It is well known to us that the conductivity of a material depends upon the concentration of free electrons in it. Good conductors consist large concentration of free electrons whereas insulators consist very small concentration of free electrons. The concentration of free electron in semiconductors is in between the values of concentration of free electrons in conductor and insulator. That is why the conductivity of semiconductor is moderate not very high and not very low. The typicality of semiconductor is that the valance electrons in the semiconductor are not free like metal instead they are trapped in the bond between two adjacent ions. Germanium and Silicon is two very popularly used semiconductors. The crystal structure of both semiconductors consist a regular repetition of three-dimensional unit.
Let us take the example of germanium where there are 32 orbiting electrons across the nucleus in each atom. Each atom in the germanium contributes four valance electrons to make covalent bond with four adjacent germanium atoms in the crystal. So the atoms are tetravalent. The inert ionic core of the germanium acts as a positive charge of +4 electronic charges. The valance electrons in germanium crystal serve to bind one atom to the next hence it can be said that the valance electron is tightly bounded with atom in the crystal. This is why although a germanium atom has four valance electrons in it but germanium crystal as a whole is not a very good conductor of electricity. At absolute zero temperatures a semiconductor crystal behaves just like an insulator as there are no free carriers of electricity available. However at room temperature (300°K), some of the covalent bonds in the crystal are broken due to available energy and this phenomenon makes availability of free electrons in the crystal and hence conduction of semiconductor may be some extend possible at room temperature. The energy required to break covalent bond is about 0.72 eV in germanium and that is 1.1 eV in silicon at room temperature.
When one covalent bond is broken, the either of electrons that previously involved in the bond formation comes out with keeping a vacant place behind it on the bond. This vacancy is referred as hole. The significance of hole in the semiconductor is that they can also be referred as a carrier of electricity compared to electrons. The mechanism by which the holes carry electricity is somewhat different from the mechanism by which electrons carry electricity. When there is an incomplete bond in a semiconductor crystal, a hole exists in the bond. It is little bit easier for the electron, to form a bond in neighborhood atoms, hence it leaves its previous position for occupying the newly created hole nearby. When an electron moves to fill a hole from its previous position in the bond, it leaves another new hole behind it. When the second hole is created then electron of any other neighborhood bond may come out to fill up the second hole with creating a new hole behind it. Hence it can be visualized that as such holes are moving in the direction opposite to the movement of electrons. In this way semiconductor conducts electricity with help of these two types of electricity or charge carriers (electrons and holes). From the above explanation if we deeply think this can be visualized that while a hole moves from one direction to other direction at the same time electron moves in just opposite direction of that. It means whenever holes move in respective forward direction, the negative charge moves in opposite or backward direction. Negative charge moves in backward direction can be considered as positive charge moving in forward direction. Hence it can be concluded that the movement of hole is involved for carrying positive charge in a semiconductor crystal. In an ideal semiconductor crystal number of holes created per unit time is exactly equal to the number of electrons becomes free during this time. If the temperature increases the rate of creation of electron hole pair increases and when the temperature decreases, number electron - hole pairs is decreased due to recombination of electrons and holes in the crystal.
When one electron-hole pair is created, there are two charge carriers produced. One is negative charge carrier associated with electron and other is positive charge carrier associated with hole. Say the mobility of the hole in the crystal is μh and the mobility of electron in the same crystal is μe. These holes and electrons move in opposite direction. The electrons always tend to move in opposite to the applied electric field, the current density due to drift of holes is given by,
The current density due to drift of electrons is given by,
As the drift of holes contributes current in the same direction and drifting of electrons contributes current in opposite direction, in both cases currents are in same direction that is in the direction of drifting of hole. Hence resultant current due to these both charge carriers will be arithmetic sum of two currents and hence resultant current density would be,
Where 'n' is the magnitude of free electron concentration, 'p' is the magnitude of hole concentration and 'σ' is the Conductivity of Semiconductor
If the semiconductor is ideally pure then there would be same number of free electrons and holes. That means n=p=ni (say). If the temperature of the semiconductor increases, the concentration of charge carriers (electrons and holes) is also increased. Hence the conductivity of semiconductor is increased accordingly. The relation between temperature and concentration of charge career in a pure or intrinsic semiconductor is given as
Where, T is the temperature in Kelvin Scale. From the above equation it is found that the concentration of charge carriers in a semiconductor exponentially increases very rapidly with increase of temperature. It is found that the concentration of hole and electrons in germanium increases 6% for increase of every degree centigrade in temperature. And it is of 8% for silicon. This phenomenon makes a semiconductor device much sensitive to temperature. This change of concentration of charge carriers in semiconductor due to temperature affects on characteristics and performance of semiconductor devices. Hence special care is to be taken to maintain the temperature within a specified limit during operation of this type of semiconductor devices. Although, this prompt sensitivity to variation of temperature makes the semiconductor useful for many applications. Many specially made semiconductors are used as transducer for measuring temperature and the device called thermistor.
