Tag Archives: Solid State Physics

Photovoltaic Effect and Theory of Solar Cells

Just as plants receive energy from the sun and use it to produce glucose, a photovoltaic cell receive energy from the sun and generates an electrical current. The working principle is based on the PN junction, which will be revisited here.

Silicon can be subdivided into several discrete energy levels called “bands”. The major bands of concern are the valence and conduction bands. The bottom bands are fully occupied and don’t change.


For silicon, the bandgap energy is 1.1eV. For an intrinsic semiconductor, the Fermi level is directly between the conduction and valence band. This is because there is an equal number of holes in the valence band as electrons in the conduction band. This means the probability of occupation of energy levels in both bands are equal. The Fermi level rises in the case of an n-type semiconuctor (doped with Phosphorous) and declines towards the valence band in a p-type (doped with Boron).

The following illustrates an energy band diagram for a semiconductor with no bias across it. Photodiodes (light sensors) operate in this manner.


The Fermi energy is shown to be constant. On the far right hand side away from the depletion region, the PN junction appears to be only P-type (hence the low Fermi level with respect to the conduction band). Likewise, on the left the Fermi level is high with respect to the conduction band. The slope of the junction is proportional to the electric field. A strong electric field in the depletion region makes it harder for holes and electrons to move away from the region. When a forward bias is applied, the barrier decreases and current begins to flow (assuming the applied voltage is higher than the turn on voltage of 0.7V). Current flows whenever recombination occurs. This is because every time an electron recombines on the P side, an electron is pushed out of the N side and beings to flow in an external circuit. The device wants to stay in equilibrium and balance out. This is why solar cells (as opposed to photodiodes) are designed to operate in a forward bias mode.

The sunlight produces solar energy in the frequency bands of Ultraviolet, infrared and visible light. In order to harness this energy, silicon is employed (made from sand and carbon). Silicon wafers are employed in solar cells. The top layer of the silicon is a very thin layer doped with phosphorous (n-type). The bottom is doped with P-type (doped with Boron). This forms the familiar PN junction. The top layer has thin metal strips and the bottom is conductive as well (usually aluminum). Only frequencies around the visible light spectrum are absorbed into the middle region of the solar cell. The photon energy from the sun knocks electrons loose in the depletion region which causes a current to flow. The output power of a single solar cell is only a few watts. To increase power, solar cells are wired in series and parallel to increase the voltage and current. Because the output of the solar cells is DC, the output is run through an inverter, a high power oscillator that converts the DC current to an 240V AC current compatible with household appliances.


Crystal Structures

Crystal Structures

Crystalline structures are noted by their regular, predictable and periodic arrangement of atoms or molecules. The  arrangement of atoms and molecules for crystal structures is called a lattice. Crystalline materials include many metals, chemical salts and semiconductors.


Solid crystals are classified by the cohesive forces that hold the lattice together and the shape or arrangement of the atoms in the material. Different arrangements include a simple cubic crystal, a face-centered cubic structure and a body-centered cubic structure.


In metals, each atom contributes at least one loosely bound electron to build an electron gas of nearly free electrons that move throughout the lattice structure. When an electric field E is applied to a metal, a current flows in the direction of the field. The flow of charges is described in terms of a current density J, or current per unit cross-sectional area. The current density is proportional to the applied electric field by a factor of the electrical conductivity σ of the material.

J = σ*E

The electrons in the lattice material experience a force F = -e*E due to the field and become accelerated. The velocity of electrons in the lattice is known as the drift velocity.


Bonding and the formation of Semiconductors

In atomic structures, different types of molecules have a varying number of electrons in the outer atomic rings or shells (valence electrons). Ionic bonding is performed by electrons present in the outermost shell, easily forming a positive ion by releasing the outer electron (net positive charge) or enter the outermost shell of another atom to make it a negative ion (net negative charge). Metallic bonding uses a loosely bound electron in an outermost shell to contribute to the crystal as a whole, creating a metallic crystal.

periodic table

The method of bonding for Ge, C and Si can be quite different however, since they have four valence electrons in the outermost shell. These four electrons can be shared with four neighboring molecules. The bonding force that results from this phenomenon is covalent bonding. In this formation however, electrons belonging to the same bond do not have a definite position in any one atom, meaning they may move between atoms that are bonded. Compound semiconductors such as GaAs (Gallium Arsenide), AlAs (Aluminum Arsenide) and InP (Indium Phosphide) have mixed bonding including both covalent and ionic bonding. These bonding characteristics and the ability for electrons to both move throughout atoms in the structure and to form ionic bonds are the basis for the use of semiconductor materials.