Dislocation density evaluation using dislocation kinetics model

Numerical Analysis of the Dislocation Density in Multicrystalline Silicon for Solar Cells by the Vertical Bridgman Process

“…The creep strain is related to the dislocation density, which can be described using the Haasen-Alexander-Sumino (HAS) model [13,14]. In the HAS model for a multiaxial stress state [15], the creep ratėand the mobile dislocation density multiplication ratėare given bẏ=…”

3D numerical analysis of the influence of material property of a crucible on stress and dislocation in multicrystalline silicon for solar cells

“…The creep strain rate, _ e c ij , is related to the dislocation density, which can be described by the HAS model. In the HAS model for a multiaxial stress state [14], the creep strain rate, _ e c ij , and the multiplication rate of mobile dislocation density, _ N m , are given by …”

Three-dimensional global analysis of thermal stress and dislocations in a silicon ingot during a unidirectional solidification process with a square crucible

“…The creep strain rate, _ e c ij , is related to the dislocation density, which can be described by the HAS model [14,15]. In the HAS model for a multiaxial stress state [16], the creep strain rate, _ e c ij , and the multiplication rate of mobile dislocation density, _ N m , are given by where b is the magnitude of the Burgers vector, k is Boltzman's constant, T is absolute temperature in a silicon crystal, Q is the Peierls potential, k 0 , K, p and l are some material constants, D is the strain hardening factor, S ij and J 2 are the deviatoric stress and the second invariant of the deviatoric stress, respectively, and ffiffiffiffi J 2 p indicates the equivalent shear stress. The value of t eff is set to zero…”