Calculation of Secondary Electron Emission Coefficient of Al-Doped MgO Protective Layer

DENG Jiangand ZENG Bao-qing

(1. College of Optoelectronic Technology, Chengdu University of Information Technology Chengdu 610225; 2. School of Physical Electronic, University of Electronic Science and Technology of China Chengdu 610054)

Calculation of Secondary Electron Emission Coefficient of Al-Doped MgO Protective Layer

DENG Jiang1and ZENG Bao-qing2

(1. College of Optoelectronic Technology, Chengdu University of Information Technology Chengdu 610225; 2. School of Physical Electronic, University of Electronic Science and Technology of China Chengdu 610054)

In this work, a first-principle calculation method is introduced to analyze the secondary emission coefficient of Mg1-xAlxO protective layer of a plasma display panel (AC PDP). The band gaps and the electronic structures of pure MgO and Mg1-xAlxO layers with different Al doping ratios are calculated based on Hagstrum’s theory. The secondary electron emission coefficient of Mg1-xAlxO layers in various gases environments based on Auger neutralization and Auger de-excitation are obtained. The calculated results show the secondary electron emission coefficient of Mg1-xAlxO layer is higher than that of pure MgO, especially in helium environment. When Al doping ratio is 0.375, the secondary electron emission coefficient in He based on Auger neutralization and Auger de-excitation theory is 0.4191 and 0.4316, respectively, compared with pure MgO of 0.3543 and 0.4060. Thus, using an Mg1-xAlxO protective layer is an effective method to improve the secondary electron emission coefficient of AC PDP.

Al-doped MgO; first-principle; plasma display panel; protective layer; secondary electron emission coefficient

As we know, alternating-current plasma display panels (AC PDPs) have great marketability in the large flat-panel display market due to their fast operating speed and simple manufacturing process[1-3]. Generally, AC PDPs consist of electrodes, barrier ribs, discharge cell, dielectric layers, and a protective layer. The protective layer plays an important role in the decrease of power consumption and protection from bombardments of numerous particles such as ions, electrons, and metastable atoms.

On the other hand, AC PDPs have some disadvantages, including lower luminous efficacy and higher power consumption than other flat panel displays such as a liquid crystal display (LCD) or an organic light emitting diode (OLED)[4]. It is known that MgO is the only commercially available protective material of AC PDP presently. Thus, in order to reduce the electrical power consumption further, it is necessary to develop a new protective material based on MgO with higher SEE yield to reduce the firingvoltage and sustain voltage of AC PDPs[5-6]. For example, Motoyama et al. obtained formulas for the simple calculation of the secondary electron yield from Hagstrum’s theory, and calculated the secondary electron yield values of BaO and MgO for He, Ne, Ar, Kr, and Xe ions and metastable atoms[7]. The impact of Si-doping on the electronic properties of the MgO layer was studied in Ref.[8]. Secondary electron emission yield of the Mg1-xSixO in the plasma display panel cell filled with a mixture of Ne and Xe gas was also discussed.

In this paper, the electronic structure, band structure, and density of states of the Mg1-xAlxO crystal are analyzed. Then the secondary electron emission coefficient (γ) values of Mg1-xAlxO for various gases are calculated by Hagstrum’s theory. The calculated results show that with the addition of Al atoms, the γ values increase, especially in helium gas.

1 Band Structures and Density of States Calculation

The MgO crystal model used in our paper is shown in Figure 1. MgO is NaCl-type crystal with space group of FM-3M. The lattice constant is 0.421 12 nm, and bond angles are α = β =γ = 90°.

In order to investigate the band structure and density of states, the cambridge serial total energy package (CASTEP) simulation program is introduced, using the Kohn-Sham formation that is based on the density functional theory. The exchange and correlation potentials among electrons are corrected by local density approximation (LDA). Firstly, the geometry optimization of the MgO crystal is performed by the LDA and ultrasoft pseudopotential method. During the calculation, plane-wave cut-off energy is 340 eV, k points set in reciprocal space is 6×6×6, and the self-consistent field (SCF) tolerance is 10?6eV.atom-1. The iteration is repeated until the energy is less than 0.001 meV/atom and root-meansquare (RMS) stress is less than 0.05 Gpa. Then, the partial density of states of Mg and O and the total density of states of MgO are obtained, respectively.

