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Thermal stability factor Δ of the recording layer was studied in perpendicular anisotropy CoFeB/MgO magnetic tunnel junctions (p-MTJs) with various CoFeB recording layer thicknesses and junction sizes. In all series of p-MTJs with different thicknesses, Δ is virtually independent of the junction sizes of 48-81 nm in diameter. The values of Δ increase linearly as the recording layer thickness increases. The slope of the linear fit is explained well by a model based on nucleation-type magnetization reversal.