Effect of external applied electric field on the silicon solar cell’s thermodynamic efficiency
This paper presents a possible solution to improve the efficiency of photovoltaic solar cells. An external electric field is applied on a silicon photovoltaic solar cell, inducing band-trap ionization of charge carriers. Output current is then monitored and the thermodynamic efficiency is calculated. Results show on the one hand a significant increase in efficiency for a certain margin of applied electric field, and on the another hand the instabilities of efficiency. A simple approach is then suggested for the implementation of these results. An efficiency of 67% has been reached for an applied electric of 1586 V/Cm.
KeywordsImprove efficiency External applied electric field Band-trap ionization of charge carriers Silicon solar cell
Planck’s constant (6.626 × 10−34 Js)
Photons propagation speed (3 × 108 m/s)
Charge of electron (1.6 × 10−19 C)
Boltzmann’s constant: (1.38 × 10−23 J/K)
Cell’s temperature (K)
Sun’s temperature (6000 °K)
Gap energy (for silicon E G = 1.12 eV)
- τn, τp
Recombination life time of electrons and holes, respectively (s)
- Ln, Lp
Electron diffusion length and hole diffusion length, respectively
Area of surface subject to the radiation (Cm2)
Intrinsic concentration of electrons and holes (n i = 1.45 × 1010 Cm−3 for silicon)
Number of quanta
Probability that incident photon will produce a hole-electron pair
External applied electric field (V/Cm)
Developing new concepts to improve the efficiency of photovoltaic solar cells is a well-known challenge for the scientific community. In 1961 Shockley and Queisser  brought out the theoretical limit of a photovoltaic solar cell. The results of their study are worldwide recognized as theoretical limit of efficiency for a single pn-junction solar cell. After them, many studies have been carried out to explore the possibilities of exceeding this limit. Different technologies and methods were used for that purpose [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Among these approaches, we could cite tandem cells, concentrator cell, carrier multiplication, down conversion, hot carriers, etc.
In 1997, by considering the impact ionization phenomenon to generate hot electrons, Würfel  found a maximum efficiency of 85% for a vanishing band gap of the solar cell. In 1993, Landsberg et al.  reported an efficiency of 60.3% at E G = 0.8 eV for a solar cell submitted to band–band impact ionization effect. By considering the impact ionization effects on the efficiency of intermediate band solar cells, Gorji  has obtained a thermodynamic efficiency of 81.2%, which was higher than the maximum efficiency of 63.2% for an intermediate band without impact ionization mechanism. All these results show that the impact ionization phenomenon is very promising for the improvement of solar cell efficiency.
A single pn-junction of the solar cell is considered in this work. In Ref.  it has been shown that outside an electron diffusion length L n to the right or a hole diffusion length L p to the left of the pn-junction, the charge current through a pn-junction is a pure electron current in the n-region and a pure hole current in the p-region. This charge current is then given by integrating over the contributions to the electron current (alternatively, the contributions to the hole current). Knowing the number of free electrons in n-region (or free holes in p-region) could be sufficient to evaluate the charge current through a pn-junction and thus the open circuit voltage. In this paper, the number of free electrons in n-region of the pn-junction is evaluated by solving the reaction diffusion equation. This equation is solved with the factorization method. The total hole-electron generation rate due to the solar radiation is evaluated by following the Shockley–Queisser approach .
Thermodynamic efficiency calculation
Resolution of the reaction–diffusion equation
Charge current density through the pn-junction
Typical materials parameters corresponding to α-si near room temperature for the g–r process of band-trap impact ionization 
3 × 10−5exp (−2 × 104/E o) Cm3 S−1
10−10 Cm3 S−1
N D *
2 × 1015 Cm−3
3 × 1015 Cm−3
μ n /μ p
In this paper, the effect of an external applied electric field on the thermodynamic efficiency of a silicon photovoltaic solar cell has been studied. Theoretically, it has been shown that an auxiliary applied electric field could be a very promising solution to reach a high efficiency of the solar cells. However, it is not always the stronger electric field which is necessary to induce the higher efficiency. There are efficiency instabilities for strong applied electric field to solar cells.
The authors thank Taku Agbor Junior for his useful comments.
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