This file for Education only.

1. Chapter 9
Electrical properties

2. I.Electrical conductivity in Metals
1. Ohm’s law
ohm’s law states that the current (I), that floe in a circuit is
directly proportional to the voltage(V), across the circuit and
inversely proportional to the resistance(R) of the circuit.
𝐼 =
𝑉
𝑅

3. When R is the resistance of the material through which the current is
passing. The units for V, I and R are respectively, Volts(J/C), amperes
(C/s) and ohms(V/A). The value of R is influenced by specimen
configuration and many materials is independent of current. The related
to R through the expression.
R =
𝜌𝑙
𝐴

4. 2. Drift velocity and Current density
The metal structure formed by metal bonds between atoms is an atom that
arranged and pulled together neatly, as shown in Figure 9.1 (a). positive ions are
the core and electrons flow freely around them that make are good thermal and
electrical conduction.
Figure 9.1 (b) shows the relationship between drift velocity of the electron
and the time. begins with the free electrons moving to structure at any speed, and
the velocity increasing with the acceleration constant until the time equal 2𝜏
electrons will be a collision, after that the speed will change from maximum
𝑉𝑚𝑎𝑥 to zero and then electrons will move with the acceleration constant and
collision again. the average velocity of the electrons equal to
𝑣 𝑚𝑎𝑥
2
and average
collision time equal to 2𝜏, where 𝜏 is relaxation time.

5. Figure 9.1 (a) Metal structure (b) shows the relationship between
Drift velocity the of the electron and the time
(a) (b)

6. The average velocity of electrons call Drift velocity 𝑣 𝑑 (m/s) related to electron mobility ( 𝑚2
/𝑉. 𝑠) and
electric field (V/m).
𝑣 𝑑 = μE
The current density (A/𝑚2) can be expressed in term of the free electron density as:
𝐽 = 𝑛𝑒𝑉𝑑
𝑛 = free electron density
e = electric charge of electron −1.6 × 10−19
𝐶
J = σE
And can be expressed current density related to electrical conductivity and electric field as follow:

7. 3. Electrical resistivity
Figure 9.2. The related between resistivity and temperature

8. The resistivity is relative to temperature. In picture showing when temperature increase the
resistivity constant, but temperature increase at some point ions in the lattice structure is vibration
s, so at high temperature the vibration of ions increases and affect to the resistivity increases too,
we called the resistivity independent with temperature is residual component(𝜌𝑟) and called the
resistivity to depend on temperature is temperature component 𝜌 𝑇 . The total of resistivity can be
found as follows:
𝜌𝑡𝑜𝑡𝑎𝑙 = 𝜌 𝑇 + 𝜌 𝑟
𝜌 𝑟 not depend on temperature but depend on imperfections in crystalline such as: dislocation, gain
boundaries or impurities.
• 𝜌 𝑇 depend on temperature:
𝜌 𝑇 = 𝜌0℃ 1 + 𝛼 𝑇 𝑇
𝜌 𝑇 = resistivity at temperature 0℃
𝛼 𝑇 = the temperature coefficient of resistivity
T = temperature in ℃

9. Table 9.1: the resistivity and temperature coefficients of resistivity for various materials.
metal
Resistivity ρ at temperature
0℃ 𝜇Ω. 𝑐𝑚)
Temperature
coefficient α ℃−1)
Aluminum 2.70 0.0039
Copper 1.60 0.0039
Gold 2.30 0.0034
Iron 9.00 0.0045
Silver 1.47 0.0038

10. II. Energy band structure in metals
• In all conductors, semiconductors, and many insulating materials, the electrical conduction is
occur by electron moving.
• The electrical conductivity depends on the number of electrons available to participate in the
conduction process. However, not all electrons accelerate in the presence of an electric field.
The number of electrons available is related to the arrangement of electron states or levels with
respect to energy.
• When two atoms approach one another, the energy level will split into two separate but closely
spaced levels, thereby resulting in an essentially continuous band of energy.
• The energy band splits into two, the conduction band and the valence band, as the two atoms
approach the equilibrium interatomic spacing.
• The region separating the conduction and valence bands is called the forbidden gap or bandgap.

