Catastrophic Transformation of Electron Stress and Electron Stiffness Parameter on Metal and Semiconductor

In this study, we calculated the quantum stress of electrons, called electron stress (ES), in a metal and a semiconductor under uniaxial tensile and compressive deformation (−50% to 50%) by using the pseudopotential method. Since the positions of atoms are fixed with external forces, the ES of a stationary electron shows the internal stress among atoms. From the derivative of ES with strain, we defined a “quantum stiffness parameter (ESP)”. We calculated ES and ESP in Al, K and Si during deformation. From the results of the calculation, we consider the following points: (i) Change of ES and ESP during deformation, (ii) ES and ESP demonstrate the difference between a metal and a semiconductor. During uniaxial tensile deformation, alter showing a gradual decrease, ESP shows a sudden divergence from positive to negative values at a certain critical strain. Under compression, a merely gradual increase of ESP was observed. Strain at the critical transformation of ESP, termed “critical strain (ε cr)”, shows a material dependence; 20% in Al, 30% in K, but only 2.5% in Si. The result of a low ε cr in Si and high ε cr values in metals corresponds to the general knowledge on mechanical properties of materials; metals are more ductile than semiconductors. The critical transitions of ES and ESP in solids could be explained from the electric properties in solids. These parameters might provide a key to understand ideal fractural properties in solid.