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Fundamental Concepts

A semiconductor is a material that has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity generally falls as its temperature rises; metals behave in the opposite way

Bonds in the materials

Conductor – Metallic bond

Semiconductor – Covalent bond

Insulator- Ionic bond

Conductivity range of a semiconductor

$≈ 10^{-8}Ω^{-1}m^{-1} \;   to   \; 10^{3}Ω^{-1}m^{-1}$

Conductivity dependence on temperature

Conductor – Positive temperature coefficient – when temperature increases, the resistance also increases, and decreases the conductivity

Semiconductor – negative temperature coefficient(NTC) at very high temperature – resistance decreases with increasing temperature

  • Pure semiconductor shows NTC behaviour 
  • Silicon, Germanium, Selenium, Antimony, Gallium Arsenide, Boron

Elements showing semiconductor behaviour

  • Carbon is not a semiconductor. Allotrope of carbon, that is Diamond,  has a semiconducting behaviour

Semiconductor materials are divided in to

  1. Elemental semiconductors
  2. Compound semiconductors

Elemental semiconductors

  • Constituted by single atoms
  • Fourth group elements such as Si and Ge
  • Si is abundant in nature
  • Si withstand high temperature and high current
  • Si has low leakage current
  • $SiO_2$ is a stable oxide used as gate oxide in MOSFET
  • Si: high voltage handling capacity

Compound Semiconductor

  • Constituted by two or more different species of
    atoms is called compound semiconductor.
  • Binary compounds:
    SiC , SiGe, GaAs, GaP, InP, InAs, InSb, ZnS, CdSe
  • Ternary Compounds: GaAsP, AlGaAs
  • Quaternary Compounds: AlGaAsP, InGaAsP

Semiconductor devices

Energy Gap

The energy gap inside materials expalin the conductive and insulative behavior of a material. If the band gap of the material increased then the resistance of the material increases and decreases the conductivity. Energy bandgap is the difference between the energy of the lowest conduction band level and the energy of the highest valance band level

  • $E_g = E_c – E_v$
  • $1eV=1.6 \times 10^{-19} J$
  • The unit of energy gap is eV
  • Conductivity of Ge is greater than Si
  • Ge has a lower band than Si
  • The energy bandgap
    • At room temperature(300k), for Silicon is 1.1 eV and that a Germanium is 0.7 eV 
    • At 0K, for Silicon is 1.2 eV and that a Germanium is 0.78 eV
  • Energygap is inversely proportional to the wavelength
    • $E_g= \frac{hc}{\lambda}=E_c – E_v$

ELECTRON & HOLE Concept

  • A vacant state in the valence band is called as hole.
  • If an electron is removed hole is generated
  • Electron and hole are generated in pairs.
  • Hole movement is in opposite direction of electrons
  • Holes are found in V.B of semiconductor
  • electron effective mass is smaller than hole effectivemass
  • Electron mobility is higher than hole

Generation

  • Electrons in the V.B is excited to C.B by supplying energy greater than or equal to band gap energy.

  • A hole is created in V. B and electron is created inC.B

  • This process is called Generation of e-h pairs.

  • Photo generation: Generation is due to optical energy

  • Thermal generation: Generation is due to thermal energy

Recombination

  • Combining an electron in the conduction band with a hole in the valence band.
  • As a result of recombination an electron in the C.B and a hole in the V.B vanishes.
  • Two types: Direct and indirect recombination
    • Direct recombination: recombination between the C.B(min) and V.B(max) without any intermediate level.
      • Releases radiation
    • Electrons in the $VB_max$ and $CB_min$ has same momentum
    • Electron-hole recombination releases photon with difference in energy
  • $$E_g = hv = \frac{hc}{\lambda}$$
    • Radiative recombination.
    • D.B.S.C materials are used for making LED
      • eg:- GaAs

GaAs $\Rightarrow$ Infrared 

GaP $\Rightarrow$ Red and Green

GaAsP $\Rightarrow$ Red and Yellow 

  • Indirect recombination:
    • Recombination between the C.B(min) and V.B(max) with intermediate level
    • Thermal energy is released
  • electron-hole recombination releases heat with the difference in energy
  • nonradiative recombination
  • Eg:- Ge, Si

Relation with Temperature 

  • Semiconductor is an insulator at $^{o}$ K (absolute zero) hence conductivity is zero.
  • Energy gap decreases with a rise in temperature
  • Mobility of charge carrier first increases with temperature and then decreases
  • Pure semiconductor resistance decreases with the rise in temperature
  • Si withstands high temperature than Ge

Intrinsic Semiconductors

  • purest for of semiconductor
  • The free electron and hole concentrations are equal in an intrinsic semiconductor
  • Crystalline form of Si, Ge
  • if total number of intrinsic charge carriers is $n_{i}$, then

                    $\Rightarrow n_{0}=p_{0}=n_{i}$

  • By mass action law;

                    $\Rightarrow n_{0}p_{0}=n_{i}^{2}$

  • valid for any semiconductor at thermal equilibrium
  • Temperature dependance ;   $n_{i} ∝ T^{1.5} $

Drawbacks of Intrinsic semiconductors

  • The conductivity of an instrinsic semiconductor is highly temperature dependent
  • Conductivity is zero at $^{0}K$ and increases as temperature increases

             $\Rightarrow σ = q n μ$ 

Extrinsic Semiconductor

  • A semiconductor doped with an impurity is called an extrinsic semiconductor
  • Electrical conductivity is high compared to ISC
  • The free electron and hole concentrations are unequal
  • Electrical conductivity depends on temperature and doping
  • Conductivity if ESC remains constant for a wide range of temperature
  • extrinsic semiconductor NTC up to 300K and PTC(positive temperature coefficient) after 300K to a range

Types of SC

  1. P-type
    1. No of holes – high
  2. N-type
    1. No of electron – high

Doping 

  • Additional energy levels are introduced
  • process of adding impurities
  • There are different types of impurities
    • Acceptor Impurities: B, Al, Ga, In $\Rightarrow$ 3 valance electron
    • Donor Impurities: P, As, Sb, Bi $\Rightarrow$ 5 valance electron
    • Amphoteric impurities: impurities act as both acceptor and donor
  • Based on the concentration; doping is divided in to 3
    • Lightly dopped; $1:10^{11}$
    • Moderately dopped; $1:10^{6}$
    • Heavily dopped; $1:10^{3}$
  • intrinsic SC+ Acceptor impurities $\Rightarrow$ P-type SC
    • Majority carriers: Holes
    • Minority carriers : Electrons
    • Acceptor concentration is high
  •  
  • Intrinsic SC+ Donor impurities $\Rightarrow$ N-type semiconductor
    • Majority carriers: Electrons
    • Minority carriers: Holes
    • Donor concentration is high
  •  

Fermi Level

  • The highest energy level that an electron can occupy at the absolute zero temperature
  • Fermi level depends upon doping concentration
  • Intrinsic SC: at the middle of the energy band gap
  • Extrinsic SC: 
    • P-type SC: Near valance band of the energy gap
    • N-type: Near conduction band of energy band gap

Comparison between intrinsic and extrinsic SC

  • Fermi level increases, then the fermi level moves towards the center of forbidden gap irrespective of whether it is p type or n-type