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Optical and electrical properties of transparent conductive air-stable C-axis aligned crystalline InGaZnON thin films

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Abstract

The concentrations of N (CN) and interstitial metal defects (CMi) and the film thickness (d) dependent microstructure and optical and electrical properties of InGaZnON thin films deposited by RF sputtering are studied. The thin films have a C-axis aligned crystalline structure with increased grain size and CMi and CN with rising substrate temperature and power during sputtering. The average visible optical transmittance (Tr) of 80% decreases with the increased d. The lowered Tr in the infrared region with the increment of free carrier absorption is observed. The refractive index and extinction coefficient and dielectric constants increase, and band gap decreases from 2.8 to 2.2 eV, due to the increased CN and d. The electrical resistivity decreases from 0.1 to 5.0 E-3 Ω.cm and the work function increases from 2.8 to 3.7 eV with the increased free carrier concentration (Ne). The electrical properties are air-stable stored for 1000 hrs due to the N passiviated surface. The thermoelectric properties, including the Seebeck coefficient (S) and power factor and electric thermal conductivity from 300 to 673 K, are evaluated. The S and extracted electron effective mass are temperature and Ne depended. The electron mean path and scattering time and plasma energy at room temperature are calculated.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The InGaZnON (IGZON) thin films are now enormously researched as the active [1–4] or passivation [5] layers of thin film transistors (TFTs) to improve TFTs' air [1, 5] or electrical [2–4] stabilities for next generation flat panel display. However, the optical and electrical properties of IGZON thin films should be further studied for improving the performance of TFTs [6] or finding new application fields for IGZON thin films such as transparent electrodes for TFTs [7] or n-type semiconductor material for thermoelectric device [8].

The formerly deposited IGZON thin films are with high electrical resistivity (ρ) decreased with the increase of N content (CN) in thin film suggesting transparent conductive air-stable IGZON thin films can be prepared [9]. Improving the air stability of electrical properties for transparent conductive oxide (TCO) thin films is still the main research focus now for flexible and transparent electronics [10–14]. However, improving the stability of TCO thin films by nitrogen doping have never been reported. Moreover, for accurate characterization the transport properties of IGZON thin films the free carriers' effective mass (me*) and scattering time (τ) should be determined together with the concentration (Ne) and mobility (μ) [6].

Moreover, the amorphous [15], C-axis aligned crystalline (CAAC) [8] and super-lattice [16, 17] InGaZnO (IGZO) thin films have been recently reported with higher thermoelectric figure of merits than those of ZnO [8] and In2O3 [18] thin films. However the thermoelectric properties at temperature higher than 373 K for IGZO based thin films which are important for thermoelectric power generation [18] have not been reported till now.

In the work, the structure, electrical properties with the air stability, and thermoelectric properties, and me* and τ for IGZON thin films are studied.

2. Experiment details

The IGZON thin films were deposited by RF sputtering from InGaZnO4 target with base and working pressures of 9.0 × 10−4 Pa and 0.5 Pa and Ar: N2 flow rates of 40: 10 sccm in 1 h. The IGZON1 and IGZON2 thin films were sputtered at power (P) of 200 W and substrate temperature (Ts) of 300 °C and 400 °C, respectively. The IGZON3 and IGZON4 thin films were sputtered at P of 400 W and Ts of 500 °C. Moreover the IGZON4 thin film was co-sputtered by IGZO and Zn targets with extra-Zn doping by DC sputtering of Zn target in P of 50 W.

The structure and surface morphology of thin films were studied by a X-ray diffraction (XRD) meter and a Scanning electron microscope (SEM). The surface chemical states and work functions of thin films were characterized by a Thermo ESCALAB 250 X-ray and Ultra-violet photoelectric spectroscopy (XPS and UPS) with a mono-chromate Al Kα X-ray source of energy 1486.6 eV. The X-ray spot size was 500 μm. The test was taken at chamber pressure of 10 mbar. The XPS spectra were collected in conditions with pass energy of 20 eV and a 0.05 eV/step for high-resolution scans. The low-energy electron flood gun with voltage of 3 V and current of 200 μA was applied to compensate for charging effects due to the poor conductivity of samples. The spectra were calibrated using the absorbed C1s peak at 284.8 eV and fitted by Avantage software with Gaussian-Lorenzian curve in shape of all peaks assumed to be 80% Gaussian and 20% Lorentzian. A Smart mode was used to calculate the background. A UV-Vis spectrometer was used to measure the transmittance (Tr) of thin films. The optical constants and film thickness (d) were fitted by a spectroscopic ellipsometry (SE). The Seebeck coefficients (S) were measured by a commercial apparatus in Helium ambient. The Ne and μ and ρ were obtained by a Hall system using the van der Pauw configuration.

