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Field Emission Enhancement in Semiconductor Nanofilms by Engineering the Layer Thickness: First-Principles Calculations Wei Zhao,† Ru-Zhi Wang,*,† Song Han,‡ Kun Xue,§ Hao Wang,† and Hui Yan† Laboratory of Thin Film Materials, College of Materials Science and Engineering, Beijing UniVersity of Technology, Beijing 100124, China, College of Forestry, Northeast Forestry UniVersity, Harbin, 150040, China, and Australian Research Council Centre of Excellence for Quantum Computer Technology and School of Physics, UniVersity of New South Wales, Sydney, New South Wales 2052, Australia ReceiVed: February 6, 2010; ReVised Manuscript ReceiVed: April 21, 2010
We investigated the field emission (FE) enhancement of semiconductor thin films on metal substrate by firstprinciples calculations. For the FE structure of GaN or AlN thin films on aluminum substrate, the calculated results show that by fine-tuning the film thickness, the FE current can be enhanced nearly 2 orders. It should be originated from reducing the surface work function. When the film thickness is less than ∼10 nm, the work function can be reduced as much as 0.5 eV by film thickness modulation of only several nanometers. The remarkable thickness effects on the work function for the semiconductor/metal structure result mainly from surface/interface charge transfer and interface states. I. Introduction Field emission (FE) materials for cold cathodes have attracted considerable attention due to their prominent electronic properties, which demonstrate potential applications in ultrathin flat panel displays and other vacuum microelectronic devices.1,2 Recently, the effects of semiconductor films’ thickness on their FE properties have been extensively studied both experimentally3-6 and theoretically.7-9 Semet et al.7 reported that an ultrathin wide band gap semiconductor layer of less than 10 nm can emit stable electron currents with a threshold field 2-3 orders of magnitude less than that of conventional FE materials. Sugion et al.4 found that in the case of film thicknesses as thin as 8-10 nm, the turn-on electric field is remarkably reduced. In the abovementioned studies, to explain the mechanism of the field emission enhancement, simple qualitative models based on the traditional Fowler-Nordheim theory10 have been proposed. However, these models lack accuracy for FE from the ultrathin film. Therefore, first-principles calculations based on the density functional theory are highly desired. In recent years, firstprinciples calculations have been successfully utilized to study the FE property.11,12 However, to the best of our knowledge, there is a lack of systematical study of the FE enhancement by thickness modulation and considering the effects of the substrate. GaN is a potential material for field emitters due to its low electron affinity and excellent physical and chemical stability.13 AlN is even better, since it may exhibit a negative electron affinity.14 In this work, we select GaN and AlN film to clarify a general law of thickness effect on the FE of semiconductor nanofilms. We focus on the work function change of the GaN films with different thicknesses by employing density functional theory (DFT).15 AlN films are also investigated for comparison. The results show that by fine-tuning the film thickness, a dramatic lowering of the surface work function can be achieved. As a result, the field emission current can be enhanced nearly 2 orders. * To whom correspondence should be addressed. E-mail:
[email protected]. † Beijing University of Technology. ‡ Northeast Forestry University. § University of New South Wales.
