The concept of the effective mass in crystals shows that the electron mass is affected by the crystal field and was experimentally verified. A useful expression for effective mass was obtained. Unfortunately this expression showed that the effective mass vanishes in the ab-sence of the external field. This is in conflict with observations which show that it reduces to the ordinary mass. To cure this defect a new model is developed assuming the existence of vacuum force as verified experimentally as shown by Casimir effect. Using Newton’s second law and the quantum expression of momentum, useful expressions were found. The same expression was found using generalized special relativity. Strikingly the three models reduced to the conventional one in the absence of vacuum, they also reduced to the ordinary electron mass in the absence of all forces.
References
[1]
Ibach, H. and Luth, H. (2009) Solid State Physics: An Introduction to Principles of Materials Science. Springer, Berlin. https://doi.org/10.1007/978-3-540-93804-0
[2]
Mehta, N. (2011) Applied Physics for Engineers. PHI Learning Private Limited, New Delhi.
[3]
Siddalingappa, B. (2010) Engineering Physics. Himalaya Publishing House, Mumbai.
[4]
Hook, J.R. and Hall, H.E. (1991) Solid State Physics (Manchester Physics Series). Wiley, Hoboken.
[5]
Wassif, R.K. (1998) Theory of Solids. Universities Publishing House, Cairo.
[6]
Kittle, C. (1976) Introduction to Solid State Physics. John Wiley and Sons, New York.
[7]
Derck, F.L. (1982) An Introduction to Tensor Calculus and Relativity. John Wiley and Sons, New York.
[8]
Ahang, Y.Z. (1998) Special Relativity and Its Experimental Foundations. World Scientific, Singapore.
[9]
Beser, A. (2002) Concept of Modern Physics. McGraw Hill, London.
[10]
Dirar, M., Hillo, M.H.M., Abd Elgani, R. and Bakheet, A.M.A. (2013) Neutrino Speed Can Exceed the Speed of Light within the Framework of the Generalized Special Relativity and Savckas Model. Natural Science, 5, 685-688. https://doi.org/10.4236/ns.2013.56084
[11]
Hillo, M.H.M., Abd Elgani, R., Abd Elhai, R., Abd Allah, M.D. and Elfaki, A.A.A. (2014) Deriving of Generalized Special Relativity (GSR) by Using Mirror Clock and Lorentz Transformations. Natural Science, 6, 1275-1281.
[12]
Hillo, M.H.M. (2011) Using the Generalized Special Relativity in Deriving the Equation of the Gravitational Redshift. Journal of Modern Physics, 2, 370-373.
[13]
Dirar Abdalla, M., et al. (2016) The Effect of Speed and Potential on Time, Mass and Energy on the Basis of Newton and Relativity Prediction. International Journal of Engineering Science and Management, 6, 63-79.
[14]
Lodari, M.M.M., Tosato, A.A.A., Sabbagh, D., Schubert, M.A., Capellini, G., Smmak, A., Veldhorst, M. and Scappucci, G. (2019) Light Effective Hole Mass in Undoped Ge/SiGe Quantum Wells. Physical Review B, 100, 041304(R). https://doi.org/10.1103/PhysRevB.100.041304
[15]
Khordad, R. (2011) Effect of Position Dependent Effective Mass on Linear and Non Linear Optical Properties of Cubic Quantum Dot. Physica B, 406, 3911-3916. https://doi.org/10.1016/j.physb.2011.07.022
[16]
Hatke, A.T., Zudo, M.A., Watson, J.D., Manfra, M.J., Peiffer, L.N. and West, K.W. (2013) Evidence of Effective Mass Reduction in GaAs/AlGaAs Quantum Wells. Physical Review B, 87, 161307(R). https://doi.org/10.1103/PhysRevB.87.161307
[17]
Hauteir, G., Miglio, A., Waroquiers, D., Rignanese, G.M. and Gonze, X. (2014) How Does Chemistry Influence Electron Effective Mass in Oxides? A High Throughput Computational Analysis. Chemistry of Materials, 26, 5447-5458. https://doi.org/10.1021/cm404079a
[18]
Hai, G.Q., Peeler, F.M. and Devreese, J.T. (1990) Polaron Energy and Effective Mass in a Quantum Wells. Physical Review B: Condensed Matter, 42, 11063-11072. https://doi.org/10.1103/PhysRevB.42.11063