3. Results and discussion

Figure 1 shows the XRD patterns of IGZON thin films. All thin films have the CAAC orientation structure with IGZO (009) major peak and (0015) minor peak. The intensity of (009) diffraction peak slightly increases indicating the growing of crystal size with rise of Ts and P. Figure 2 shows the surface morphology by SEM for IGZON thin films. The IGZON1 to IGZON3 thin films have the hexagonal crystal structures with grain size slightly increased which is coincided with XRD result. The IGZON4 thin film forms ZnN like structure [19] with increase of Zn and N contents (CZn and CN) compared with IGZON3 thin film. The composition of thin films are analyzed by Energy dispersive spectroscopy attached with SEM. The IGZON1 to IGZON4 thin films have the compositions of InGa0.5Zn0.4O2.5N0.07, InGa0.6Zn0.5O2.1N0.12, and InGa0.5Zn0.3O2.4N0.11 and InGa0.7Zn0.5O1.9N0.6, respectively. The CN slightly increases and content of O (CO) slightly decreases with the rise of Ts and P. With Zn and IGZO co-sputtered, the CZn and CN increase and CO decreases obviously, and the thin film forms ZnN like structure.

 figure: Fig. 1

Fig. 1 XRD patterns of IGZON thin films.

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 figure: Fig. 2

Fig. 2 The surface morphology by SEM for IGZON thin films.

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Figure 3 shows the concentration of donor defects including interstitial metal (CMi) and oxygen vacancy (CVO) and the atomic ratio of O and N by XPS and work function (φ) analyzed by UPS. The In3d5/2 have two peaks at 443.9 eV and 444.9 eV for Ini and In-O bonds in lattice [20]. The Ga2p3/2 have two peaks at 1116.7 eV and 1117.8 eV for Gai and Ga-O bonds in lattice [20]. The Zn2p3/2 have two peaks at 1021.8 eV and 1022.5 eV for Zni and Zn-O bonds in lattice [20]. The atomic ratio of Ini and Gai and Zni calculated by peak divided software all increase from IGZON1 to IGZON4 thin films due to the increase of Ts and P. Meanwhile, as shown in Fig. 3(d) and (e), the Gaussian fittings are also used to de-convolute the combined O1s and N1s peaks. The resulting sub-peaks at binding energy of 530.3 and 530.9 and 533.2 eV [4] attribute to O2- surrounded by metals atoms, VO and OH−1 impurities, respectively. The atomic ratio of total O and VO decrease apparently with the increase of P. The signals of Ga Auger at 396.7 eV and Ga-N bonds at 397.8 eV are observed [4]. The CN in IGZON thin films slightly increases with Ts and P and Zn extra-doping. As discussed in ZnON thin film [21] with the increase of CN in thin films the CVO near the valence band maximum and the total O and the band gap all decrease which are coincided with our results. The N in thin films are usually considered as acceptor defects. But the total Ne generated by Mi and VO are larger than the concentration of holes generated by N doping. The all thin films are still n-type and the Ne increase with CN due to the increase Mi. The φ [22] is an important parameter for IGZON thin films used in transparent electrodes, which is in the range of 2.8 to 3.7 eV and slightly increases with Ne seen later.

 figure: Fig. 3

Fig. 3 In3d, Ga2p, and Zn2p and O1s and N1s XPS spectra and φ by UPS of IGZON films.

