, by a misfit dislocation of length, l, at an epitaxial layer
depth below a free surface, d, is given by (illustrated in Figure 2.9):
(2.6)
where G is the shear modulus and is Poisson’s ratio. For derivation see example in Capewell (2002).
The elastic strain energy associated with screw, edge and mixed dislocations
differs (section 2.3.3), however a further approximation of the strain energy per unit
length is valid for all:
(2.7)
where 0.5-1.0, G is shear modulus, b is Burgers vector.
ld b G Er eff 1 1 2 cos b beff 2 b G Eelasticstrain
Importantly, the elastic strain energy is proportional to the square of the dislocations Burgers vector and as a result smaller Burgers vectors are favoured, the energy of a
dislocation clearly also increases linearly with misfit length (Hull et al. 2002).
Figure 2.9 – Diagram illustrating the strain relief provided by an expanding misfit dislocation as the threading arms glide apart.
A dislocation cannot terminate within the crystal bulk, it must either terminate upon itself, at a node with another defect or at a free surface (Kasper 1995). Dislocations are usually connected at either end to the growth surface (closest free
surface) by a threading dislocation. Propagation of a dislocation will occur until (a) it
reaches a wafer edge, where the misfit will terminate directly; (b) sufficient strain has been relieved by the misfit that further expansion is energetically unfavourable; (c) it meets another threading dislocation mutually annihilating; or (d) it is unable to pass
another orthogonally placed dislocation becoming pinned (trapped). The annihilation
of two threading dislocations requires them to share equal Burgers vectors, forming a continuous misfit dislocation.
l
Region of strain relief
Threading arm Expansion of dislocation
d
Misfit dislocation Substrate Epitaxial layer
Ideally all threading dislocations will either mutually annihilate or reach the edge of the wafer reducing the number of threading dislocations remaining at the surface to zero. Surface threading dislocations are unwelcome in virtual substrates (buffers) used for device processing, with a clear link between current leakage and
threading density, that leads to degraded performance (Giovane et al. 2001). Surface
undulations have also been found to be increased when large numbers of threading
dislocations pile-up along orthogonal misfit dislocations (Fitzgerald et al. 1999). The
annihilation of threading dislocations is statistically unlikely, although LeGoues (1994) has found that the modified Frank-Read multiplication mechanism can lead to self-aligned dislocations where the likelihood of annihilation is greatly increased (discussed in section 2.3.7.3).