SEMICONDUCTOR PHYSICS DEPARTMENT OF APPLIED PHYSICS UNIT –IV SEMICONDUCTOR PHYSICS DEPARTMENT OF APPLIED PHYSICS

Band Theory of Solids Every atom is associated with its own energy level. When two atoms are placed apart then, they do not interact. Two atoms close together causes particular energy level to split into two energy levels. Band Theory of Solid explain how energy bands are formed within solid.

Energy level splitting in a solid (a)Energy band structure of the solid corresponding to the actual spacing of atoms in the body. (b) Energy level splitting as a function of distance. (c) Discrete energy levels in an isolated atom.

Energy Bands in Semiconductors The Energy level splitting and Energy band Configuration In Silicon Crystal

Valence Band: Conduction Band: “The band formed by series of energy levels containing valence electron is called Valence Band”. It may be completely filled or partially filled with electrons. Conduction Band: “The Band formed by energy values of free electron that have broken their covalent bonds is called Conduction band”. Conduction band is the next permitted energy band. It may be empty or partially filled with electrons.

Forbidden energy Gap The energy gap between the valence band and conduction band is called the Forbidden energy gap or Forbidden Band or Band gap. This band is formed by series of non permitted energy levels above the top of valence band and below the bottom of conduction band. Energy gap is denoted by Eg and it is the amount of energy supplied, to excite the electron from valence band to conduction band. It is measured in eV.

Classification of solid: On the basis of energy band diagram Insulator Material which do not conduct current is called insulator. C.B. and V.B. separates with large energy gap, which is greater than 5 eV.

Semiconductor Materials which have conductivity lies between insulator and conductor are called Semiconductor. Energy gap is small and it is of the order of 1eV.

Conductor Material which conduct current is called Conductor As valence band overlaps with conduction band, energy gap is zero If an electric field is applied to this solid, electrons in the V.B. have easy asses to move in C.B. and current flows through material.

Types of Semiconductor Intrinsic Semiconductor: Chemically pure semiconductor is called Intrinsic Semiconductor. Extrinsic Semiconductor: Semiconductor doped with some external impurity are called Extrinsic semiconductor. Doping: It is the Process of adding impurities into an intrinsic semiconductor .

Intrinsic Semiconductor(Si): Fig. A Fig. B Fig. A- Two dimensional representation of Si crystal Fig. B- The Band Structure View

N-type Semiconductor: Two dimensional representation The Band Structure View Semiconductors doped with pentavalent impurity (P,As) are called N-type semiconductor. As pentavalent impurity atom donate free electrons it is called Donor impurity. Donor impurities “create” an energy level, close to the conduction band & represented by ED .

P-type Semiconductor: Two dimensional representation The Band Structure View Semiconductors doped with trivalent impurity (Al, B) are called P-type semiconductor. As trivalent impurity accept free electrons, so we call them Acceptors. Acceptor impurities “create” discrete energy level, close to the valence band & represented by EA .

Concept of Holes: Hole is nothing but the absence of electron. “Deficiency” of negative charge can be treated as a positive charge. Holes are positive charge carriers. Movement of electrons from nearby sites gives rise to movement of holes in apposite direction. Hole is just like a bubble in liquid.

Fermi level & Fermi Energy For conductor: The highest occupied energy level at 0ok is called Fermi level and the Energy corresponding to it is called the Fermi Energy. For semiconductor: Fermi level is the reference energy level and it correspond to the center of gravity of conduction electron and valence hole.

Fermi-Dirac Distribution Function f(E) is the function that gives the probability that particular energy level having energy E is occupied by an electron at Temperature T0 Kelvin. Where EF is the Fermi energy, k is Boltzmann's constant. For conductor: The highest occupied energy level at 0K is called Fermi level and the Energy corresponding to it is called the Fermi Energy. For semiconductor: Fermi level is the reference energy level and it correspond to the center of gravity of conduction electron and valence hole.

Effect of temperature on Fermi Function The above diagram represents variation of f(E) as a function of temperature. All the curves pass through cross-over point C corresponding to f(E) =1/2.