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Figure 4 shows the relation of ρ, μ and Ne and the ambient stability as exposed in air for six weeks. With the increase of Ts and P the ρ decreases and μ and Ne increase due to the growing of crystal size and increased CMi. The μ decreases obviously for IGZON4 thin film due to the increase content of ZnN as the In-O being the main origin of large mobility for IGZO based thin film. The lowest ρ of 5E-3Ω.cm is obtained. As shown in Fig. 4(b) and (c) and (d), the ρ, μ and Ne show no apparent variation exposed in air for six weeks. For TCO thin films such as Ga and Al doped ZnO, the ρ increased as exposed in air six weeks [11] due to the oxidation which suggests that minor nitrification can passivate the surface from oxygen absorption and reduces the potential barrier for electron transport therefore increases the air stability for IGZON thin films. This indicates that especially the IGZON4 film can be used as air stable transparent electrodes for IGZO TFTs instead of use another doped ZnO sputtering target to lowering the materials cost which is previously not reported for IGZO based film.

 figure: Fig. 4

Fig. 4 (a) The relation between ρ, μ and Ne and the variation of (b) ρ (c) μ and (d) Ne with exposure time in air for IGZON films.

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Figure 5(a) shows the Tr spectra for IGZON thin films. The CN and d and Ne together influence the Tr. In the ultra-violet region, the cut-off wavelength (λc) at first slightly shifts to shorter wavelength (blue-shift) as compared the IGZON1 with IGZON2 thin films, then shifts to longer wavelength (red shift) for IGZON3 and IGZON4 thin films obviously due to the lowering of band gap (Eg) by the evident rise of CN [21]. Figure 5 (b) shows the Eg for IGZON thin films fitted by (αE)1/2~E where α is the absorption coefficient calculated by

α=ln(Tr/d).
The Eg widen by Burstein-Moss effect with increased Ne is not observed due to the counteracting by Eg narrowed with the increased CN in thin films. In the visible region the thin films are transparent with average Tr near 80%. With the increase of d and CN the Tr slightly decreases. In the infrared region the free carrier absorption is obvious that the Tr decreases with the increase of Ne and d.

 figure: Fig. 5

Fig. 5 (a) Transmittance and (b) band gap for IGZON thin films.

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Figure 6 shows the electrical conductivity (σ), S, and power factor (PF) and electronic thermal conductivity (κe) for IGZON thin films. The IGZON1 to IGZON3 thin films behave as semiconductors that σ increases with temperature (T). From RT to 373 K, the IGZON4 thin film behaves as metal that σ decreases with T but from 373 K to 673 K the thin film behaves as semiconductor that σ increases with T. The T depended σ can be expressed as:

σ=σ0exp[Eσ/(kBT)],
where σ0 is a constant and kB is the Boltzmann constant and Eσ is the activation energy for conductivity. The Eσ are calculated as shown in Fig. 6 (a). Different Eσ indicates different T dependent conductivity mechanism. The electrons are excited thermally from donor levels to the conduction band as T increased. With increased T more charge carriers overcome the Eσ barrier and participate in the electrical conduction. The Eσ increases with T. Figure 6 (b) shows that all S are negative values indicating the n-type conductivity for IGZON thin films in the whole temperature range. The PF and κe are calculated by
PF=σS2,
and the Wiedemann-Franz relation
κe=LoTσ,
where
Lo=πkB/(3q),
and kB is the Boltzmann constant and q is the electron charge and T is the temperature. The relation of PF and κe with T coincide with variation of σ(T). Performance of thermoelectric materials is generally represented by a dimensionless figure of merit,
ZT=S2σT/κ,
where S is the Seebeck coefficient, σ is the electrical conductivity, and κ is the thermal conductivity. Superior thermoelectric materials are achieved by obtaining high power factors and low thermal conductivity. The κ includes the κe and lattice thermal conductivity (κl) in which κe is positive proportional to the σ. The IGZON2 film has the highest PF though with the highest κe. The κl plays a dominant role over κe. The material always has lower κl if κe is higher [8]. Therefore the IGZON2 film may have the lowest κl and κ and highest ZT and be best for thermoelectric device application which is either previously not reported. To verify this, the measurement of κ is ongoing. The S values depend on the T and me* at Fermi level and Ne as [18]:
S=8π2kB2T3qh2me*(π3Ne)2/3,
where kB is the Boltzmann constant and q is the electron charge and h is the Plank constant. The T depended Ne is measured by Hall instrument. The relation of S with T and Ne are shown in Fig. 7(a) from which found that the absolute value of S increases with T and decreases with Ne obeyed well with Eq. (1). From Eq. (1) with the measured S and Ne the me* are calculated as shown in Fig. 7(b) from which found that the me* increases with Ne and decreases with T obeyed well with Eq. (1). The function of me*(Ne, T) is not reported for IGZON even for IGZO films before which are key parameters for accurate characterization the transport properties of films.

 figure: Fig. 6

Fig. 6 Electrical properties of IGZON thin films with temperature (a) σ (b) S and (c) PF and (d) κe.

