**Author details**

Bruno Ullrich1,2,3\* and Haowen Xi4

\*Address all correspondence to: bruno.ullrich@yahoo.com

1 Ullrich Photonics LLC, USA

2 Air Force Research Laboratory, Materials & Manufacturing Directorate, Wright Patterson, USA

3 Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos, México

4 Department of Physics and Astronomy, Bowling Green State University, USA

#### **References**

exp −(*t* / *τs*,*b*)*<sup>γ</sup>* = *∫*

introduced by Eq. (29).

i.e., the use of carrier lifetimes.

Bruno Ullrich1,2,3\* and Haowen Xi4

1 Ullrich Photonics LLC, USA

\*Address all correspondence to: bruno.ullrich@yahoo.com

**Author details**

USA

Morelos, México

**6. Conclusion**

0

time τ=uτs,b. The mean relaxation time is<*τ* > = *∫*

*p*(*u*, *γ*)exp −*t* / (*uτs*,*b*) *du*, where p(u,γ) is the weight function for the decay

exp −(*t* / *τs*,*b*)*<sup>γ</sup> dt* =

*τs*,*<sup>b</sup> γ Γ*( 1

*<sup>γ</sup>* ), where Γ is the

0

gamma function. For a simple exponential decay, <*τ* > = *τs*,*b*, and, therefore, the necessity of the Kohlrausch function to fit the temporal PC decay confirms the involvement of various time constants and is strong supportive evidence for the multi-time scale relaxation model

We have derived a spectral PC formula based on general principles for the standard set‐ up used in experiments. By explicitly including the spatial variation of the recombina‐ tion rate along the light propagation - i.e., at the surface and in the bulk region – we were able to demonstrate that PC spectra can be accurately described by the BU model. Equivalently good agreements between theory and experiment were found by using *α*(ℏ*ω*) values either experimentally determined or straightforwardly modeled by the density of states and the modified Urbach rule. Furthermore, we have shown that the detailed the‐ oretical model of the spatial variation of τ(z) is not critical for the generation of the PC near the band gap. However, the presented detailed theory correctly fit and explains the experimental observations. It reveals the firm physical key mechanism for understand‐ ing of the PC peak near the gap energy: The peak takes place due to the different recom‐ bination rates of the excited carries near the surface and bulk. We also showed that the τs/τb ratio found by temporally resolved PC measurements reasonably agrees with the results from the PC fits, accommodating the commonly used concept in optoelectronics,

2 Air Force Research Laboratory, Materials & Manufacturing Directorate, Wright Patterson,

3 Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca,

*∞*

*∞*

204 Optoelectronics - Advanced Materials and Devices


[14] Ullrich, B., & Bouchenaki, C. (1991). Bistable Optical Thin CdS Film Devices: All-opti‐ cal and Optoelectronic Features. *Jap. J. Appl. Phys.*, 30, L 1285-L1288.

**Chapter 9**

**Recent Progress in the Understanding and**

**Photovoltaic Cells**

http://dx.doi.org/10.5772/51115

**1. Introduction**

Gabriel Bernardo and David G. Bucknall

Additional information is available at the end of the chapter

**Manipulation of Morphology in Polymer: Fullerene**

The morphology of the active layer in OPV devices is widely recognized as being crucial for their photovoltaic performance [1-4]. The physics of the system dictates that excitons must dissociate efficiently at a donor-acceptor interface, and that sufficient pathways for charge transport to the electrodes are also required. Conjugated polymer crystals are considered to be the primary hole carrier and thus are essential for effective charge transport. With this in mind, the ideal morphology for an organic photovoltaic BHJ film was often considered until a few years ago to be a bicontinuous, interpenetrating network morphology composed of pure P3HT and pure PCBM phases, with both phases of order ∼20 nm in size [5, 6] and numer‐ ous cartoon depictions have helped to propagate this view, as the one shown in Figure 1.

In this idealized model, the two pure phases of donor and acceptor within the bulk hetero‐ junction are interdigitated in percolated highways with an average length scale of around 10-20 nm, equal to or less than the exciton diffusion length, to ensure exciton dissociation and high mobility charge carrier transport with reduced recombination. Furthermore, a pure donor phase at the hole collecting electrode and a pure acceptor phase at the electron collect‐ ing electrodes should exist in order to minimize the losses by recombination of opposite charges or acting as diffusion barriers for the opposite sign charge carriers at the respective electrodes. The presence of mixed phases in these BHJ were considered to be counterpro‐ ductive to device performance, since isolated molecules could act as traps for separated

Many efforts have used this ideal model to design studies that examine the effect of the chemical structure of conjugated polymer, composition, and processing methods on the abil‐

> © 2013 Bernardo and Bucknall; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Bernardo and Bucknall; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

charges and centers for charge recombination within the percolation pathways.

