Significances: ||Modified Versions of Einstein and Boltzmann Relations for Mobility (via entropy-ruled method) - A Unified Approach for Band & Hopping Transport||
||Charge Disorder Variance Principle on Electron-Hole Symmetry-to-Asymmetry Transport Transition||
||Quantum-Classical Phase Changes via Chemical Potential Scaled Entropy (or DOS Proportion)||
Over the one decade of Navamani’s research works, some of the important findings are observed which are listed below:
Continuum Time-Delayed Hopping Model & Entropy-Ruled Method
The developed continuum time-delayed (i.e., restricted-charge transport) hopping model (K. Navamani, J. Phys. Commun., 2021, 5, 075012) is more precise model to explore the vibronic coupled charge transport (CT) in the extended dynamical molecular systems. This work mainly elucidates "dispersion weighted charge transfer delay" at each hopping step, which can be modified by electric field assisted site-energy difference and molecular vibrations. By this continuum time-delayed CT (or dispersion-corrected CT) model, one can easily switch over the dynamic to static disordered transport or vice-versa or intermediate transport in molecular semiconductors with the help of two descriptors, bias voltage (or electric field) and molecular vibrational frequency.
The proposed entropy-ruled charge transport method is the generalized method for both degenerate and nondegenerate semiconducting materials, which is useful to study the validity and limitations of original Einstein relation. Here, the traversing chemical potential along the consequential hopping sites decides whether the Einstein relation is valid or not. According to our Entropy-ruled Einstein relation, we have modified the Shockley diode equation for organic semiconducting devices and is referred as Navamani-Shockley diode equation.
Implication for Material Scientists/Device Physicists & Manufactures:
The main implication of this work for device performance is that the cooperative behavior between the molecular vibration and applied electric field (or bias voltage) is important factor to functionalize the appropriate properties (either CT or light emission) in any molecular devices; and thus these two descriptors (vibrational frequency and applied voltage) are indeed ideal for better device performance. This continuum model provides the microscopic level of energy disorder-charge transport property relationship for dynamical systems, which will be helpful to understand the effect of biasing, thermal fluctuation, dispersion effect and contact phenomena (including interfaces effect) on charge transport in molecular electronic devices.
Multiscale Modeling of Charge Transport
(on the basis of 3-set of analytical procedures)
The proposed multi-scale model (Navamani et al., J. Chem. Phys., 2019, 151, 224301) is useful to classify the given (chosen) molecular systems whether it follows Langevin or Shockley-Read-Hall (SRH) mechanism. The Langevin mechanism based materials are suitable for charge transport devices (OPVs) due to trap free transport, and the SRH mechanism based materials are more appropriate for light emitting devices (OLEDs) due to trap-assisted mechanism, which leads to recombination current.
Implications for device performance (from his model based analysis):
The obtained results from his model suggest that the possibility of dual mechanism in molecular electronic devices (e.g., OPVs or OLEDs):
(i) “Slow fluctuations (static disorder) with large amplitude of electric field assisted site energy gap” between the adjacent sites facilitates trap assisted recombination process (Shockley-Read-Hall Mechanism). For large site energy fluctuations, there is a significant loss in charge transfer rate at every hopping site leads to incoherent transport and vice versa.
(ii) “Fast fluctuations (dynamic disorder) with low amplitude of field-assisted site energy gap” facilitates trap-free Langevin recombination mechanism.
The first one occurs due to the diffusion limitation by dispersion initiated trap mechanism and the later one is due to trap-free (absolute) diffusion by non-dispersive (coherent) mechanism.
“Langevin transport is expected for small energy disordered dynamical systems, and Shockley-Read-Hall (SRH) charge recombination transport will be expected in the highly energy disordered systems.”
Diffusion-Mobility Relation for Quantum Materials
The proposed D/μ formalism relies on the chemical potential which provides the cooperative nature between electronic and temperature counterparts on fundamental transport. The symmetrical nature of electron-hole transport in highly degenerate twodimensional quantum materials gives linear dispersion, preserving the time-reversal invariance property, while the symmetry is found to be broken in the nonlinear regime. His generalized diffusion-mobility relation explains both the relativistic (Dirac particles) and non-relativistic regimes (Schrödinger particles) from low temperature to high temperature, and reproduces the classical Einstein relation in appropriate limit.
Other Significant Observations
The developed carrier drift energy-current density and momentum-energy redistribution approach helps to study the electric field coupled disorder (static & dynamic) effect on charge transport property in molecular solids. Theoretical results suggest the validity and limitation of Einstein diffusion equation at applied electric field conditions, which is verified by multi-scale modeling study (DFT+MD+KMC), (Navamani et al., RSC Adv., 2018, 8, 30021-30039). Also, we find the possible enhancement of recombination mechanism via 'electric field stretched dispersion and its consequence of charge trapping'.
The site energy gap fluctuation in the dynamically disordered molecular system controls the forth-back oscillation of charge carrier (i.e., electron/hole dynamics) which is responsible for unidirectional charge transport mechanism (Navamani et al., Phys. Chem. Chem. Phys., 2015, 17, 17729-17738). In this work, we have proposed forth-back oscillated diffusion coefficient to examine the charge transfer kinetics in such dynamical systems.
Effect of dynamic fluctuations on charge transport in π-stacked molecules (or conjugated organic molecules) follows the static non-Condon principle which facilitates the non-dispersive charge transfer kinetics (Navamani et al., Phys. Chem. Chem. Phys. 2013, 15, 17947-17961).
Also refer, Important formulas*
