What is it about?
We have derived the generalized quantum classical relationship of the diffusion-mobility ratio for relativistic and non-relativistic quantum systems of any dimensionality in a wide range of temperatures. Interestingly, our derived formulation is easy to tune, as all the quantities which quantum systems generally have, like various types of electronic interactions, coupled strength of electric and thermal energy quantities like charge-heat current, environmental effects, etc., are tunable by one parameter, i.e., the chemical potential. Our exact solution of the D/μ ratio for 2D devices explains the particle-hole symmetry, also its absence in other classes of materials. From our model, it is observed that the ideality factor (g) is nonlinear with the chemical potential (η) and temperature (T). For highly degenerate limit (η kBT), the factor g linearly depends on a single parameter of the chemical potential.
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Why is it important?
Several experimental results clearly indicate that the deviation of classical Einstein diffusion-mobility relation is due to nonlinear transport phenomena. The Einstein relation does not work for high charge density materials and also not valid for nonequilibrium cases. In this scenario, we are developing a generalized model to overcome these failures of Einstein relation. Our unified expression provides completely new insight on electrical transport for all dimensional (1D, 2D and 3D) ordered and disordered semiconductors in both relativistic (Dirac particles) and nonrelativistic limits (Schrödinger particles) with wide range of temperatures. Importantly, here the developed formalism well settles the earlier experimental findings in electronic transport; also reproduce the classical Einstein relation in nondegenerate cases. This paradigm predicts both the electron-hole symmetrical transport in highly degenerated two-dimensional semiconductors, which assures the time-reversal invariance property. It shows linear dispersion, and also dictates the broken symmetry due to nonlinear dispersion for all other cases.
Perspectives
While the Einstein relation (diffusionmobility ratio, D/μ) works only for classical systems under equilibrium cases, our generalized paradigm is quite general and works for systems ranging from classical to quantum systems in any dimensions. The proposed D/μ formalism relies on the chemical potential which provides the cooperative nature between electronic and temperature counterparts on fundamental transport. Our generalized paradigm is applicable to both degenerate and non-degenerate cases, and explains the transition from linear to nonlinear relationship between the charge density and chemical potential. The symmetrical nature of electron-hole transport in highly degenerate two-dimensional quantum materials gives linear dispersion, preserving the time-reversal invariance property, while the symmetry is found to be broken in the nonlinear regime. Notably, for certain combinations of temperature and chemical potential, we reproduce the original Einstein equation from our paradigm. Noteworthy, this study is very important to get a clear understanding of carrier dynamics in a different range of systems of the device interest and related process, from molecules to materials, at different physical domain
Dr. K. NAVAMANI
KPR Institute of Engineering and Technology
Read the Original
This page is a summary of: Revisiting Einstein's diffusion-mobility relation for universal quantum materials: A generalized paradigm, EPL (Europhysics Letters), May 2021, Institute of Physics Publishing,
DOI: 10.1209/0295-5075/134/47001.
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