Abstract

We propose a novel scheme of surface plasmon polariton (SPP) amplification that is based on a minority carrier injection in a Schottky diode. This scheme uses compact electrical pumping instead of bulky optical pumping. Compact size and a planar structure of the proposed amplifier allow one to utilize it in integrated plasmonic circuits and couple it easily to passive plasmonic devices. Moreover, this technique can be used to obtain surface plasmon lasing.

© 2011 OSA

1. Introduction

Operation frequency of modern microprocessors does not exceed a few gigahertz due to high heat generation and interconnect delays. SPPs, which are surface electromagnetic waves propagating at the interface between a metal and an insulator, are considered as very promising information carriers that can replace electrons in integrated circuits [13]. An exceedingly short wavelength and a very high spatial localization of the electromagnetic field near the interface allow to get over the usual diffraction limit and design ultracompact interconnects with the transverse size of the order of 100 nm [1,4] that is comparable with electronic components. Unfortunately, high propagation losses due to Joule heating restrict the application of SPPs. Thus, one should increase the SPP propagation length, i.e. partially or fully compensate Joule losses. This can be done by using an active media placed near a metal surface [5]. In recent years, a number of paper devoted to the SPP amplification have been published [614] and several methods have been proposed. Despite the advantages of these methods, the necessity of an external high power pump laser prevents us to use them in nanoscale circuits.

In this paper, we propose a different technique that is based on a minority carrier injection effect in metal-semiconductor contacts that gives one a possibility to use compact electrical pumping instead of a bulky optical approach.

2. Schottky barrier diode

Usually, Schottky diodes are treated as majority carrier devices. For instance, if one has an n-type semiconductor-metal contact, the electron concentration is much greater than the concentration of holes all over the semiconductor at all bias voltages (here and below, only the case of forward bias is considered) and the hole current is much less than the electron one. However, the situation changes drastically when the metal work function ψM exceeds χe+Eg/2, where χe and Eg are the electron affinity and the band gap of the semiconductor, respectively. In this case, the concentration of holes (minority carriers) near the metal-semiconductor contact becomes greater than the concentration of electrons (majority carriers) and it is said that an inversion layer is formed. Under forward bias, holes are injected into the bulk of the semiconductor and recombine with electrons that results in light emission [15]. So, Schottky barriers can be used to design efficient and compact light- [15] and plasmon-emitting diodes [16], but what about lasers and amplifiers? To design a laser, one should satisfy the condition for net stimulated emission or gain [17,18]

FeFhωEg.
Here, ω is the SPP frequency, Fe, Fh are quasi-Fermi levels for electron and holes, respectively.

How can we satisfy inequality (1)? Firstly, if we use a degenerate semiconductor, FeEc is positive nearly everywhere inside the semiconductor under sufficient forward bias. Hence, one should only maximize the difference EvFh. It is obvious that, near the metal-semiconductor contact, Fh is very close to the metal Fermi level Fm=0 and one can increase EvFh by increasing the metal work function or decreasing the electron affinity of the semiconductor. Inside the semiconductor, EvFh will decrease but in the region near the Schottky contact condition (1) is still satisfied. Thus, one should maximize ψMχeEg and make it positive.

To demonstrate the principle of operation of the proposed device, consider a structure depicted in Fig. 1(a) . For simplicity, assume the back contact to be an ideal ohmic contact, i.e.

Fe|z=L=Fh|z=L=Efs|V=0+V=Fm+V=V
where Efs is the Fermi level under zero bias. The boundary conditions at z=0 are [1922]
{Jn|z=0=eυnr(n|z=0n0)Jp|z=0=eυpr(p|z=0p0)
where, Jn and Jp are the electron and hole current densities, e is the electron charge, n0=NcF1/2((ψMχe)/kBT) and p0=NvF1/2((ψMχeEg)/kBT) are quasi-equilibrium electron and hole concentrations at z=0 (F1/2 is the Fermi-Dirac integral), υnr and υpr are effective recombination or collection velocities. We neglect the effect of surface states and image forces on the barrier height, assume the donor concentration to be independent on z and suppose mobilities and diffusion constants to obey the Einstein relation.

