Improved model for solar cells with up-conversion of low-energy photons

Abstract

In this paper we analyze the system proposed by Trupke T, Green MA, Würfel P. [Improving solar cell efficiencies by up-conversion of sub-band-gap light. J Appl Phys 2002; 92: 4117–22] to increase solar cells efficiency. The system consists in adding to the cell a so-called up-converter, which is a device able to convert the low-energy (sub-band gap) incident solar photons into photons of higher energy. The main novelty of the present model consists in taking into account appropriately the refractive index of solar cell and converter materials. Two configurations are studied: cell and rear converter (C–RC) and front converter and cell (FC–C), respectively. The main conclusions of this work are as follows: (1) The maximum solar energy conversion efficiency increases in case of the C–RC system as compared to the efficiency of a solar cell operating alone, especially at higher values of the concentration ratio; (2) the solar energy conversion efficiency of the C–RC system increases by increasing both the cell and the up-converter refractive indices; (3) the energy conversion efficiency does not increase by adding a front up-converter to the cell, whatever the value of the concentration ratio is.

Introduction

Techniques based on photon recycling [1], [2] and impact-ionization [3], [4], [5] have been proposed in the last 20 years to increase the efficiency of solar cells. More recently, two other processes were investigated. They were called ‘down-conversion’ and ‘down-shifting’, respectively, in Ref. [6]. In the first process, which is sometimes referred to as ‘quantum-cutting via down-conversion’ [7], [8], [9], [10], [11], [12], more than one low-energy photons are produced from absorption of one high-energy photon. Consequently, the number of hot charge carriers generated by the high-energy photons decreases and the available energy lost by thermalization of carriers is diminished. In the second process, a ‘down-shifting’ layer is used to transform any high-energy photon for which the cell quantum efficiency (QE) is low to a lower energy photon for which the cell QE is high, thereby increasing the short-circuit current and the solar cell efficiency. This second process has been most discussed in the literature [13], [14], [15], [16], [17]. A combination of down-shifting and down-conversion processes was studied in Ref. [18]. A more involved model for the down-conversion technique was proposed in Ref. [19] and used in Ref. [20].

An interesting technique has been proposed in Trupke et al. [21] to convert the incident low-energy (sub-band gap) solar photons into photons of energy higher than solar cell band gap. In this way the number of high-energy photons absorbed in the cell increases. Trupke et al. [21] have taken account that the radiation fluxes coming from a medium depends on the refractive index of that medium. However, the quoted authors did not include in their analysis all the effects that normally a different from unity refractive index has. Mainly, the fact that the radiation flux is changed when passing through interfaces of different refractive indexes was not considered. In this paper we propose a more involved model for the up-conversion technique, which takes into account the effects of the radiation transfer through interfaces. Also, Trupke et al. [21] considered only cells and up-converters of equal refractive index. Our analysis refers to cells and up-converters of different refractive indices. Finally, only the configuration solar cell- (rear) up-converter has bee considered in Ref. [21]. Here the configuration (front) up-converter - solar cell is analyzed, too.

We tried to keep the model as close as possible to the original model proposed in Ref. [21]. Therefore, it is free from the additional possible improvements (consideration of non-radiative recombination processes, anti-reflection layers, light trapping structures, etc). The main question we want answer is the following: adding an up-converter to the solar cell really improves the solar energy conversion efficiency?