Brian K. Ridley
      
        A brief summary is made of the models used
          to describe the interaction between electrons and polar
          optical phonons in nanostructures. Simpler models are compared
          with the model that describes optical modes that satisfy both
          mechanical and electrical boundary conditions. Satisfaction of
          these boundary conditions requires modes to be a linear
          combination (LC) of longitudinal (LO), transverse (TO) and
          interface (IF) modes. The role of lattice dispersion turns out
          to be crucial. If accuracy is not essential, the simple models
          can provide adequate results, provided that coupled-mode and
          hot-phonon effects are absent.
          
         Keywords:
        electron–phonon interactions, electronic transport,
        nanostructures
        
PACS: 72.10.Di, 73.63.-b
      
 
      
      References
/
          Nuorodos
        
        [1] M.G. Burt, An exact
        formulation of the envelope function method for the
        determination of electronic states in semiconductor
        microstructures, Semicond. Sci. Technol. 
3, 739 (1988),
        
        
http://dx.doi.org/10.1088/0268-1242/3/8/003
        [2] M.G. Burt, The justification for applying the effective-mass
        approximation to microstructures, J. Phys. Condens. Matter. 
4,
        6651 (1992), 
        
          http://dx.doi.org/10.1088/0953-8984/4/32/003
        [3] B.A. Foreman and B.K. Ridley, in: 
Proc. ICPS24 CDROM
          Section V-E3 (1999), 
        
          http://dx.doi.org/10.1142/3915
        [4] B.K. Ridley, 
Electrons and Phonons in Semiconductor
          Multilayers, 2nd ed. (Cambridge University Press, 2009), 
        
          http://dx.doi.org/10.1017/CBO9780511581496
        [5] F.A. Riddoch and B.K. Ridley, On the scattering of electrons
        by polar optical phonons in quasi-2D quantum wells, J. Phys. C 
16,
        6971 (1983), 
        
          http://dx.doi.org/10.1088/0022-3719/16/36/012
        [6] R. Fuchs and K.L. Kliewer, Optical modes of vibration in an
        ionic crystal slab, Phys. Rev. 
140, A2076 (1965), 
        
          http://dx.doi.org/10.1103/PhysRev.140.A2076
        [7] M. Babiker, Longitudinal polar optical modes in
        semiconductor quantum wells, J. Phys. C 
19, 683 (1986),
        
        
http://dx.doi.org/10.1088/0022-3719/19/5/008
        [8] J.E. Zucker, A. Pinczuk, D.S. Chemla, A. Gossard, and W.
        Wiegman, Optical vibrational modes and electron-phonon
        interaction in GaAs quantum wells, Phys. Rev. Lett. 
53,
        1280 (1984), 
        
http://dx.doi.org/10.1103/PhysRevLett.53.1280
        [9] H. Akero and T. Ando, Envelope-function formalism for
        phonons in heterostructures, Phys. Rev. B 
40, 2914
        (1989), 
        
http://dx.doi.org/10.1103/PhysRevB.40.2914
        [10] C. Trallero-Giner, F. García-Moliner, V.R. Velasco, and M.
        Cardona, Analysis of the phenomenological models for long
        wavelength polar optical modes in semiconductor layered systems,
        Phys. Rev. B 
45, 11944 (1992), 
        
http://dx.doi.org/10.1103/PhysRevB.45.11944
        [11] K.J. Nash, Electron-phonon interactions and lattice
        dynamics of optic phonons in semiconductor heterostructures,
        Phys. Rev. B 
46, 7723 (1992), 
        
http://dx.doi.org/10.1103/PhysRevB.46.7723
        [12] B.K. Ridley, Continuum theory of optical phonon hybrids and
        their interaction with electrons in a quantum well, Proc. SPIE 
1675,
        492 (1992), 
        
http://dx.doi.org/10.1117/12.137633
        [13] B.K. Ridley, Electron-hybridon interaction in a quantum
        well, Phys. Rev. B 
47, 4592 (1993), 
        
http://dx.doi.org/10.1103/PhysRevB.47.4592
        [14] M.P. Chamberlain, M. Cardona, and B.K. Ridley, Optical
        modes in GaAs/AlAs superlattices, Phys. Rev. B 
48, 14356
        (1993), 
        
http://dx.doi.org/10.1103/PhysRevB.48.14356
        [15] J. Požela, G. Butkus, and V. Jucienė, Electron-optical
        phonon scattering rates in 2D structures: effects of independent
        electron and phonon confinement, Semicond. Sci. Technol. 
9,
        1480 (1994), 
        
http://dx.doi.org/10.1088/0268-1242/9/8/006
        [16] J. Požela, V. Jucienė, and K. Požela, Confined
        electron-optical phonon scattering rates in 2D structures
        containing electron and phonon walls, Semicond. Sci. Technol. 
10,
        1076 (1995), 
        
http://dx.doi.org/10.1088/0268-1242/10/8/004