 

Fig. 1 (a) Sketch of the ideal Schottky barrier diode and schematic band diagram under zero bias, L = 400 nm, ψ M = 5.4 eV [34,35], ε st = 13.94 [36], χ e = 4.5 eV [36], E g = 0.75 eV that correspond to Ga0.47In0.53As at T = 300 K and donor concentration N d = 9.3 × 1017 cm−3. (b) Carrier density distribution and (c) band diagram under zero bias.

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Thus, we have four boundary conditions (Eqs. (1) and (2)) and six nonlinear first order differential equations that describe the carrier behavior within the semiconductor:

{dϕ/dz=EzdEz/dz=4πe(pn+Nd)/εstdndz=1eDnJnμnnDnEzdpdz=1eDpJp+μppDpEzdJn/dz=eUdJp/dz=eU
where, symbols have their usual meaning [20]. Two missing boundary conditions are certainly ϕ|z=0=0 and ϕ|z=L=V.

The carrier recombination rate consists of three components U=Uspont+Ustim+Unr, as long as there are three recombination processes: spontaneous emission (Uspont), stimulated emission (Ustim) and non-radiative Schockley-Read-Hall and Auger recombination (Unr). In direct-band-gap semiconductors, Unr is usually much less than Uspont, therefore it is not discussed in the present work.

To begin with, we demonstrate that it is possible to satisfy inequality (1). For this purpose, let Ustim be zero, while Uspont=B(npneqpeq), where neq and peq are the equilibrium concentrations and B=1.43×1010cm3s1 for In0.53Ga0.47As [23]. In the presence of degeneracy and in the case of high minority carrier injection, system of Eqs. (4) cannot be solved analytically and we have to implement the Newton-Raphson method. Under zero bias, namely at thermal equilibrium, Fe=Fh=Fm=0 (Figs. 1(b) and 1(c)). As the bias increases, holes are injected into the bulk of the semiconductor and Fh shifts downward. At the same time, the concentration of electrons changes slightly and Fe remains constant (Fig. 2 ). Under high forward bias (Fig. 2(b)), the difference between quasi-Fermi levels exceeds Eg and we satisfy inequality (1). This clearly demonstrates that it is possible to realize a SPP amplifier based on a Schottky barrier diode [24].

 

Fig. 2 Quasi-Fermi levels at V = 0.8 V (a) and V = 0.85 V (b).

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3. SPP dispersion

The dispersion relation for SPPs propagating along the planar interface between a metal and a semiconductor (Fig. 3(a) ) with permittivities ε1 and ε2, respectively, has the form κ2ε1=κ1ε2, where κi=β2(ω/c)2εi is the penetration constant (i=1,2 and β is the SPP wavevector). Assuming the semiconductor to be lossless and taking into account losses in the metal [25], we calculate the propagation length of the SPP at the interface between Au and Ga0.47In0.53As. At a light wavelength of 1.7 µm (0.73 eV), β=(143926+806i)cm1 that corresponds to a wavelength of 436 nm and a propagation length of 6.2 µm. The imaginary part of β is much less than the real one and losses almost do not affect the field distribution and SPP wavelength, therefore we will use the power flow approach. The essence of the method is that only the real parts of permittivities are used to determine the real part of the wavevector (Reβ=144018   cm1), while Imβ is found from the power flow equation [26,27]. This method provides a simple treatment and gives a clear physical interpretation of the SPP attenuation or amplification. Let us denote by P the power flow per unit guide width (P=+Sxdz, where Sx is the x-component of the complex Poynting vector) and by R the Joule loss power per unit guide length per unit guide width (R=ω/8π0Imε1|E|2dz). Then dP/dx=2ImβP=R [27] and consequently Imβ=R/2P=815 cm1. The power flow in the metal is much less than in the semiconductor that is due to the great difference in penetration depths of the SPP field inside the metal (22 nm) and semiconductor (223 nm). Despite that, the absorption in the metal is high enough and the material gain of the order of 2Imβ=1630 cm1 is required in the semiconductor medium to compensate losses.