II. Models and Methods In this work, to simulate the real FE cathode structure, both the wurtzite GaN and AlN nanofilms on Al substrate are taken into account in our calculations. It should be noted that the integration of substrate has scarcely been considered in previous theoretical studies of the field emission. For the present work, the Ga (Al)-terminated (0001) surfaces are modeled using a (1 × 1) surface unit cell (Figure 1) considering that the N-terminated surfaces are generally unstable,16,17 and the most common growth direction of epitaxial hexagonal GaN is normal to the (0001) basal plane.18 Each (1 × 1) unit cell contains one atom per layer. Periodic boundary conditions are applied with 20 Å of vacuum between periodic slabs. DFT calculations are carried out using the projected augmented wave19 pseudopotentials as implemented in the Vienna ab initio simulation package.20 The Perdew-Wang 91 form of the generalized gradient approximation21 for exchange-correlation functional is employed. To achieve high precision, the kinetic energy cutoff is set to 520 eV, and the k-point sampling is set at 15 × 15 × 1. The calculations are converged to 10-5 eV/cell. The work functions are determined from the difference between the Fermi level and the vacuum level. To expediently investigate the surface work functions of the FE cathode structure, three supercell models are constructed. In model 1 (GaN/Al), as shown in Figure 1a, the supercell is modeled by Ga-terminated GaN(0001) on the fcc Al(111) substrate. To build the supercell model of the integrated cathode structure in our calculations, the atoms of GaN and Al substrate are relaxed to compensate for the epitaxial strain because of the lattice mismatch.22-24 The GaN/Al supercell with an in-plane lattice constant of 3.0 Å before relaxation is modeled, and all atoms are fully relaxed until the forces are converged up to 0.01 eV/Å per atom. Because of the asymmetry of the slabs, the vacuum level in our calculations is defined as the potential in the vacuum region where it approaches an extremum (maximum value). The vacuum level must, of course, be determined from the test for a distance in the vacuum that is long enough. Similarly, for the AlN/Al structure, the supercell has the same structure as model 1, except that the Ga atoms are replaced by Al atoms. For model
10.1021/jp101164h 2010 American Chemical Society Published on Web 06/10/2010
FE Enhancement in Semiconductor Nanofilms
J. Phys. Chem. C, Vol. 114, No. 26, 2010 11585
Figure 2. Work functions of GaN/Al, AlN/Al, H-GaN, and G-GaN as a function of the NLs.
Figure 1. Atomistic representations of the semiconductor nanofilm surface structures: (a) side view of the GaN/Al structure, (b) side view of the H-GaN (G-GaN) structure before relaxation, and (c) top view of (1 × 1) unit cells used to model the GaN(0001) surfaces.
2 (H-GaN), as shown in Figure 1b, to compare the GaN/Al structure with the intrinsic GaN structure without substrate, the supercell is constructed of the GaN layer adopting the bulk phase parameter and without the Al substrate. The bottom side of the GaN layer is saturated with pseudohydrogen atoms of fractional charge to recover a bulklike behavior.17,25 Model 3 (G-GaN) is similar to model 2. The bottom side of the GaN layer is saturated with pseudohydrogen atoms, but the lattice parameters of the GaN layer are taken from the GaN/Al structure after relaxation. As a result, this structure retains the epitaxial strain induced by GaN/Al structure formation, but the effects of charger transfer from Al substrate can be eliminated. Therefore, it is reasonable to analyze the effects of epitaxial strain induced by the Al substrate. III. Results and Discussion 1. Surface Work Function. In Figure 2, the calculated work functions of GaN/Al (AlN/Al) structures with thicknesses ranging from 4 to 38 layers are shown. For GaN/Al, the increase in GaN layer thickness leads to a significant decrease in the surface work function (from 4.9 to 4.4 eV). Similar behavior is also observed in the AlN/Al. It is clear that the dramatic changes of the work function for nanofilm FE cathodes can be achieved by film thickness modulation. Then FE current enhancement is expected due to reduction of the surface work function. On the other hand, the values of the work function for H-GaN are independent of thickness modulation. Therefore, the remarkable work function variation of the GaN/Al structure results mainly from the substrate-induced effects. By our calculations, the substrate-induced effects are composed of three aspects: (a) the surface charge transfer, (b) the interface charge transfer, and (c) the interface states. Moreover, the three aspects contributed different effects to the work function variation and acted on a
Figure 3. Averages of the electron density difference density in GaN/ Al with different NLs. (a) GaN with 4 layers, (b) GaN with 16 layers, (c) GaN with 36 layers. Solid vertical line denotes the position of the surface first atoms layer (Ga); dashed vertical line denotes the position of the second atoms layer to surface (N).
