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Efficiency enhancement for SiN-based light emitting device through introduction of Si nanocones in emitting layer

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Abstract

Silicon nitride-based light-emitting devices were fabricated with a SiNx emitting layer grown on annealed Si film of dense nano-crystalline cones. Comparative studies revealed that the patterned SiNx emitting layer, with embedding nanocrystalline Si cones and a rough surface morphology of its own, manifests a much enhanced, even doubled at sufficiently large injected current density, electroluminescence efficiency. Both the increased light-extraction capability and the effective hole-blocking by the presence of Si nanocones, the latter is favorable for the balance of carrier injection in emitting layer, are responsible for this remarkable efficiency enhancement. The current work established an alternative approach toward the fabrication of more efficient SiN-based light-emitting devices.

© 2015 Optical Society of America

1. Introduction

In order to realize monolithic integration of electronic and optical devices on mass-produced Si chips, lots of research has been conducted in pursuit of more efficient Si-based light sources operating at room temperature [17]. Of the various Si-based materials investigated, Si nanostructures embedded in a Si oxide matrix were found to exhibit excellent photoluminescence properties [4]. Unfortunately, the electroluminescence (EL) from this system suffers from the difficulty of electron injection as there an oxide-based matrix is confronted. Besides the work following various strategies to increase carrier injection efficiency in the Si/silicon dioxide systems [8], much effort has been devoted to searching for other Si-based materials [916]. In particular, the Si/silicon nitride system has attracted considerable interest, because it not only exhibits excellent photoluminescence properties but also features narrow band gaps (2.0-5.1 eV) which constitute a low injection barrier for carrier transport. This makes it quite favorable for designing stable and efficient EL structures [1113, 17, 18]. Even though good progress has been made, it still remains a great challenge to develop more efficient SiN-based light-emitting devices (LEDs). For LEDs, the external quantum efficiency depends strongly on the internal quantum efficiency (ηin) and the light extraction efficiency (ηex). The internal quantum efficiency is associated with the recombination probability of electron-hole pairs, which relies on the nature of the active layer and the device design. For example, the asymmetric band offset between SiN and Si may result in an unbalanced electron- and hole- transport in device, which inevitably deteriorates the radiative recombination probability and thus lowers the internal quantum efficiency of the SiN-based devices [15]. On the other hand, the large refractive index contrast between air (n = 1) and SiNx (n≈2.3) also leads to considerable Fresnel loss and total internal reflection at the abrupt interface, reducing significantly the light extraction efficiency [19].

In this work we report the fabrication of SiN-based LEDs with a SiNx emitting layer grown on an annealed Si film of dense nano-crystalline cones, inspired by our previous work on fabricating Si quantum dot-assisted silicon nitride-based LEDs [20]. The patterned SiNx emitting layer, with embedding nanocrystalline Si cones and a rough surface morphology of its own, gives rise to a much enhanced, even doubled at sufficiently large injected current density, EL efficiency, which can be attributed to both the increased light-extraction efficiency and the effective hole-blocking by Si nanocones. This established an alternative approach toward the fabrication of more efficient SiN-based LEDs.

