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UNIT- 1
REVIEW OF SEMICONDUCTOR PHYSICS
Atomic Structure
According to the modern theory, All the materials are composed of
very small particles called atoms. The atoms are the building bricks of
all matter.
Various scientists have given different theories regarding the structure of
atom. However, for the purpose of understanding electronics, the study of
Bohr’s atomic model is adequate.
Bohr’s Atomic Model
In 1913, Neils Bohr, Danish Physicist gave clear explanation of atomic structure. According to Bohr: (i) An atom consists of a positively charged nucleus around which negatively charged electrons revolve in different circular orbits. (ii) The electrons can revolve around the nucleus only in certain permitted orbits i.e. orbits of certain radii are allowed. The number of electrons in any orbit is given by 2 n^2 where n is the number of the orbit. For example, First orbit contains 2 12 = 2 electrons Second orbit contains 2 22 = 8 electrons Third orbit contains 2 32 = 18 electrons (iii) The electrons in each permitted orbit have a certain fixed amount of energy. The larger the orbit ( i.e. larger radius), the greater is the en- ergy of electrons. (iv) If an electron is given additional energy ( e.g. heat, light etc.), it is lifted to the higher orbit. The atom is said to be in a state of excitation. This state does not last long, because the electron soon falls back to the original lower orbit. As it falls, it gives back the acquired energy in the form of heat, light or other radiations. Fig. shows the structure of silicon atom. It has 14 electrons. Two electrons revolve in the first orbit, 8 in the second orbit and 4 in the third orbit. The first, second, third orbits etc. are also known as K , L , M orbits respectively. These electrons can revolve only in permitted orbits ( i.e. orbits of *radii r 1 , r 2 and r 3 ) and not in any arbitrary orbit. Thus, all radii between r 1 and r 2 or between r 2 and r 3 are forbidden. Each orbit 1 has fixed amount of energy associated with it.
Energy Levels
It has already been discussed that each orbit has fixed amount of energy associated with it. The electrons moving in a particular orbit possess the energy of that orbit. The larger the orbit, the greater is its energy. It becomes clear that outer orbit electrons possess more energy than the inner orbit electrons. A convenient way of representing the energy of different orbits is shown in Fig. 4.2 ( ii ). This is known as energy level diagram. The first orbit represents the first energy level , the second orbit indicates the second energy level and so on. The larger the orbit of an electron, the greater is its energy and higher is the energy level. Fig. 4. Fig. 4.
current in a conductor. For this reason, they are called conduction electrons. The range of energies ( i.e. band ) possessed by conduction band electrons is known as conduc- tion band. All electrons in the conduction band are free electrons. If a substance has empty conduction band, it means current conduction is not possible in that substance. Generally, insulators have empty conduction band. On the other hand, it is partially filled for conductors. (vii) Forbidden energy gap. The separation between conduction band and valence band on the energy level diagram is known as forbidden energy gap. No electron of a solid can stay in a forbidden energy gap as there is no allowed energy state in this region. The width of the forbidden energy gap is a measure of the bondage of valence electrons to the atom. The greater the energy gap, more tightly the valence electrons are bound to the nucleus. In order to push an electron from valence band to the conduction band ( i.e. to make the valence electron free), external energy equal to the forbidden energy gap must be supplied.
Based on the electrical conductivity all the materials in nature are classified as insulators,
semiconductors, and conductors.
PARAMATER CONDUCTORS SEMICONDUCTORS INSULATORS
Conduction
The conduction in
conductors is due to the
free electrons in metal
bonding.
The conduction in
semiconductor is due to
the movement of electron
& holes.
There are no free
electrons or holes thus,
there is no conduction.
Band gap
There is no or low
energy gap between the
conduction & valance
band of a conductor. It
does not need extra
energy for the
conduction state.
The band gap of
semiconductor is greater
than the conductor but
smaller than an insulator
i.e. 1 eV. Their electrons
need a little energy for
conduction state.
The band gap in
insulator is huge (+
eV), which need an
enormous amount of
energy like lightning to
push electrons into the
conduction band.
Valence Electron in
Outer Shell
1 Valence electron in
outer shell.
4 Valence electron in
outer shell.
8 Valence electron in
outer shell.
Conductivity High (10- 7 mho/m)
Medium (10- 7 to 10-
13 mho/m)
Very Low (10- 3 mho/m)
Almost negligible.
