## Solar energy conversion

### Physical Background

A semiconductor diode with PN junction (photovoltaic cell, resp. PV cell) is a well-known device. Its volt-ampere characteristics in the dark is

*I*is current through the diode,

*I*

_{0}is the reverse diode current,

*e*

*is the elementary charge*

*, U*is the voltage,

*k*is the Boltzmann constant,

*T*is the temperature and

*a*is the coefficient of diode ideality, e is the base of the natural logarithm e = 2,71 (Fig. 1), [1].

**Figure 1 Dark**

*I-U*characteristic of the semiconductor diode with PN junction
The diode changes in the light into a source of electromotive voltage (and a corresponding source of current) *ε*_{photo }~ *I*_{photo}, which is generated as a result of the radiation, so the volt-ampere (*I-U*) characteristics changes its form into

*I-U*characteristics under illumination for three light intensities

*L*are in Figure 2. Conversion of radiant energy into the electric energy is a complicated physical phenomenon. Efficiency of the conversion of radiant energy into the electric energy or the ratio of electric power

*P*

_{el}=

*I*

_{m}

*U*

_{m}from the cell (

*I*

_{m}and

*U*

_{m}are the current and the voltage of the photovoltaic cell for a maximum power into the external load) and the

*P*

_{rad}( the power of the solar radiation) is defined as

Figure 2 Example of

*I*-

*U*characteristics of real photovoltaic cell in the light - 0.4 L, 0.7 L and 1.0 L.

*I*

_{sc}is a short - circuit current in the cell,

*U*

_{oc }is open circuit voltage,

*U*

_{m}and

*I*

_{m}is current and voltage corresponding to maximum electric power of the photovoltaic cell

*P*

_{m}

Conversion efficiency may be expressed by means of partial efficiencies

*η*

_{r}=

*P*

_{abs}/

*P*

_{rad}= 0,70 is a ratio of the power of reflected radiation to the power of falling down radiation (on average, the reflectance of silicon is

*R*= 0,30 [1]),

*η*

_{e}= 1-

*T*/

*T*

_{s}is the efficiency of the Carnot heat cycle, where

*T*= 300 K and

*T*

_{s}= 6000 K are the ambient temperature and the Sun temperature ,

*η*

_{e}= 1-

*T*/

*T*

_{s}= 0.95;

*η*

_{p}= 0,42 [2] is a contribution to efficiency (Fig. 3) affected by non-adjustment of silicon to the spectrum of solar radiation (as can be seen from the following picture, which clearly indicates that the optimum material for the Sun conversion is CdTe semiconductor, or amorphous silicon a-Si). And finally

*η*

_{el}, which is a contribution to efficiency given by cumulative electronic parameters of the photovoltaic cell, accessible for the measurements

*I*

_{sc}is a short-circuit current through the cell which may be influenced mainly by optimisation of transport properties, flexibility, cell geometry and the width of an active layer,

*U*

_{oc}is open circuit voltage which my be influenced by the choice of materials and

*FF*is the so called the filling factor of the photovoltaic cell given by the quality of contacts and material morphology and also dependent on the resistance of an active semiconductive layer. Efficiencies of contemporary photovoltaic cells range from 1-30 %.

Figure 3 Dependence of the theoretical efficiency of the photovoltaic cells on the bandgap ΔW of the semiconductor, c-Si-crystalline silicon, a-Si amorphous silicon.

Likewise significant is a relation between the short-circuit current in the cell *I*_{sc} and open circuit voltage *U*_{oc}

The optimum load resistance

#### Literature

- R. Bonnefille and J. Robert, Principes generaux des convertisseurs directs d energie, Dunod, Paris, 1971.
- J. R. Chelikowsky and M. L Cohen.: Phys. Rev. B14, 2 556-582 (1976).

- D. Halliday - R. Resnick – J. Walker: Fyzika, Vysoké učení technické v Brnĕ – Nakladatelství VUTIUM, 2000, ISBN 80-214-1868-0

Author of study text: Prof. Dr. František Schauer, Univerzita Tomáše Bati ve Zlíně