2. Experimental

An a-Si:H layer 20 nm in thickness was initially deposited onto p-type Si (100) wafers (2 Ωcm) in a plasma enhanced chemical vapor deposition system using a mixture of SiH4 and H2 in a flux ratio of 1:7 as working gas. The pressure in the chamber was kept at 60 Pa, and the substrate maintained at 250 °C. An RF power of 30 W was supplied. To fabricate the Si nanocones, the a-Si:H layer was subjected to thermal annealing at 1100 °C in the N2 atmosphere for half an hour. Onto the thermally annealed Si layer, a 40 nm-thick SiNx layer would be grown by using the hydrogen and ammonia-diluted silane as working gases, other parameters were specified in the previous work [20]. Such SiNx layers were also directly grown onto the Si (100) substrate for comparative study. For brevity and clarity, the SiNx layers grown on the annealed Si layer will be referred to as patterned SiNx layer, while those grown directly on the Si substrate are referred to as flat SiNx layer, in the following discussion. At the final stage, dot-shaped aluminum-doped zinc oxide (AZO) top electrode of 1.5 mm in diameter was deposited onto the SiNx active layer. Aluminum layer was evaporated on the back of the substrate to serve as the bottom electrode. Surface morphology of the layers at different stages was inspected by using an atomic force microscope (AFM, NanoscopeII) operated in the tapping mode. The AFM tip is made from n-type Si (0.01-0.025 ohm•cm−1). The tip radius is less than 10 nm, and the geometry of the cantilever is specified by a length of 125 μm, a width of 35 μm, and a thickness of 4.5 μm, respectively, while the probe is 15 μm in height. The force constant of the cantilever was adjusted between 25 and 75 N• m−1. Room-temperature electroluminescence driven by a dc power source was recorded by using a Jobin-Yvon fluorolog-3 spectrophotometer, with the frontispiece of the device rightly facing the photo multiplier of the spectrophotometer. Reflectance measurements were performed before metallization. The reflectance spectra were measured by using an UV/Visible/NIR spectrophotometer (Shimadzu UV-3600) with an integrating sphere. The optical bandgap, Eopt, of the nc-Si thin layers with nanocones was calculated from the absorption coefficient [11]. A Keithley 2611A source meter was employed for the measurement of the I–V characteristic of the devices.

3. Results and discussion

The morphological features of the precursor Si-layer with nanocones and the subsequently grown SiNx layer were characterized by using AFM. Fig. 1(a) displays the image of a Si layer, ~20 nm in thickness in the as-deposited status, which had been annealed at 1100 °C. Vertically aligned Si nanocones are clearly observed, arising from the formation of Si nanocrystals. The nanocones have a base diameter of 15-40 nm, and are generally 2-10 nm in height. The SiNx emitting layer subsequently grown on such an annealed Si-layer also reveals a surface morphology with nanocones (Fig. 1(b))—thus it can be referred to as patterned SiNx layer—though the cones are now less dense and also appear smaller in size. For comparison, the AFM image for a SiNx layer directly grown on the substrate is presented in Fig. 1(c), which reveals a very flat surface –the root-mean-square roughness measures only 0.4 nm in contrast to the value of 1.8 nm for Fig. 1(b). Obviously, the Si nanocones in the precursor Si-layer survived the subsequent growth of SiNx emitting layer, and further defined the structure and consequently the surface morphology of the latter.

 figure: Fig. 1

Fig. 1 Atomic force microscopic images of (a) a ~20 nm thick layer of Si showing dense nanocones arising from thermal annealing; (b) the Si layer in (a) covered with a SiNx layer of 40 nm in thickness; and (c) a SiNx layer directly grown onto the Si substrate for comparison.

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The differing surface morphology for the SiNx emitting layers brings with it a significant variation to the efficacy of light trapping. As in shown in Fig. 2, the reflectance spectrum for the patterned SiNx layer with nanocones is much lower in the whole spectral range of concern (400-1200 nm) than that for the flat SiNx layer. In the wavelength range from 500 to 850 nm, the reflectance drop measures within 40-90%, which implies that the presence of embedding Si nanocones can increase light extraction from the sample. This is because the nanocones serve as an effective medium with gradient refractive index, thus extending the critical angle and enhancing the light extraction efficiency [21].

 figure: Fig. 2

Fig. 2 Reflectance spectra from the patterned SiNx layer (solid line) and from the flat SiNx layer (dashed line), respectively.

