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Transactions on Engineering and Computing Sciences - Vol. 12, No. 3
Publication Date: June 25, 2024
DOI:10.14738/tecs.123.17127.
Chanana, R. K. (2024). Constant Total Energy for A Given Mass and At A Given Temperature Is the Source of The Universal Mass- Energy Equivalence Relation in Semiconductor and Insulator Materials Having A Bandgap. Transactions on Engineering and
Computing Sciences, 12(3). 101-103.
Services for Science and Education – United Kingdom
Constant Total Energy for A Given Mass and At A Given
Temperature Is the Source of The Universal Mass-Energy
Equivalence Relation in Semiconductor and Insulator Materials
Having A Bandgap
Ravi Kumar Chanana
Self-Employed Independent Researcher, Gr. Noida-201310, India
ABSTRACT
In this research article it is shown that the motion of an electron or hole in
semiconductor and insulator materials having a bandgap is similar to the falling
object on the surface of the earth at constant acceleration due to gravity g of 9.8
meters/sec2. The constant total energy for a given mass and at a given temperature
is the source of the universal mass-energy equivalence relation in materials having
a bandgap. This relation is given as dE/E = dm/m. In materials, dE is the differential
potential energy from the intrinsic Fermi energy level Ei to the conduction band of
the materials, and E is the semiconductor bandgap as the total potential energy of
the electrons. These energies are also the total mechanical energies of the electrons
at the cathode of the materials where the velocity of the electron in the material is
zero at zero electric field, and so it possesses only potential energy as the total
mechanical energy. The dm is the differential mass as the longitudinal electron
effective mass and m is the free electron mass.
Keywords: Bandgaps, Energy, Materials, Mass-Energy equivalence.
SHORT COMMUNICATION
In Classical mechanics at the school level, it is taught that the change in potential energy is equal
to a change in kinetic energy for an object of mass m dropped from a height h at constant
acceleration due to gravity g of 9.8 meters/sec2, ignoring the friction on the falling object due
to air. The potential energy of the object at height h is given as mgh. Since the velocity before
dropping the object is zero, therefor the kinetic energy of the object at height h is zero. The total
mechanical energy which is the sum of the kinetic and potential energy is therefore equal to
mgh at height h. When the object is dropped, it reaches the ground with a final velocity v in
meters/sec. The kinetic energy of the object is now 0.5mv2 and the potential energy is zero after
reaching the ground. So, the total mechanical energy is 0.5mv2. The total mechanical energy is
constant due to conservation of energy and so mgh equals 0.5mv2. In other words, the potential
energy of the object changes from mgh at height h to zero at the ground and the kinetic energy
of the object changes from zero at height h before being dropped, to 0.5mv2 when dropped and
at the time of reaching the ground. The change in potential energy equals the change in kinetic
energy.
The final velocity of the object when reaching the ground can analogous to the saturated drift
velocity of electron in a material at high field at a given temperature. This saturated drift
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Transactions on Engineering and Computing Sciences (TECS) Vol 12, Issue 3, June - 2024
Services for Science and Education – United Kingdom
velocity is constant. At zero electric field at the cathode across a semiconductor or insulator,
the kinetic energy of the electron is zero and the potential energy of the electron is the energy
from the metal to the conduction band of the material. So, the total mechanical energy of the
electron at the cathode is the same as the total potential energy because the kinetic energy of
the electron at the cathode is zero. After applying the field, for example a 10 to 20KV across a Si
semiconductor, the saturated and constant drift velocity is reached at the anode where the
potential energy is zero. The total energy being constant, the change in potential energy of the
electron at the cathode equals the change in kinetic energy of the electron of 0.5mv2 at the
anode having a constant drift velocity v meters/sec. Thus, the motion of the electron in a
semiconductor or insulator material is similar to the falling object from height h at constant
acceleration due to gravity. For both, constant velocity and constant acceleration due to gravity,
the total energy is constant due to conservation of energy and gives the same universal mass- energy equivalence relation dE/E =dm/m when the total energy is differentiated once giving a
first-order differential equation as above [1-4]. This universal mass-energy equivalence
relation is discussed in more detail in the author’s earlier studies [1-4]. In materials, the total
potential energy of the electron E, as the semiconductor bandgap, is the total mechanical energy
of the electron at the cathode where the field is zero with respect to the anode at voltage V, and
thus the kinetic energy of the electron is zero.