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 figure: Fig. 7

Fig. 7 (a) S and (b) me*as a function of Ne and T.

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The refractive index (n) and extinction coefficient (k) are fitted with SE spectral based on Tauc-Lorentz model describing the band-to-band energy absorption and Drude model describing the free-carrier absorption (ANe). Figure 8(a) shows that the n increases with d and CN. With the increase of d, the thin film becomes more crystalline with grain size and packing density rising. The atomic radii of N is larger than that of the O. The larger atomic radius the larger its polarizability. The n is proportional to the polarizability. Therefore the n increases with CN due to the increased polarizability. The k is proportional to the absorption of thin films. The decrease of Tr and increase of absorption attribute to the increase of k. No ANe is observed for the fitted k values of nearly equal to zero at E<1.5 eV considering the fitted errors. The real and imaginary parts of dielectric functions are calculated by

ε1=n2k2,
ε2=2nk,
which coincide well with the variation of n and k. Seen in Fig. 8(c) the ε1 peak near 3.5 eV show clearly shifts to lower energies with increasing CN which counteracts the Burstein-Moss effect with increasing Ne. Also due to the fitted errors of k values equal to zero the ε2 values are equal to zero at E<1.5 eV with no ANe observed. The decrease of ε1 at E<1.5 eV by ANe is also counteracted by the increase effects of d and CN. The ε1 are calculated by Eq. (8). The n are larger than k by several order. Therefore ε1 are mainly n dependent and ε1 (E) almost follow the same variation trends as n (E). The n (E) are fitted by SE method with fitting errors which is the main reason for the curling of the tail in the plot for IGZON4 film in Fig. 8(a) and (c).The structural model of four medium system consisting of the ambient, a surface roughness layer, IGZON layer and the glass substrate is used during fitting the optical constants for IGZON films by SE method. Therefore the different structure as shown in Fig. 2(d) and the abrupt increase of film thickness for IGZON4 film due to the Zn and IGZO co-sputtering are other reasons for the abnormal curling of the tail in the plots for IGZON4 film in Fig. 8(a) and (c).The high frequency dielectric function ε is calculated by the Cole-Cole plots [23] shown in Fig. 8(e). The ε almost decreases with Ne. The mean path of the free electron is estimated by
le=h2q(3Neπ)1/3μ,
where q is the electron charge, h is the Plank constant, and Ne is the free carrier concentration and μ is the mobility. The le increases with Ne and decreases with μ for IGZON4 thin film. The le is smaller than the crystal size seen in Fig. 2 indicating the grain boundary not having significant effects on the transport properties. The plasma energy is calculated by
Ep=(h2q2Ne4π2m*eεε0)1/2,
where h is the Plank constant, q is the electron charge, and Ne is the electron charge, and me* is the electron effective mass and ε and ε0 are the high frequency and free space dielectric constants as shown in Fig. 8(e). The Ep almost increases with Ne. Also the d has positive relation with Ep. With the improvement of polycrystalline grain structure with increased d increases the Ne. The carrier scattering time at RT is calculated by
τ=me*μ/q,
where μ is the mobility and me* is the effective mass of electron and q is the electron charge. The calculated τ are 0.095, 0.34, and 0.78 and 0.92 fs from IGZON1 to IGZON4 thin films.

 figure: Fig. 8

Fig. 8 Calculated (a) n (b) k and (c) ε1 and (d) ε2 and (e) ε and (f) le and Ep for IGZON films.

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4. Summary

The structure and optical and electrical properties of sputtered IGZON thin films are studied. With N doping the transparent conductive air-stable IGZON thin films can be deposited for optical-electronic device application. The thermoelectric properties of IGZON thin films are also studied which suggesting IGZO based films be promising application in device. The temperature depended electron effective mass and scattering time and plasma energy for IGZON thin films are also calculated.