The structure of Mg1-xAlxO is obtained by replacing Mg atom with Al atom in the cubic rock-salt structure. We set up a 2×2×2 super cell to model the Mg1-xAlxO structure. For each Mg1-xAlxO super cell with symmetry P1, the geometrical optimization is performed by the CASTEP simulation program. In this step, atomic positions are relaxed and optimized with a density mixing scheme by using the Pulay method for eigenvalues minimization. Finally, the energy band structure and density of states of Mg1-xAlxO are obtained. In addition, it is known that LDA pseudopotential calculation may underestimate band gap energy, although the estimation of valence band is accurate. Thus, we amend band gap using scissors operation with a rigid upward shift of the conduction band with respect to the valence band from the experimental value of the band gap of 0.78 eV. The amendment does not prevent us from analyzing our results qualitatively.

2 Secondary Electron Emission Coeffi-Cient Calculation

In order to study the characteristics of Mg1-xAlxO used in AC PDP, the secondary electron emission coefficient of Mg1-xAlxO for different gases is calculated. As we know, the plasma display discharge cell is very small and the firing voltage of discharge cell is about 200V, and the priming electrons can’t get enough energy. Hence, it is difficult to form fast electron, and the contribution of fast electron to secondary electron is very small. According to the theory and experimental results of Hagstrum[9-10], the mechanism of secondary electron emission consists ofthe following two processes: Auger neutralization and Auger deexcitation, as shown in Fig.2a and Fig.2b. During our simulation, the bottom of the valence band and electronic affinity of MgO are defined as zero and 0.85 eV, respectively.

From Fig.2a, when electron 1 moves to the ground state of an atom and electron 2 is excited simultaneously, the energy distribution Ni(E) of the excited electron could be given by the following expression[7].

whereδ( ), T[E], and n(E) are delta function of Dirac, Auger transform function, and valence band electron density of states function, respectively. ρ0(E) is the state density of the excited electron, which is considered proportional to (E?EC)1/2. If E>E0, an electron could be excited to escape from the solid surface. Assuming this escape probability is Pe(E) is given by expression (2), we could obtain the expression (3) for the secondary electron yield γNcaused by Auger neutralization at a distance s.

where α and β are constants of 0.248 and 1.0 determined by Hagstrum, respectively. αi≡Ei/E0?1; βi≡(Ei?2ξ)/E0+1; Pe*(x)=(?1x?β)α/2. The function T*(x), which is assumed for parabolic band of state density and finite only in αi

From Fig.2b, when an ion approaches a solid surface and resonance neutralization occurs, the ion becomes an excited atom. Then, the excited atom returns to the ground state by Auger deexcitation, unless resonance ionization occurs with the condition Ei?Em

Similar with the process of Auger neutralization, the secondary electron yieldDγ caused by Auger deexcitation can be obtained as follows:

Putting x≡E/E0and σ≡EC/E0, γDcould be defined by another expression, i.e.

where αm=Em/E0，βm=(Em?ξ)/E0+1. The function n*(x), which is assumed for parabolic bandof state density and finite only in αm

3 Simulation Results

Fig.3a and Fig.3b show the partial density of states of MgO. The electronic states of Mg mainly distribute in the valence band and conduction band, and O atoms almost appear in the valence band. The possible reason is that the valence band is constituted by O-2p with some small peaks of Mg-3s, while conduction band is mainly composed of Mg-3s. In addition, there is obvious a hybrid phenomenon between Mg-O bonds, which means a strong interaction between the Mg-O constructions.

Fig. 4a～4e show the total density of states of Mg1-xAlxO with different Al doping ratios (x=0, 0.125, 0.25, 0.375, 0.5), respectively. The Mg1-xAlxO layer has a smaller band gap than the pure MgO layer. Furthermore, compared with the pure MgO layer, the Mg1-xAlxO layer has a relatively small band gap energy and large valence bandwidth. The higher the Al concentration is, the smaller the band gap is. It also can be seen that the density of states of valence band and conduction band both have gained a great increase because of the contribution of Al-3p. This can make the electrons of conduction band excite more easily. Combined with the results from other literatures[11-12], we think that narrowing of the band gap is favorable for the enhancement of secondary emission coefficient.

