Semiconductors PDF

At T = 0 K, the Fermi level lies exactly in midway between conduction band and Valence band. At T > 0 K, the Fermi level rises slightly upward since mh > me. 8-ELECTRICAL CONDUCTIVITY IN INTRINSIC SEMI-CONDUCTOR Expression for electrical conductivity in intrinsic semiconductor...

At T = 0 K, the Fermi level lies exactly in midway between conduction band and Valence band. At T > 0 K, the Fermi level rises slightly upward since mh > me. 8-ELECTRICAL CONDUCTIVITY IN INTRINSIC SEMI-CONDUCTOR Expression for electrical conductivity in intrinsic semiconductor The general expression for the electrical conductivity, The intrinsic electrical conductivity, The electrical conductivity depends on the negative exponential of band gap Eg between the valance band and conduction band and also for the mobilities of both holes and electrons. The mobilities in a pure semiconductor are determined by the interaction of electron with lattice waves or phonons.  Fig. 2.4 Variation of Electrical with temperature in intrinsic semiconductor A graph is drawn between 1/T and Log i from the graph it is noted that this electrical conductivity increases with temperature. 9-DETERMINATION OF BAND GAP ENERGY OF A SEMICONDUCTOR We know that the electrical conductivity, We know resistivity is resistance per unit area per unit length The above equation gives us a method of determining the energy gap of an intrinsic material. If we find the resistance of the intrinsic semiconductor using post office box or carry Foster’s bridge at various temperatures, we can plot a graph between 1/T and log Ri Fig. 2.5 Variation of resistance with temperature in intrinsic semiconductor Therefore by finding the slope of line we can calculate the energy band gap with the following expression. 10-EXTRINSIC SEMICONDUCTOR A semiconductor in which the impurity atoms are added by doping process is called Extrinsic semiconductor. The addition of impurities increases the carrier concentration and conductivity. There are two types of impurities. Donor impurity which leads to N-type semiconductor. Acceptor impurity which leads to P-type semiconductor. 10.1 N-type Semiconductor (Donor impurity) Donor impurity means it donates the electron to the semiconductor materials. Pentavalent atoms (five valence electrons in their outer most orbit) are called as donor impurities. Example : Phosphorous, Arsenic and Antimony.  When a pentavalent atom is added with tetravalent atoms (Ge and Si), the covalent bond is formed and one element is left free. Thus one impurity atom is surrounded by four Ge or Si atoms. The remaining electron is loosely bound to the parent impurity atom is detached from the impurity atom by supplying ionization energy. Each impurity atom donates one free electron. Thus this type of semiconductor is called as N-type semiconductor. The donor atoms form the new energy level called donor energy level ( E D ) very near and below the conduction band. At room temperature, almost all the excess electrons donated by the donor atoms are raised to the conduction band as majority charge carriers (free electrons) in N-type semiconductor. 10.2 P – type Semiconductor (Acceptor Impurities) Acceptor impurity means it ready to accept an electron to form the covalent bond in semiconductor materials. Trivalent atoms (three valence electrons in their outer most orbits) are called as acceptor impurities. Example: Aluminum, Gallium, Boron and Indium. When a trivalent atom is added with tetravalent atoms (Ge or Si), the covalent bond is formed and there is one vacancy (hole) for one electron in one of the covalent bonds, thereby one impurity atom is surrounded by four Ge or Si atoms. Thus each impurity atom hole is ready to accept an electron. Thus this type of semiconductor is called P-type semiconductor. The Acceptor atoms form the new energy level called acceptor energy level (EA) very near and above the valence band. When a small amount of energy is applied, the electrons from valence band are moved to the acceptor level and creating holes in the valence band. These valence band holes are the majority charge carriers in the P-type semiconductor material.  Fig. 2.7 P type semiconductor 11-CHARGE DENSITIES IN A SEMICONDUCTOR In intrinsic semiconductor, the electron density is equal to hole density. In Extrinsic semiconductor the electron and hole densities are related by The law of charge neutrality also relate the densities of free electron and holes in an Extrinsic semiconductor. The law of charge neutrality states that the total positive charge density is equal to the total negative charge density. Case 1: In N-type semiconductors, there is no acceptor doping atoms. i.e., NA =0 and also the majority carriers are electrons. The number of electrons is greater than the number of holes.  