Chapter 16
Polarized Semiconductors
Abstract In this chapter semiconductors with a spontaneous polarization and ferroelectric semiconductors are discussed. Also the effect of piezoelectricity is treated in some detail for zincblende and
wurtzite materials.
16.1 Introduction
Semiconductors can have an electric polarization. Such polarization can be induced by an external
electric field (Fig. 16.1a). This phenomenon, i.e. that the semiconductor is dielectric, has been discussed
already in Chap. 9. In this chapter, we discuss pyroelectricity, i.e. a spontaneous polarization without
an external field (Fig. 16.1b), ferroelectricity,
1 i.e. pyroelectricity with a hysteresis (Fig. 16.1c) and
piezoelectricity, i.e. a polarization due to external stress.
16.2 Spontaneous Polarization
The reason for a spontaneous polarization P sp (without external electric field) is the static, relative shift
of positive and negative charges in the unit cell. For a slab of semiconductor material (thus ignoring
depolarization effects present in other geometries), the polarization causes polarization charges located
at the upper and lower surfaces (Fig. 16.2a). The polarization vector P points from the negative to the
positive charge. The electric field due to the polarization charges has the opposite direction. In the
absence of free charges, the Maxwell equation ∇ · D = 0 yields for piecewise constant fields at
a planar interface (Fig. 16.2b) (D 2 − D 1 ) · n 12 = 0 where n 12 is the surface normal pointing from
medium 1 to medium 2. Therefore, the polarization charge σ P = 0 ∇ · E is given by
σ P = −(P 2 − P 1 ) · n 12 .
(16.1)
Polarization charges develop at interfaces where the polarization is discontinuous, e.g. an interface
between two semiconductors with different spontaneous polarization. Vacuum (at a surface) represents
a special case with P = 0.
1 Ferromagnetic semiconductors are discussed in Chap. 17. We note that there exist so called multiferroic materials that
possess more than one ferroic property [1485, 1486].
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_16
451
Polarized Semiconductors
Abstract In this chapter semiconductors with a spontaneous polarization and ferroelectric semiconductors are discussed. Also the effect of piezoelectricity is treated in some detail for zincblende and
wurtzite materials.
16.1 Introduction
Semiconductors can have an electric polarization. Such polarization can be induced by an external
electric field (Fig. 16.1a). This phenomenon, i.e. that the semiconductor is dielectric, has been discussed
already in Chap. 9. In this chapter, we discuss pyroelectricity, i.e. a spontaneous polarization without
an external field (Fig. 16.1b), ferroelectricity,
1 i.e. pyroelectricity with a hysteresis (Fig. 16.1c) and
piezoelectricity, i.e. a polarization due to external stress.
16.2 Spontaneous Polarization
The reason for a spontaneous polarization P sp (without external electric field) is the static, relative shift
of positive and negative charges in the unit cell. For a slab of semiconductor material (thus ignoring
depolarization effects present in other geometries), the polarization causes polarization charges located
at the upper and lower surfaces (Fig. 16.2a). The polarization vector P points from the negative to the
positive charge. The electric field due to the polarization charges has the opposite direction. In the
absence of free charges, the Maxwell equation ∇ · D = 0 yields for piecewise constant fields at
a planar interface (Fig. 16.2b) (D 2 − D 1 ) · n 12 = 0 where n 12 is the surface normal pointing from
medium 1 to medium 2. Therefore, the polarization charge σ P = 0 ∇ · E is given by
σ P = −(P 2 − P 1 ) · n 12 .
(16.1)
Polarization charges develop at interfaces where the polarization is discontinuous, e.g. an interface
between two semiconductors with different spontaneous polarization. Vacuum (at a surface) represents
a special case with P = 0.
1 Ferromagnetic semiconductors are discussed in Chap. 17. We note that there exist so called multiferroic materials that
possess more than one ferroic property [1485, 1486].
© Springer Nature Switzerland AG 2021
M. Grundmann, The Physics of Semiconductors, Graduate Texts in Physics,
https://doi.org/10.1007/978-3-030-51569-0_16
451