Abstract

n-GaAs can be so highly doped that its plasma frequency is larger than the associated frequency of a CO2 laser emission line, leading to a negative real part of the dielectric permittivity. We studied linear and nonlinear reflection properties of structures composed of such thin highly doped n-GaAs film in an attenuated total reflection (ATR) configuration. We show that deep reflection minima coincide with the excitation of Brewster-type modes of the multilayer structure. These minima feature strong nonlinear and bistable behavior and are sensitive to geometrical and material parameters. The proposed ATR configuration can be used to determine doping concentrations with an accuracy of better than 1 part per thousand and different deformation potentials of the higher-conduction bands in n-GaAs.

© 2003 Optical Society of America

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  1. G. Shkerdin, J. Stiens, R. Vounckx, “Comparative study of the infra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs,” J. Appl. Phys. 87, 3807–3818 (1999).
    [CrossRef]
  2. G. Shkerdin, J. Stiens, R. Vounckx, “A multi-valley model for hot free-electron nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 12, 169–180 (2000).
    [CrossRef]
  3. G. Shkerdin, J. Stiens, R. Vounckx, “Influence of leaky waves on free-electron-induced nonlinear reflection properties of highly doped n-GaAs layer at medium IR-wavelength,” J. Opt. A Pure Appl. Opt. 3, 493–499 (2001).
    [CrossRef]
  4. K. Welford, “Surface plasmon polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
    [CrossRef]
  5. M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, Cambridge, UK, 1989), Chap. 6.
    [CrossRef]
  6. J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
    [CrossRef]
  7. G. Shkerdin, J. Stiens, R. Vounckx, “X-valley influence on hot free electron absorption and nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 19, 29–37 (2002).
    [CrossRef]
  8. J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53, R123–R181 (1982).
    [CrossRef]
  9. S. Adachi, “GaAs, AlAs, and AlxGa1-xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
    [CrossRef]
  10. J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
    [CrossRef] [PubMed]
  11. S. Zollner, S. Gopalan, M. Cardona, “Microscopic theory of intervalley scattering in GaAs: k dependence of deformation potentials and scattering rate,” J. Appl. Phys. 68, 1682–1693 (1990).
    [CrossRef]
  12. M. A. Littlejohn, J. R. Hauser, T. H. Glisson, “Velocity-field characteristics of GaAs with Γ6c-L6c-X6c conduction-band ordering,” J. Appl. Phys. 48, 4587–4590 (1977).
    [CrossRef]
  13. M. N. Zervas, “Surface plasmon-polariton waves guided by thin metal films,” Opt. Lett. 16, 720–722 (1991).
    [CrossRef] [PubMed]

2002

G. Shkerdin, J. Stiens, R. Vounckx, “X-valley influence on hot free electron absorption and nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 19, 29–37 (2002).
[CrossRef]

2001

G. Shkerdin, J. Stiens, R. Vounckx, “Influence of leaky waves on free-electron-induced nonlinear reflection properties of highly doped n-GaAs layer at medium IR-wavelength,” J. Opt. A Pure Appl. Opt. 3, 493–499 (2001).
[CrossRef]

2000

G. Shkerdin, J. Stiens, R. Vounckx, “A multi-valley model for hot free-electron nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 12, 169–180 (2000).
[CrossRef]

1999

G. Shkerdin, J. Stiens, R. Vounckx, “Comparative study of the infra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs,” J. Appl. Phys. 87, 3807–3818 (1999).
[CrossRef]

1991

K. Welford, “Surface plasmon polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
[CrossRef]

M. N. Zervas, “Surface plasmon-polariton waves guided by thin metal films,” Opt. Lett. 16, 720–722 (1991).
[CrossRef] [PubMed]

1990

S. Zollner, S. Gopalan, M. Cardona, “Microscopic theory of intervalley scattering in GaAs: k dependence of deformation potentials and scattering rate,” J. Appl. Phys. 68, 1682–1693 (1990).
[CrossRef]

1987

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

1986

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

1985

S. Adachi, “GaAs, AlAs, and AlxGa1-xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

1982

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53, R123–R181 (1982).
[CrossRef]

1977

M. A. Littlejohn, J. R. Hauser, T. H. Glisson, “Velocity-field characteristics of GaAs with Γ6c-L6c-X6c conduction-band ordering,” J. Appl. Phys. 48, 4587–4590 (1977).
[CrossRef]

Adachi, S.

