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Basic Electronics (Module 1 – Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering. Indian Institute of Technology, Guwahati Lecture - 1 Semiconductor Materials: Intrinsic and Extrinsic
Today we will discuss about semiconductor materials. Semiconductor materials are the backbone of electronic devices and circuits. What is a semiconductor material? Probably all of you know about conductors and insulators. Conductor is a material which when you apply a voltage source creates a generous flow of charges like for example copper. Copper is a metal and metals are conductors. Insulator is a material that offers a very low level of conductivity when a voltage is applied; for example mica. Semiconductor material is in between this conductor and insulator. It is a material that has conductivity level somewhere between the extremes of an insulator and a conductor.
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For example germanium and silicon are these two materials which are semiconductors showing similar property. The resistivity of a material is inverse of conductivity. If we compare the resistance levels of conductors, insulators and semiconductors we see that
the conductor has resistivity value which is the least among the three. That is, a copper which is a conductor has a maximum conductivity so its resistivity value is around 10 - ohm centimeter whereas an insulator has a resistivity of 10^12 ohm centimeter. This is much more than conductor but semiconductor like germanium and silicon have resistivity values in between these two. For example if we consider germanium semiconductor it has resistivity value of 50 ohm centimeter and silicon has resistivity value of 50 x 10 3 ohm centimeter.
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You can see that semiconductor has resistivity in between conductor and insulator. If we consider these three, i.e insulators, conductors and semiconductors and see their energy band diagrams, then we find that the energy gap between the valence band and the conduction band in an insulator is very high.
That is because the semiconductor like germanium and silicon have some unique qualities which are due to their position in the periodic table and their atomic structure. These are group IV elements. The atoms of these materials like germanium and silicon have a very different and definite pattern that is periodic in nature. That is it continuously repeats itself and one complete pattern is called a crystal and the periodic arrangement of the atoms is a lattice. Both germanium and silicon have 4 electrons in the outer most orbit which are called valence electrons. In order to complete the structure of inert gas they will always try to complete the 8 electrons in the outer most orbit.
In the pure germanium or silicon crystal these 4 valence electrons will be bonded to 4 neighboring atoms as shown in this diagram. If I consider a germanium atom it has 1, 2, 3, 4 electrons in the outer most orbit which are called valence electrons. Similarly silicon will also have 4 electrons in the outer most orbit because they are group IV materials.
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An increase in temperature is naturally the reason for more conductivity in semiconductors. This increase in temperature of a semiconductor results in increase in the number of free electrons in the material so they become more and more conductive. Even though they may be not so conductive at certain temperature but if we increase the temperature they will absorb more kinetic energy and will become more conductive. The semiconductors like germanium and silicon they have negative temperature coefficient as the resistance will decrease with increase in temperature. This is a peculiar phenomena that is seen in semiconductors which is just opposite to your conductors like metal.
We have been talking about the intrinsic semiconductors. Those are the purest form of semiconductors without any impurity in them. But there is another type of semiconductor which is extrinsic semiconductor.
This extrinsic semiconductor has the characteristics such that their property can be significantly altered by addition of certain impurity atoms into the pure semiconductor material. The impurities added to the purest semiconductor to make an intrinsic into extrinsic semiconductor are defined. We can add pentavalent impurity materials like antimony, arsenic and phosphorous which are group V elements and have 5 electrons in the outer most orbit or we can add trivalent materials like boron, gallium and indium which are group III materials and have 3 electrons in their outer most orbit and the standard norm of adding is that they are added 1 part in 10 millions. That is to 10 million atoms of intrinsic semiconductor you add one impurity atom.
We will discuss how the addition of this impurity totally changes the electrical properties of the intrinsic semiconducting material. When certain impurity atoms like antimony or boron are added to a pure semiconductor material we get an extrinsic semiconductor and this process of adding certain impurity atoms like antimony or boron into pure semiconductor like silicon is called the doping process. As a result of this doping we get extrinsic semiconductor either n-type or p-type.
This is called n-type semiconductor. What happens when we add p-type semiconductor? We have seen how n-type semiconductor is formed by adding pentavalent impurity material to intrinsic semiconductor like germanium or silicon. Let us see how p-type semiconductor is formed from pure semiconductor like germanium or silicon by adding trivalent impurity material like boron or indium. Let us add boron impurity which is a group III material having 3 electrons in the outer most orbit to a silicon semiconductor. This boron has 3 electrons in the outer most orbit. It will complete its covalent bond with neighboring silicon atom having shared these 2 electrons as is seen here. These 2 electrons will form a covalent bond. In this process 3 covalent bonds are now completed. What about the other covalent bond? This covalent bond is now devoid or it is short of 1 electron to complete its covalent bond. This shortage of 1 electron means it is having less negative charge. This less negative charge or a positive charge is there in this covalent bond. This is called a hole. Hole means it is basically devoid of 1 electron. So there is a hole formed here in this covalent bond and this hole is a positively charged particle.
So this p- type semiconductor basically is formed in this way which will have holes as charge carriers.