Let us take the example of germanium where there are 32 orbiting electrons across the nucleus in each atom. Each atom in the germanium contributes four valance electrons to make covalent bond with four adjacent germanium atoms in the crystal. So the atoms are tetravalent. The inert ionic core of the germanium acts as a positive charge of +4 electronic charges. The valance electrons in germanium crystal serve to bind one atom to the next hence it can be said that the valance electron is tightly bounded with atom in the crystal. This is why although a germanium atom has four valance electrons in it but germanium crystal as a whole is not a very good conductor of electricity. At absolute zero temperatures a semiconductor crystal behaves just like an insulator as there are no free carriers of electricity available. However at room temperature (300°K), some of the covalent bonds in the crystal are broken due to available energy and this phenomenon makes availability of free electrons in the crystal and hence conduction of semiconductor may be some extend possible at room temperature. The energy required to break covalent bond is about 0.72 eV in germanium and that is 1.1 eV in silicon at room temperature.
When one covalent bond is broken, the either of electrons that previously involved in the bond formation comes out with keeping a vacant place behind it on the bond. This vacancy is referred as hole. The significance of hole in the semiconductor is that they can also be referred as a carrier of electricity compared to electrons. The mechanism by which the holes carry electricity is somewhat different from the mechanism by which electrons carry electricity. When there is an incomplete bond in a semiconductor crystal, a hole exists in the bond. It is little bit easier for the electron, to form a bond in neighborhood atoms, hence it leaves its previous position for occupying the newly created hole nearby. When an electron moves to fill a hole from its previous position in the bond, it leaves another new hole behind it. When the second hole is created then electron of any other neighborhood bond may come out to fill up the second hole with creating a new hole behind it. Hence it can be visualized that as such holes are moving in the direction opposite to the movement of electrons. In this way semiconductor conducts electricity with help of these two types of electricity or charge carriers (electrons and holes). From the above explanation if we deeply think this can be visualized that while a hole moves from one direction to other direction at the same time electron moves in just opposite direction of that. It means whenever holes move in respective forward direction, the negative charge moves in opposite or backward direction. Negative charge moves in backward direction can be considered as positive charge moving in forward direction. Hence it can be concluded that the movement of hole is involved for carrying positive charge in a semiconductor crystal. In an ideal semiconductor crystal number of holes created per unit time is exactly equal to the number of electrons becomes free during this time. If the temperature increases the rate of creation of electron hole pair increases and when the temperature decreases, number electron - hole pairs is decreased due to recombination of electrons and holes in the crystal.
When one electron-hole pair is created, there are two charge carriers produced. One is negative charge carrier associated with electron and other is positive charge carrier associated with hole. Say the mobility of the hole in the crystal is μh and the mobility of electron in the same crystal is μe. These holes and electrons move in opposite direction. The electrons always tend to move in opposite to the applied electric field, the current density due to drift of holes is given by,
The current density due to drift of electrons is given by,
As the drift of holes contributes current in the same direction and drifting of electrons contributes current in opposite direction, in both cases currents are in same direction that is in the direction of drifting of hole. Hence resultant current due to these both charge carriers will be arithmetic sum of two currents and hence resultant current density would be,Where 'n' is the magnitude of free electron concentration, 'p' is the magnitude of hole concentration and 'σ' is the Conductivity of Semiconductor
If the semiconductor is ideally pure then there would be same number of free electrons and holes. That means n=p=ni (say). If the temperature of the semiconductor increases, the concentration of charge carriers (electrons and holes) is also increased. Hence the conductivity of semiconductor is increased accordingly. The relation between temperature and concentration of charge career in a pure or intrinsic semiconductor is given as
Where, T is the temperature in Kelvin Scale. From the above equation it is found that the concentration of charge carriers in a semiconductor exponentially increases very rapidly with increase of temperature. It is found that the concentration of hole and electrons in germanium increases 6% for increase of every degree centigrade in temperature. And it is of 8% for silicon. This phenomenon makes a semiconductor device much sensitive to temperature. This change of concentration of charge carriers in semiconductor due to temperature affects on characteristics and performance of semiconductor devices. Hence special care is to be taken to maintain the temperature within a specified limit during operation of this type of semiconductor devices. Although, this prompt sensitivity to variation of temperature makes the semiconductor useful for many applications. Many specially made semiconductors are used as transducer for measuring temperature and the device called thermistor.
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