Abstract
The nature of the motion of charge carriers is reflected in the temperature dependence of their mobility. Photo-injected carriers in aromatic hydrocarbon crystals had shown puzzling behavior particularly in naphthalene in which the mobility drops with an increase in temperature from 30 to 100 K and is then unaffected by it as temperature varies further from 100 to 300 K. Many theories had been developed to explain the phenomenon. The chapter showed how they all fail when put to quantitative test. These qualitatively (apparently) successful explanations included standard acoustic phonon scattering formalisms, SLE considerations, and polaron considerations as well. It was shown how the GME theory with its specific calculational scheme applied to a system of polaronic transfer finally succeeded for the entire temperature interval and in all crystallographic considerations. Further calculations, some of them about the saturation of mobility with increasing field, and others designed to address materials with carrier bands broader than in narrow-band polaronic materials were developed. The latter showed how a mobility dependence could arise with the appearance of a band-hopping transition for intermediate width bands.
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Notes
- 1.
The last two of the publications mentioned provided visually impressive quantitative fits of the theory to the data as well.
- 2.
Throughout my scientific life I have wondered what precisely “essential” means in this context. When do I know I have captured the essence of a problem through my theory? Did Einstein capture the essence in his theory of specific heats of insulators based on dispersionless oscillators? Does Debye’s innovation in this subject address an essential ingredient or is it a “mere matter of detail”? Is knowing whether one’s theory has captured the essence of an experiment an inner phenomenon only? Are there no criteria more objective than for knowing if one has fallen in love?
- 3.
In this chapter we show all occurrences of ħ explicitly to avoid any confusion because of the plentiful discussion of experimental data here.
- 4.
David Dunlap who collaborated on this fitting did not work further on crystal mobilities. He went on to produce, in collaboration with Paul Parris, a remarkable theory of the field-dependence of mobilities in the presence of dipolar disorder that will be mentioned passingly in Chap. 13 (Dunlap et al. 1996, 1999; Novikov et al. 1998; Kenkre et al. 1998a; Parris et al. 2001b). It has not been described in this book because it does not fit in with the flow of the book’s topics. However, I heartily recommend to the interested reader that fine work by Dunlap and Parris on the description of carrier transport in statically disordered systems.
- 5.
They went on to remark (Swenberg and Pope 1998) that “This surprisingly close agreement between the two approaches strengthens the validity of each...”.
- 6.
The late Larry Schein said to me when I asked him to push the measurements to that region, “I would if I could but the *&%*%&crystal melts at that point.”
- 7.
I find this topic powerful but personally rather mystifying and beset with logic that, to my uneducated eye, appears a tad confusing.
- 8.
Cautionary conclusions of this kind were also drawn by Conwell and Basko (2003) on independent grounds.
- 9.
This B to B 2 transition as temperature increases is reminiscent of the V to V 2 behavior we discussed in the Perrin-Förster problem of excitation transfer in Chap. 3 but arises here from a completely different source!
- 10.
We have kept to the definition of B here used in Kenkre (2002) rather than in Kenkre et al. (1989) although there is unfortunately a discrepancy of a factor of 4 in the two. B is simply the assumed matrix element V in the tightbinding model in the former but the actual bandwidth that results from it in the latter. Quantitative precision is not being sought here and I hope my pointing this out will help rather than harm the explanations.
- 11.
It was unfortunately not pursued further because of the data falsification situation in the field alluded to earlier. I believe that serious theoretical analysis should return with renewed intensity now that the field appears to have bounced back again under the leadership of inspired scientists such as Biscarini, Dodabalapur, and their collaborators. See, e.g., Cramer et al. (2009), Shehu et al. (2010), Wang and Dodabalapur (2018), Wang et al. (2019), and Wang and Dodabalapur (2020).
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Kenkre, V.M.(. (2021). Application to Charges Moving in Crystals: Resolution of the Mobility Puzzle in Naphthalene and Related Results. In: Memory Functions, Projection Operators, and the Defect Technique. Lecture Notes in Physics, vol 982. Springer, Cham. https://doi.org/10.1007/978-3-030-68667-3_6
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