 

Fig. 3 (a) Schematic view of the SPP propagation along the metal-semiconductor interface. (b) Dependence of the material gain on the minority carrier density in In0.53Ga0.47As at a light wavelength of 1.7 µm. (c) Gain spectra of In0.53Ga0.47As.

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4. SPP amplification by stimulated emission of radiation

Stimulated emission recombination rate is given as

Ustim=gS/ω,
where S is the local optical power density and g is the local optical gain. In a one-electron model, the optical gain connected with band-to-band transitions is given as [18]
g(Fe,Fh)=4π2e2cn¯me02ω|Mb|2+|Menv(E,Eω)|2ρc(EEc)ρv(EvE+ω)[11+exp((EFe)/kBT)11+exp((EωFh)/kBT)]dE,
where me0 is the free-electron mass, ρc and ρv are the densities of states in the conduction and valence bands, n¯ is the refractive index of the semiconductor, Mb is the average matrix element connecting Bloch states near the band edges (6|Mb|2/me0=12.7 eV for Ga0.47In0.53As [28]) and Menv is the envelope matrix element. When the semiconductor is heavily doped, the parabolic band approach becomes inapplicable and band tails must be taken into account [29,30]. We follow Stern's [31,32] approach to calculate the envelope matrix element and use the Gaussian Halperin-Lax band-tail (GHLBT) model to calculate the densities of states. Finally, we fit Eq. (6) to a linear function and use the obtained expression in our solver substituting it into Eqs. (4) and (5). In a heavily doped Ga0.47In0.53As (Nd=4.3×1018cm3) at T=300  K and ω=0 .73 eV, g(n,p)8.76×1016×(min(n,p)3.7×1016) and it is possible to achieve the material gain greater than 1630 cm1  (Figs. 3(b) and (3c)) that is required for the SPP amplification.

Taking into account stimulated emission, we solve Eq. (4) numerically in the same way as it was done in section 2 (Fig. 4 ). For a small signal of 5 mW/µm or less (Fig. 4(a)), the stimulated emission recombination rate is greater than the spontaneous but its absolute value is nevertheless quite small (eU<<(Jn+Jp)/L) and does not affect the carrier distribution (Fig. 4(a)). In this case, the net SPP gain G at V=1.07 V is positive and equals 1/P×(0Lg(z)Sx(z)dzR)=17801630=150cm1. At a high signal power (Fig. 4(b)), eU>(Jn+Jp)/L in the region near the metal-semiconductor interface that affects the carrier density distribution. The material gain is smaller (Fig. 4(b)) and the net SPP gain becomes negative (G=620   cm1 at V=1.07 V and P=50 mW/μm).

 

Fig. 4 Gain, current density (dashed lines correspond to the electron current and solid lines to the hole current) and carrier density distribution across the active region of the plasmonic waveguide at four different biases for two different values of the power per unit guide width.

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5. Conclusion

To conclude, we have proposed a novel SPP amplification scheme that utilizes a compact electrical pumping and gives an ability to design really nanoscale amplifiers and spasers [33]. For the analysis of the scheme, we have developed a fully self-consistent one-dimensional steady-state model of the amplifier and presented an accurate numerical solution.

Acknowledgments

This work was supported in part by the Russian Foundation for Basic Research (grants no. 09-07-00285, 10-07-00618 and 11-07-00505), by the Ministry of Education and Science of the Russian Federation (grants no. P513 and P1144) and by the grant MK-334.2011.9 of the President of the Russian Federation.

References and links

1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef]   [PubMed]  

2. M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010). [CrossRef]   [PubMed]  

3. A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18(11), 11791–11799 (2010). [CrossRef]   [PubMed]  

4. J. A. Conway, S. Sahni, and T. Szkopek, “Plasmonic interconnects versus conventional interconnects: a comparison of latency, crosstalk and energy costs,” Opt. Express 15(8), 4474–4484 (2007). [CrossRef]   [PubMed]  

5. M. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004). [CrossRef]   [PubMed]  

6. J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005). [CrossRef]   [PubMed]  

7. M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008). [CrossRef]   [PubMed]  

8. A. Kumar, S. F. Yu, X. F. Li, and S. P. Lau, “Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides,” Opt. Express 16(20), 16113–16123 (2008). [CrossRef]   [PubMed]  

