Solids Class 11 Physics Notes | 2080 | NEB

Syllabus

1. Energy bands in solids (qualitative ideas)
2. Difference between conductors, insulators and semi-conductors using band theory
3. Intrinsic and extrinsic semi-conductors

Band theory of metals:

In an atom, there are fixed energy levels with definite energies that an electron occupies in accordance with Pauli’s exclusion principle. If two atoms are brought closer to each other, due to repulsion interaction between the valence electron, their energy levels are changed ever so slightly. Similarly, if multiple atoms are brought closer to each other like in the case of crystalline solids, due to mutual interaction between valence electrons, the energy levels are further changed. Thus, due to mutual interaction between valence electrons, the valence electrons in different atoms now have different energies that differ by a very small amount. The energy difference is so small that it forms a continuous range of allowed energy states. This is called an energy band. It is divided into three regions:

1. Valence band (VB):

   The electron in the outermost orbit of an atom is called a valence electron. The region of the energy band where valence electrons are present is called the valence band. This band is either completely filled or partially filled depending upon the type of atom but it isn’t fully empty.

2. Conduction band (C.B):

   The electrons that have left the valence band are called conduction electrons. These electrons are weakly held by the nucleus of an atom. The region of the energy band where these free electrons are present is called the conduction band. This band can be either empty or partially filled depending upon the type of material but is never completely full.

3. Energy gap (E.G.):

   The region of the energy band which separates the valence band and the conduction band is called the energy gap. It is also called the forbidden gap. This gap corresponds to the energy that must be supplied in order to excite an electron from the valence band to the conduction band. This band is completely empty as there are no allowed energy states.

Difference between conductor, semi conductor and Bad conductor:

Conductor	Semi-conductor	Bad conductor
Those substance whose energy gap of energy band is zero are called conductor.	Those substances with small energy gap of energy band has value close to 1 ev are called semi–conductor.	Those substance whose energy gap of energy band is wide are called bad conductor.
Conductors have large number of free electrons.	Semi-conductors have less number of free electrons.	Bad conductors have very less number of free electrons.
It has positive temperature coefficient.	It has negative temperature coefficient.	It has negative temperature coefficient.
At normal temperature V.B and C.B. are partially filled.	At normal condition V.B. and C.B are partially filled.	At normal condition V.B. is completely filled but C.B. is completely empty.
Example: Copper,Iron,etc.	Example: Silicon,Germanium,etc.	Example: Wood,Plastic,etc.

Hole and electron current:

In semiconductor, the valence electron moves from the end of negative potential to the end of positive potential and the holes moves from the end at positive potential to the end at negative potential is called hole current.
The electric current set up in the semi – conductor due to the flow of the free electron is called electron current.
Now, let us consider the semiconductor is connected to a battery. The free electron in the conduction bond will be attracted by the anode of battery, it neutralizes a positive charge on it. At the same time, an electron leaves the cathode of the battery and enters into the semi-conductor to take the place of the previous electron. In this way, if a large number of electrons in an electric current is set up in the circuit.

Fig. Hole current in the valence band of a semi-conductor

Consider atoms (Say L, M, N, P, etc) in the semi conductor. Also consider the electron of L has jumped from valence bond to conduction bond. As a result, a hole has been created in L. The valence electron in M and N are still in valence bond. If the battery is connected, the valence electron of atom N is pushed towards atom M and that of M is pushes towards the atom L. The result is that the valence electron of the atom M moves to the hole in the atom L and a hole is created in M. The valence electron in N jumps into the hole in M and a hole is created in atom N.

This way is a hole is created of the extreme end of the semiconductor which is connected to the cathode of the battery; an electron from the cathode enters into the hole neutralizes the atom. At the same time, the anode of the battery detaches an electron from an atom which lies at the other extreme end of the semiconductor. As a result, a new hole is created which moves towards the cathode.

Thus, the hole moves towards the cathode and the electron moves towards the anode. This is called hole current.

Semiconductor:

A semiconductor is a material whose electrical conductivity lies between those of conductors and insulator. It has a small forbidden gap energy which is nearly equal to 1 ev. Due to its small forbidden gap, comparatively smaller electric field could cause the electrons in the valence band to jump to conduction band. It has a negative coeffient of resistance. i.e. its resistivity decreases as the temperature rises. E.g: Silicon (1.1 ev), Germanium (0.7 ev), etc. It has four valence electrons in the valence shell.

Types of Semiconductor:

There are two types of semiconductor:

1. Intrinsic semi conductor

   The semi conductor having tetravalent atoms and found in nature is called Intrinsic or pure semiconductors.
   Pure Silicon or pure Germanium is intrinsic semi-conductors. In these types of atoms, 4 valence shell electrons are involved in the formation of 4-covalent bond with the neighbouring atoms in a crystalline structure. Since, all the valence electrons are bound at ordinary temperatures forming bonds, they behave as insulators. However, at room temperature, some of the electrons jump to conduction band due to thermal energies which account for the perceived conductivity of the semi conductors. In this case, the number of electrons in valence shell is always equal to the number of holes in the valence band.

   
2. Extrinsic semi conductor

   The semi conductor formed by addition of impurities like trivalent or pentavalent atoms to the intrinsic semi conductor is called extrinsic semi conductor. Eg: SiB, GeP, etc. Doping (semiconductor), intentionally introducing impurities into an extremely pure semiconductor to change its electrical properties. The process of adding a measured quantity of a trivalent or a pentavalent impurity to a pure semi conductor is called doping in a semi – conductor.
   In semiconductor production, doping intentionally introduces impurities into an extremely pure (also referred to as intrinsic) semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic.

   

P-type of semiconductor

When trivalent impurities like boron is mixed with pure semiconductor, the semiconductor thus obtained is classified as p-type semiconductor. In this case, the 3-valence electron share the electron with 3e of the semiconductor atom i.e. Si, and hence 3 covalent bonds are formed. But as the semiconductor has 4-valence electrons, out of which, 3 are involved in the formation of covalent bond, one remains unattended, which leaves a vacancy in the structure. As this type of impurity seeks electrons due to the presence of electron vacancies, they are called Acceptor atoms. These electron vacancies are termed as hole or electron holes. These particle behaves has positive charge but are nevertheless, virtual in nature. These structures, holes, have less mobility as compared to the free electrons and they always move in the opposite direction to the direction of movement of free electrons.
In p-type of semiconductor, the majority charge carrier is holes while electrons are minority charge carrier. The holes shift from positive side to negative side whenever the structures are subjected to external electric fields like a battery.

N-type semiconductor:

When pentavalent impurities like Phosphorous or Arsenic is mixed with pure semiconductor, the semiconductor thus obtained is classified as n-type semiconductor. In this case, the 4-valence electron share the electron with 4e of the semiconductor atom i.e. Si, and hence 4 covalent bonds are formed. But as the impurity has 5-valence electrons, out of which, 4 are involved in the formation of covalent bond, one remains unattended, which is free and is available for conduction in n-type structures. Since, this type of impurity provides an extra free electron for conduction, they are called Donor atoms.
In n-type of semiconductor, the majority charge carrier is electrons while holes are minority charge carrier. It should be noted here that, the semi-conductor material as a whole is electrically neutral.