Intrinsic Semiconductors

Intrinsic Semiconductors

• A sample of semiconductor in its purest form is called an intrinsic semiconductor.

• The impurity content in intrinsic semiconductor is very very small, of the order of one part in 100 million parts of semiconductor.

1. Crystal Structure of Intrinsic Semiconductor

• Consider an atomic structure of an intrinsic semiconductor material like silicon.

• The outermost shell of an intrinsic semiconductor like silicon has only four electrons. Each of these four electrons form a bond with another valence electron of the neighbouring atoms. This is nothing but sharing of electrons. Such bonds are called covalent bonds. The atoms align themselves to form a three dimensional uniform pattern called a crystal.

• A symbolic two dimensional structure is used to represent a three dimensional crystal form, as shown in Fig. 1.3.1 (a).

• The covalent bonds are represented by a pair of dotted lines encircling the two electrons forming the covalent bond. The more clear understanding of the covalent bonds can be obtained from Fig. 1.3.1 (b) which shows the sharing of valence electrons.

• Both the electrons are shared by the two atoms. Hence the outermost shell of all the atoms is completely filled, and the valence electrons are tightly bound to the parent atoms.

• No free electrons are available at absolute zero temperature. Hence such an intrinsic semiconductor behaves as a perfect insulator at absolute zero temperature.

2. Thermal Generation in Intrinsic Semiconductors

• At room temperature, the number of valence electrons absorb the thermal energy, due to which they break the covalent bond and drift to the conduction band. Such electrons become free to move in the crystal as shown in Fig. 1.3.2 (a).

• Once the electrons are dislodged from the covalent bonds, then they become free. Such free electrons wander in a random fashion in a crystal.

• The energy required to break a covalent bond is 0.72 eV for germanium and 1.1 eV for silicon, at room temperature.

• When a valence electron drift from valence to conduction band breaking a covalent bond, a vacancy is created in the broken covalent bond. Such a vacancy is called a hole. Whenever an electron becomes free, the corresponding hole gets generated.

• So free electrons and holes get generated in pairs. The formation of electron‒hole pair is shown in Fig. 1.3.2 (b) while the corresponding energy band diagram is shown in Fig. 1.3.2 (c). Such a generation of electron hole pairs due to thermal energy is called thermal generation.

• The concentration of free electrons and holes is always equal in an intrinsic semiconductor. The hole also serves as a carrier of electricity similar to that of free electron.

• An electron is negatively charged particle. Thus a hole getting created due to electron drift is said to be positively charged.

Key Point: Thus in an intrinsic semiconductors both holes as well as free electrons are the charge carriers.

3. Conduction in Intrinsic Semiconductors

• When a battery is connected to a semiconductor, free electrons move towards positive of battery and constitute a current called an electron current. The free electrons move in conduction band.

• Consider three atoms as shown in Fig. 1.3.3.

• There is a hole in atom 1. When battery is applied, electron from atom 2 shifts into hole of atom 1, creating hole in atom 2.

• Then electron from atom 3 shifts into hole of atom 2 creating hole in atom 3.

• Thus hole moves from atom 1 to atom 3 and like this it gets attracted towards negative of battery.

• As holes are positively charged, movement of hole constitutes a current called hole current. The holes to always move in valence band.

• In semiconductors, the total current is combination of electron current and hole current.

• The direction of conventional current is always opposite to the direction of free electrons i.e. from positive to negative of battery, external to the battery.

Key Point: The current due to movement of free electrons in the conduction band is an electron current. The current due to movement of holes in the valence band is a hole current. The electron as well as hole current together constitutes current in an intrinsic semiconductor.

Total current = Electron current + Hole current

4. Conductivity of Intrinsic Semiconductor

• The property called conductivity indicates the ease with which a material can carry the current. Thus more conductivity means that material can carry high current, very easily.

• The conductivity of a good conductor is high while that of an insulator is low.

• In intrinsic semiconductor, very few electron‒hole pairs get generated at room temperature. Hence very small current can be constituted, due to the application of voltage to an intrinsic semiconductor.

• Thus the conductivity of an intrinsic semiconductor at room temperature is very low. Such a low conductivity has very little practical significance.

Key Point: Due to low conductivity, the intrinsic semiconductors are not used used in practice for manufacturing of electronic devices.

5. Recombination of Electrons and Holes

• The movement of holes in the valence band is always random and similarly the movement of free electrons in the conduction band is also random.

• Thermal agitation continues to produce new hole‒electron pairs.

• Occasionally, a free electron approaches a hole and falls into it. This merging of a free electron and a hole is called recombination.

• After the recombination, an electron‒hole pair gets disappeared.

• Due to recombination the number of charge carriers decreases.

• The amount of time between the creation and disappearence of a free electron or hole is called the mean life time of the charge carrier.

• At any temperature, at any instant, the free electrons and holes, the two types of charge carriers are present in equal numbers. This concentration is called intrinsic concentration. Mathematically this is indicated as,

n = p = n_i;      

where volume

n = Number of free electrons per unit

p = Number of holes per unit volume

n_i = Intrinsic concentration.

• The concentration is measured in the units number per m³ or per cm³.

6. Energy Band Diagram for Intrinsic Semiconductor

• In the energy band diagram of semiconductors, the probability of occupancy of an energy level by an electron is indicated by a level called fermilevel denoted as E_F.

• In intrinsic semiconductors, the number of electrons and holes are always equal in number.

• If Ec is the lowest energy level of conduction band and E_V is the highest energy level of valence band then the probability of finding electron in conduction band and probability of finding hole in valence band is same.

• Hence the fermilevel in such a case lies exactly at the centre of forbidden energy band and given by

E_F = [ Ec + Ev ] / 2

• Thus energy band diagram for intrinsic semiconductor is as shown in Fig. 1.3.4.

Review Questions

1. Explain intrinsic semiconductor.

2. Explain generation of electron‒hole pairs in an intrinsic semiconductor.

3. Explain how conduction takes place in an intrinsic semiconductor.

4. Describe the generation and recombination of charge carriers in intrinsic semiconductors.