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The inset of Fig. 3 displays the EL spectra for the two devices, one made of a patterned SiNx emitting layer with Si nanocones and the other made of a flat SiNx emitting layer, under the same injected current density of 793 mA/cm2. Both EL spectra feature a broad band centered at around 750 nm. However, the EL from the device made of patterned SiNx emitting layer is remarkably more intensive. The integrated EL intensities of the devices as a function of injected current density are depicted in Fig. 3. The EL intensities in both devices increase monotonically with the increasing injected current density. However, the EL intensity from the device made of patterned SiNx emitting layer is much intensive, particularly when the injected current density is raised over 500 mA/cm2, and it is doubled at 793 mA/cm2 than that from the device made of flat SiNx layer, of which the emission seems saturated from 700 mA/cm2. At this stage, one may speculate that the increased light-extraction efficiency resulting from Si nanocones in the emitting layer is responsible for the enhanced EL efficiency of the device. However, reflectance spectra reveal that the reflectance of the device made of patterned SiNx emitting layer has been reduced only by 40-90% in the wavelength range from 500 to 850 nm (Cf. Figure 2), the EL enhancement cannot be accounted for by the presence of Si nanocones in emitting layer alone. There might be other factors responsible for the large ratio of EL efficiencies for the two devices operated under large injected current density. In fact, from Fig. 4 we can found that the EL efficiency for the device made of flat SiNx emitting layer begins to drop down when the injected current density is greater than 450 mA/cm2. This efficiency drop has been observed in SiN-based LEDs long before, which is ascribed to carrier overflow and/or the process of Auger non-radiative recombination [22]. Obviously, this efficiency drop has not been confronted by the device made of patterned SiNx emitting layer, even for an injected current density up to ~800 mA/cm2. This is to say that the presence of Si nanocones might bring about an effective suppression of carrier overflow and/or the Auger nonradiative recombination process.

 figure: Fig. 3

Fig. 3 Integrated EL intensities as a function of the injected current density for devices prepared with the patterned SiNx emitting layer (empty square) and with a flat SiNx emitting layer (solid square), respectively. Inset shows the EL spectra of corresponding devices, driven by an injected current density of 793 mA/cm2. The driving voltage for the former (referring to the solid line) is 28 V, while for the latter (referring to the dashed line) it is 24 V.

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 figure: Fig. 4

Fig. 4 Ratios of the integrated EL intensity to the injection current density as a function of the latter for the devices made of a patterned (empty square) and of a flat (solid square) SiNx emitting layer, respectively.

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To further understand the improved EL characteristics, the tentative dominant process of recombination in the devices was investigated. Theoretically, the dominant process of recombination in LED can be described by the Z parameter. Given the Boltzmann statistics of carriers and an absence of leakage currents, the injected current can be expressed as

I=NZ(1<Z<3)
where N is the carrier concentration and Z is power index [22, 23]. Z = 1, 2 and 3 represent the recombination of carriers via defect states, radiative and Auger process, respectively [22, 23]. Assuming that the EL intensity (P) is proportional to the radiative recombination of electron-hole pairs, that is P~N2, Eq. (1) can be transformed to show the Z parameter as follows [22]:
1n(I) =Z ln (P1/2)+C
where C is constant. Thus, the Z parameter can be estimated from the ln (P1/2)-dependence of ln (I). From Fig. 5, a Z value of 1.44 is obtained for the device made of flat SiNx emitting layer, while for the device made of patterned SiNx emitting layer the Z value is approximately 1.61. This is to say that with the presence of Si nanocones in the emitting layer, the dominant recombination mechanism makes a shift towards the bimolecular radiative recombination process, or in other words the nonradiative recombination process has been suppressed to some extent [22]. For the emitting medium here concerned, the valence band offset between Si and SiNx is smaller than the conduction band offset. Consequently, hole injection is much easier than electron injection. This will cause an unbalanced electron- and hole- transport in the SiNx emitting layer. In fact, the unbalanced carrier injection in SiNx emitting layer would be more serious due to the fact that the injection barrier for holes from the p-Si anode is much lower than that for electrons from the AZO cathode. Undoubtedly, the hole overflow lowers the electron-hole pair recombination probability. For the device made of a patterned SiNx emitting layer with Si nanocones, it is speculated that the larger band gap of Si nanocrystals (1.4 eV) with respect to p-Si (1.1 eV) anode can create a quite effective energy barrier, as is shown in the inset of Fig. 6(a).This energy barrier alleviates the overflow of the holes, and thus balances to some extent the injected electrons and holes in the emitting layer, resulting in an increase of radiative recombination probability. This well explains the enhancement in EL efficiency and the reduction of efficiency drop in the device made of patterned SiNx emitting layer. Therefore, we can say that the improved performance of the LED device by the introduction of Si nanocones in the emitting layer comes also partly from the increased radiative recombination probability resulting from the suppression of hole overflow.

 figure: Fig. 5

Fig. 5 Ln (I) as a function of ln (P1/2) for the devices made of a patterned (empty triangle) and of a flat (solid triangle) SiNx emitting layer. The calculated Z parameter for each curve is also specified.