S. Adachi, “GaAs, AlAs, and AlxGa1-xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

Blakemore, J. S.

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53, R123–R181 (1982).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

Cardona, M.

S. Zollner, S. Gopalan, M. Cardona, “Microscopic theory of intervalley scattering in GaAs: k dependence of deformation potentials and scattering rate,” J. Appl. Phys. 68, 1682–1693 (1990).
[CrossRef]

Cossard, A. C.

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

Cottam, M. G.

M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, Cambridge, UK, 1989), Chap. 6.
[CrossRef]

Damen, T. C.

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

Deveaud, B.

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

Glisson, T. H.

M. A. Littlejohn, J. R. Hauser, T. H. Glisson, “Velocity-field characteristics of GaAs with Γ6c-L6c-X6c conduction-band ordering,” J. Appl. Phys. 48, 4587–4590 (1977).
[CrossRef]

Gopalan, S.

S. Zollner, S. Gopalan, M. Cardona, “Microscopic theory of intervalley scattering in GaAs: k dependence of deformation potentials and scattering rate,” J. Appl. Phys. 68, 1682–1693 (1990).
[CrossRef]

Hauser, J. R.

M. A. Littlejohn, J. R. Hauser, T. H. Glisson, “Velocity-field characteristics of GaAs with Γ6c-L6c-X6c conduction-band ordering,” J. Appl. Phys. 48, 4587–4590 (1977).
[CrossRef]

Littlejohn, M. A.

M. A. Littlejohn, J. R. Hauser, T. H. Glisson, “Velocity-field characteristics of GaAs with Γ6c-L6c-X6c conduction-band ordering,” J. Appl. Phys. 48, 4587–4590 (1977).
[CrossRef]

Lugli, P.

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

Shah, J.

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

Shkerdin, G.

G. Shkerdin, J. Stiens, R. Vounckx, “X-valley influence on hot free electron absorption and nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 19, 29–37 (2002).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “Influence of leaky waves on free-electron-induced nonlinear reflection properties of highly doped n-GaAs layer at medium IR-wavelength,” J. Opt. A Pure Appl. Opt. 3, 493–499 (2001).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “A multi-valley model for hot free-electron nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 12, 169–180 (2000).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “Comparative study of the infra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs,” J. Appl. Phys. 87, 3807–3818 (1999).
[CrossRef]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

Stiens, J.

G. Shkerdin, J. Stiens, R. Vounckx, “X-valley influence on hot free electron absorption and nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 19, 29–37 (2002).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “Influence of leaky waves on free-electron-induced nonlinear reflection properties of highly doped n-GaAs layer at medium IR-wavelength,” J. Opt. A Pure Appl. Opt. 3, 493–499 (2001).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “A multi-valley model for hot free-electron nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 12, 169–180 (2000).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “Comparative study of the infra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs,” J. Appl. Phys. 87, 3807–3818 (1999).
[CrossRef]

Tamir, T.

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

Tilley, D. R.

M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, Cambridge, UK, 1989), Chap. 6.
[CrossRef]

Tsang, W. T.

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

Vounckx, R.

G. Shkerdin, J. Stiens, R. Vounckx, “X-valley influence on hot free electron absorption and nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 19, 29–37 (2002).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “Influence of leaky waves on free-electron-induced nonlinear reflection properties of highly doped n-GaAs layer at medium IR-wavelength,” J. Opt. A Pure Appl. Opt. 3, 493–499 (2001).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “A multi-valley model for hot free-electron nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 12, 169–180 (2000).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “Comparative study of the infra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs,” J. Appl. Phys. 87, 3807–3818 (1999).
[CrossRef]

Welford, K.

K. Welford, “Surface plasmon polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
[CrossRef]

Zervas, M. N.

Zollner, S.

