محاضرة 1

University of Babylon-Faculty of Science-Physics department
Undergraduate stage 2
Integrated electronic (Analogue circuits)
Dr. Burak Kadem
Chapter 1:Conduction in semiconductors
1.1.Introduction:
The charge of the electron (q) = 1.6 x10-19 C
The mass of the electron (Me) = 9.11 x 10-31 Kg
The radius of electron is 10-15m
The number of electrons per second is known as current (I)
The energy of electron (E) is:
(1-1)
Where
, h is Blank constant, c is the speed of light, ? is the wavelength.
? The electric field intensity is the force (f) on a unit positive charge (q):
(1-2)
i.e. (1-3)
? The force is directed from the higher potential region to the lower potential region.
? The electron charge is (-q), therefore the force on the electron is:
(1-4)
? Unit of energy is Joule (J) ? where, Watt=J/sec.
? The energy that the electron can gain when its voltage increases to 1volt is known as electronvolt
(eV).
? If an electron falls through a potential of 1volt, its kinetic energy will increase by decreasing the
potential energy, or:
( ) ( )
University of Babylon-Faculty of Science-Physics department
Undergraduate stage 2
Integrated electronic (Analogue circuits)
Dr. Burak Kadem
1.2.The Bohr atom:
In 1913, Bohr has postulated the following 3 laws:
1- The atom can possess only certain discrete energy, and the electron does not emit radiation in
states corresponding to these energies, and the electron is said to be in a stationary or nonradiating
state.
2- In a transition from one stationary state with energy (W) to another one, radiation will be
emitted. The frequency of this radiated energy is :
(1-5)
Where W in (J) and f in cycle/sec or hertz.
3- A stationary state is determined by the condition that the angular momentum of the electron
in this state is quantized and must be an integral multiple of ? .
(1-6)
Where n is an integer. The energy level of each state is:
(1-7)
(1-8)
? The lowest energy state is called normal or ground state and other levels are called excited
levels.
? As the electron is given more and more energy, it moves into the stationary states which are
farther and farther away from the nucleus.
? When its energy is large enough it will detached out of the field of influence of ion, this
energy is called ionization energy; is represented as the highest state in the energy level
diagram.
University of Babylon-Faculty of Science-Physics department
Undergraduate stage 2
Integrated electronic (Analogue circuits)
Dr. Burak Kadem
1.3.Field intensity, Potential and Energy:
Definition of the electric field intensity: is the force (f) on a unit positive charge in an electric
field at a certain point.
Newton’s second law determines the motion of a particle with charge “q” in (Coulomb) and
mass “m” in (kg), moving with a velocity “v” in (m/sec) in a field “E” in (volt/m).
(1-9)
For 3D field, the potential V (volt) of point B with respect to point A is the work done against
the field in taking a unit positive charge from A to B.
For 1D with A at the point xo and B at an arbitrary distance x
?
(1-10)
(1-11)
Where E represents the X component of the field.
The minus sign shows that the electric field is directed from the higher potential region to the
lower potential region.
The potential energy “U” (Joules) = Potential (V) x electronic charge (q):
(1-12)
If an electron is being considered, q is replaced by –q and U has the same shape as V but is
inverted.
The law of conversion of energy states that the total energy (W) which is equals the sum of the
potential energy (U) and the kinetic energy (
) remains constant, therefore at any point in
space:
(1-13)
Q: Consider two plates A & B (Fig.1.1(a)) separated by a distance (d); B at a negative potential
(Vd) with respect to A. When an electron leaves the surface of A with the velocity (vo) towards
B, how much speed (v) will it have if it reaches B?
University of Babylon-Faculty of Science-Physics department
Undergraduate stage 2
Integrated electronic (Analogue circuits)
Dr. Burak Kadem
Answer: page 3, with Figure 1-1 (the English book).
1.4.Concept of a potential-energy barrier:
Fig.1-1 (b, c) shows a linear relation between Potential (V) and distance (x) and the
corresponding potential energy (U) versus (x), respectively.
? V = U/q from eq.1-4
? Then Fig.1.1 (c) is obtained by multiplying the each ordinate in the Fig.1.1 (b) curve with
q (negative value).
? Since W of electron remains constant, it will be represented as horizontal line.
? From eq.1-6:
(
) ( ) (1-14)
(
) is max. at x=0, which means that kinetic energy in the greatest when the electron
leaves electrode A.
? At point P: (
) , so the particle is at rest at this point (xo).
? Xo is the max distance that the electron can travel from A.
Q: What is the possibility of traveling the electron from A to reach distance S in Fig.1.1(c)?
This leads to an important conclusion: The electron can never penetrate the shaded part of
Fig.1.1(c), and point P is a potential-energy barrier.
1.5.The atomic nature of atom:
In 1911, Rutherford has found that the atom consists of positively charged nucleus and
surrounding by negatively charged electrons.
The hydrogen atom, as an example, consists of positively charged nucleus (a proton which is
equal in magnitude to the electron charge with opposite sign) and a single electron. Hence, the
atom is electrically neutral.
University of Babylon-Faculty of Science-Physics department
Undergraduate stage 2
Integrated electronic (Analogue circuits)
Dr. Burak Kadem
Because the proton has practically all the mass of atom, proton is substantially immobile and the
electron moves around it in a closed circular of elliptical orbit, under the force of attraction
which follows Coulomb’s law.
Now assume the orbit is circle, and the nucleus is fixed, so it is easier to calculate the radius in
term of W of electron.
The force of attraction between proton and electron in hydrogen atom is ? . By
Newton’s 2nd law,
(1-15)
Where v is the speed of electron in the circle path (m/sec), m is the mass of the electron (kg),r is
the separation distance between two particles (m),
is the acceleration towards the nucleus and
is the permittivity of free space.
Moreover, the potential energy at a distance r from nucleus is ? , and the kinetic
energy is ? . Then, according to the conservation of energy:
(1-16)
From eq. (1-8) and (1-9):
(1-17)
This equation gives the desire relation between the radius and the energy of the electron which is
always negative.
The negative sign means:
.
University of Babylon-Faculty of Science-Physics department
Undergraduate stage 2
Integrated electronic (Analogue circuits)
Dr. Burak Kadem
And
( )
All the accelerated charges must radiate energy with the same frequency (f) of the charge
oscillation. Therefore, the energy of the emitted radiation is equal to the frequency at which the
electron is rotating in its circular orbit.
Therefore, as the atom radiates energy, the electron must move in smaller and smaller orbits,
eventually falling into the nucleus.