7.1 Chapter 5_section 5.2. direct and in-direct band gap

Chapter 5_Section 5.2. Direct and in-direct Band Gap Materials.

Section 5.2.

As seen in Figure 5.3, in Direct Band Gap materials the Energy Minima of Conduction Band and Energy Maxima of Valence band lie along the vertical line which passes through identical momentum value. So when electron in conduction band and hole in valence band recombine then there is : ∆E = E _g and ∆p = 0. Therefore a photon which has an energy packet = hγ = E _g and momentum ‘p’ = negligible, such a photon can successfully mediate such a recombination. These are called Radiative Transitions where for every electron and hole recombination there is the emission of a photon.

Therefore we say that Vertical Transitions cause Radiative Transitions or Emissive Transitions. In such Direct Band-Gap materials, internal Quantum Efficiency is 100% and if there are 1000 EHPs recombining then through Vertical Transitions 1000 photons of requisite wavelength given by Equation 5.1 are emitted.

In Figure 5.3., E-p or E-k diagram of a In-direct Band Gap material is given.AS can be seen the electrons at the bottom of conduction band and holes at the top of the valence band must recombine obliquely. They cannot recombine vertically. This oblique recombination is called in-direct recombination. In this oblique recombination ,for the conservation law to hold good after the recombination of electrons and holes, extra Energy ∆E = E _g and extra ∆p =p2-p1, both have to be carried away. Photon has very little momentum. So only Phonons can do this job. It can take away the extra Energy as well as the extra Momentum generated by in-direct recombination.

Now the question arises as to what is phonons.

Phonons are quanta of lattice vibrational energy. They travel with the velocity of sound in the dielectric medium. The phonons which travel as longitudinal waves are called acoustic mode phonon and phonons which travel as transverse waves are called optical mode phonon. Here I may just refresh the terms “longitudinal” and “transverse”. Light travel as a Transverse Wave. Here the medium moves transverse to the direction of propagation. Whereas Sound transmission medium moves in the same direction as the direction of propagation. Here I may also point out that in stable state every component of a system is in minimum energy state. Electrons in the bottom of Conduction Band and holes at the top of the Valence Band are also in minimum energy state.

Since all elemental semi-conductors have in-direct Energy Band Diagram, hence their EHPs recombination or transitions are always accompanied with increased lattice vibration which is tantamount to heating. Hence here we have non-radiative transition and Quantum Efficiency is zero.

Since Compound Semiconductors are Direct Band-Gap materials they are suitable as Optical Sources. But Optical Detectors can be either Direct or In-Direct Band Gap material since both respond to optical excitation except that in-Direct material will have to be thicker to be able to give equivalent response for a given optical input.