Physics Group - II (3110018)

BE | Semester-1   Winter-2019 | 02-01-2020

Q4) (c)

Discuss UV-VIS method for band gap measurement of semiconductor.

  • UV- Vis Spectroscopy is related to the interaction of light with matter.
  • As light is absorbed by matter, the result is an increase in the energy content of the atoms or molecules. 
  • This method is used to measure the energy band gap of different materials, by measuring absorption spectrum.
  • Bandgap refers to the energy difference between bottom of conduction band and top of valence band, through which electrons are able to jump from one band to another.
  • The instrument used in UV-Vis spectroscopy is called UV-Vis spectro-photometer.
  • It measure the intensity of light after passing through a sample (I), and compares it to the intensity of light before it passes through the sample (I0).
  • A light of wavelength (λ) and energy (hv) is made to pass through monochromator to get a parallel beam.
  • It then passes through a beam splitter and is incident on two cells, a reference cell and a sample cell.
  • The intensities of light from reference and sample cells is collected by the detector. 
  • The ration of intensities is called transmittance (T).

          i.e.  T = II0

  • The transmittance (T) is usually expressed in percentage (%T).
  • If we plot %T w.r.t. to concentration of sample, we get an exponential decrease in transmittance, with an increase in concentration.
  • Higher the concentration, more is the absorption so less is the value of I, through the sample cell.
  • As it is difficult to extract characteristics from the exponential relation, we define a relation absorption (A)

          Absorption  (A) = logI0I

  • The Tauc’s relation is used to determine the bandgap in semiconductor.

           α h v = A  h v - Eg n

           α = A  h v - Eg nh v  ,

    Rearranging above relation, we can have

    α hv1n  = A1n hv - A1n Eg  

    Where, α = absorption coefficient  = ln1Tx 

    Where, T = transmittance  =  l  I0  

    Where, x = Thickness of the sample  

    Where, n = 2, 12, 23 and 13 for direct allowed, indirect allowed, direct forbidden and indirect forbidden transitions respectively. 
    Where,
    Now, we can plot a graph of  α hv 1n  along x - axis vs hv (along y - axis), we will get slop as A1n and y intercept as A1n Eg. Dividing y intercept by An we can estimate the band gap.