# QMU – July 2012

The second lecture was given by Dr Theo Kreouzis about photovoltaic cells. The intensity of direct sunlight is about 1000 Wm^-2 (which is an awful lot). This gives about 150Wm^-2 over a year in the UK. Solar power is now a viable option as photovoltaics are much cheaper now.

Students often get the photovoltaic effect mixed up with the photoelectric effect. In the photoelectric effect high energy photons (ultra violet light) can free electrons from the surface of certain metals. This can’t be used for power generation. In the photovoltaic effect visible light can excite electrons and holes) across the bandgap of the semiconductor to provide useful current. The term “band gap” refers to the energy difference between the top of the valence band and the bottom of the conduction band. The valence band describes electrons fixed to their atoms and the conduction band describes electrons free to move and form a current. Photovoltaic electrons don’t escape from the material. Energy level diagram for a single atom A simplified energy band diagram used to describe semiconductors. Shown are the valence and conduction band as indicated by the valence band edge, Ev, and the conduction band edge, Ec. The vacuum level, Evacuum, and the electron affinity, X, are also indicated on the figure. It identifies the almost-empty conduction band by a set of horizontal lines. The bottom line indicates the bottom edge of the conduction band and is labeled Ec. Similarly, the top of the valence band is indicated by a horizontal line labeled Ev. The energy band gap, Eg, is located between the two bands. The distance between the conduction band edge, Ec, and the energy of a free electron outside the crystal (called the vacuum level labeled Evacuum) is quantified by the electron affinity, c multiplied with the electronic charge q. The electron affinity of an atom or molecule is defined as the amount of energy released when an electron is added to a neutral atom or molecule to form a negative ion. X + e → X

The energy E = hf where f is the frequency of the electromagnetic wave and h is Planck’s constant. Electrons can only exist in discrete energy levels.

When solar radiation falls on a silicon n-p junction, photons with wavelength less than 1.13 µm generate electron-hole pairs. The electric field in the depletion layer drives the electrons to the n-type side and the holes to the p-type side. This separates most of the electrons and holes before they can recombine. A solar photovoltaic cell consists of a thick n-type crystal covered by a thin p-type layer exposed to the sunlight. An electrical load resistance R is connected across the junction. The electrons and holes produce a current, and the energy in the solar radiation is converted into electrical energy in the circuit. Photovoltaic solar cell circuit.

The diode is the simplest type of semiconductor device.

Forbidden Zone That energy range between the valence band and the conduction band. Electrons cannot remain within this range of energy; they must either gain or lose energy so as to attain either the conduction band or the valence band.

Fermi Level The highest energy level in the crystal that can remain populated by electrons at a temperature of Absolute Zero. Electrons with greater energy than this may be available for conduction; electrons with less energy are bound to the crystal structure.

Looking at the electrical characterisation of diodes is a practical carried out both at GCSE and A level. This is the simplest set up for the experiment although a variable power supply would be better than using a variable resistor

Apparatus and materials

• Semiconductor diode – e.g. IN 5401

• Protective resistor, at least 10 ohm

• Power supply, 0 to 12 V, DC (or, better, small smooth stabilized 5 V supply)

• Multimeters, 2, or 1 ammeter and 1 voltmeter of suitable ranges

• Rheostat as a variable resistor.

The rheostat in this case is used as a potential divider. This allows you to get a full range of current and pd readings.  When the voltage is applied this way round it tends to push the electrons and holes towards the junction. It also reduces the height of the energy barrier and reduces the width of the depletion zone. These effects make it easier for free electrons and holes with modest amounts of thermal (kinetic) energy to cross the junction. As a result, we get a sizeable current through the diode when we apply a forward bias voltage.

When the voltage is applied the other way round it tends to pull the free electrons and holes apart, and increases the height of the energy barrier between the two sides of the diode. As a result it is almost impossible for any electrons or holes to cross the depletion zone and the diode current produced is virtually zero. A few lucky electrons and holes may happen to pick up a lot of thermal (kinetic) energy. This gives them enough ‘go’ to cross the barrier; hence the reversed biased current is not zero, just very, very small.

The depletion layer is an insulating region within the doped semiconductor where the charge carriers have been forced away by an electric field. The Shockley equation. Current through a diode varies exponentially with the applied voltage. The shape of this exponential curve depends upon various factors which include a ‘fiddle factor’ called the saturation current.
At a finite temperature –eV >> kT (eV is energy in electron volts, k is the Boltzmann’s constant and T is the absolute temperature in kelvins).   When light shines on the photocell, the I-V curve shifts as the cell begins to generate power. The greater the light intensity the greater the amount of shift. Light generates electron-hole pairs on both sides of the junction, in the n-type emitter and in the p-type base. The generated electrons (from the base) and holes (from the emitter) then diffuse to the junction and are swept away by the electric field, thus producing electric current across the device. The electric currents of the electrons and holes reinforce each other since these particles carry opposite charges. The p-n junction therefore separates the carriers with opposite charge, and transforms the generation current between the bands into an electric current across the p-n junction. The short circuit current is the maximum current from the solar cell and occurs when the voltage is zero. The open circuit pd is the maximum voltage from a solar cell and occurs when the net current through the device is zero. The cell generates no power in short-circuit (when current Isc is produced) or open-circuit (when cell generates voltage Voc). The cell delivers maximum power Pmax when operating at a point on the characteristic where the product IV is at a maximum. The efficiency (n) of a solar cell is defined as the power Pmax supplied by the cell at the maximum power point under standard test conditions, divided by the power of the radiation incident upon it. Most frequent conditions are: irradiance 100 mW/cm2 , standard reference spectrum, and temperature 25 0 C. The use of this standard irradiance value is particularly convenient since the cell efficiency in percent is then numerically equal to the power output from the cell in mW/cm^2. When using photovoltaic cells there are things we need to consider. Is the sunlight going to hit the cell at the optimum angle? What are the power requirements of the household? The inverse square law tells us that if the distance from the light source doubles then the power developed drops by a factor of four. What type to we go for? Multicrystalline silicon, amorphous silicon or organic solar cells? The latter has the benefit of being flexible.

Photovoltaic cells can be bought quite cheaply now. Amorphous photovoltaic cells are about 10% efficient but they are inexpensive and the sunlight is free. Organics are 8% efficient but the maximum efficiency from certain photovoltaic cells is 40%. This will improve with time.

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