different range of the number of layers (NLs), which can be seen in Figure 2. Surface Charge Transfer. It is an effective method to analyze the surface charge transfer from the electron density difference at the direction normal to the surface (z) averaged over the xy plane, which is given by:
∆F(z) )
1 S
∫0L1 dx ∫0L2 dy ∆F(x, y, z)
(2)
where S is the area of the (1 × 1) surface unit cell. L1 and L2 are the length and width of the unit cell, respectively. Figure 3 shows the electron density difference of GaN/Al with GaN thicknesses of 4, 16, and 36 layers, respectively. In these curves,
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Figure 4. Surface separation, dsur, and interface separation, dsep, as a function of the NLs for GaN/Al and H-GaN.
a positive ∆F(z) means an increase in electrons, and a negative ∆F(z) means a decrease in electrons. From Figure 3, it is clear that, independent of the thickness of the GaN layers, there is always a charge transfer from the Ga atoms to the N atoms at the surface. Although the shapes of these curves are quite similar, the surface separation, dsur, between the first atomic layer and the second atomic layer decreases gradually. As a result, more electrons are transferred from the vacuum regions to the N atomic layer. This kind of charge transfer reduces the surface dipole; thus, it leads to the dramatic decrease in the work functions, as shown in Figure 2. Due to the lattice mismatch between GaN(0001) and Al(111) in the GaN/Al structure, the epitaxial strain must exist. As a result, the dsur values and the in-plane lattice constant of GaN/ Al will deviate from that of H-GaN. As shown in Figure 4, the dsur values of H-GaN can be fitted by a horizontal straight line, which means the dsur values of the intrinsic GaN structure without substrate are independent of thickness modulation. However, for GaN/Al, the dsur values first decrease quickly and then slowly. It is obvious that the changes in the dsur values of GaN/Al have the same trend, as compared with that in Figure 2. It means that the variation of dsur originates from the different strain states, which results from the substrate-induced thickness effects rather than the thickness modulation itself. Moreover, when compared with H-GaN, the G-GaN has a similar structure but with the lattice parameters of the GaN/Al structure after relaxation. Thus, the G-GaN structure retains the epitaxial strain of the GaN/Al structure. As a result, the strain-induced surface charge transfer can be easily analyzed by the difference in the work function between H-GaN and G-GaN, as can be seen in Figure 2. Interface Charge Transfer. As shown in Figure 2, when compared with the work functions of G-GaN, the GaN/Al exhibits significantly different features: (i) In regions I, there is a larger slope when the layer is less than 10 layers. (ii) In regions II, the slopes are similar but the values of the work function are ∼0.2 eV larger. The first feature can be reasonably explained by the electron density difference in GaN/Al interface. From the averages of the electron density difference in GaN/Al interface, there is a net transfer of the charge from Al to N atoms, inducing excess negative charges on the film side and excess positive charges on the Al substrate side near the interface. Therefore, a dipole with an electric field pointing toward the film side is, hence, generated at the interface, which can result in a work function increase for the ultrathin films.26 For a nanofilm with only several layers (in regions I), our calculations show that the interface negative dipole reinforces
Figure 5. LDOS of GaN/Al through the stack to identify the spatial electronic structure of the interface. On the right-hand side, we show the geometric structure, with local sliced regions corresponding to LDOS graphs on the left-hand side. Projections on both interfacial (solid lines) and bulk (dashed lines) atoms are plotted. The Fermi energy is 0 eV.
