Definitions [2]
Calculate electron & hole concentration in intrinsic Si at room temperature if
its electrical conductivity is 4x10-4 mho/m.Given that mobility of electron=
0.14m2/V-sec and mobility of holes=0.04m2/V-sec.
Data: μe=0.14m2/V-sec,μh=0.040m2/V-sec,σ=4×10-4mho/m
Formula:σi= ni(μe+μh).e
Calculations: ni=σi/e(μe+μh)
=4×10-4/1.6×10-19(0.14+0.040)
= ni=1.388×1016/m3
Answer: Carrier concentration=1.388×1016/m3
Show that for intrinsic semiconductors of the Fermi level lies midway between the conduction band and the valence band .With the help of diagram explain effect of impurity concentration on Fermi level of N type semiconductor.
• At any temperature T > OK is an intrinsic semiconductor, a number of electrons are
found in the conduction band and the rest of the valence electrons are left behind in
the valence band.
• Let there be nc number of electrons in the conduction band and nv number of
electrons in the valence band.
Hence, the total number of electrons in the intrinsic semiconductor is
N=nc +n ................................. (7)
At T = 0 K all N electrons occupy energy states in the valence band.
• Out of these total N number of valence electrons Amy NC number of electrons cam
reach the conduction band.
The probability of occupancy of an energy level in the conduction band can be written
from equation (7) as
` f (EC)= 1/(1+e ^(Ec Et)//kT)`
where Ec is the potential energy of a rest electron in conduction band.
• Here, Ec is the minimum energy required for the electron to reach the bottom level of
the conduction band. The extra energy is converted to its kinetic energy with which it
moves freely in the conduction band at any energy level.
• Hence, the number if electrons found in the conduction band is
nc= Nf(Ec} = `N/(7 +e(Ec-EtJ JkT)` ........................ {2}
• Similarly, any nv number if valence electrons from the total of N electrons can bring
left behind in the valence band.
• The probability of occupancy of a level in the valence band is given by
f(Ev} = `1/(7 +e·(Et-Ev) /kT)`......................... {3}
• Hence, the number of electrons in the valence band can bring written as
nV=NF{Ev} =`N/(7 +e {Ef-Ev) /kT)....................... (4}`
• Substituting equations (2} and ( 4} in {7 ), it is found that.
` N = N/(1 +e(Ec-Et) JkT) + N/(7 +e {Et-Ev) / kT)`
`[1 + e ^(Ec -Et )//kt]` `[1+e^((- Et-Ev)//kT)]= 2 + e ^(-(Et-Ev)//kT)+e^((Ec-Et )//Kt)`
`1 + e ^((Ec -Et )//kt)` `+e^((- Et-Ev)//kT)= 2 + e ^(-m(Et-Ev)//kT)+e^((Ec-Et )//Kt)`
`e^((Ec-2Ef+Ev)//kT)=1`
`Ec -2EF + Ev//kT = 0`
`Ec+Ev= 2EF`
`(EF = Ec+Ev)/2`
Thus the Fermi energy /eve/lies in the middle of the forbidden energy gap in an intrinsic
semiconductor.
Vsristlon of Fermi Level with Impurity concentrstlon:
• At low impurity concentration the impurity atoms do not interact with each
other. Hence, the extrinsic carriers have their own discrete energy levels.
• With the increase in impurity concentration the interaction of the impurity atoms start
and the Fermi level varies in the following way.
• As the impurity atoms interacts the donor electron are shared by the neighbouring
atoms.
• This results in splitting of the donor level and formation of the donor band below the
conduction band. With the increase in impurity concentration the width of the band
increases. At one stage it overlaps with the conduction band. As the donor band widens the forbidden gap decreases.ln the process the Fermi level shifts upwards
and finally enters the conduction band as shown:
Important Questions [25]
- Define drift current, diffusion current and P-N junction. The electrical conductivity of a pure silicon at room temperature is 4×10-4 mho/m .
