Non linear piezoelectric effects in polar semiconductors

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 and zincblende 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.^[1] 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.^[2] and by M.A. Migliorato et al.,^[3] in relation to zincblende GaAs and InAs. 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,^[4] 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 e_ij, the second and third order coefficients are in the form of a higher rank tensor, expressed as e_ijk and e_ijkl. 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 GaAs and InAs, under pseudomorphic strain,^[5] using Harrison's Model
• zincblende GaAs and InAs, for any combination of diagonal strain components,^[6] using Harrison's Model
• All common III-V semiconductors in the zincblende structure ^[7] using ab initio
• GaN, AlN, InN in the wurtzite structure,^[8] using Harrison's Model
• GaN, AlN, InN in the wurtzite structure,^[9] using ab initio
• ZnO in the wurtzite structure ,^[10] using Harrison's Model
• wurtzite GaN, InN, AlN and ZnO,^[11] using ab initio
• wurtzite GaAs, InAs, GaP and InP,^[12] using Harrison's Model

Experimental Evidence

Particularly for III-N semiconductors, the influence of non linear piezoelectricity was discussed in the context of light-emitting diodes:

• Influence of external pressure ^[13]
• Increased efficiency ^[14]

See also

• Piezotronics
• Piezoelectricity
• Light-emitting diode
• Wurtzite

References

1. Migliorato, Max; et al. "A Review of Non Linear Piezoelectricity in Semiconductors". AIP Conf Proc (AIP Publishing) 1590 (N/A): 32–41. doi:10.1063/1.4870192.
2. Bester, Gabriel; X. Wu; D. Vanderbilt; A. Zunger. "Importance of Second-Order Piezoelectric Effects in Zinc-Blende Semiconductors". Physical Review Letters (APS) 96 (N/A): 187602. doi:10.1103/PhysRevLett.96.187602.
3. Migliorato, Max; D. Powell; A.G. Cullis; T. Hammerschmidt; G.P. Srivastava. "Composition and strain dependence of the piezoelectric coefficients in InxGa1−xAs alloys". Physical Review B (APS) 74 (N/A): 245332. doi:10.1103/PhysRevB.74.245332.
4. Harrison, Walter. Electronic Structure and Properties of Solids. Dover Publications Inc, New York (1989).
5. Garg, Raman; A. Hüe; V. Haxha; M. A. Migliorato; T. Hammerschmidt; G.P. Srivastava. "Tunability of the piezoelectric fields in strained III-V semiconductors". Appl. Phys. Lett. (AIP) 95 (N/A): 041912. doi:10.1063/1.3194779.
6. Tse, Geoffrey; J. Pal; U. Monteverde; R. Garg; V. Haxha; M. A. Migliorato; S. Tomic´. "Non-Linear Piezoelectricity in Zinc Blende GaAs and InAs Semiconductors". J. Appl. Phys. (AIP) 114 (N/A): 073515. doi:10.1063/1.4818798.
7. A. Beya-Wakata; et al. Phys. Rev B (APS) 84 (N/A): 195207. doi:10.1103/PhysRevB.84.195207. Missing or empty |title= (help)
8. Pal, Joydeep; G. Tse; V. Haxha; M.A. Migliorato; S. Tomic´. "Non-Linear Piezoelectricity in Zinc Blende GaAs and InAs Semiconductors". Phys. Rev B (APS) 84 (N/A). doi:10.1103/PhysRevB.84.085211.
9. L. Pedesseau; C. Katan; J. Even. Appl. Phys. Lett. (AIP) 100 (N/A): 031903. doi:10.1063/1.3676666. Missing or empty |title= (help)
10. Al-Zahrani, Hanan; J.Pal; M.A. Migliorato. "Non Linear Piezoelectricity in Wurtzite ZnO Semiconductors". Nano Energy (Elsevier) 2 (N/A): 1214. doi:10.1016/j.nanoen.2013.05.005.
11. Pierre-Yves Prodhomme; Annie Beya-Wakata; Gabriel Bester. Phys. Rev B (APS) 88 (N/A): 121304(R). doi:10.1103/PhysRevB.88.121304. Missing or empty |title= (help)
12. Al-Zahrani, Hanan; J.Pal; M.A. Migliorato; G. Tse; Dapeng Yu. "Piezoelectric Field Enhancement in III-V Core-Shell Nanowires". Nano Energy (Elsevier) N/A (N/A): N/A. doi:10.1016/j.nanoen.2014.11.046.
13. Crutchley, Benjamin; I. P. Marko; S. J. Sweeney; J. Pal; M.A. Migliorato. Phys. Stat. Sol (B) (Wiley) 250 (N/A): 698. doi:10.1002/pssb.201200514. Missing or empty |title= (help)
14. Pal, Joydeep; M. A. Migliorato; C.-K. Li; Y.-R. Wu; B. G. Crutchley; I. P. Marko; S. J. Sweeney. "Enhancement of Efficiency of InGaN-based LEDs through Strain and Piezoelectric Field Management". J. Appl. Phys. (AIP) 114 (N/A): 073104. doi:10.1063/1.481879.