## Theoretical studies of the intermidiate band solar cell

##### Abstract

This thesis presents theoretical work on the intermediate band solar cell (IBCS). It is divided into two main parts: The first part is an introduction to basic solar cell physics and a presentation of central parts of the physics of the IBSC. The intention is not to give a complete review of these topics, but to provide readers unfamiliar to solar cell physics the basic knowledge needed to understand the scientific papers that constitutes part two of the thesis.
The intermediate band solar cell is a photovoltaic concept with a theoretical efficiency limit of 63:2%. This is over 50% higher than the 40:7% limit for conventional photovoltaic cells. The feature that distinguishes the IBSC from other photovoltaic concepts is that it allows electrons to be excited from low energy electron states to high energy states in a two-step process via an intermediate band (IB). This allows a more effective harvest of the energy of the photons impinging on the cell, than in ordinary solar cells where only transitions directly from the low energy states to the high energy states are allowed.
Theoretical efficiencies can be calculated for various combinations of band gaps and light concentrations. For conventional solar cells it has been shown that the theoretical efficiency of cells with band gaps lower than the optimal can be increased when spectral selectivity is applied. Spectral selectivity means that the cell absorptivity of certain photon energies above the band gap is set to zero. In this work it is shown that the theoretical efficiency increases for several band gap combinations and light concentrations for the IBSC, when spectral selectivity is applied. For some spectra, the efficiency of a spectrally selective IBSC can surpass the efficiency limit found without spectral selectivity. To give an example, the efficiency limit for an IBSC under the 1 sun 6000K black body spectrum increases from 46:8% to 48:5% when spectral selectivity is applied. No change is found for the fundamental 63:2% limit for fully concentrated black body radiation.
For the two-step generation process to work properly, the intermediate band has to be partially filled with electrons to allow transitions both to and from the IB. It has previously been assumed that one either has to use materials that have a partially filled IB in thermal equilibrium or use doping to assure that the IB is partially filled. This work investigates the possibility of partially filling the IB with electrons that are photogenerated from the valence band, so called photofilling. In a model based on detailed balance principles it is found that a practically usable photofilling can be obtained when the density of states in the IB has values typical for IBs formed by quantum dot superlattices, particularly when the light is concentrated. It is also shown how the filling varies with the voltage of the solar cell and the position of the IB in the main band gap.
A drift-diffusion model for the IBSC which allows for photofilling, that is, the IB-filling is treated as a variable, is also developed. By use of this model it is shown how the mutual sizes of the absorption cross-sections for transitions over the sub-band gaps can give rise to spatial variations in the filling. These spatial variations will result in electric fields that can drive the carriers in the conduction band and valence band in opposite directions. If this effect is present in real cells this observation has the practical consequence that the cell should be designed in a way which assures that the electric field push the electrons in the right direction.
The drift-diffusion model is also used to determine whether an unfilled or a half-filled IB in thermal equilibrium results in the highest efficiency. This is found to depend on the mutual sizes of the absorption cross sections for transitions via the IB. The optimal filling is examined for a particular example.
To investigate the optimal filling further, models based on detailed balance principles are applied to see how the optimal filling is affected by various parameters. The optimal filling is found to vary with the band gaps, the overlap between the absorption coefficients, the light concentration and the mutual sizes of the absorption cross-sections for transitions over the subband gaps. The negative effect of a non-optimal filling is shown to depend on the absorptivity of the cell, the overlap between the absorption coefficients as well as the density of states in the IB. Two main effects are identified as determinative for the optimal filling. The first is the pursuit for a maximized net generation rate via the IB. The second effect is the irreversible losses due to overlapping absorption coefficients. These should be as small as possible.
An ideality that is assumed in most theoretical work on the IBSC is that the IB has no energetical width. Previously a fundamental limit has been found by Levy and Honsberg for the minimal effect of this width on the cell efficiency. In this thesis an attempt is made to investigate how the thermalized nature of the IB-electrons affects the efficiency of IBSCs with a wide IB. To obtain numerical results, two sets of idealized absorption coefficients based on different assumptions are derived. For IBs with nonoverlapping absorption coe_cients, the efficiency deviates only slightly from the fundamental limit when the IB-width is below 0:15 eV. When the width increases, so does the difference between the fundamental limit and the efficiency calculated with the thermalized nature of the IB-electrons taken into account. One of the sets of absorption coefficients increases more steeply with the photon energy than the other. It is found that the reduction in effciency is smaller for the absorption coefficients with the steeper increase.
Efficiencies are also calculated when the absorption coe_cients are overlapping in the energy range which is assumed to be affected by the IB-width. The difference in efficiency between the fundamental limit and the efficiencies found in this work can be reduced, as compared to in the non-overlapping case, when the IB-width approaches 1 eV. In some of the investigated cases, the decrease in efficiency due to an increase in the IB-width is still significantly higher than the efficiency limit for single band gap cells. In other cases, however, the efficiency shows a devastating drop when the width of the IB goes from 0 to 1 eV.
The models presented in the thesis are idealized and based on assumptions that might not be fulfilled in real devices. Before transferring the results to real devices one should first be assured that the assumptions that have been made in the modeling are valid. If not, analyzes based on more advanced models might be required before conclusions can be drawn.

##### Has parts

Strandberg, Rune. Initial theoretical study of solar cells with an inter-mediate band of non-zero width and a thermalized electron population. .Strandberg, Rune. Optimal filling of Intermediate Bands in Intermedi-ate Band Solar Cells. .