semiconductor textbooks. They can also be approximated by two oppositely charged
point charges at some distance apart, forming a dipole or double layer.
Figure 2.5 shows the electric field and potential near the interface, i.e., the
so-called built-in electric field and potential in a PN junction. These are familiar
results in semiconductor textbooks.
Since the material is piezoelectric, the electric field causes mechanical deformation. The strain field associated with the PN junction is shown in Fig. 2.6 which
localizes near the interface. In the present analysis, T 33 ¼ 0. A small T 33 can be
included to study its effects on the PN junction without mathematical difficulty.
However, the above linear analysis cannot describe the typical nonlinear currentvoltage relations or I-V curve of a PN junction. They will be treated by numerical
methods later.
Interfaces between metal conductors and semiconductors (MS junctions) are also
common and are fundamentally important in devices. The analysis of an MS
junction is similar to the above and is simpler in the sense that on the metal side
there is a concentrated point charge described by a delta function [2] instead of a
distribution.
2.3 Circular PN Junction
Figure 2.7 shows the cross section of a circular piezoelectric semiconductor cylinder
with radius a embedded in another unbounded piezoelectric semiconductor material.
The two materials are doped oppositely and form a PN junction at their interface [3].
Fig. 2.4 Δp À Δn near the
interface
18
2 Exact Solutions
point charges at some distance apart, forming a dipole or double layer.
Figure 2.5 shows the electric field and potential near the interface, i.e., the
so-called built-in electric field and potential in a PN junction. These are familiar
results in semiconductor textbooks.
Since the material is piezoelectric, the electric field causes mechanical deformation. The strain field associated with the PN junction is shown in Fig. 2.6 which
localizes near the interface. In the present analysis, T 33 ¼ 0. A small T 33 can be
included to study its effects on the PN junction without mathematical difficulty.
However, the above linear analysis cannot describe the typical nonlinear currentvoltage relations or I-V curve of a PN junction. They will be treated by numerical
methods later.
Interfaces between metal conductors and semiconductors (MS junctions) are also
common and are fundamentally important in devices. The analysis of an MS
junction is similar to the above and is simpler in the sense that on the metal side
there is a concentrated point charge described by a delta function [2] instead of a
distribution.
2.3 Circular PN Junction
Figure 2.7 shows the cross section of a circular piezoelectric semiconductor cylinder
with radius a embedded in another unbounded piezoelectric semiconductor material.
The two materials are doped oppositely and form a PN junction at their interface [3].
Fig. 2.4 Δp À Δn near the
interface
18
2 Exact Solutions