Fermi level in Intrinsic semiconductor Conduction band m*h>m*e Energy m*h = m*e m*h < m*e Valence band Temperature At T=0K the number of electrons in conduction band equals the number of holes in valence band, ne = nh = ni . Fermi level lies in the middle of the band gap. At T≠ 0 K, it depends upon the effective mass of electron and hole.

Fermi level in p-type semiconductor Energy Band Diagram of n-type semiconductor at 0K and 300K The number of holes in valence band are greater than number of electrons in conduction band, nh > ne So the Fermi level shift towards the valence band. With temperature fermi level shifts towards Efi .,

Fermi level in n-type semiconductor Energy Band Diagram of p-type semiconductor at 0K and 300K The number of electrons in conduction band are greater than number of holes in valence band, ne > nh So the Fermi level shift towards the conduction band . With temperature Fermi level shifts towards the EFi

Variation of Fermi level with impurity concentration in n-type semiconductor: Eg Conduction band Valence band ED EF EC EV E Impurity Concentration Fig: (a) Fig: (b) Fig: (c) Conduction band Fig. (a): At low impurity concentration Fig. (b): At moderate impurity concentration Fig. (c): At high impurity concentration

Drift Current Drift current: The current due to (motion) drifting of charge carrier under application of electric field is called Drift Current. Drift current density is given by Where are the constants called mobility of electrons and holes respectively.

Diffusion current Diffusion current: The directional movement of charge carriers due to concentration gradient is called Diffusion Current. Diffusion current density due to electron is given by Diffusion current density due to hole is given by Where De and Dh are the diffusion coefficient for electron and hole respectively.

Conductivity of semiconductor Conductivity of intrinsic semiconductor: σi = ni e( μe + μh) Conductivity of Extrinsic semiconductor: For n – type semiconductor: σn = n e μe = ND e μe For p – type semiconductor: σp = p e μh = NA e μh Where ND and NA are the concentration of donor and acceptor impurity.

p – n junction Diode The diode is just like a current valve. It allows unidirectional flow of current. Diode conduct only when it is in forward bias and do not conduct ideally in reverse bias. It is used in rectifiers. Diode has a nonlinear voltage - current characteristics.

Formation of p-n Junction Diode Holes are the majority charge carriers and electrons are the minority charge carriers in p- region. Electrons are the majority charge carriers and holes are the minority charge carriers in n- region. p-n junction is the boundary between p-type and n-type semiconductor.

Physical Structure and Symbol Physical structure Diode circuit symbol

Biasing of p-n junction diode Biasing of diode: Terminals of external battery is connected to the terminals of diode is called as biasing of diode. Forward Biasing: p terminal of diode is connected to +ve and n terminal is connected to –ve terminal of battery. Reverse Biasing: n terminal of diode is connected to +ve and p terminal is connected to –ve terminal of battery.

Energy Band Diagram of p-n junction diode At equilibrium mode

In Forward Bias mode Energy of electron Energy of holes

In Reverse Bias mode. Energy of holes Energy of electron

The V-I Characteristics of p-n Junction diode.

Pictorial History of Transistors http://www.bellsystemmemorial.com/belllabs_transistor.html

Transistor = Trans + resistor Bipolar Junction Transistor Transistor = Trans + resistor The transistor can be thought as a device in which current travels from low resistance to high resistance path.

Common base mode Common emitter mode Common collector mode Modes of operation of Transistor Common base mode Common emitter mode Common collector mode For efficient action of a transistor, emitter- base junction is forward biased and collector is reverse biased.

Energy band Diagram of a transistor n-p-n Transistor in unbiased mode Energy of electrons Energy of holes

n-p-n Transistor in Common Base mode Energy of electrons Energy of holes

The Hall Effect: Discovered in 1897 by Edwin H. Hall Lorentz Force F= -eBVd d e- + VH - When a current carrying conductor is placed in a transverse magnetic field, a potential difference is generated in the direction perpendicular to both the current and the magnetic field, the voltage developed is known as Hall voltage VH and the effect is known as Hall effect.

Application of Hall Effect Determination of the “type of semiconductor” Determination of the “concentration” of charge carrier (p or n). Determination of the “mobility” of charge carrier (µ). Measurement of “magnetic field” (B). Measurement of “Hall coefficient” (RH).

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