9. I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010). [CrossRef]  

10. I. Radko, M. G. Nielsen, O. Albrektsen, and S. I. Bozhevolnyi, “Stimulated emission of surface plasmon polaritons by lead-sulphide quantum dots at near infra-red wavelengths,” Opt. Express 18(18), 18633–18641 (2010). [CrossRef]   [PubMed]  

11. M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008). [CrossRef]   [PubMed]  

12. M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010). [CrossRef]  

13. A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011), doi:. [CrossRef]   [PubMed]  

14. P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35(8), 1197–1199 (2010). [CrossRef]   [PubMed]  

15. H. C. Card and B. L. Smith, “Green injection luminescence from forward-biased Au-GaP Schottky barriers,” J. Appl. Phys. 42(13), 5863 (1971). [CrossRef]  

16. D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008). [CrossRef]  

17. N. K. Dutta and Q. Wang, Semiconductor Optical Amplifiers (World Scientific, 2006).

18. H. C. Casey and M. B. Panish, Heterostructure Lasers, Part A (Academic, 1978).

19. C. R. Crowell and S. M. Sze, “Current transport in metal-semiconductor barriers,” Solid-State Electron. 9(11-12), 1035–1048 (1966). [CrossRef]  

20. S. M. Sze, Physics of Semiconductor Devices (Wiley, 1981).

21. J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992). [CrossRef]  

22. M. A. Green and J. Shewchun, “Minority carrier effects upon the small signal and steady-state properties of Schottky diodes,” Solid-State Electron. 16(10), 1141–1150 (1973). [CrossRef]  

23. R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998). [CrossRef]  

24. D. Yu. Fedyanin, A. V. Arsenin, and D. N. Chigrin, “Semiconductor surface plasmon amplifier Based on a Schottky barrier diode,” AIP Conf. Proc. 1291, 112–114 (2010). [CrossRef]  

25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]  

26. D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010). [CrossRef]  

27. D. Yu. Fedyanin and A. V. Arsenin, “Stored light in a plasmonic nanocavity based on extremely-small-energy-velocity modes,” Photonics Nanostruct. Fundam. Appl. 8(4), 264–272 (2010). [CrossRef]  

28. L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

29. B. I. Halperin and M. Lax, “Impurity-band tails in the high-density limit. I. Minimum counting methods,” Phys. Rev. 148(2), 722–740 (1966). [CrossRef]  

30. E. O. Kane, “Thomas-Fermi approach to impure semiconductor band structure,” Phys. Rev. 131(1), 79–88 (1963). [CrossRef]  

31. F. Stern, “Band-tail model for optical absorption and for the mobility edge in amorphous silicon,” Phys. Rev. B 3(8), 2636–2645 (1971). [CrossRef]  

32. H. C. Casey and F. Stern, “Concentration-dependent absorption and spontaneous emission on heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976). [CrossRef]  

33. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef]   [PubMed]  