Funding

National Natural Science Foundation of China (No.61674107); Shenzhen Key Lab Fund (ZDSYS 20170228105421966); Science and Technology Plan of Shenzhen (JCYJ20170302150335518).

References

1. P. Liu, Y. Chou, L. Teng, F. Li, and H. P. Shieh, “Nitrogenated amorphous InGaZnO thin film transistor,” Appl. Phys. Lett. 98(5), 052102 (2011). [CrossRef]  

2. J. Raja, K. Jang, N. Balaji, W. choi, T. Thuy Trinh, and J. Yi, “Negative gate-bias temperature stability of N-doped InGaZnO active-layer thin-film transistors,” Appl. Phys. Lett. 102(8), 083505 (2013). [CrossRef]  

3. C. Fuh, P. Liu, L. Teng, S. Huang, Y. Lee, H. P. Shieh, and S. M. Sze, “Effects of microwave annealing on nitrogenated amorphous In-Ga-Zn-O thin-film transistor for low thermal budget process application,” IEEE Elec. Dev. Lett. 34(9), 1157–1159 (2013). [CrossRef]  

4. X. Huang, C. Wu, H. Lu, F. Ren, D. Chen, R. Zhang, and Y. Zheng, “Enhanced bias stress stability of a-InGaZnO thin film transistors by inserting an ultrathin interfacial InGaZnO: N layer,” Appl. Phys. Lett. 102(19), 193505 (2013). [CrossRef]  

5. P. Liu, Y. Chou, L. Teng, F. Li, C. Fuh, and H. P. Shieh, “Ambient stability enhancement of thin-film transistor with InGaZnO capped with InGaZnO: N bilayer stack channel layers,” IEEE Elec. Dev. Lett. 32(10), 1397–1399 (2011). [CrossRef]  

6. T. Kamiya, K. Nomura, and H. Hosono, “Origins of high mobility and low operation voltage of amorphous oxide TFTs: electronic structure, electron transport, defects and doping,” J. Disp. Technol. 5(12), 468–483 (2009). [CrossRef]  

7. J. Y. Kwon, D. J. Lee, and K. B. Kim, “Transparent amorphous oxide semiconductor thin film transistor,” Electron. Mater. Lett. 7(1), 1–11 (2011). [CrossRef]  

8. N. H. Tran Nguyen, T. H. Nguyen, Y. R. Liu, M. Aminzare, A. T. Pham, S. Cho, D. P. Wong, K. H. Chen, T. Seetawan, N. K. Pham, H. K. Ta, V. C. Tran, and T. B. Phan, “Thermoelectric properties of indium and gallium dually doped ZnO thin films,” ACS Appl. Mater. Interfaces 8(49), 33916–33923 (2016). [CrossRef]   [PubMed]  

9. P. T. Liu, C. H. Chang, C. S. Fuh, Y. T. Liao, and S. M. Sze, “Effects of nitrogen on amorphous nitrogenated InGaZnO (a-IGZO:N) thin film transistors,” J. Disp. Technol. 12(10), 1070–1077 (2016). [CrossRef]  

10. B. Cho, H. Kim, D. Yang, N. Shrestha, and M. Sung, “Highly conductive air-stable ZnO thin film formation under in situ UV illumination for an indium-free transparent electrode,” RSC Advances 6(73), 69027–69032 (2016). [CrossRef]  

11. L. Zhang, R. Yang, K. Chen, X. Wang, Y. Tang, F. Yang, R. Liu, Z. Ye, and Y. Li, “The fabrication of Cu nanowire/graphene/Al doped ZnO transparent conductive film on PET substrate with high flexibility and air stability,” Mater. Lett. 207, 62–65 (2017). [CrossRef]  

12. W. Xiong, H. Liu, Y. Chen, M. Zheng, Y. Zhao, X. Kong, Y. Wang, X. Zhang, X. Kong, P. Wang, and L. Jiang, “Highly conductive, air-stable silver nanowire@Iongel composite films toward flexible transparent electrodes,” Adv. Mater. 28(33), 7167–7172 (2016). [CrossRef]   [PubMed]  

13. T. Minami, “Present status of transparent conducting oxide thin-film development for Indium-Tin-Oxide (ITO) substitutes,” Thin Solid Films 516(17), 5822–5828 (2008). [CrossRef]  

