3 S.No.ModuleLectur e No. PPT Slide No. 1IntroductionL Extrinsic semiconducto rs L EINSTEIN EQUATION L UNIT INDEX
4 Lecture-1 Solids are classified as metals, semiconductors and insulators. Solids with either overlapping valence band and conduction band or partially filled valence bands are metals. Solids with finite forbidden gap in the range 1-3ev are semi conductors. Insulators have much larger band gap.
5 Germanium and silicon are important semiconductors which are widely used in the manufacturing of diodes and transistors. Germanium and silicon are tetravalent atoms i.e they have four valence electrons. Since all the four valence electrons are covalently bound to the four neighboring atoms the crystal acts as a perfect insulator at 0k.
6 Germanium and silicon are pure semiconductors with no impurities. At room temperature the thermal enrgy is sufficient to break covalent bonds. When a covalent bond is broken a free electron-hole pair is generated. Conductivity increases with temperature as more and more electrons cross over the small energy gap.
7 Lecture-2 In an intrinsic semiconductor, the Fermi energy level is at the middle of valence and conduction bands. If Ev and Ec are the energy levels respectively at the top of the valance band and bottom of conduction band, the enerrgygap E g is given by E g =Ec-Ev And E F =(E c +E v )/2
8 The density of electrons is given by n= 2(2пm e * kT/h 2 ) 3/2 exp[ (E F - E c )/kT] The density of holes is given by p = 2(2пm h *kT/h 2 ) 3/2 exp[ (E v - E F )/kT]
9 Extrinsic semiconductors A semiconducting material in which the charge carriers originate from impurity atoms added to the material is called impurity semiconductor or extrinsic semiconductor. The addition of impurity increases the carrier concentration and hence the conductivity of the conductor. Lecture-3
10 N-type semiconductor There are two types of impurities possible namely pentavalent and trivalent. If a pentavalent atom is doped to the tetravalent host crystal, four of the five valence electrons of the impurity atom form covalent bonds with four neighboring host atoms and one electron is left unpaired.
11 Antimony, phosphorous, arsenic etc., are examples of pentavalent elements. When they are added to Si or Ge as impurities, they are called donors as they donate free electrons. The semiconductor prepared in this way will have more electrons than holes. Since the excess free charge is negative, these are named as N-type semiconductors.
12 At 0k E F =(E d +E c )/2 i.e. at 0k Fermi level lies exactly at the middle of the donor level E d and the bottom of the conduction band E c. The density of electrons in the conduction band is given by n = 2(2пm e * kT/h 2 ) 3/4 exp[ (E d -E c )/kT]
13 P-type semiconductor If a trivalent atom is doped into the trivalent host crystal, its three valence electrons fill only three of the four covalent bonds of the host atoms and one vacancy exists in the fourth bond. Thus in this case one extra hole per doped atoms is formed. The examples of trivalent atoms are boron, gallium, indium etc.
14 When they are added to Si or Ge as impurities, they are called acceptors as they readily accept electrons due to the presence of the hole. Since the holes behave like positive charges, the acceptors are called P- type impurities and these impure semiconductors are called P-type semiconductors. Lecture-3Lecture-3
15 At 0k E F =(E v +E a )/2 i.e. Fermi level lies exactly at the middle of the acceptor level and the top of the valence band. Density of holes in valence band is given by p = 2(2пm h *kT/h 2 ) 3/4 exp[ (E v - E a )/kT]
16 For a semiconducting material the electrical conductivity σ is given by σ = (neμ e + peμ h ) Since n=p=n i σ = (μ e + μ h ) 2e (2пkT/h 2 ) 3/2 (m e * m h * ) 3/4 exp(-E g /2kT)
17 EINSTEIN EQUATION The relation between diffusion coefficient and mobility of a charge carrier is termed Einstein equation. D n = μ e kT/e (For electrons) Dp = μ f kT/e (For holes) Lecture-4
18 HALL EFFECT When a piece of semiconductor carrying a current is placed in a transverse magnetic field, an electric field is produced inside the conductor in a direction normal to both the current and magnetic field. This phenomenon is known as the Hall effect and the generated voltage is known as Hall voltage.
19 Lecture-5 The Hall coefficient R H = -1/ne (for n-type semiconductors) = 1/pe (for p-type semiconductors)
20 Mean life time is the time taken for the injected concentration to fall to 1/e of its initial value. Minority carrier life time can be defined as the time taken for the excess charge carriers to reduce to 1/e times its initial value, once the source generating these excess charge carriers is cut off.