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 figure: Fig. 6

Fig. 6 (a) Current-voltage characteristics of devices made of a patterned (empty triangle) and of a flat (solid triangle) SiNx emitting layer, respectively. Inset shows the band diagram for the LED made of patterned SiNx emitting layer, which is drawn according to the electron affinity (χe) and band gaps (Eg) of Si quantum dots, SiNx layer, nanocrystalline Si (nc-Si), bulk Si and aluminum-doped zinc oxide, respectively. The values are taken from Refs [2427]. (b) The trap-assisted tunneling plot based on the In(I)-E−1 relation for the device made of patterned SiNx emitting layer and the Poole-Frenkel plots based on the ln(J/E)-E1/2 relation for the device made of flat SiNx emitting layer, respectively. E is in MV cm−1.

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Figure 6(a) presents the I-V characteristics of the devices made of a patterned and of a flat SiNx emitting layer, respectively. The injected current in the device made of patterned emitting layer with Si nanocones is obviously lower at the same forward applied voltage. Since hole conduction by the Poole-Frenkel emission process dominates the current at high voltages, as confirmed in our previous work [20], the decrease of the injected current in this device strongly indicates that hole injection could have been partially suppressed. From Fig. 6(b) it is also found that the I-V characteristic for the device made of patterned emitting layer could be better fitted by the ln(I)-E−1 relation rather than the ln(J/E)-E1/2 relation. This indicates that the carrier transport process in such a device is dominantly governed by the trap-assisted tunneling behavior rather than the Poole-Frenkel hole conduction [28]. In other words, the PF hole conduction in the device with Si nanocones was suppressed to some extent.

4. Conclusion

In summary, the improved performance of Si quantum dot-based silicon nitride light-emitting devices was investigated. With introduction of Si nanocones in the working layer, the EL efficiency of the device can be significantly enhanced, in some cases even more than doubled. The improved EL efficiency comes presumably from, besides the increase of the light-extraction efficacy, also the hole-blocking by Si nanocones, which can effectively suppress the overflow of holes. The present advancement provides an alternative approach toward the fabrication of more efficient SiN-based light-emitting devices.

Acknowledgments

This work was supported by the national natural science foundation of China grant nos. 61274140 and 61306003.

References and links

1. D. J. DiMaria, J. R. Kirtley, E. J. Pakulis, D. W. Dong, T. S. Kuan, F. L. Pesavento, T. N. Theis, J. A. Cutro, and S. D. Brorson, “Electroluminescence studies in silicon dioxide films containing tiny silicon islands,” J. Appl. Phys. 56(2), 401–416 (1984). [CrossRef]  

2. A. G. Cullis and L. T. Canham, “Visible light emission due to quantum size effects in highly porous crystalline silicon,” Nature 353(6342), 335–338 (1991). [CrossRef]  

3. K. Chen, X. Huang, J. Xu, and D. Feng, “Visible photoluminescence in crystallized amorphous Si:H/SiNx:H multiquantum-well structures,” Appl. Phys. Lett. 61(17), 2069–2071 (1992). [CrossRef]  

4. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408(6811), 440–444 (2000). [CrossRef]   [PubMed]  

5. N. M. Park, C. J. Choi, T. Y. Seong, and S. J. Park, “Quantum confinement in amorphous silicon quantum dots embedded in silicon nitride,” Phys. Rev. Lett. 86(7), 1355–1357 (2001). [CrossRef]   [PubMed]  

6. R. J. Walters, G. I. Bourianoff, and H. A. Atwater, “Field-effect electroluminescence in silicon nanocrystals,” Nat. Mater. 4(2), 143–146 (2005). [CrossRef]   [PubMed]  

7. H.-Y. Tai, C.-H. Cheng, and G.-R. Lin, “Blue-green light emission from Si and SiC quantum dots co-doped Si-rich SiC p-i-n junction diode,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200507 (2014).

