Photovoltaics: Doping

In the previous post, we explained that semiconductors do not conduct electricity very well. One way to manipulate electrical conductivity in semiconductors is to manipulate the concentration of electrically charged carriers. We can do this by using doping. In this post, we will first introduce what doping is. Then we will discuss how doping changes important material properties in semiconductors. The concentration of charge carriers in a semiconductor can be manipulated by doping the material. Doping means that we add impurities in a controlled way to the material. Let’s take the example of silicon. Silicon has four valence electrons. In a silicon lattice, each atom is bonded, covalently, to four other silicon atoms.

We can take that silicon lattice and substitute a small amount of silicon atoms with different atoms. This is commonly done with atoms of two different elements: Boron and Phosphorus. Boron atom has three valence electrons, while phosphorus atom has five valence electrons. When Boron is used as a dopant, the resulting material is called p-type. When phosphorus is used, we call that material n-type. So what actually happens when we substitute silicon atoms with these impurities?

However, one of the silicon atoms has a funny looking bond with the Boron atom. This is because Boron atom shares only one valence electron. This bond is missing one electron. This missing electron is denoted as a hole. Four valence electrons of the phosphorus atom form four covalent bonds with neighbouring silicon atoms. Because phosphorus atom has five valence electrons, there is an extra electron floating around and not being involved in a bond. What we just explained can be better visualized with the help of the two-dimensional bonding model.

Let’s start comparing intrinsic and doped semiconductors at zero Kelvin. We can see that in the lattice of an n-type semiconductor, there are “extra” electrons carried by phosphorous atoms. Similarly, the p-type lattice contains extra holes carried by boron atoms. If the temperature increases, some silicon-silicon bonds can break and electrons are liberated from the bonds. The missing electrons in the bonds represent virtual particles that we call holes. So, breaking the bonds results in the formation of electron-hole pairs.

These electrons and holes are mobile and can move through the material. The same process of breaking bonds also occurs if the material is doped. However, in doped material thermal excitation also affects the dopant atoms. In n-type materials, the extra phosphorus’ electron needs a very small amount of thermal energy to get loose from the phosphorus atom and become mobile. Hence, we say that the phosphorus atom “donates” a free mobile electron into the silicon lattice. For this reason, phosphorous is also called to be a “donor”. If this mobile electron leaves the phosphorus atom, the phosphorus atom becomes positively charged. This is because it has more protons than electrons now. In p-type materials, electrons can be readily accepted by Boron atoms to fill the holes and complete the covalent bond with silicon atom. We call dopants like Boron “acceptors”. The Boron atom becomes negatively charged since it now has accepted an extra electron. We say that boron atoms are negatively ionized. Ionization of dopant atoms can affect locally the charge neutrality of the lattice itself. This happens when mobile carriers deplete the region with fixed ionized dopant atoms.

As a consequence, the lattice will become locally positively charged in the n-type, while in the ptype it will become negatively charged. Nevertheless, the charge neutrality of the whole material is still maintained. In the previous posts we stressed out the relationship between electron’s energy and material’s composition and structure. Moreover, we also introduced the Fermi energy level and showed that its position depends on the effective density of states in the conduction and valence bands. We can therefore expect that, when inserting donor and acceptor atoms, these properties will be affected. Let’s see how. Let’s start by looking at the band diagrams of our three materials.

In previous posts I showed you the band diagram of an intrinsic semiconductor. The position of the Fermi level which I have labeled E_Fi is here of major importance. E_Fi stands for the Fermi level of an intrinsic semiconductor. In the band diagram of the n-type material, the energy level denoted as E D represents energy of the “extra” electrons of phosphorus atoms that are not involved in bonds. The energy level of this weakly bonded electron lies close to the conduction band. Once liberated from the atom, it will gain energy and occupy an energy level in the conduction band. Since by doping we increase number of electrons with energies in the conduction band the average energy of electrons will increase.

This will result in a shift of the Fermi level towards the conduction band. You can see that it is between the intrinsic Fermi level and the conduction band and the more we dope the material, the closer the Fermi level will be to the conduction band. If we look at a p-type material we can see a similar, but opposite effect. Now we have an energy level, denoted as E_A, which is occupied by electrons that are accepted to form covalent bonds. Since in this case most of the electrons occupy energy levels in or close to the valence band the average energy of electrons will decrease. The Fermi level is shifted towards the valence band.

Again, the higher the doping with acceptor atoms, the closer the Fermi level will be to the valence band. Before we move forward with some calculations to determine the concentration of mobile charge carriers, it is important to understand some important terminology. In semiconductors we often distinguish between majority and minority charge carriers. As you already understand we deal with two types of charge carriers in semiconductors. Negatively charged electrons and positively charged holes. In an intrinsic semiconductor we have the same number of electrons and holes. However with doping we manipulate the concentration of only one type of the charge carriers.

We call the carriers whose concentration is much larger than that of the other type majority carriers. These are holes in p-type materials and electrons in n-type materials. Minority charge carriers are the carriers with much lower concentration than the majority carriers.

These are electrons in in p-type materials and holes in n-type materials. The dopant concentration can be selectively chosen according to the application. For crystalline Silicon we may have three levels of doping, low, moderate and heavy, whose ranges can be seen in this picture. For illustration when we take a moderate doping of 10 to power of 16 dopant atoms per cubic centimeter this means that we have substituted just ONE silicon atom out of 1 million silicon atoms. For solar cell applications, we generally use layers with moderate to high dopant concentrations. In this post we looked at how doping affects some of the semiconductor properties qualitatively. In the next post we will learn how to calculate the carrier concentrations and the position of Fermi levels of semiconductors depending on their doping concentration.