information from x ray diffraction that samples grown at t gt 750c are approximately 15 completely relaxed the average length of a misfit dislocation and therefore length a threading dislocation has traveled is u03bb avg u03c1 u03bb u03c1 t 1 s ue89e ue89e u03c1 t u03b4 b eff ue89e u03c1 t 3 where u03c1 l is the interface dislocation density inverse of the interface dislocation spacing s for the 30 ge alloy example u03c1 1 22 u00d7 10 u2212 2 for complete relaxation this results in a total misfit length per thread of approximately 5 cm using equation 3 since the experiments were performed on 4 inch 10 cm substrates it is possible that a significant number are escaping at the edges of the wafer it must be remembered that the total length of 5 cm is distributed over a number of interfaces in a graded layer in the case of graded sige typically a graded layer is composed of for example 15 layers each layer with an increment of 2 ge if one also imagines a typical 5 grading rate of 10 ge u03bcm each of the 15 layers is 2000 u00e5 thick thus each thread is creating about 5 cm 15 0 33 cm of misfit length in each interface v by m ue89e u025b eff m ue89e uf74d u kt 4 estimates the dislocation velocity the minimum time u03b4t to ensure close to maximum relaxation is u03b4 ue89e ue89e t t v u2248 0 1 ue89e ue89e seconds 5 where it is assumed that annealing occurs at 1100 c thus the annealing time required at the elevated temperature need not be longer than a matter.