If we consider again the n-type material we have seen that in n-type material which is an extrinsic semiconductor it has donated 1 electron. As it has donated 1 electron, the atom of this extrinsic semiconductor is now having 1 positive charge which is called an ion. 1 atom of this extrinsic semiconductor when it donates one electron it becomes ion having 1 positive charge which is shown here. The donor ions are having 1 positive charge and there will be electrons which are in abundance in the n-type material. These are called majority carriers. In an n-type material the majority carriers are electrons but there will also be in less number the minority carriers which are holes. These holes will be from this intrinsic material that is coming. If n-type material is considered altogether we will see majority carriers as electrons, minority carriers as holes and immobile ions which are positively charged or donor ions.
That means in a p-type material the atom of the impurity will be an acceptor ion having a negative charge and there will be holes which are positively charged as majority carriers and also very less in numbers although there will be presence of minority carriers which are electrons which are coming from the intrinsic semiconductor. This is p-type material where all these carriers and ions you see here. We can summarize that in n-type semiconductor the majority carriers are electrons and minority carriers are holes and in p- type semiconductor majority carriers are holes but minority carriers are electrons.
These are the charge carriers available in n-type and p-type semiconductors. How does the current flow in a semiconductor? Current flow is due to the movement of electrons and conventional current is always against the direction of movement of electrons. Suppose if electron moves in this way then conventional current direction will be in opposite way. This is electron movement direction and this is conventional current direction. But we have seen that another type of charge carrier is also there in semiconductors which are holes and which are positively charged. So the current flow will be now due to these two types of carriers; one is electron and other is hole and both are opposite in charge. That is electron is negatively charged and hole is positively charged.
We are having a semiconductor. We have the silicon atom and this is an impurity atom which is boron. It is creating a hole as is seen here. In order to fill up this hole electron from a neighboring atom will come. This movement of electron will be in this direction. When this electron comes and fills up this hole then this place will be now devoid of electron. It will be now a hole. Now hole movement will be from this position to this position. It is just opposite to the electron movement. Electron movement is in the direction of this solid arrow and hole movement is in the direction of this dotted arrow. If
This is a very fundamental law in electronics which is mass action law. Now let us consider about the charge densities in a semiconductor. We will consider charge density later. Before that you must also know what is the law of electrical neutrality that is satisfied in the semiconductor? Let us consider a semiconductor material and consider a situation where it is doped by both n-type and p-type materials and let ND be the concentration of donor atoms. These donor atoms are all ionized and already we have seen that these will be positively charged donor atoms. We have ND positive charges per cubic meter which are contributed by these donor ions and let p be the hole concentration in the semiconductor so that the total positive charge density in the semiconductor is ND plus p. That is total positive charge density in the semiconductor which is contributed by donor atoms as well as holes. Similarly if we consider that NA is the concentration of acceptor ions then these contribute NA negative charges per cubic meter and let small n be the electron concentration in the semiconductor. So the total negative charge density in the semiconductor will be now NA plus n and since the semiconductor is electrically neutral we have this law to be satisfied that ND plus p is equal to NA plus n. Let us number this equation as 2.
That means this electrical neutrality must be satisfied in a semiconductor given by this equation. Consider solely n-type material. We can either dope by n-type or by p-type impurity. So in an n-type material doping NA will be zero and then the equation 2 will be now N (^) D plus p is equal to n since NA is equal to zero or ND is equal to n minus p. As it is an n-type material the concentration of electrons is much much more than concentration of the holes. So n minus p we can roughly say that equal to n. Then from this equation we will get that the electron concentration is almost equal to the concentration of the donor atoms ND and if we use a subscript small n, the electron concentration in an n-type material nn is equal to capital N subscript capital D. From this equation we can get now hole concentration for this n-type material which is given by p (^) n is equal to n (^) i square by ND. Here we are using equation number 1, mass action law.
Here I am substituting in this equation np is equal to n (^) i square. I am substituting this p with NA. Then I get this n equal to ni square by NA. The fundamental difference between a metal and a semiconductor is that metal is unipolar since current conduction is taking place only by electrons which are having only one sign that is negative sign.
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But in semiconductor there are two charge carriers having negative as well as positive charges which are known as electrons and holes. Semiconductor is a bipolar material. There are 2 types of charge carriers positive as well as negative. Holes are positively charged and electrons are negatively charged. Whenever you apply an electric field, E then your holes and electrons will move in opposite directions since they are of opposite sign but the current due to both these two components will be in one direction.
If you want to find out the current density after the application of an electrical field E, that is given by this expression. The current density J is equal to n times mu n plus p times mu p into q into E which is known as sigma into E. What are those terms? n is magnitude of free electron concentration, mu n is mobility of the electrons, p is magnitude of the hole concentration and mu p is the mobility of holes, q is the charge of an electron and sigma is known as conductivity which is given by this expression n mu n plus p mu p into q. For intrinsic semiconductor as n is equal to p which is equal to ni that is intrinsic concentration, we get for intrinsic semiconductor if you want to find out the current density you will have to simply substitute ni both for n and p.
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