11. • In insulators, the bandgap is relatively large and thermal energy or an applied electric field cannot raise the
uppermost electron in the valence band to the conduction band.
• In metals or conductors, the conduction band is either partially filled or overlaps the valence band such that
there is no bandgap and current can readily flow in these materials.
• In semiconductors, the bandgap is smaller than insulators, and thermal energy can excite electrons to the
conduction band. The bandgap of a semiconductor decreases with higher temperature.
Figure 9.3. A diagram showing the valence and conduction bands of insulators, metals, and semiconductors.

12. III. electrical properties of Intrinsic semiconductor
- Intrinsic semiconductor is pure material such as silicon, germanium. They have 4 valence electrons
and they are covalent bond at absolute zero temperature.
- When the temperature increases electrons are unbounded and will be knocked loose from its position
and become free to move through the lattice and leaving behind an electron vacancy called a hole as
a positive charge occur in structure.
Figure 9.4 Electrons and holes in Silicon structure

13. If a voltage is applied, both electrons and holes contribute to current flow in an intrinsic semiconductor. Electrons
will move to positive side and holes move to negative side.
Figure 9.5 The motion of electrons and holes in electrical field

14. The current density equal to the sum of electron conduction and hole conduction.
𝐽 = 𝑛𝑞𝑣 𝑛
∗ + pq𝑣 𝑝
∗
P and n is a number of hole and electron per unit volume
q is an electrical charge of electron and hole 1.6 × 10−19
𝐶
𝑣 𝑛
∗
and 𝑣 𝑝
∗
is drift velocity of electron and hole m/s
From equation: J = σ. E => σ =
𝐽
𝐸
Can be written as: σ =
𝐽
𝐸
=
𝑛𝑞𝑣 𝑛
∗
𝐸
+
pq𝑣 𝑝
∗
𝐸
Where
𝑣 𝑛
∗
𝐸
= 𝜇 𝑛 ,
𝑣 𝑝
∗
𝐸
= 𝜇 𝑝 ( electron and hole mobility 𝑚2
/𝑉. 𝑠 )
Conductivity in intrinsic semiconductor can also be written as:
σ = nq𝜇 𝑛 + pq𝜇 𝑝 = 𝑛𝑖 𝑞 𝜇 𝑛 + 𝜇 𝑝
intrinsic semiconductor: p = n = 𝑛𝑖

15. In general, the motion of electron is better than hole. We can see it on the table. Germanium is
a good conductor when compared with silicon.
Table 9.2 : Electrical properties of Silicon and Germanium
property Silicon Germanium
Energy gap, eV 1.1 0.76
Electron mobility 𝜇 𝑛 , 𝑚2
/𝑉. 𝑠 0.135 0.39
Hole mobility 𝜇 𝑛 , 𝑚2
/𝑉. 𝑠 0.048 0.19
Intrinsic carrier density 𝑛𝑖, carriers /𝑚3
1.5× 1016
2.4× 1019
Intrinsic resistivity ρ, Ωm 2300 0.46
Density, g/𝑚3
2.33× 106
5.23× 106

16. Number of electron is activation depend on temperature as follows:
𝑛𝑖 ∝ 𝑒− Τ𝐸 𝑔−𝐸 𝑎𝑣 𝑘𝑇
𝐸 𝑔 = energy band gap
𝐸 𝑎𝑣 = average energy
K = Boltzmann’s constant ( 1.38× 10−23 J/ atom.K )
T = Temperature in Kelvin
When 𝐸 𝑎𝑣 =
𝐸 𝑔
2
can write as: 𝑛𝑖 ∝ 𝑒− Τ𝐸 𝑔 2𝑘𝑇
Electrical conductivity in intrinsic is direct fraction with intrinsic carriers concentration given by:
σ = 𝜎0 𝑒 Τ−𝐸 𝑔 2𝑘𝑇
lnσ = ln𝜎0 −
𝐸𝑔
2𝑘𝑇
𝜎0 is constant value depends on moving ability of electron and hole
or