- Show that for Intrinsic Semiconductors of the Fermi Level Lies Midway Between the Conduction Band and the Valence Band .With the Help of Diagram Explain Effect of Impurity Concentration on Fermi Level
- Calculate Electron and Hole Concentration in Intrinsic Si at Room Temperature If Its Electrical Conductivity is 4x10-4 Mho/M.Given that Mobility of Electron= 0.14m2/V-sec and Mobility of Holes=0.04m2/
- Define Super Conductivity and Critical Temperature. Plot the Variation of Resistance Versus Temperature in Case of Superconducting State of the Material.
- Mobility of electron and hole in a sample of Ge at room temperature are 0.36 m2 /V-sec and 0.17m2 /V-sec respectively. If electron and holes densities are equal and it is 2.5 ×1013 /cm3
- Define the term drift current and mobility of a charge carriers. Calculate the current product in a germanium sample of area of cross section 1 cm2 and thickness of 0.01 m,
- The mobility of holes is 0.025m2 /V-sec. what would be the resistivity of n- type Si if the Hall coefficient of the sample is 2.25× 10-5m3/C.
- Write Fermi Dirac distribution function. With the help of diagram. Explain the variation of Fermi level with temperature in n-type semiconductor.
- Write the Fermi Dirac distribution function and terms in it. What is the probability of an electron being thermally excited to the conduction band in Si at 30 ℃. The band gap energy is 1.12 eV.
- What is the Probability of an Electron Being Thermally Excited to Conduction Band in Si at 27°C.The Band Gap Energy is 1.12 Ev.
- How does the position of fermi energy level changes with increasing doping concentration in p-type semi-conductor ? sketch diagram.
- Find the minimum energy of neutron confined to a nucleus of size of the order of 10-14m. Given mass of neutron = 1.675×10-27kg
- Explain the Concept of Fermi Level. Prove that the Fermi Level Exactly at the Centre of the Forbidden Energy Gap in Intrinsic Semiconductor.
- In a solid the energy level is lying 0.012 eV below Fermi level. What is the probability of this level not being occupied by an electron 27℃?
- Show that fermi energy level in intrinsic semiconductor is at the Centre of forbidden energy gap. What is the probability of an electron being thermally excited to the conduction band in Si at 30℃.
- With energy band diagram ,explain the variation of fermi energy level with temperature in extrinsic semiconductor.
- With energy band diagram , explain the variation of fermi energy level with impurity concentration in extrinsic semiconductor.
- Find the depth of sea water from a ship on the sea surface it the time interval of two seconds is required to receive the signal back. Given that:
- Draw the Energy Band Diagram of P-n Junction Diode in Forward and Reverse Bias Condition .
- State application of Hall effect. In a Hall effect experiment a potential difference of 4.5 μV is developed across a foil of zinc of thickness 0.02mm when a current of 1.5
- Derive an Expression for Hall Voltage and Hall Coefficient with Neat Labelled Diagram.
- State the Hall Effect. Derive the Expression for Hall Voltage and Hall Coefficient with Neat Diagram.
- Distinguish Between Type I and Type Ii Superconductor.
- Draw the I-v Characteristics of a Photo -diode. What is Meant by Dark Current?
- What is photovoltaic effect? Explain the principle and working of solar cell.
Concepts [12]
- Splitting of Energy Levels for Band Formation
- Electrical Conduction in Solids
- Conductivity, mobility, current density (drift & diffusion) in semiconductors(n type and p type)
- Fermi Dirac Distribution Function
- Fermi Energy Level in Intrinsic Semiconductors
- Fermi energy level in extrinsic semiconductors
- Effect of Impurity Concentration on Fermi Level
- Effect of Temperature on Fermi Level
- Fermi Level Diagram for P-N Junction
- Breakdown Mechanism
- Hall Effect
- Applications of semiconductors : Rectifier diode, LED, Zener diode, Photo diode, Photovoltaic cell, BJT, FET, SCR., MOSFET
