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.