34. M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998). [CrossRef]  

35. S. Adachi, Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors (Wiley, 2009).

36. Yu. A. Goldberg and N. M. Schmidt, Handbook Series on Semiconductor Parameters, Vol. 2 (World Scientific, 1999).

References

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  • |
  • |

  1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
    [Crossref] [PubMed]
  2. M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
    [Crossref] [PubMed]
  3. A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18(11), 11791–11799 (2010).
    [Crossref] [PubMed]
  4. J. A. Conway, S. Sahni, and T. Szkopek, “Plasmonic interconnects versus conventional interconnects: a comparison of latency, crosstalk and energy costs,” Opt. Express 15(8), 4474–4484 (2007).
    [Crossref] [PubMed]
  5. M. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004).
    [Crossref] [PubMed]
  6. J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
    [Crossref] [PubMed]
  7. M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008).
    [Crossref] [PubMed]
  8. A. Kumar, S. F. Yu, X. F. Li, and S. P. Lau, “Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides,” Opt. Express 16(20), 16113–16123 (2008).
    [Crossref] [PubMed]
  9. I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
    [Crossref]
  10. I. Radko, M. G. Nielsen, O. Albrektsen, and S. I. Bozhevolnyi, “Stimulated emission of surface plasmon polaritons by lead-sulphide quantum dots at near infra-red wavelengths,” Opt. Express 18(18), 18633–18641 (2010).
    [Crossref] [PubMed]
  11. M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
    [Crossref] [PubMed]
  12. M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
    [Crossref]
  13. A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011), doi:.
    [Crossref] [PubMed]
  14. P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35(8), 1197–1199 (2010).
    [Crossref] [PubMed]
  15. H. C. Card and B. L. Smith, “Green injection luminescence from forward-biased Au-GaP Schottky barriers,” J. Appl. Phys. 42(13), 5863 (1971).
    [Crossref]
  16. D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
    [Crossref]
  17. N. K. Dutta and Q. Wang, Semiconductor Optical Amplifiers (World Scientific, 2006).
  18. H. C. Casey and M. B. Panish, Heterostructure Lasers, Part A (Academic, 1978).
  19. C. R. Crowell and S. M. Sze, “Current transport in metal-semiconductor barriers,” Solid-State Electron. 9(11-12), 1035–1048 (1966).
    [Crossref]
  20. S. M. Sze, Physics of Semiconductor Devices (Wiley, 1981).
  21. J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992).
    [Crossref]
  22. M. A. Green and J. Shewchun, “Minority carrier effects upon the small signal and steady-state properties of Schottky diodes,” Solid-State Electron. 16(10), 1141–1150 (1973).
    [Crossref]
  23. R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998).
    [Crossref]
  24. D. Yu. Fedyanin, A. V. Arsenin, and D. N. Chigrin, “Semiconductor surface plasmon amplifier Based on a Schottky barrier diode,” AIP Conf. Proc. 1291, 112–114 (2010).
    [Crossref]
  25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  26. D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010).
    [Crossref]
  27. D. Yu. Fedyanin and A. V. Arsenin, “Stored light in a plasmonic nanocavity based on extremely-small-energy-velocity modes,” Photonics Nanostruct. Fundam. Appl. 8(4), 264–272 (2010).
    [Crossref]
  28. L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).
  29. B. I. Halperin and M. Lax, “Impurity-band tails in the high-density limit. I. Minimum counting methods,” Phys. Rev. 148(2), 722–740 (1966).
    [Crossref]
  30. E. O. Kane, “Thomas-Fermi approach to impure semiconductor band structure,” Phys. Rev. 131(1), 79–88 (1963).
    [Crossref]
  31. F. Stern, “Band-tail model for optical absorption and for the mobility edge in amorphous silicon,” Phys. Rev. B 3(8), 2636–2645 (1971).
    [Crossref]
  32. H. C. Casey and F. Stern, “Concentration-dependent absorption and spontaneous emission on heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976).
    [Crossref]
  33. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
    [Crossref] [PubMed]
  34. M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998).
    [Crossref]
  35. S. Adachi, Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors (Wiley, 2009).
  36. Yu. A. Goldberg and N. M. Schmidt, Handbook Series on Semiconductor Parameters, Vol. 2 (World Scientific, 1999).

2011 (1)

A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011), doi:.
[Crossref] [PubMed]

2010 (9)

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35(8), 1197–1199 (2010).
[Crossref] [PubMed]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

I. Radko, M. G. Nielsen, O. Albrektsen, and S. I. Bozhevolnyi, “Stimulated emission of surface plasmon polaritons by lead-sulphide quantum dots at near infra-red wavelengths,” Opt. Express 18(18), 18633–18641 (2010).
[Crossref] [PubMed]

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18(11), 11791–11799 (2010).
[Crossref] [PubMed]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

D. Yu. Fedyanin, A. V. Arsenin, and D. N. Chigrin, “Semiconductor surface plasmon amplifier Based on a Schottky barrier diode,” AIP Conf. Proc. 1291, 112–114 (2010).
[Crossref]

D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010).
[Crossref]

D. Yu. Fedyanin and A. V. Arsenin, “Stored light in a plasmonic nanocavity based on extremely-small-energy-velocity modes,” Photonics Nanostruct. Fundam. Appl. 8(4), 264–272 (2010).
[Crossref]