8. G. R. Lin, C. J. Lin, and H. C. Kuo, “Improving carrier transport and light emission in a silicon-nanocrystal based MOS light-emitting diode on silicon nanopillar array,” Appl. Phys. Lett. 91(9), 093122 (2007). [CrossRef]  

9. R. Huang, K. Chen, B. Qian, S. Chen, W. Li, J. Xu, Z. Ma, and X. Huang, “Oxygen induced strong green light emission from low-temperature grown amorphous silicon nitride films,” Appl. Phys. Lett. 89(22), 221120 (2006). [CrossRef]  

10. R. Huang, K. Chen, P. Han, H. Dong, X. Wang, D. Chen, W. Li, J. Xu, Z. Ma, and X. Huang, “Strong green-yellow electroluminescence from oxidized amorphous silicon nitride light-emitting devices,” Appl. Phys. Lett. 90(9), 093515 (2007). [CrossRef]  

11. R. Huang, Z. Lin, Y. Guo, C. Song, X. Wang, J. Song, H. Lin, L. Xu, and H. Li, “Bright red, orange-yellow and white switching photoluminescence from silicon oxynitride films with fast decay dynamics,” Opt. Mater. Express 4(2), 205–212 (2014).

12. Z. H. Cen, T. P. Chen, L. Ding, Y. Liu, J. I. Wong, M. Yang, Z. Liu, W. P. Goh, F. R. Zhu, and S. Fung, “Strong violet and green-yellow electroluminescence from silicon nitride thin films multiply implanted with Si ions,” Appl. Phys. Lett. 94(4), 041102 (2009). [CrossRef]  

13. S. Yerci, R. Li, S. O. Kucheyev, T. V. Buuren, S. N. Basu, and L. D. Negro, “Visible and 1.54 m emission from amorphous silicon nitride films by reactive cosputtering,” IEEE J. Sel. Top. Quantum Electron. 16(1), 114–123 (2010). [CrossRef]  

14. J. Wang, V. Suendo, A. Abramov, L. Yu, and P. Roca i Cabarrocas, “Strongly enhanced tunable photoluminescence in polymorphous silicon carbon thin films via excitation-transfer mechanism,” Appl. Phys. Lett. 97(22), 221113 (2010). [CrossRef]  

15. L. Kamyab, M. B. Yu. Rusli, L. Ding, and G.-Q. Lo, “Electroluminescence from amorphous-SiNx:H/SiO2 multilayers using lateral carrier injection,” Appl. Phys. Lett. 98(6), 061105 (2011). [CrossRef]  

16. X. Wang, R. Huang, C. Song, Y. Guo, and J. Song, “Effect of barrier layers on electroluminescence from Si/SiOxNy multilayer structures,” Appl. Phys. Lett. 102(8), 081114 (2013). [CrossRef]  

17. B. H. Kim, R. F. Davis, C.-H. Cho, and S.-J. Park, “Effect of injection current density on electroluminescence in silicon quantum dot light-emitting diodes,” Appl. Phys. Lett. 95(15), 153103 (2009). [CrossRef]  

18. F. Wang, D. Li, D. Yang, and Q. Que, “Tailoring effect of enhanced local electric field from metal nanoparticles on electroluminescence of silicon-rich silicon nitride,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4602504 (2013). [CrossRef]  

19. K.-H. Kim, J.-H. Shin, N.-M. Park, C. Huh, T.-Y. Kim, K.-S. Cho, J. C. Hong, and G. Y. Sung, “Enhancement of light extraction from a silicon quantum dot light-emitting diode containing a rugged surface pattern,” Appl. Phys. Lett. 89(19), 191120 (2006). [CrossRef]  

20. R. Huang, J. Song, X. Wang, Y. Q. Guo, C. Song, Z. H. Zheng, X. L. Wu, and P. K. Chu, “Origin of strong white electroluminescence from dense Si nanodots embedded in silicon nitride,” Opt. Lett. 37(4), 692–694 (2012). [CrossRef]   [PubMed]  

21. Y. Liu, J. Xu, H. Sun, S. Sun, W. Xu, L. Xu, and K. Chen, “Depth-dependent anti-reflection and enhancement of luminescence from Si quantum dots-based multilayer on nano-patterned Si substrates,” Opt. Express 19(4), 3347–3352 (2011). [CrossRef]   [PubMed]  

22. D. Li, F. Wang, D. Yang, and D. Que, “Reduction of the efficiency droop in silicon nitride light-emitting devices by localized surface plasmons,” Appl. Phys. Lett. 102(8), 081108 (2013). [CrossRef]   [PubMed]  

23. W. Mu, P. Zhang, J. Xu, S. Sun, J. Xu, W. Li, and K. Chen, “Direct-current and Alternating-current Driving Si Quantum Dots-based Light Emitting Device,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200106 (2014).

