4.1 Basic Concepts of Semiconductor Physics
153
4.1.2 Intrinsic and Extrinsic Materials
A perfect material containing no impurities is called an intrinsic material. Because
of thermal vibrations of the crystal atoms, some electrons in the valence band gain
enough energy to be excited to the conduction band. This thermal generation process
produces free electron−hole pairs because every electron that moves to the conduction band leaves behind a free hole. Thus for an intrinsic material the number of
electrons and holes are both equal to the intrinsic carrier density, as denoted by
Eq. (4.1). In the opposite recombination process, a free electron in the conduction
band releases its energy and drops into a free hole in the valence band. For an extrinsic
semiconductor, the increase of one type of carrier reduces the number of the other
type. In this case, the product of the two types of carriers remains constant at a given
temperature. This gives rise to the mass-action law
pn = n
2
i
(4.2)
which is valid for both intrinsic and extrinsic materials under thermal equilibrium.
Because the electrical conductivity is proportional to the carrier concentration,
two types of charge carriers are defined for this material:
1. Majority carriers refer either to electrons in n-type material or to holes in p-type
material;
2. Minority carriers refer either to holes in n-type material or to electrons in p-type
material.
The operation of semiconductor devices is essentially based on the injection and
extraction of minority carriers.
Example 4.2 Consider an n-type semiconductor that has been doped with a net
concentration of N D donor impurities. Let n N and p N be the electron and hole concentrations, respectively, where the subscript N is used to denote n-type semiconductor
characteristics. In this case, holes are created exclusively by thermal ionization of
intrinsic atoms. This process generates equal concentrations of electrons and holes,
so that the concentration of holes in an n-type semiconductor is
p N = p i = n i
Because both impurity and intrinsic atoms generate conduction electrons, the total
concentration of conduction electrons n N is
n N = N D + n i = N D + p N
Substituting Eq. (4.2) for p N (which states that, in equilibrium, the product of the
electron and hole concentrations equals the square of the intrinsic carrier density, so
that p N = n
2
i /n N ), it follows that
153
4.1.2 Intrinsic and Extrinsic Materials
A perfect material containing no impurities is called an intrinsic material. Because
of thermal vibrations of the crystal atoms, some electrons in the valence band gain
enough energy to be excited to the conduction band. This thermal generation process
produces free electron−hole pairs because every electron that moves to the conduction band leaves behind a free hole. Thus for an intrinsic material the number of
electrons and holes are both equal to the intrinsic carrier density, as denoted by
Eq. (4.1). In the opposite recombination process, a free electron in the conduction
band releases its energy and drops into a free hole in the valence band. For an extrinsic
semiconductor, the increase of one type of carrier reduces the number of the other
type. In this case, the product of the two types of carriers remains constant at a given
temperature. This gives rise to the mass-action law
pn = n
2
i
(4.2)
which is valid for both intrinsic and extrinsic materials under thermal equilibrium.
Because the electrical conductivity is proportional to the carrier concentration,
two types of charge carriers are defined for this material:
1. Majority carriers refer either to electrons in n-type material or to holes in p-type
material;
2. Minority carriers refer either to holes in n-type material or to electrons in p-type
material.
The operation of semiconductor devices is essentially based on the injection and
extraction of minority carriers.
Example 4.2 Consider an n-type semiconductor that has been doped with a net
concentration of N D donor impurities. Let n N and p N be the electron and hole concentrations, respectively, where the subscript N is used to denote n-type semiconductor
characteristics. In this case, holes are created exclusively by thermal ionization of
intrinsic atoms. This process generates equal concentrations of electrons and holes,
so that the concentration of holes in an n-type semiconductor is
p N = p i = n i
Because both impurity and intrinsic atoms generate conduction electrons, the total
concentration of conduction electrons n N is
n N = N D + n i = N D + p N
Substituting Eq. (4.2) for p N (which states that, in equilibrium, the product of the
electron and hole concentrations equals the square of the intrinsic carrier density, so
that p N = n
2
i /n N ), it follows that