Resistivity Low Moderate High
Temperature coefficient
of resistance
Positive Negative Negative
Charge carriers in
conduction band
Completely filled Partially filled Completely vacant
Charge carriers in
valence band
Almost vacant Partially filled Completely filled
Example
Copper, Aluminium,
graphite etc.
Silicon, Germanium,
arsenic etc.
Paper, rubber, glass,
plastic etc.
Application
The metals like iron &
copper etc. that can
conduct electricity are
made into wires and
cable for carrying
electric current.
Semiconductors are used
every day electronic
devices such as
cellphone, computer,
solar panel etc as
switches, energy
converter, amplifiers, etc.
The insulators are used
for protection against
high voltages &
prevention of electrical
short between cables in
circuits.
( ii ) Silicon. Silicon is an element in most of the common rocks. Actually, sand is silicon diox- ide. The silicon compounds are chemically reduced to silicon which is 100% pure for use as a semiconductor. The atomic number of silicon is 14. Therefore, it has 14 protons and 14 electrons. Two electrons are in the first orbit, eight electrons in the second orbit and four electrons in the third orbit [See Fig. 5.3 ( i )]. It is clear that silicon atom has four valence electrons i.e. it is a tetravalent element. Fig. 5. (ii) shows how various silicon atoms are held through co-valent bonds. Like germanium, silicon atoms are also arranged in an orderly manner. Therefore, silicon has crystalline structure.
Energy Band Description of Semiconductors
It has already been discussed that a semiconductor is a substance whose resistivity lies between conductors and insulators. The resistivity is of the order of 10 ^4 to 0.5 ohm metre. However, a semi- conductor can be defined much more comprehensively on the basis of energy bands as under : A semiconductor is a substance which has almost filled valence band and nearly empty conduc- tion band with a very small energy gap (j 1 eV) separating the two. Figs. 5.4 and 5.5 show the energy band diagrams of germanium and silicon respectively. It may be seen that forbidden energy gap is very small; being 1.1 eV for silicon and 0.7 eV for germanium. Therefore, relatively small energy is needed by their valence electrons to cross over to the conduction band. Even at room temperature, some of the valence electrons may acquire sufficient energy to enter Fig. 5.4 Fig. 5. Fig. 5. 7
into the conduction band and thus become free electrons. However, at this temperature, the number of free electrons available is very *small. Therefore, at room temperature, a piece of germanium or silicon is neither a good conductor nor an insulator. For this reason, such substances are called semi- conductors. The energy band description is extremely helpful in understanding the current flow through a semiconductor. Therefore, we shall frequently use this concept in our further discussion.
Effect of Temperature on Semiconductors
The electrical conductivity of a semiconductor changes appreciably with temperature variations. This is a very important point to keep in mind. (i) At absolute zero. At absolute zero temperature, all the electrons are tightly held by the semiconductor atoms. The inner orbit electrons are bound whereas the valence electrons are engaged in co-valent bonding. At this temperature, the co-valent bonds are very strong and there are no free electrons. Therefore, the semiconductor crystal behaves as a perfect insulator [See Fig. 5.6 ( i )]. In terms of energy band description, the valence band is filled and there is a large energy gap between valence band and conduction band. Therefore, no valence electron can reach the conduction band to become free electron. It is due to the non-availability of free electrons that a semiconductor behaves as an insulator. (ii) Above absolute zero. When the temperature is raised, some of the covalent bonds in the semiconductor break due to the thermal energy supplied. The breaking of bonds sets those electrons free which are engaged in the formation of these bonds. The result is that a few free electrons exist in the semiconductor. These free electrons can constitute a tiny electric current if potential difference is applied across the semiconductor crystal [See Fig. 5.7 ( i )]. This shows that the resistance of a semi- conductor decreases with the rise in temperature i.e. it has negative temperature coefficient of resis- tance. It may be added that at room temperature, current through a semiconductor is too small to be of any practical value. Fig. 5.