17. VI. Electrical properties of Extrinsic semiconductor
Extrinsic semiconductor is a substitutional solid solution by adding impurity to intrinsic semiconductor.
• Impurity atoms with 5 valence electrons are called donor impurities (atoms from group V A i.e., P,
As, Sb) produce n-type semiconductors by contributing extra electrons.
• Impurity atoms with 3 valence electrons are called acceptor impurities (atoms from group III i.e.,
B, Al, Ga) produce p-type semiconductors by producing a “hole” or electron deficiency.
Figure 9.6 P- and N- Type Semiconductors

18. The application of band theory to n-type and p-type semiconductors shows that extra levels have been
added by the impurities. In n-type material, there are electron energy levels near the top of the bandgap
so that they can be easily excited into the conduction band. In p-type material, extra holes in the band
gap allow excitation of valence band electrons, leaving mobile holes in the valence band.
Figure 9.7 Bands energy of extrinsic semiconductor

19. In Extrinsic semiconductor, the electron and hole densities are related by:
𝑛𝑝 = 𝑛𝑖
2
(1)
The law of charge neutrality states that the total positive charge density is equal to the total
negative charge density.
𝑁𝐴 + 𝑛 = 𝑁 𝐷 + 𝑝 (2)
𝑁𝐴 concentration of acceptor atom
𝑁 𝐷 concentration of donor atom

20. Equation (1) becomes: 𝑝 𝑛 =
𝑛𝑖
2
𝑛 𝑛
≈
𝑛𝑖
2
𝑁 𝐷
• In N-type semiconductors, there is no acceptor doping atoms. i.e., 𝑁𝐴 =0 and also the majority
carriers are electrons. The number of electrons is greater than the number of holes.
From equation (2) becomes: 𝑛 𝑛 = 𝑁𝐴
𝑛 𝑛 concentration of electron in N-type semiconductor
𝑝 𝑛 concentration of hole in N-type semiconductor
• In the P-type semiconductor, there is no donor doping atoms. i.e.,𝑁 𝐷 =0 and also the majority
carriers are holes. The number of holes is greater than the number of electrons.
𝑝 𝑝 = 𝑁𝐴
𝑝 𝑝 concentration of hole in P-type semiconductor
𝑛 𝑝 =
𝑛𝑖
2
𝑝 𝑝
≈
𝑛𝑖
2
𝑁𝐴
𝑛 𝑝 concentration of electron in P-type semiconductor

21. Group Material ( )gE eV ( )2
/n m V s  ( )2
/p m V s  ( )3
/in carrier m
IVA Si 1.100 0.135 0,048
16
1,50 10
Ge 0.670 0.390 0,190
19
2,4 10
IIIA-VA GaP 2.250 0.030 0,015
GaAs 1.470 0.720 0.020
12
1,4 10
InAs 0.360 3.300 0.045
InSb 0.170 8.000 0.045
22
1,35 10
IIA-VIA ZnSe 2.670 0.053 0.002
CdSe 2.590 0.034 0.002
Table9.3: Electrical properties of semiconductor at temperature 300K

22. V. Compound semiconductor
Compound semiconductor composed of many single elements. They have two types:
composed from two elements and composed of three elements.
1. Compound semiconductor composed of two elements
- 2-6 compound semiconductors are made from Groups II and VI (CdTe, ZnSe and others).
- 3-5 compound semiconductors are from combinations of elements from GroupIII and GroupV
(GaAs, GaP, InP and others).
2. Compound semiconductor composed from three elements
This compound semiconductor composed of combinations of three element and adding to
group 2-6 or 3-5 compound semiconductor.
- 1-3-62 composed from group I ( Cu, Ag…), III ( Al, Ga, I,…) VI ( S, Se, Te…) e.g, CuGaS2,
AgInTe2 and CuInSe2 adding to group 2-6 compound semiconductor.
- 2-4-52 composed from group II ( Zn, Cd…), IV ( Si, Ge, Sn…) and V ( P, As, Sb…) e.g, ZnGeP2,
CdSiP2, and ZnSnS2 adding to group 3-5 compound semiconductor.

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