14. C. Guillén and J. Herrero, “Stability of sputtered ITO thin films to the damp-heat test,” Surf. Coat. Tech. 201(1-2), 309–312 (2006). [CrossRef]  

15. Y. Fujimoto, M. Uenuma, Y. Ishikawa, and Y. Uraoka, “Analysis of thermoelectric properties of amorphous InGaZnO thin film by controlling carrier concentration,” AIP Adv. 5(9), 097209 (2015). [CrossRef]  

16. S. Cho, M. Jeong, J. Kim, Y. Kwon, H. Kim, J. Lee, and H. Cho, “A combinatorial approach to solution-processed InGaO3(ZnO)m superlattice films: growth mechanisms and their thermoelectric properties,” CrystEngComm 18(5), 807–815 (2016). [CrossRef]  

17. S. Cho, S. Baek, D. Kim, Y. Kim, and H. Cho, “Microstructure-dependent thermoelectric properties of polycrystalline InGaO3(ZnO)2 superlattice films,” J. Vac. Sci. Technol. A 35(1), 01B126 (2017). [CrossRef]  

18. G. Korotcenkov, V. Brinzari, and M. Ham, “In2O3-based thermoelectric materials: the state of the art and the role of surface state in the improvement of the efficiency of thermoelectric conversion,” Crystals 8(14), 1–37 (2018).

19. C. Nunez, J. Pau, E. Ruız, and J. Piqueras, “Thin film transistors based on zinc nitride as a channel layer for optoelectronic devices,” Appl. Phys. Lett. 101(25), 253501 (2012). [CrossRef]  

20. T. Li, C. Han, T. Kuan, and J. Lin, “Effects of sputtering-deposition inclination angle on the IGZO film microstructures, optical properties and photoluminescence,” Opt. Mater. Express 6, 343–366 (2016). [CrossRef]  

21. M. Ryu, T. Kim, K. Son, H. Kim, J. Park, J. Seon, S. Seo, S. Kim, E. Lee, H. Lee, S. Jeon, S. Han, and S. Lee, “High mobility zinc oxynitride-TFT with operation stability under light-illuminated bias-stress conditions for large area and high resolution display applications,” IEDM 12, 112–114 (2012).

22. J. K. Yao, S. Chen, X. Sun, and H. Kwok, “He plasma treatment of transparent conductive ZnO thin films,” Appl. Surf. Sci. 355, 702–705 (2015). [CrossRef]  

23. K. S. Cole and R. H. Cole, “Dispersion and absorption in dielectrics I. alternating current characteristics,” J. Chem. Phys. 9(4), 341–351 (1941). [CrossRef]  

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Figures (8)

Fig. 1
Fig. 1 XRD patterns of IGZON thin films.
Fig. 2
Fig. 2 The surface morphology by SEM for IGZON thin films.
Fig. 3
Fig. 3 In3d, Ga2p, and Zn2p and O1s and N1s XPS spectra and φ by UPS of IGZON films.
Fig. 4
Fig. 4 (a) The relation between ρ, μ and Ne and the variation of (b) ρ (c) μ and (d) Ne with exposure time in air for IGZON films.
Fig. 5
Fig. 5 (a) Transmittance and (b) band gap for IGZON thin films.
Fig. 6
Fig. 6 Electrical properties of IGZON thin films with temperature (a) σ (b) S and (c) PF and (d) κe.
Fig. 7
Fig. 7 (a) S and (b) me*as a function of Ne and T.
Fig. 8
Fig. 8 Calculated (a) n (b) k and (c) ε1 and (d) ε2 and (e) ε and (f) le and Ep for IGZON films.

Equations (12)

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

α=ln ( T r /d ).
σ= σ 0 exp[ E σ /( k B T)],
PF=σ S 2 ,
κ e = L o Tσ,
L o =π k B /(3q),
ZT= S 2 σT/κ,
S= 8 π 2 k B 2 T 3q h 2 m e * ( π 3 N e ) 2/3 ,
ε 1 = n 2 k 2 ,
ε 2 =2nk,
l e = h 2q ( 3 N e π ) 1/3 μ,
E p = ( h 2 q 2 N e 4 π 2 m * e ε ε 0 ) 1/2 ,
τ= m e * μ/q,
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