S. Zollner, S. Gopalan, M. Cardona, “Microscopic theory of intervalley scattering in GaAs: k dependence of deformation potentials and scattering rate,” J. Appl. Phys. 68, 1682–1693 (1990).
[CrossRef]

Eur. Phys. J. AP

G. Shkerdin, J. Stiens, R. Vounckx, “A multi-valley model for hot free-electron nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 12, 169–180 (2000).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “X-valley influence on hot free electron absorption and nonlinearities at 10.6 μm in highly doped n-GaAs,” Eur. Phys. J. AP 19, 29–37 (2002).
[CrossRef]

J. Appl. Phys.

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53, R123–R181 (1982).
[CrossRef]

S. Adachi, “GaAs, AlAs, and AlxGa1-xAs: material parameters for use in research and device applications,” J. Appl. Phys. 58, R1–R29 (1985).
[CrossRef]

G. Shkerdin, J. Stiens, R. Vounckx, “Comparative study of the infra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs,” J. Appl. Phys. 87, 3807–3818 (1999).
[CrossRef]

S. Zollner, S. Gopalan, M. Cardona, “Microscopic theory of intervalley scattering in GaAs: k dependence of deformation potentials and scattering rate,” J. Appl. Phys. 68, 1682–1693 (1990).
[CrossRef]

M. A. Littlejohn, J. R. Hauser, T. H. Glisson, “Velocity-field characteristics of GaAs with Γ6c-L6c-X6c conduction-band ordering,” J. Appl. Phys. 48, 4587–4590 (1977).
[CrossRef]

J. Opt. A Pure Appl. Opt.

G. Shkerdin, J. Stiens, R. Vounckx, “Influence of leaky waves on free-electron-induced nonlinear reflection properties of highly doped n-GaAs layer at medium IR-wavelength,” J. Opt. A Pure Appl. Opt. 3, 493–499 (2001).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

K. Welford, “Surface plasmon polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
[CrossRef]

Phys. Rev. B

J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

Phys. Rev. Lett.

J. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Cossard, P. Lugli, “Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy,” Phys. Rev. Lett. 59, 2222–2225 (1987).
[CrossRef] [PubMed]

Other

M. G. Cottam, D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge U. Press, Cambridge, UK, 1989), Chap. 6.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Geometry of multilayer structure.

Fig. 2
Fig. 2

Dependencies of the dielectric permittivity ∊ n on electron temperature t e for Λ LL = 1 × 106 eVcm-1, Λ XL = Λ XX = 0.7 × 109 eV/cm, ΛΓX = 0.8 × 109 eV/cm, λ = 10.6 μm, and t L = 300 K. Different curves correspond to different doping concentrations. (a) Real part and (b) imaginary part.

Fig. 3
Fig. 3

(a) Dependencies of the linear reflection coefficient r lin on the angle of incidence θ for n 0 = 1.2 × 1019 cm-3, buffer thickness b = 0.3 μm, t L = 300 K, and λ = 10.6 μm. Different curves correspond to different n-GaAs layer thicknesses. (b) Dependence of Brewster-type mode conditions: n-GaAs layer thickness and angle of incidence versus doping concentration for a buffer thickness b = 0.3 μm, t L = 300 K, and λ = 10.6 μm.

Fig. 4
Fig. 4

Dependencies of the real (solid curves) and imaginary (dashed curves) parts of the normalized wave vector k/ k 0 of the TM mode exhibiting Brewster-type mode characteristics on the thickness d of the n-GaAs layer for n 0 = 1.2 × 1019 cm-3, buffer thickness b = 0.3 μm, λ = 10.6 μm, and t L = 300 K for two electron temperatures t e = 300 and 800 K.

Fig. 5
Fig. 5

Dependencies of the minimum reflection angle θmin (dashed curves) and the propagation angle ϕ (solid curves) of the Brewster-type mode in the substrate on the thickness d of the n-GaAs layer for n 0 = 1.2 × 1019 cm-3, buffer thickness b = 0.3 μm, λ = 10.6 μ and t L = 300 K for two electron temperatures t e = 300 and 800 K.