equation (2) becomes ND = Ne Thus in N-type material, the free electron concentration equals to the density of donor atoms. Case 2: In the P-type semiconductor, there is no donor doping atoms. i.e., ND 0 and also the majority carriers are holes. The number of holes is greater than the number of electrons. Thus P-type material, the hole concentration equals to the density of acceptor atoms. According to the law of mass action. 12-CARRIER CONCENTRATION IN P-TYPE SEMI- CONDUCTOR P-Type Semiconductor : If trivalent (Aluminum, Gallium, Indium) impurities are doped with pure semiconducting material the holes are produced, this is called P - type semiconductor.  Fig. 2.8 Energy level diagram for P-type Semiconductor We know that, Density of holes in the valence band in an intrinsic semiconductors is  At 0 K fermi level in p type semiconductor lies exactly at the middle of the acceptor level and the top of the valance band. Expression for the density of holes in valence band in termsof NA As the temperature is increased more and more the acceptor atoms are ionized. Further increase in temperature results in generation of electron hole pairs due to breaking of covalent bonds and materials tends to behave in a intrinsic manner. The fermi level gradully moves towards the intrinsic fermi level. We know density of holes in valence band  Here EA – EV = E is known as ionisation energy of acceptors i.e. E represents the energy required for an electron to move from valance band (EV) to acceptor energy level (EA) 13-CARRIER CONCENTRATION IN N-TYPE SEMI CONDUCTOR If pentavalent (Phosphorous, Arsenic, Antimony) impurities are doped with pure semiconducting material the free electrons are produced, this is called N-type semiconductor. Fig. 2.9 Energy level diagram for N-type Semiconductor We know that, Density of electrons in conduction band in an intrinsic semiconductor is  At T = 0 K. Thus, the Fermi level in N-type semiconductor lies exactly in middle of the conduction level (EC) and donor level (ED).  This equation shows that the electron concentration in the conduction band is proportional to the square root of the donor concentration. 13.1 Expression for the density of electrons in conduction band in terms of ND As the temperature is increased more and more the donor atoms are ionized and the fermi level drops. For a particular temperature all donor atoms are ionized, further increase in temperature results in generation of electron hole pairs due to breaking of covalent bonds and materials tends to behave in a intrinsic manner. We know density of electrons in conduction band  Here EC – ED = E is known as ionisation energy of donars i.e. E represents the amount of energy required to transfer on an electron to from donor envergy level (ED) to conduction band (EC) 14-VARIATION OF FERMI LEVEL WITH TEMPERATURE AND CONCENTRATION OF IMPURITIES IN P-TYPE SEMICONDUCTOR mid way between the acceptor level and valence level. When temperature increases, some of the electrons from valence band will go to acceptor energy level [EA]. Therefore the Fermi level shifts upward. At high temperature 500 K, the Fermi level reaches intrinsic levelEi. If the impurity atoms are increased from 1021 atoms /m3 to 1024 atoms / m3 the hole concentration increases and hence the Fermi level decrease. Fig. 2.10 variation of Fermi level with Temperature and Concentration of Impurities in P-type Semiconductor. 15-VARIATIONOF FERMI LEVEL WITH TEMPERATURE AND CONCENTRATION OF IMPURITIES IN N-TYPE SEMICONDUCTOR mid way between the Donar level and valence level. When temperature increases, some of the electrons moves from valence band to Donar energy level [ED]. Therefore the Fermi level shifts upward. At high temperature 500 K, the Fermi level reaches intrinsic level ED. If the impurity atoms are increased from 1021 atoms /m3 to 1024 atoms / m3, the electron concentration increases and hence the Fermi level decrease. Fig. 2.11 variation of Fermi level with Temperature and Concentration of Impurities in N-type Semiconductor. SOLVED PROBLEMS 1.Calculate the intrinsic concentration of charge carriers at 300 K given that m*e =0.12mo ,m*h =0.28mo and the value of band gap = 0.67 eV. Solution: Given: 2.The intrinsic carrier density is 1.5 × 1016 m–3. If the mobility of electron and hole are 0.13 and 0.05 m2 V–1 s–1, calculate the conductivity. 3. The Intrinsic carrier density at room temperature in Ge is 2.37 × 10 m if the electron and hole mobilities are 0.38 and 0.18 m2 V–1 s– 19 3 1 respectively, calculate the resistivity. 4. In a P-type germanium, ni = 2.1 × 1019 m–3density of boran 4.5 × 1023 atoms /m3. The electron and hole mobility are 0.4 and 0.2 m2 v–1 s–1 respectively. What is its conductivity before and after addition of boron atoms. ………………………………………….. 5. For an intrinsic Semiconductor with a band gap of 0.7 eV, determine the position of EF at T = 300 K if m*h = 6m*e. …………………………………………………………….. 6. Find the resistance of an intrinsic Ge rod 1 mm long, 1 mm wide and 1 mm thick at 300 K. the intrinsic carrier density 2.5 ×1019 m–3 is at 300 K and the mobility of electron and hole are 0.39 and 0.19 m2 v–1 s–1.