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

equation 1
where I is current through the diode, I0 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
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) εphoto ~ Iphoto, which is generated as a result of the radiation, so the volt-ampere (I-U) characteristics changes its form into

equation 2
and the corresponding 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 Pel = Im Um from the cell (Im and Um are the current and the voltage of the photovoltaic cell for a maximum power into the external load) and the Prad ( the power of the solar radiation) is defined as
equation 3
Figure 2
Figure 2 Example of I-U characteristics of real photovoltaic cell in the light - 0.4 L, 0.7 L and 1.0 L. Isc is a short - circuit current in the cell, Uoc is open circuit voltage, Um and Im is current and voltage corresponding to maximum electric power of the photovoltaic cell Pm

Conversion efficiency may be expressed by means of partial efficiencies

equation 4
where ηr = Pabs/Prad = 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]), ηe = 1-T/Ts is the efficiency of the Carnot heat cycle, where T = 300 K and Ts = 6000 K are the ambient temperature and the Sun temperature , ηe = 1- T/Ts = 0.95; ηp = 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 ηel, which is a contribution to efficiency given by cumulative electronic parameters of the photovoltaic cell, accessible for the measurements
equation 5
where Isc 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, Uoc 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
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 Isc and open circuit voltage Uoc

equation 6

The optimum load resistance

equation 7


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

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