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3.4 The p-n junction

N-type semiconductors are characterized by electron conduction, while p-type semiconductors conduct mostly through holes.
In conductors, electrons are free charge carriers forming an "electron gas" (the Drudy-Lorentz theory) [1]. The consequence of the possibility of free movement of electrons is high conductivity in metals. In semiconductors, on the other hand, valence electrons are bonded to atoms and only some of them, after being pulled out of valence orbitals, take part in current flow.
The introduction of dopants into semiconductors generates an increase in the concentration of majority charges. For donor dopants these are electrons, and for acceptor dopants these are holes.
The transport of electrons from the valence level to the conduction band is accomplished by absorption of electromagnetic radiation energy or thermal energy. The absorbed energy should be greater than the energy gap \( E_{g} \). Thanks to their properties, semiconductors have been used in many technology domains. The quantities influencing the electro-optical properties of semiconductors are: mobility of charge carriers, expressing the relationship between the charge drift velocity and the external electric field, quantum properties such as the lifetime of electrons in individual states, and the absorption coefficient, which depends on the wavelength. These properties determine the possible use of semiconductor materials for the production of solar cells.
Connecting n-type and p-type conductors creates at their boundary a so-called p-n type junction ( Fig. 1 ). The formation of the junction results in the flow of electrons from the n-type region to the p-type region and the formation of holes in the n-type region. The separation of electrons (-) and holes (+) leads to an electric field that produces a potential barrier.

Semiconductors p and n before bonding with no charge (a) and (b) after the bonding of semiconductors p and n, a depleted region w is formed, an electric field appears, (c) symbol of a semiconductor diode. Own elaboration.
Figure 1: Semiconductors p and n before bonding with no charge (a) and (b) after the bonding of semiconductors p and n, a depleted region w is formed, an electric field appears, (c) symbol of a semiconductor diode. Own elaboration.


When p-type and n-type semiconductors are combined, the Fermi levels are aligned, as visualized in Fig. 2. This causes a curvature of the valence and conduction levels in the region (width of the p-n junction). A layer is formed at the junction where charges exist that cause the disruption of the levels. This is a layer that is depleted of positive charges on one side and negative charges on the other.

Energy levels at the junction of p- and n-type semiconductors. {OPENAGHMATHJAX()}E_{f}{OPENAGHMATHJAX} - Fermi energy, w - width of the p-n junction region, {OPENAGHMATHJAX()}E_{g}{OPENAGHMATHJAX} - energy gap in a semiconductor, {OPENAGHMATHJAX()}E_{c}{OPENAGHMATHJAX} - energy level of conduction band, {OPENAGHMATHJAX()}E_{v}{OPENAGHMATHJAX} - energy level of valence band. Own elaboration.
Figure 2: Energy levels at the junction of p- and n-type semiconductors. \( E_{f} \) - Fermi energy, w - width of the p-n junction region, \( E_{g} \) - energy gap in a semiconductor, \( E_{c} \) - energy level of conduction band, \( E_{v} \) - energy level of valence band. Own elaboration.


Such an array of semiconductors is called a semiconductor diode.

Connecting a p-type semiconductor to a positive potential and an n-type semiconductor to a negative potential - that is, applying an external electric field - causes the potential barrier to decrease and the width of the p-n junction region to decrease. There is a flow of electrons from the p area to the electrode and an injection of electrons from the other electrode to the n area of the semiconductor, current flows through the system ( Fig. 3 on the positive side of the voltage). Reverse polarization increases the height of the potential barrier and the width of the depleted region, and no current flows through such a circuit ( Fig. 3 on the negative voltage side). The junction of a semiconductor p and n is called a diode.

Schematic current-voltage characteristics for a p-n type semiconductor diode. Own elaboration.
Figure 3: Schematic current-voltage characteristics for a p-n type semiconductor diode. Own elaboration.