same time, another current – the hole current – also flows in the semiconductor. When a covalent bond is broken due to thermal energy, the removal of one electron leaves a vacancy i.e. a missing electron in the covalent bond. This missing electron is called a *hole which acts as a positive charge. For one electron set free, one hole is created. Therefore, thermal energy creates hole-electron pairs ; there being as many holes as the free electrons. The current conduction by holes can be explained as follows : The hole shows a missing electron. Suppose the valence electron at L (See Fig. 5.8) has become free electron due to thermal energy. This creates a hole in the co-valent bond at L. The hole is a strong centre of attraction **for the electron. A valence electron (say at M ) from nearby co-valent bond comes to fill in the hole at L. This results in the creation of hole at M. Another valence electron (say at N ) in turn may leave its bond to fill the hole at M , thus creating a hole at N. Thus the hole having a positive charge has moved from L to N i.e. towards the negative terminal of supply. This constitutes hole current. It may be noted that hole current is due to the movement of ***valence electrons from one co- valent bond to another bond. The reader may wonder why to call it a hole current when the conduc- tion is again by electrons (of course valence electrons !). The answer is that the basic reason for current flow is the presence of holes in the co-valent bonds. Therefore, it is more appropriate to consider the current as the movement of holes. Energy band description. The hole current can be beautifully explained in terms of energy bands. Suppose due to thermal energy, an electron leaves the valence band to enter into the conduc- tion band as shown in Fig. 5.9. This leaves a vacancy at L. Now the valence electron at M comes to fill the hole at L. The result is that hole disappears at L and appears at M. Next, the valence electron at N moves into the hole at M. Consequently, hole is created at N. It is clear that valence electrons move along the path PNML whereas holes move in the opposite direction i.e. along the path LMNP. Fig. 5. Fig. 5.
Intrinsic Semiconductor
A semiconductor in an extremely pure form is known as an intrinsic semiconductor. In an intrinsic semiconductor, even at room temperature, hole-electron pairs are created. When electric field is applied across an intrinsic semiconductor, the current conduction takes place by two processes, namely ; by free electrons and holes as shown in Fig. 5.10. The free electrons are pro- duced due to the breaking up of some covalent bonds by thermal energy. At the same time, holes are created in the covalent bonds. Under the influence of electric field, conduction through the semicon- ductor is by both free electrons and holes. Therefore, the total current inside the semiconductor is the sum of currents due to free electrons and holes. It may be noted that current in the ex- ternal wires is fully electronic i.e. by electrons. What about the holes? Re- ferring to Fig. 5.10, holes being posi- tively charged move towards the negative terminal of supply. As the holes reach the negative terminal B , electrons enter the semiconductor crys- tal near the terminal and combine with holes, thus cancelling them. At the same time, the loosely held electrons near the positive terminal A are attracted away from their atoms into the positive terminal. This creates new holes near the positive terminal which again drift towards the negative terminal.
5.6 9 Extrinsic Semiconductor
The intrinsic semiconductor has little current conduction capability at room temperature. To be useful in electronic devices, the pure semiconductor must be altered so as to significantly increase its conducting properties. This is achieved by adding a small amount of suitable impurity to a semicon- ductor. It is then called impurity or extrinsic semiconductor. The process of adding impurities to a semiconductor is known as doping. The amount and type of such impurities have to be closely controlled during the preparation of extrinsic semiconductor. Generally, for 108 atoms of semicon- ductor, one impurity atom is added. The purpose of adding impurity is to increase either the number of free electrons or holes in the semiconductor crystal. As we shall see, if a pentavalent impurity (having 5 valence electrons) is added to the semiconductor, a large number of free electrons are produced in the semiconductor. On the other hand, addition of trivalent impurity (having 3 valence electrons) creates a large number of holes in the semiconductor crystal. Depending upon the type of impurity added, extrinsic semicon- ductors are classified into: (i) n - type semiconductor ( ii ) p - type semiconductor
5.7 0 n - type Semiconductor
When a small amount of pentavalent impurity is added to a pure semiconductor, it is known as n-type semiconductor. Fig. 5.