The γNvalues of Mg1-xAlxO for all noble gas ions are shown in Tab. 1, which are calculated by the formulas relevant to Auger neutralization. Wherein, Ei(He)=24.58 eV, Ei(Ne)=21.56 eV, Ei(Ar)=15.76 eV, Ei(Kr)=14.00 eV, and Ei(Xe)=12.13 eV. We observe three important phenomena in the calculated results:

1) As Al atoms are doped in MgO crystal, the γNvalue increases in all gases. Especially in He, the maximum of γNis up to 0.419 1 at the Al doping ratio of 0.375.

2) When the Al doping ratio is 0 and 0.125 in Kr and Xe, it does not meet the conditions of Ei<2ξ[13-14]. Thus, Auger neutralization does not occur and the γNvalues are zero.

3) There are optimum values of Al doping ratio with the highest γNin various gases. For example, the optimum value of Al doping ratio for He, Ne, and Ar is 0.375.

The γDvalues of Mg1-xAlxO calculated by the formulas relevant to Auger deexcitation for various gas ions are shown in Tab. 2, where Em(He)= 19.81 eV, Em(Ne)= 16.61 eV, Em(Ar)= 11.55 eV, Em(Kr)= 9.91 eV, and Em(Xe)= 8.31 eV. Mg1-xAlxO almost presents higher γDvalues than pure MgO in every gas. As the Al doping ratio increases, the γDincreases accordingly and reaches the maximums at Al doping ratio of 0.375 for all gases except for Xe. In He environment, the maximum ofDγ is up to 0.431 6.

4 Conclusions

In this paper, the band structure and density of states of pure MgO and Mg1-xAlxO protective layer with different x values have been investigated by using the first principles theory. The results show that with the increase of Al concentration, the band gap energy of Mg1-xAlxO becomes smaller. The secondary electron emission coefficients of both MgO and Mg1-xAlxO protective layers have also been calculated under different inert gases based on Auger neutralization and Auger exexcitation. The γ values of Mg1-xAlxO are always higher than those of pure MgO, which can reduce the firing voltage and sustain voltage of AC PDP effectively. Moreover, there are optimum values of Al doping ratio with the highest γ value in various gases based on Auger neutralization and Auger deexcitation.

References

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編 輯 稅 紅

Al摻雜MgO保護(hù)層對(duì)二次電子發(fā)射系數(shù)的影響

鄧 江1，曾葆青2
(1. 成都信息工程學(xué)院光電技術(shù)學(xué)院 成都 610225；2. 電子科技大學(xué)物理電子學(xué)院 成都 610054)

采用基于密度泛函理論的第一性原理贗勢(shì)法，研究了Al摻雜對(duì)于MgO保護(hù)層電子結(jié)構(gòu)的影響。采用Hagstrum’s 理論計(jì)算了在不同放電氣體環(huán)境下，不同Al摻雜比例的Mg1-xAlxO的能帶結(jié)構(gòu)和態(tài)密度分布，分別獲得了基于俄歇中和和俄歇退激理論的二次電子發(fā)射系數(shù)。結(jié)果表明，Al摻雜MgO能有效提高二次電子發(fā)射系數(shù)，且在氦氣環(huán)境下二次電子發(fā)射系數(shù)的提高尤為顯著。當(dāng)Al摻雜比例為0.375時(shí)，在氦氣環(huán)境下基于俄歇中和和俄歇退激理論的二次電子發(fā)射系數(shù)最大，分別為0.419 1和0.431 6(純MgO為0.354 3、0.406 0)。

Al摻雜MgO; 第一性原理; 等離子體顯示器; 保護(hù)層; 二次電子發(fā)射系數(shù)

O461.2

A

10.3969/j.issn.1001-0548.2015.03.010

2014 ? 04 ? 11；

2014 ? 07 ? 24

鄧江(1978 ? )，男，博士，主要從事氣體放電、等離子體顯示等方面的研究.

data：2014 ? 04 ? 11；Revised date：2014 ? 07 ? 24

Biography：DENG Jiang was born in 1978, and his research interests include gas discharge and plasma display.