The properties of semiconductor diodes are used in a number of different ways. Depending on their structure and purpose, they include rectifier diodes, capacitive diodes, light emitting diodes, laser diodes, pulse diodes, tunnel diodes, Zener diodes, and photovoltaic diodes. A diode used to convert solar energy into electricity is called a photovoltaic cell shown in Fig. 4. Absorption of incident photons on a photovoltaic diode results in the transfer of an electron from the valence band to the conduction band and the formation of a hole-electron pair. This pair can move in a semiconductor. The binding energy of the hole-electron pair is at an energy level of 16 meV (the thermal energy at room temperature is 25 meV). The hole-electron pair called an exciton decays into a free electron and a free hole [2]. Free electrons are attracted by the positive space charge at the p-n junction. The holes are transferred to the p-type region. The separation of positive and negative charges produces a potential difference.

Photovoltaic cell (photovoltaic diode) and its symbol. Own elaboration.
Figure 4: Photovoltaic cell (photovoltaic diode) and its symbol. Own elaboration.


A cross section through the structure of a simple monocrystalline photovoltaic cell is shown in Fig. 5, [3]. The following elements are present:

  • the front electrode - on the side of the incident sunlight,
  • n-type layer – up to 2 μm thick,
  • n-p junction layer,
  • p-type layer – 100-300 μm thick layer,
  • back electrode (from the side opposite to incident sunlight).

A photovoltaic cell is a diode in which hole-electron pairs are additionally produced under the influence of electromagnetic radiation. The cell structure - as shown in Fig. 5 - is used for all inorganic materials that photovoltaic cells are made of.

Structure of a monocrystalline solar cell. Own elaboration.
Figure 5: Structure of a monocrystalline solar cell. Own elaboration.


The case is different for organic compounds. For organic semiconductors, single molecules are considered. Each molecule is characterized by energy levels. In the ground state, all levels are occupied up to the Highest Occupied Molecular Orbital called HOMO ( Fig. 6a). Above these there are unoccupied levels. The Lowest Unoccupied Molecular Orbital is called LUMO. The difference between the positions of the HOMO and LUMO levels is treated in organic materials as an energy gap \( E_{g} \).
These levels in organic semiconductors are treated as equivalents of the valence and conduction bands in inorganic semiconductors. The energy structure of the molecules is shown in ( Fig. 6a). These apply only to the one molecule.
An incident radiation quantum, when absorbed, will transfer an electron from the HOMO level to the LUMO level in the molecule. The hole-electron pair thus formed (called an exciton) can move through the material. In organic compounds, the binding energy of the exciton is at the level of 0.4 eV. To break the resulting exciton in organic materials, energies much higher than in inorganic semiconductors are required.

The arrangement of two molecules with different HOMO-LUMO levels results in a potential difference ( Fig. 6b). The exciton, upon encountering such an arrangement, can be separated into charges. The resulting positive and negative charges in this system are in the same region, which unfortunately allows them to recombine. To force a proper flow of charges, electrodes with different exit works ( \( W_{w} \)) are used. The work of exit is the least amount of energy required for an electron to leave a material and become a free electron. A metal electrode with a smaller exit work accumulates electrons, while an electrode with a larger one accumulates holes.

Thus, for photovoltaic cells made of organic semiconductors, contact electrodes play an important role.

(a) Energy levels in an organic molecule, (b) Energy levels of an organic photovoltaic cell. Own elaboration.
Figure 6: (a) Energy levels in an organic molecule, (b) Energy levels of an organic photovoltaic cell. Own elaboration.

Bibliography

1. N. W. Ashcroft, N. D. Mermin: Fizyka ciała stałego, PWN, Warszawa 1986.
2. M. A. Green: Silicon Solar Cells : Advanced Principles & Practice, Centre for Photovoltaic Devices and Systems – University of New South Wales, Sydney 1995.
3. M. S. Tyagi: Introduction to semiconductor materials and devices, Wiley, New York 1991.

Ostatnio zmieniona Wtorek 04 z Styczeń, 2022 14:00:13 UTC Autor: Konstanty Marszałek, Katarzyna Dyndał, Gabriela Lewińska, Jerzy Sanetra
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