Dr Paul Kinsler. [Acknowledgements & Feedback]
This is part of a hyperlinked notes maze -- please read the index-file for important information about the nature and reliability of this document.
*199708xx Read Educato-LBVJ-1993
*19970826 Think about needed code in context of existing srph.c program. i The bulk phonon rates depend on the wavefunction overlaps, as defined by the form factors. However, the interface-phonons will have a spatial term (sinh or cosh, from memory) that is a function of position, and will be inside the integral.
*19970924 Reading Ridley-1993 and Ridley-ACB-1994 suggests that our GaAs AlxGa(1-x)As wells will not have independent LO-phonons and IP-phonons as Educato-LBVJ-1993 assume, but that a hybrid-phonon consisting of a combination of all these will exist. This gives us a single phonon reservior, not the multiple ones resulting from the (DC) Educato-LBVJ-1993 model, and so will significantly affect the phonon rates.
*19971028 Attempts to solve the Ridley-1993 case with mathematica have stalled, but I need also to consider the E-field boundary conditions, which may resolve the difference between my answers and Ridley-1993's. Currently I am looking at a numerical solution to the hybrid-phonon modes, starting from a multi-slab model (TFM-model) using the LO-phonon, TO-phonon, IP-phonon modes as a basis. This can then be taken to the infinitesimal limit to get a differential equation (or integral solution).
*19971127 Have done a lot of reading, mostly from bids-Babiker_M, re the DC-model versus HD-model controversy. Notes have been typed up, and my new 'hyperindex' script has been used to hyperlink the files here (after minor modifications). The pressure boundary-condition for LO-phonons given in Babiker-1986 and Ridley-B-1991 gives me an extra equation for the TFM-model, which now requires solution of a 5x6 matrix. Ridley-B-1991 suggests a corresponding TO-phonon boundary-condition, which might give me the 6x6 matrix I need for easy inversion.
*19971210
(1) I have looked at the proceedings to Phonon'95 conference in
Physica B, but there
was little of interest -- the least irrelevant being
concerned with phonon transport. The only citation of a
Ridley or Babiker paper in the proceedings was "AB-INITIO
CALCULATIONS OF PHONONS AT SEMICONDUCTOR SURFACES" Schroeder-FP-1996
(see BIDS-phonon-theory-GaAs-marked).
(2) boundary-conditions, in terms of which variables to match
across an interface are not necessarily always the same -- a free
surface has "stress free" boundary-conditions, whereas a
layer-to-layer interface might have others. Probably
the EM ones (DC-model) are always enforced,
but mechanical ones (HD-model) may vary.
(see eg Ridley-ACB-1994).
(3) It seems that adding extra interfaces
restricts the scattering into LO-phonon modes, but adds
new scattering into IP-phonon (interface) modes that are only
allowed at interfaces. In simple situations (?assumed equal coupling
constants, or something (see Babiker-Z-1998), the new
IP-phonon rates exactly
compensate for the reduced LO-phonon rates.
This is a consequence of a sum-rule.
So while extra interfaces
might restrict the "mode-space" spanned by spanned by the LO-phonon modes,
the total phonon "mode-space" (ie that spanned by all phonon modes)
remains the same -- and only details (eg different coupling constants etc)
will affect the total electron-phonon scattering rate.
*19971212 I now understand the nature of the sum-rule, it relies on (nearly) dispersionless phonons -- see Register-1992.
*19980123 following meeting with Essex group, I have updated the notes.
One) what is the Delta_mod line in SR_LOP in srph.c for?
Two) calculate hybrid-phonon for two -slab model analytically
XINDEX: sum-rule, phonon, phonon-polariton, ph-rwk-discuss, index-file, hybrid-phonon, boundary-condition, BIDS-phonon-theory-GaAs-marked, BIDS-confined, BIDS-cite-Register-1992, BIDS-cite-Mori-A-1989, BIDS-Ridley_BK, BIDS-Ridley-etc, BIDS-Babiker_M, none, TO-phonon, TFM-model, Ridley-B-1991, Ridley-ACB-1994, Ridley-1997, Ridley-1993, Register-1992, LO-phonon, Jiang-L-1993, IP-phonon, HD-model, FK-phonon, Educato-LBVJ-1993, DC-model, Babiker-Z-1998, Babiker-1992, Babiker-1986, index-file, log-file.
19908xx 09xx 10xx 1127 1210 12
Email Feedback: Dr.Paul.Kinsler@physics.org
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