5.8 1 p - type Semiconductor
When a small amount of trivalent impurity is added to a pure semiconductor, it is called p-type semiconductor. The addition of trivalent impurity provides a large number of holes in the semiconductor. Typical examples of trivalent impurities are gallium (At. No. 31) and indium (At. No. 49). Such impurities which produce p - type semiconductor are known as acceptor impurities because the holes created can accept the electrons. To explain the formation of p - type semiconductor, consider a pure germanium crystal. When a small amount of trivalent impurity like gallium is added to germanium crystal, there exists a large number of holes in the crystal. The reason is simple. Gallium is trivalent i.e. its atom has three valence electrons. Each atom of gallium fits into the germanium crystal but now only three co-valent bonds can be formed. It is because three valence electrons of gallium atom can form only three single co-valent bonds with three germanium atoms as shown in Fig. 5.14. In the fourth co-valent bond, only germanium atom contributes one valence electron while gallium has no valence electron to contribute as all its three valence electrons are already engaged in the co-valent bonds with neighbouring germanium atoms. In other words, fourth bond is incomplete; being short of one electron. This missing electron is called a hole. Therefore, for each gallium atom added, one hole is created. A small amount of gallium provides millions of holes. Fig. 5.15 shows the energy band description of the p - type semiconductor. The addition of triva- lent impurity has produced a large number of holes. However, there are a few conduction band electrons due to thermal energy associated with room temperature. But the holes far outnumber the conduction band electrons. It is due to the predominance of holes over free electrons that it is called p - type semiconductor ( p stands for positive). Fig. 5. Fig. 5.
p-type conductivity. The current conduction in p - type semiconductor is predominantly by holes i.e. positive charges and is called p-type or hole-type conductivity. To understand p - type conductiv- ity, refer to Fig. 5.16. When p.d. is applied to the p - type semiconductor, the holes (donated by the impurity) are shifted from one co-valent bond to another. As the holes are positively charged, there- fore, they are directed towards the negative terminal, constituting what is known as hole current. It may be noted that in p - type conductivity, the valence electrons move from one co-valent bond to another unlike the n - type where current conduction is by free electrons.
5.9 2 Charge on n - t ype and p - type Semiconductors
As discussed before, in n - type semiconductor, current conduction is due to excess of electrons whereas in a p - type semiconductor, conduction is by holes. The reader may think that n - type material has a net negative charge and p - type a net positive charge. But this conclusion is wrong. It is true that n - type semiconductor has excess of electrons but these extra electrons were supplied by the atoms of donor impurity and each atom of donor impurity is electrically neutral. When the impurity atom is added, the term “excess electrons” refers to an excess with regard to the number of electrons needed to fill the co-valent bonds in the semiconductor crystal. The extra electrons are free electrons and increase the conductivity of the semiconductor. The situation with regard to p - type semiconductor is also similar. It follows, therefore, that n-type as well as p-type semiconductor is electrically neutral.
5.10 3 Majority and Minority Carriers
It has already been discussed that due to the effect of impurity, n - type material has a large number of free electrons whereas p - type material has a large number of holes. However, it may be recalled that even at room temperature, some of the co-valent bonds break, thus releasing an equal number of free electrons and holes. An n - type material has its share of electron-hole pairs (released due to breaking of bonds at room temperature) but in addition has a much larger quantity of free electrons due to the effect of impurity. These impurity-caused free electrons are not associated with holes. Consequently, an n - type material has a large number of free electrons and a small number of holes as shown in Fig. 5.17 ( i ). The free electrons in this case are considered majority carriers — since the majority portion of current in n - type material is by the flow of free electrons — and the holes are the minority carriers. Similarly, in a p - type material, holes outnumber the free electrons as shown in Fig. 5.17 ( ii ). Therefore, holes are the majority carriers and free electrons are the minority carriers. Fig. 5.15 Fig. 5.
Difference Between Intrinsic and Extrinsic semicoductors
Parameter Intrinsic Semiconductor Extrinsic Semiconducto
Form of semiconductor Pure form of semiconductor. Impure form of semico
Conductivity It exhibits poor conductivity. It possesses comparativ
better conductivity tha
intrinsic semiconducto
Band gap The band gap between conduction and
valence band is small.
The energy gap is high
than intrinsic semicon
Fermi level It is present in the middle of forbidden
energy gap.
The presence of Fermi
level varies according
the type of extrinsic
semiconductor.
Dependency The conduction relies on temperature. The conduction depend
on the concentration o
doped impurity and
temperature.
Carrier concentration Equal amount of electron and holes are
present in conduction and valence band.
The majority presence
electrons and holes
depends on the type of
extrinsic semiconducto
Type It is not further classified. It is classified as p type
and n type semiconduc
Example Si, Ge etc. GaAs, GaP etc.
