1.7. FURTHER READING 27
composition of In that can be tolerated. Assume that the lattice constant of the alloy can be
linearly interpolated from its components.
Problem 1.9Assume that in a semiconductor alloy, the lattice constant scales as a linear
weighted average. Find the composition of the InxGa 1 −xAs alloy that lattice matches with
an InP substrate.
Problem 1.10Calculate the critical thickness for the growth of AlAs on a GaAs substrate.
Problem 1.11A 100AIn ̊ 0. 2 Ga 0. 8 As film is grown on a GaAs substrate. The film is
coherent. Calculate the strain energy per cm^2 in the film.
Problem 1.12Consider a coherently grown film of Si 0. 8 Ge 0. 2 grown on a Si substrate.
Calculate the thickness of the film at which the strain energy density (eV cm−^2 ) becomes
equal to the energy density arising from a square array of dislocations in the film.
Assume that the dislocations are on a planar square grid with one broken bond per spacing
ofa/whereais the film lattice constant andis the strain. The energy per broken bond
is 1.0 eV.
1.7 FURTHERREADING
- Crystal Structure
- M. M. Woolfson,AnIntroductiontoCrystallography, Cambridge University Press
(1997).
- McGraw-HillEncyclopediaofScienceandTechnology, Volume 4, McGraw-Hill
(1997).
- A. C. Gossard (ed.),EpitaxialMicrostructuresinSemiconductorsandSemi
metals, Volume 40, Academic Press (1994).
- G. Benedek (ed.),PointandExtendedDefectsinSemiconductors, Plenum Publish-
ing Press (1989).
- Landolt-Bornstein,NumericalDataandFunctionalRelationshipsinScienceand
Technology, (O. Madelung, M. Schultz, and H. Weiss, eds.), Springer (1985).
- Strained Structures
- J. F. Nye,PhysicalPropertiesofCrystals: TheirRepresentationbyTensorsand
Matrices, Oxford University Press (1987).
- T. Ikeda,FundamentalsofPiezoelectricity, Oxford University Press (1990).
- E. Bernardini, V. Fiorentini, and D. Vanderbilt,SpontaneousPolarization,and
PiezoelectricConstantofIII-VNitrides,PhysicalReviewB, vol. 56, p. R10024
(1997).
- J. H. Edgar,PropertiesofGroupIIINitrides, INSPEC, London (1994).