2008 (4)

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008).
[Crossref] [PubMed]

A. Kumar, S. F. Yu, X. F. Li, and S. P. Lau, “Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides,” Opt. Express 16(20), 16113–16123 (2008).
[Crossref] [PubMed]

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

2007 (1)

2006 (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

2005 (1)

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

1998 (2)

M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998).
[Crossref]

R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998).
[Crossref]

1992 (1)

J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992).
[Crossref]

1976 (1)

H. C. Casey and F. Stern, “Concentration-dependent absorption and spontaneous emission on heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976).
[Crossref]

1973 (1)

M. A. Green and J. Shewchun, “Minority carrier effects upon the small signal and steady-state properties of Schottky diodes,” Solid-State Electron. 16(10), 1141–1150 (1973).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1971 (2)

F. Stern, “Band-tail model for optical absorption and for the mobility edge in amorphous silicon,” Phys. Rev. B 3(8), 2636–2645 (1971).
[Crossref]

H. C. Card and B. L. Smith, “Green injection luminescence from forward-biased Au-GaP Schottky barriers,” J. Appl. Phys. 42(13), 5863 (1971).
[Crossref]

1966 (2)

C. R. Crowell and S. M. Sze, “Current transport in metal-semiconductor barriers,” Solid-State Electron. 9(11-12), 1035–1048 (1966).
[Crossref]

B. I. Halperin and M. Lax, “Impurity-band tails in the high-density limit. I. Minimum counting methods,” Phys. Rev. 148(2), 722–740 (1966).
[Crossref]

1963 (1)

E. O. Kane, “Thomas-Fermi approach to impure semiconductor band structure,” Phys. Rev. 131(1), 79–88 (1963).
[Crossref]

Adegoke, J. A.

Ahrenkiel, R. K.

R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998).
[Crossref]

Albrektsen, O.

Ambati, M.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

Arsenin, A. V.

D. Yu. Fedyanin, A. V. Arsenin, and D. N. Chigrin, “Semiconductor surface plasmon amplifier Based on a Schottky barrier diode,” AIP Conf. Proc. 1291, 112–114 (2010).
[Crossref]

D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010).
[Crossref]

D. Yu. Fedyanin and A. V. Arsenin, “Stored light in a plasmonic nanocavity based on extremely-small-energy-velocity modes,” Photonics Nanostruct. Fundam. Appl. 8(4), 264–272 (2010).
[Crossref]

Aussenegg, F. R.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Bahoura, M.

Bartal, G.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

Barus, M.

J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992).
[Crossref]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

Berini, P.

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

Bolger, P. M.

A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011), doi:.
[Crossref] [PubMed]

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35(8), 1197–1199 (2010).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

Brongersma, M. L.

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

Card, H. C.

H. C. Card and B. L. Smith, “Green injection luminescence from forward-biased Au-GaP Schottky barriers,” J. Appl. Phys. 42(13), 5863 (1971).
[Crossref]

Casey, H. C.

H. C. Casey and F. Stern, “Concentration-dependent absorption and spontaneous emission on heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976).
[Crossref]

Chigrin, D. N.

D. Yu. Fedyanin, A. V. Arsenin, and D. N. Chigrin, “Semiconductor surface plasmon amplifier Based on a Schottky barrier diode,” AIP Conf. Proc. 1291, 112–114 (2010).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Conway, J. A.

Crowell, C. R.

C. R. Crowell and S. M. Sze, “Current transport in metal-semiconductor barriers,” Solid-State Electron. 9(11-12), 1035–1048 (1966).
[Crossref]

Danz, N.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

De Leon, I.

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

Dickson, W.

A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011), doi:.
[Crossref] [PubMed]

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35(8), 1197–1199 (2010).
[Crossref] [PubMed]

Ditlbacher, H.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Donoval, D.

J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992).
[Crossref]

Ellingson, R.

R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998).
[Crossref]

Eng, L.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[Crossref] [PubMed]

Fainman, Y.

Fedyanin, D. Yu.

