PYL 793 ASSIGNMENT- 1 Submitted by: Sqn Ldr Himanshu Bhatt 2022JOP2829 Given the effective mass of an electron inside GaAs is around 0.067 and that of Si is 1.10. Comparatively elaborate the difference between them on the basis of Nature of Forces and E-k diagram On the basis of Nature of Forces 1. Effective Mass. The mass of an electron in the periodic potentials of the crystal is different from the free electron mass and is usually referred to as Effective Mass and is given by:- 2. GaAs is a direct band gap semiconductor, which means that the minimum of the conduction band is directly over the maximum of the valence band. Transitions between the valence band and the conduction band require only a change in energy, and no change in momentum, unlike indirect band-gap semiconductors such as Si. 3. In a semiconductor, when a carrier (an electron) is subjected to an electric field, it will experience a force (F = –qE) and will be accelerated along the field. During the time between collisions with other carrier ions and the semiconductor lattice, the carrier will achieve a velocity that is a function of the electric field strength. This velocity is defined as the drift velocity (v). From the conservation of momentum, it can be shown that the drift velocity (v) is proportional to the applied electric field and is given by:- 4. The proportionality factor depends on the mean free time between collisions (τc) and the electron effective mass (m*). The proportionality factor is called the electron mobility (µ). Mobility is an important parameter for carrier transport because it describes how strongly the motion of an electron is influenced by an applied electric field. From the equation above, it is evident that mobility is related indirectly to the effective mass of the electron. 5. So, if you compare it with silicon the effective mass of electron in Gallium Arsenide is much smaller. So, electron feels much lighter in presence of Gallium Arsenide crystal potential as compared to silicon crystal potential and that is why the mobility of electron in Gallium Arsenide is very high if you apply force because the mass is small so the electron gains a high acceleration or high drift velocity in Gallium Arsenide as compared to silicon. On the basis of E-k diagram 6. In the graph shown below, we can see that some valleys in the band structure have a sharp curvature and these correspond to the electrons with low effective mass, while valleys that are wide with gentle curvature are characterized by larger effective mass. The minimum point of gallium arsenide’s conduction band is near the zero point of crystal-lattice momentum, as opposed to silicon, where conduction band minimum occurs at high momentum. 7. For GaAs, the effective mass of these electrons is 0.067 times the mass of free electron (that is, 0.067me, where me is the free electron rest mass). Thus the shapes in the conduction band bring about a superior electron mobility. Due to this, the electrons travel faster in Gallium Arsenide (GaAs) than in Silicon. Furthermore, Gallium Arsenide is a direct-gap semiconductor. Its conduction band minimum occurs at the same wave vector as the valence band maximum , which means little momentum change is necessary for the transition of an electron from the conduction band to the valence band. Since the probability of photon emission with energy nearly equal to the band gap is somewhat high, GaAs makes an excellent lightemitting diode. Silicon on the other hand, is an indirect-gap semiconductor and on account of momenta misalignment has very low probability of photon emission.