The difference in the motion of an electron in a material and an object falling under acceleration
due to gravity g is that the electron in materials move under the electrostatic force and acquire
a constant drift velocity or saturation velocity at a high enough electric field at a given
temperature, whereas the object falling on earth move under the gravitational force and acquire
a final velocity when it reaches the earth. For a given electron mass at a given temperature, the
constant drift velocity gives a constant total energy of electrons in materials. If there is increase
in energy, say, in thermal energy caused by heating the material, then there is increase in
electron mass as shown earlier giving the relation dE/E=dm/m [1]. Similarly, for the falling
object under gravity, the total mechanical energy E is mgh with g and h being invariable, and
thus keeping the energy constant. Now a change in mass would cause a change in energy giving
again the relation dE/E=dm/m [4]. The same will be true for the falling object having total
mechanical energy as 0.5mv2 when reaching the earth’s surface. So, for both constant velocity
motion of the electron particle as it reaches the saturated drift velocity at high electric fields,
and constant acceleration motion of the falling object, the universal mass-energy equivalence
relation is manifested as dE/E=dm/m. This was first proposed by the famous scientist Albert
Einstein by the equation of the total relativistic energy equation of a relativistic moving mass
m as E = mc2, where c is the speed of light. This equation is the final form of his mass-energy
equivalence that he showed as a conclusion of his special theory of relativity. If this equation is
differentiated once, it gives the same universal mass-energy equivalence relation dE/E=dm/m
[1]. A recent article by the author describes how the discovery of the universal mass-energy
equivalence relation given as dE/E=dm/m was made in materials having a bandgap [5-7].
CONCLUSION
The universal mass-energy equivalence relation is valid for different forms of energy such as
potential, kinetic, nuclear, chemical, thermal, electrical, mechanical etc. In this paper it is shown
conclusively, the analogous behavior of a falling object under gravity to the motion of electrons
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Chanana, R. K. (2024). Constant Total Energy for A Given Mass and At A Given Temperature Is the Source of The Universal Mass-Energy Equivalence
Relation in Semiconductor and Insulator Materials Having A Bandgap. Transactions on Engineering and Computing Sciences, 12(3). 101-103.
URL: http://dx.doi.org/10.14738/tecs.123.17127
in materials having a bandgap such as semiconductors and insulators. Biological materials like
proteins and amino acids also fall in this category.
References
[1]. R.K. Channa, Linear model for the variation of semiconductor bandgap with high temperature for high
temperature electronics, IOSR-J. Electrical and Electronics Engg., 2021. 16(6), p. 5-8.
[2]. R.K. Chanana, Universal mass-energy equivalence relation in materials, European Journal of Theoretical and
Applied Sciences, 2023. 1(5), p. 612-614.
[3]. R.K. Chanana, Discussion on the electron and hole effective masses in thermal silicon dioxide, J. Materials
Science and Engg. A, 2023. 13(4-6), p. 30-34.
[4]. R.K. Chanana, Universal mass-energy equivalence relation is expressed by mechanical energy of a falling body
on earth at constant acceleraion due to gravity, Europeon Journal of Applied Sciences, 2024. 12(2), p. 45-
46.
[5]. R.K. Chanana, The discovery of the universal mass-energy equivalence relation in materials having a bandgap
as dE/E=dm/m, IOSR J. of Engineering, 2023. 13(10), p. 59-62.
[6]. R.K. Chanana, The discovery of the universal mass-energy equivalence relation in materials having a bandgap
as dE/E=dm/m, IOSR-J. of Electrical and Electronics Engineering, 2023. 18(6), p. 1-3.
[7]. R.K. Chanana, The discovery of the universal mass-energy equivalence relation in materials having a
bandgap, Transactions on Engineering and Computing Sciences, 2023. 11(6), p. 19-23.