Non Linear Piezoelectric Effects In Polar Semiconductors
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Non linear piezoelectric effects in polar semiconductors are the manifestation that the strain induced piezoelectric polarization depends not just on the product of the first order piezoelectric coefficients times the strain tensor components but also on the product of the second order (or higher) piezoelectric coefficients times products of the strain tensor components. The idea was put forward for zincblende GaAs and InAs semiconductors since 2006, and then extended to all commonly used
wurtzite Wurtzite is a zinc and iron sulfide mineral with the chemical formula , a less frequently encountered Polymorphism (materials science), structural polymorph form of sphalerite. The iron content is variable up to eight percent.Palache, Charles, Har ...
and
zincblende Sphalerite (sometimes spelled sphaelerite) is a sulfide mineral with the chemical formula . It is the most important ore of zinc. Sphalerite is found in a variety of deposit types, but it is primarily in sedimentary exhalative, Mississippi-Va ...
semiconductors. Given the difficulty of finding direct experimental evidence for the existence of these effects, there are different schools of thought on how one can calculate reliably all the piezoelectric coefficients. On the other hand, there is widespread agreement on the fact that non linear effects are rather large and comparable to the linear terms (first order). Indirect experimental evidence of the existence of these effects has been reported in the literature in relation to GaN and InN semiconductor optoelectronic devices.


History

Non linear piezoelectric effects in polar semiconductors were first reported in 2006 by G.Bester et al. and by M.A. Migliorato et al., in relation to
zincblende Sphalerite (sometimes spelled sphaelerite) is a sulfide mineral with the chemical formula . It is the most important ore of zinc. Sphalerite is found in a variety of deposit types, but it is primarily in sedimentary exhalative, Mississippi-Va ...
GaAs Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monolithic microwave integrated circui ...
and
InAs Indium arsenide, InAs, or indium monoarsenide, is a narrow-bandgap semiconductor composed of indium and arsenic. It has the appearance of grey cubic crystals with a melting point of 942 °C. Indium arsenide is similar in properties to galli ...
. Different methods were used in the seminal papers and while the influence of second (and third) order piezoelectric coefficients was generally recognized as being comparable to first order, fully ab initio and what is currently known as Harrison's model, appeared to predict slightly different results, particularly for the magnitude of the first order coefficients.


Formalism

While first order piezoelectric coefficients are of the form eij, the second and third order coefficients are in the form of a higher rank tensor, expressed as eijk and eijkl. The piezoelectric polarization would then be expressed in terms of products of the piezoelectric coefficients and strain components, products of two strain components, and products of three strain components for the first, second, and third order approximation respectively.


Available Non Linear Piezoelectric Coefficients

Since 2006 many more articles were published on the subject. Non linear piezoelectric coefficients are now available for many different semiconductor materials and crystal structures: *
zincblende Sphalerite (sometimes spelled sphaelerite) is a sulfide mineral with the chemical formula . It is the most important ore of zinc. Sphalerite is found in a variety of deposit types, but it is primarily in sedimentary exhalative, Mississippi-Va ...
GaAs Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monolithic microwave integrated circui ...
and InAs, under pseudomorphic strain, using Harrison's Model *
zincblende Sphalerite (sometimes spelled sphaelerite) is a sulfide mineral with the chemical formula . It is the most important ore of zinc. Sphalerite is found in a variety of deposit types, but it is primarily in sedimentary exhalative, Mississippi-Va ...
GaAs Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monolithic microwave integrated circui ...
and InAs, for any combination of diagonal strain components, using Harrison's Model * All common III-V semiconductors in the
zincblende Sphalerite (sometimes spelled sphaelerite) is a sulfide mineral with the chemical formula . It is the most important ore of zinc. Sphalerite is found in a variety of deposit types, but it is primarily in sedimentary exhalative, Mississippi-Va ...
structure using ab initio *
GaN The word Gan or the initials GAN may refer to: Places *Gan, a component of Hebrew placenames literally meaning "garden" China * Gan River (Jiangxi) * Gan River (Inner Mongolia), * Gan County, in Jiangxi province * Gansu, abbreviated ''Gā ...
, AlN,
InN Inns are generally establishments or buildings where travelers can seek lodging, and usually, food and drink. Inns are typically located in the country or along a highway; before the advent of motorized transportation they also provided accommo ...
in the
Wurtzite crystal structure In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crystal ...
, using Harrison's Model *
GaN The word Gan or the initials GAN may refer to: Places *Gan, a component of Hebrew placenames literally meaning "garden" China * Gan River (Jiangxi) * Gan River (Inner Mongolia), * Gan County, in Jiangxi province * Gansu, abbreviated ''Gā ...
, AlN,
InN Inns are generally establishments or buildings where travelers can seek lodging, and usually, food and drink. Inns are typically located in the country or along a highway; before the advent of motorized transportation they also provided accommo ...
in the
Wurtzite crystal structure In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crystal ...
, using ab initio * ZnO in the
Wurtzite crystal structure In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crystal ...
, using Harrison's Model *
Wurtzite crystal structure In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crystal ...
GaN, InN, AlN and ZnO, using ab initio *
Wurtzite crystal structure In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crystal ...
GaAs, InAs, GaP and InP, using Harrison's Model


Experimental Evidence

Particularly for III-N semiconductors, the influence of non linear
piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
was discussed in the context of
light-emitting diode A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (cor ...
s: * Influence of external pressure * Increased efficiency


See also

*
Piezotronics Piezotronics effect is using the piezoelectric potential (piezopotential) created in materials with piezoelectricity as a “gate” voltage to tune/control the charge carrier transport properties for fabricating new devices. Neil A Downie showed h ...
*
Piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
*
Light-emitting diode A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (cor ...
*
Wurtzite crystal structure In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crystal ...


References

{{Reflist Nanoelectronics Semiconductor devices Semiconductors