the original surface dipole. This leads to an increase in the work function, whereas with the increase in the film thickness, the surface dipole enhancement induced by interface dipole can be neglected due to the large distance between the interface and the surface. Moreover, as shown in Figure 4, the interface separation, dsep, remarkably increases when the thickness of the nanofilm is less than 10 layers. This correlates with the strength range of the interface dipole. For the second feature, it can be explained by the formation of interface states, as will be discussed below. Interface States. The LDOS of the GaN/Al interface and bulk regions are calculated and shown in Figure 5. Extra states appear only at the gap of the interface N atoms. Due to the delocalized characteristic of the Al valence band (Figure 5c), the orbital hybridization across the interface is small and induces little distortion of N LDOS in the gap, which is different from the chemical bonding appeared at the interface.27 These structureless characteristics correspond to conventional metal induced gap states (MIGS),28,29 which originate from the metal wave function penetrating into the semiconductor nanofilm band gap and screening by the GaN slab, decaying rapidly (Figure 5a). These Al-induced states are of particular importance because the density of these states sensitively influences the position of the Fermi level with respect to the semiconductor band edges. Therefore, the work function of GaN/Al is ∼0.2 eV higher than that of the G-GaN, and it should originate from the strong metaldependent MIGS density.27 2. The Influence of Surface and Interface Structure. Because of the difficulty of doing DFT calculations in such a systematical study, an ideal unreconstructed Ga (Al)-terminated (0001) surface and an atomically smooth interface are modeled for this semiconductor/metal structure. However, the ideal surface and interface can similarly affect the values of the work function as well as that in the actual structure. Surface Structure. In our calculations, the work function changes quite significantly as the surface termination changes from Ga (4.1 eV) to N (8.8 eV), which is similar to the results of Rosa et al.,17 reflecting the general instability of the N-terminated surface. This is because the N atom is more
FE Enhancement in Semiconductor Nanofilms electronegative than the Ga atom, and electrons will be transferred to the N atomic layer, causing an accumulation of negative charge on the outside and an accumulation of positive charge on the inside of the surface. This leads to a negative dipole and makes the work function increase. The reconstruction may also influence the surface charge transfer; however, the (1 × 1) structure has been experimentally and theoretically observed at Ga-rich conditions, whereas the exact Ga coverage is not definite.30-32 Rosa et al.17 showed that the work function of a (0001) clean Ga-terminated surface is 4.42 eV, which is similar to our result of 4.1 eV. The work function with different Ga coverages is observed to range from 3.1 to 5.31 eV. Interface Structure. The corresponding effects originate from the interface states and interface charge transfer. (1) For the interface charge transfer, the change in the interface structure can directly influence the space charge distribution near the interface. As a result, the work function would change accordingly. However, because of the same Al-N bond in the interface in our model, the direction of the charge transfer cannot be changed; therefore, the general behavior of the interface charge transfer cannot be affected. (2) For the interface states, the occupied states penetration inside the semiconductor layer is strongly metal-dependent rather than the interface structure.27,29 The general behavior of the interface states cannot be significantly affected by interface structure. Similar to the ideal interface (large lattice mismatch) structure adopted in our calculations, the structural and electronic properties of ideal nitride/Al interfaces have been studied.22 The calculated results show that the contact between GaN and Al was in good agreement with the experimental findings for Al films deposited on a clean GaN surface. It means that modifying the surface and interface structure can somewhat change the values of some physical parameters, in particular, the work function, but not the general behavior of the semiconductor/ metal system. Of course, a more complicated calculation and accurate analysis for the interface and surface would be needed in the future. IV. Conclusions By taking into account an Al substrate to model a real FE device, we have investigated the FE properties of nitride semiconductor nanofilms with different thicknesses by firstprinciples calculations. The results show that, by thickness modulation in a certain range, the work function can be decreased nearly 0.5 eV for GaN/Al; similar results apply for AlN/Al. FE current densities can be advanced nearly 2 orders of magnitude only by thickness modulation of several nanometers, which is very promising for engineering the thin film cathode of FE devices. The remarkable thickness effect of the nanofilms on their FE properties is closely related to the Al substrate-induced surface charge transfer, interface charge transfer, and interface states.