Fig. 6
Fig. 6

Angular dependencies of the linear reflection coefficient r lin for three-layer structures: GaAs substrate-metal (silver) layer-air for two wavelengths of λ = 10.6 μm, with silver dielectric permittivity of -6547.2 + 1383.12i and d = 4.167 nm, and λ = 0.633 μm, with silver dielectric permittivity of -19 + 0.53i and d = 55.02 nm.

Fig. 7
Fig. 7

Angular dependencies of the reflection coefficients r lin, r non and electron temperature t e for different MIR light intensities W at n 0 = 1.2 × 1019 cm-3, buffer thickness b = 0.3 μm, n-GaAs thickness d = 0.2 μm, λ = 10.6 μm, and t L = 300 K. Reflection coefficients (solid curves): r lin, unmarked and nonlinear reflection coefficient r non for W 0 = 3 MW/cm2 (double crosses) and W 0= 5 MW/cm2 (circles).

Fig. 8
Fig. 8

Intensity-dependent nonlinear reflection coefficients for a fixed angle of incidence θ = 40° and three doping concentrations: n 0 = 1.18 × 1019, 1.20 × 1019, 1.22 × 1019 cm-3. In all cases, buffer thickness b = 0.3 μm, doped layer thickness d = 0.2 μm, λ = 10.6 μm, and t L = 300 K were used.

Fig. 9
Fig. 9

Intensity-dependent nonlinear reflection coefficients for different combinations of deformation potentials. For Λ LL = 1 × 109 eV/cm (solid curves with markers): Λ XL = ΛΓX = Λ XX = 1.1 × 109 eV/cm (maximum); Λ XL = Λ XX = 0.7 × 109 and ΛΓX = 0.8 × 109 eV/cm (medium); and Λ XL = 0.34 × 109, ΛΓX = 0.5 × 109, and Λ XX = 0.27 × 109 eV/cm (minimum). For Λ LL = 0.6 × 109 eV/cm, Λ XL = Λ XX = 0.7 × 109 and ΛΓX = 0.8 × 109 eV/cm (dotted-dashed curve). In all cases, angle of incidence θ = 40°, doping concentration n 0 = 1.2 × 1019 cm-3, buffer thickness b = 0.3 μm, doped layer thickness d = 0.2 μm, λ = 10.6 μm, and t L = 300 K.

Fig. 10
Fig. 10

Dependencies of electron temperature t e on incident light intensity W 0 for different angles of incidence θ at n 0 = 1.5 × 1019 cm-3, b = 0.3 μm, d = 0.05 μm, Λ LL = 1 × 109 eV/cm, Λ XL = 0.34 × 109 eVcm, ΛΓX = 0.5 × 109 eV/cm, Λ XX = 0.27 × 109 eV/cm, λ = 10 μm, and t L = 300 K.

Fig. 11
Fig. 11

Dependencies of nonlinear reflection coefficient r non on incident light intensity W 0 for different angles of incidence θ at n 0 = 1.5 × 1019 cm-3, b = 0.3 μm, d = 0.05 μm, Λ LL = 1 × 109 eV/cm, Λ XL = 0.34 × 109 eV/cm, ΛΓX = 0.5 × 109 eV/cm, Λ XX = 0.27 × 109 eV/cm, λ = 10.6 μm, and t L = 300 K.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

nω=11-ω˜p2/ω2+iω˜p2/ω3τ˜,
ω˜p=ωp,Γ2+ωp,L2+ωp,X2,1/τ˜=ωp,Γ2/ω˜p2τΓ+ωp,L2/ω˜p2τL+ωp,X2/ω˜p2τX.
Platd=W0 cos θ1-|R|2-|Tb|2+|Rb|2, 
exp2iknd=1-α1α2+1+exp2ikbbα3-1α2-1/α3+11+α1α2-1+exp2ikbbα3-1α2+1/α3+1,
α1=n cos θ/1n/1-sin2 θ,α2=1n/1-sin2 θ/n cos θ,α3=cos θ/11/1-sin2 θ,kn=k0n-1 sin2θ1/2,kb=k01 cos θ, k0=ω/c,
α1=-nkys/1kyn, α2=1kyn/nkyb,α3=kyb/1ky0,kn  kyn=nk02-k21/2,kb  kyb=1k02-k21/2,kys=±1k02-k21/2, ky0=±k02-k21/2,

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