D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010).
[Crossref]

D. Yu. Fedyanin, A. V. Arsenin, and D. N. Chigrin, “Semiconductor surface plasmon amplifier Based on a Schottky barrier diode,” AIP Conf. Proc. 1291, 112–114 (2010).
[Crossref]

D. Yu. Fedyanin and A. V. Arsenin, “Stored light in a plasmonic nanocavity based on extremely-small-energy-velocity modes,” Photonics Nanostruct. Fundam. Appl. 8(4), 264–272 (2010).
[Crossref]

Fujimoto, Y.

M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998).
[Crossref]

Galler, N.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Gather, M. C.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

Genov, D. A.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

Gladun, A. D.

D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010).
[Crossref]

Grafström, S.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[Crossref] [PubMed]

Green, M. A.

M. A. Green and J. Shewchun, “Minority carrier effects upon the small signal and steady-state properties of Schottky diodes,” Solid-State Electron. 16(10), 1141–1150 (1973).
[Crossref]

Grmanova, A.

J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992).
[Crossref]

Halperin, B. I.

B. I. Halperin and M. Lax, “Impurity-band tails in the high-density limit. I. Minimum counting methods,” Phys. Rev. 148(2), 722–740 (1966).
[Crossref]

Hickey, S. G.

Hohenau, A.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Johnston, S.

R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998).
[Crossref]

Kane, E. O.

E. O. Kane, “Thomas-Fermi approach to impure semiconductor band structure,” Phys. Rev. 131(1), 79–88 (1963).
[Crossref]

Koller, D. M.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Krasavin, A. V.

Krenn, J. R.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Kumar, A.

Lau, S. P.

Lax, M.

B. I. Halperin and M. Lax, “Impurity-band tails in the high-density limit. I. Minimum counting methods,” Phys. Rev. 148(2), 722–740 (1966).
[Crossref]

Leiman, V. G.

D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010).
[Crossref]

Leitner, A.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Leosson, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

Li, X. F.

Liebscher, L.

List, E. J. W.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Mayy, M.

Meerholz, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

Nagl, V.

J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992).
[Crossref]

Nakamura, A.

M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998).
[Crossref]

Nam, S. H.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

Nezhad, M.

Nielsen, M. G.

Noginov, M. A.

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref] [PubMed]

Podolskiy, V. A.

Racko, J.

J. Racko, D. Donoval, M. Barus, V. Nagl, and A. Grmanova, “Revised theory of current transport through the Schottky structure,” Solid-State Electron. 35(7), 913–919 (1992).
[Crossref]

Radko, I.

Reil, F.

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Reynolds, K.

Ritzo, B. A.

Sahni, S.

Seidel, J.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[Crossref] [PubMed]

Shalaev, V. M.

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

Shewchun, J.

M. A. Green and J. Shewchun, “Minority carrier effects upon the small signal and steady-state properties of Schottky diodes,” Solid-State Electron. 16(10), 1141–1150 (1973).
[Crossref]

Skryabin, D. V.

Smith, B. L.

H. C. Card and B. L. Smith, “Green injection luminescence from forward-biased Au-GaP Schottky barriers,” J. Appl. Phys. 42(13), 5863 (1971).
[Crossref]

Stern, F.

H. C. Casey and F. Stern, “Concentration-dependent absorption and spontaneous emission on heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976).
[Crossref]

F. Stern, “Band-tail model for optical absorption and for the mobility edge in amorphous silicon,” Phys. Rev. B 3(8), 2636–2645 (1971).
[Crossref]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

Sze, S. M.

C. R. Crowell and S. M. Sze, “Current transport in metal-semiconductor barriers,” Solid-State Electron. 9(11-12), 1035–1048 (1966).
[Crossref]

Szkopek, T.

Tetz, K.

Uda, M.

M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998).
[Crossref]

Ulin-Avila, E.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

Vo, T. P.

A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011), doi:.
[Crossref] [PubMed]

Wanlass, M.

R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998).
[Crossref]

Yamamoto, T.

M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998).
[Crossref]

Yu, S. F.

Zayats, A. V.

Zhang, X.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

Zhu, G.