J. Phys. Chem. C, Vol. 114, No. 26, 2010 11587 Acknowledgment. This research was supported by Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB) (PHR201007101), the Beijing Nova Program (2008B10), the Beijing Natural Science Foundation (No. 1102006), and the Ministry of Education Scientific Research Foundation for Returnees. References and Notes (1) de Jonge, N.; Lamy, Y.; Schoots, K.; Oosterkamp, T. H. Nature 2002, 420, 393. (2) de Heer, W. A.; Chaˆtelain, A.; Ugarte, D. Science 1995, 270, 1179. (3) Forrest, R. D.; Burden, A. P.; Silva, S. R. P.; Cheah, L. K.; Shi, X. Appl. Phys. Lett. 1998, 73, 3784. (4) Sugino, T.; Kimura, C.; Yamamoto, T. Appl. Phys. Lett. 2002, 80, 3602. (5) Wang, R. Z.; Yan, H.; Wang, B.; Zhang, X. W.; Hou, X. Y. Appl. Phys. Lett. 2008, 92, 142102. (6) Zhao, J. P.; Chen, Z. Y.; Wang, X.; Shi, T. S.; Yano, T. Appl. Phys. Lett. 2000, 76, 191. (7) Binh, V. T.; Adessi, C. Phys. ReV. Lett. 2000, 85, 864. (8) Wang, R. Z.; Ding, X. M.; Wang, B.; Xue, K.; Xu, J. B.; Yan, H.; Hou, X. Y. Phys. ReV. B 2005, 72, 125310. (9) Duan, Z. Q.; Wang, R. Z.; Yuan, R. Y.; Yang, W.; Wang, B.; Yan, H. J. Phys. D: Appl. Phys. 2007, 40, 5828. (10) Fowler, R. H.; Nordheim, L. Proc. R. Soc. London A 1928, 119, 173. (11) Khazaei, M.; Farajian, A. A.; Kawazoe, Y. Phys. ReV. Lett. 2005, 95, 177602. (12) Tada, K.; Watanabe, K. Phys. ReV. Lett. 2002, 88, 4. (13) Pankove, J. I.; Schade, H. Appl. Phys. Lett. 1974, 25, 53. (14) Wu, C. I.; Kahn, A.; Hellman, E. S.; Buchanan, D. N. E. Appl. Phys. Lett. 1998, 73, 1346. (15) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, A1133. (16) Zywietz, T. K.; Neugebauer, J.; Scheffler, M. Appl. Phys. Lett. 1999, 74, 1695. (17) Rosa, A. L.; Neugebauer, J. Phys. ReV. B 2006, 73, 205346. (18) Ambacher, O. J. Phys. D: Appl. Phys. 1998, 31, 2653. (19) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (20) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (21) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (22) Picozzi, S.; Continenza, A.; Massidda, S.; Freeman, A. J. Phys. ReV. B 1998, 57, 4849. (23) Huang, F. Y. Appl. Phys. Lett. 2000, 76, 3046. (24) Tolle, J.; Roucka, R.; Chizmeshya, A. V. G.; Kouvetakis, J.; D’Costa, V. R.; Menendez, J. Appl. Phys. Lett. 2006, 88, 252112. (25) Zhou, G.; Duan, W.; Gu, B. Phys. ReV. Lett. 2001, 87, 095504. (26) Prada, S.; Martinez, U.; Pacchioni, G. Phys. ReV. B 2008, 78, 235423. (27) Goniakowski, J.; Noguera, C. Interface Sci. 2004, 12, 93. (28) Louie, S. G.; Cohen, M. L. Phys. ReV. B 1976, 13, 2461. (29) Bordier, G.; Noguera, C. Phys. ReV. B 1991, 44, 6361. (30) Yu, Z. X.; Tong, S. Y.; Xu, S.; Ma, S.; Wu, H. Surf. ReV. Lett. 2003, 831. (31) Northrup, J. E.; Neugebauer, J.; Feenstra, R. M.; Smith, A. R. Phys. ReV. B 2000, 61, 9932. (32) Smith, A. R.; Feenstra, R. M.; Greve, D. W.; Shin, M. S.; Skowronski, M.; Neugebauer, J.; Northrup, J. E. J. Vac. Sci. Technol. B 1998, 16, 2232.
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