24. J. Warga, R. Li, S. N. Basu, and L. Dal Negro, “Electroluminescence from silicon-rich nitride/silicon superlattice structures,” Appl. Phys. Lett. 93(15), 151116 (2008). [CrossRef]  

25. M. Wang, J. Huang, Z. Yuan, A. Anopchenko, D. L. D. Yang, and L. Pavesi, “Light emission properties and mechanism of low-temperature prepared amorphous SiNx films. II. Defect states electroluminescence,” J. Appl. Phys. 104(8), 083505 (2008).

26. A. J. Bennett, P. N. Stavrinou, C. Roberts, R. Murray, G. Parry, and J. S. Roberts, “A comparative study of spontaneous emission and carrier recombination processes in InGaAs quantum dots and GaInNAs quantum wells emitting near 1300 nm,” J. Appl. Phys. 92(10), 6215–6218 (2002). [CrossRef]  

27. D. Li, F. Wang, D. Yang, and D. Que, “Reduction of the efficiency droop in silicon nitride light-emitting devices by localized surface plasmons,” Appl. Phys. Lett. 102(8), 081108 (2013). [CrossRef]   [PubMed]  

28. R. Huang, D. Q. Wang, H. L. Ding, X. Wang, K. J. Chen, J. Xu, Y. Q. Guo, J. Song, and Z. Y. Ma, “Enhanced electroluminescence from SiN-based multilayer structure by laser crystallization of ultrathin amorphous Si-rich SiN layers,” Opt. Express 18(2), 1144–1150 (2010). [CrossRef]   [PubMed]  

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Figures (6)

Fig. 1
Fig. 1 Atomic force microscopic images of (a) a ~20 nm thick layer of Si showing dense nanocones arising from thermal annealing; (b) the Si layer in (a) covered with a SiNx layer of 40 nm in thickness; and (c) a SiNx layer directly grown onto the Si substrate for comparison.
Fig. 2
Fig. 2 Reflectance spectra from the patterned SiNx layer (solid line) and from the flat SiNx layer (dashed line), respectively.
Fig. 3
Fig. 3 Integrated EL intensities as a function of the injected current density for devices prepared with the patterned SiNx emitting layer (empty square) and with a flat SiNx emitting layer (solid square), respectively. Inset shows the EL spectra of corresponding devices, driven by an injected current density of 793 mA/cm2. The driving voltage for the former (referring to the solid line) is 28 V, while for the latter (referring to the dashed line) it is 24 V.
Fig. 4
Fig. 4 Ratios of the integrated EL intensity to the injection current density as a function of the latter for the devices made of a patterned (empty square) and of a flat (solid square) SiNx emitting layer, respectively.
Fig. 5
Fig. 5 Ln (I) as a function of ln (P1/2) for the devices made of a patterned (empty triangle) and of a flat (solid triangle) SiNx emitting layer. The calculated Z parameter for each curve is also specified.
Fig. 6
Fig. 6 (a) Current-voltage characteristics of devices made of a patterned (empty triangle) and of a flat (solid triangle) SiNx emitting layer, respectively. Inset shows the band diagram for the LED made of patterned SiNx emitting layer, which is drawn according to the electron affinity (χe) and band gaps (Eg) of Si quantum dots, SiNx layer, nanocrystalline Si (nc-Si), bulk Si and aluminum-doped zinc oxide, respectively. The values are taken from Refs [2427]. (b) The trap-assisted tunneling plot based on the In(I)-E−1 relation for the device made of patterned SiNx emitting layer and the Poole-Frenkel plots based on the ln(J/E)-E1/2 relation for the device made of flat SiNx emitting layer, respectively. E is in MV cm−1.

Equations (2)

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I = N Z ( 1 < Z < 3 )
1n ( I )   = Z ln  ( P 1 / 2 ) + C
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