AIP Conf. Proc. (1)

D. Yu. Fedyanin, A. V. Arsenin, and D. N. Chigrin, “Semiconductor surface plasmon amplifier Based on a Schottky barrier diode,” AIP Conf. Proc. 1291, 112–114 (2010).
[Crossref]

Appl. Phys. Lett. (1)

R. K. Ahrenkiel, R. Ellingson, S. Johnston, and M. Wanlass, “Recombination lifetime of In0.53Ga0.47As as a function of doping density,” Appl. Phys. Lett. 72(26), 3470–3472 (1998).
[Crossref]

J. Appl. Phys. (2)

H. C. Casey and F. Stern, “Concentration-dependent absorption and spontaneous emission on heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976).
[Crossref]

H. C. Card and B. L. Smith, “Green injection luminescence from forward-biased Au-GaP Schottky barriers,” J. Appl. Phys. 42(13), 5863 (1971).
[Crossref]

J. Electron Spectrosc. Relat. Phenom. (1)

M. Uda, A. Nakamura, T. Yamamoto, and Y. Fujimoto, “Work function of polycrystalline Ag, Au and Al,” J. Electron Spectrosc. Relat. Phenom. 88-91, 643–648 (1998).
[Crossref]

J. Opt. (1)

D. Yu. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12(1), 015002 (2010).
[Crossref]

Nano Lett. (2)

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[Crossref] [PubMed]

A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett. 11(6), 2231–2235 (2011), doi:.
[Crossref] [PubMed]

Nat. Photonics (3)

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

D. M. Koller, A. Hohenau, H. Ditlbacher, N. Galler, F. Reil, F. R. Aussenegg, A. Leitner, E. J. W. List, and J. R. Krenn, “Organic plasmon emitting diode,” Nat. Photonics 2(11), 684–687 (2008).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Photonics Nanostruct. Fundam. Appl. (1)

D. Yu. Fedyanin and A. V. Arsenin, “Stored light in a plasmonic nanocavity based on extremely-small-energy-velocity modes,” Photonics Nanostruct. Fundam. Appl. 8(4), 264–272 (2010).
[Crossref]

Phys. Rev. (2)

B. I. Halperin and M. Lax, “Impurity-band tails in the high-density limit. I. Minimum counting methods,” Phys. Rev. 148(2), 722–740 (1966).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Sketch of the ideal Schottky barrier diode and schematic band diagram under zero bias, L = 400 nm, ψ M = 5.4 eV [34,35], ε st = 13.94 [36], χ e = 4.5 eV [36], E g = 0.75 eV that correspond to Ga0.47In0.53As at T = 300 K and donor concentration N d = 9.3 × 1017 cm−3. (b) Carrier density distribution and (c) band diagram under zero bias.

Fig. 2
Fig. 2

Quasi-Fermi levels at V = 0.8 V (a) and V = 0.85 V (b).

Fig. 3
Fig. 3

(a) Schematic view of the SPP propagation along the metal-semiconductor interface. (b) Dependence of the material gain on the minority carrier density in In0.53Ga0.47As at a light wavelength of 1.7 µm. (c) Gain spectra of In0.53Ga0.47As.

Fig. 4
Fig. 4

Gain, current density (dashed lines correspond to the electron current and solid lines to the hole current) and carrier density distribution across the active region of the plasmonic waveguide at four different biases for two different values of the power per unit guide width.

Equations (6)

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F e F h ω E g .
F e | z = L = F h | z = L = E fs | V = 0 + V = F m + V = V
{ J n | z = 0 = e υ nr ( n | z = 0 n 0 ) J p | z = 0 = e υ pr ( p | z = 0 p 0 )
{ d ϕ / d z = E z d E z / d z = 4 π e ( p n + N d ) / ε st d n d z = 1 e D n J n μ n n D n E z d p d z = 1 e D p J p + μ p p D p E z d J n / d z = e U d J p / d z = e U
U stim = g S / ω ,
g ( F e , F h ) = 4 π 2 e 2 c n ¯ m e 0 2 ω | M b | 2 + | M env ( E , E ω ) | 2 ρ c ( E E c ) ρ v ( E v E + ω ) [ 1 1 + exp ( ( E F e ) / k B T ) 1 1 + exp ( ( E ω F h ) / k B T ) ] d E ,

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