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Characteristics of field emission from nanocrystalline metals
Physica B 324 (2002) 329–335
Characteristics of field emission from nanocrystalline metals R.R. Mulyukova, E.A. Litvinovb, L.R. Zubairova,*, Yu.M. Yumaguzinc, V.A. Ivchenkob a
Institute for Metals Superplasticity Problems, Russian Academy of Sciences, Khalturin Str. 39, Ufa 450001, Russia b Institute of Electrophysics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia c Bashkir State University, Frunze Str. 32, Ufa 450074, Russia Received 19 March 2002; received in revised form 1 July 2002
Abstract Nanocrystalline (NC) samples of tungsten have been investigated by transmission electron microscopy, field ion microscopy and field electron energy spectroscopy. It has been shown that energy distributions of field-emitted electrons from NC tungsten differ significantly from energy distributions of coarse-grained metal. Theoretical analysis shows that the revealed differences are caused by work function changes and Fermi’s level shifts due to formation of NC structure in the metal. r 2002 Elsevier Science B.V. All rights reserved. PACS: 61.46; 79.70 Keywords: Field electron emission; Nanocrystalline tungsten; Total energy distribution
1. Introduction Recent interest in nanocrystalline (NC) materials [1–4] with a mean grain size of about 10– 100 nm is due to the fact that their physical properties significantly differ from properties of usual coarse-grained materials. This opens new potentials for processing materials with prespecified properties. A large volume fraction of grain boundaries within NC metals and their special, non-equilibrium states play a significant *Corresponding author. Tel.: +7-3472-253710; fax: +73472-253759. E-mail address: [email protected] (L.R. Zubairov).
role in the formation of its specific properties. The specific behavior of physical properties from NC materials allows one to await the features of the electronic structure from these materials. The method of field electron energy spectroscopy was first applied for the investigation of NC nickel in Ref. [5]. Qualitative and quantitative changes in energy distributions, resulting from NC structure formation, were revealed. Two types of distributions for different areas of an emitting surface of a tip were observed. However, the lack of experimental data on the actually probed area of the microstructure (from grain body or from vicinity of grain boundaries) delayed the analysis of the results of this work.
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 4 1 9 - 9
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R.R. Mulyukov et al. / Physica B 324 (2002) 329–335
2. Experimental procedure In the present work transmission electron microscopy, field ion and field electron emission methods [6,7] were used to study features of microstructure and electronic structure of the NC tungsten (purity of 99.99%). The NC structure was obtained by high plastic deformations up to the true logarithmic strain e ¼ 7 by means of torsion under quasihydrostatic pressure on a Bridgemen anvil. The microstructure of the NC sample was studied using a transmission electron microscope JEM-2000EX [8]. Samples selected for investigations of the microstructure in a field-ion microscope were produced from NC tungsten in the form of point emitters with a radius of curvature, B30–50 nm, by means of electrolytic etching. The tip was spot welded to a nickel loop. The field-ion microscope was equipped with a microchannel ion–electron converter, which intensified the brightness of surface micropatterns by a factor of 104. Liquid nitrogen was used as a coolant (T ¼ 78 K). Spectroscopically pure neon was used as imaging gas. The field emitter tips, prepared for investigations using field-emission methods, had an atomically smooth surface, which was close to semi-spherical. The surface was prepared in situ by field evaporation. A controlled removal of atomic layers from the sample surface was carried out until a grain boundary appeared on a field ion image. The tip with grain boundaries at the apex was installed in a field-electron spectrometer to study the features of the electronic structure of the material. Experimental studies were conducted under conditions of ultra-high (o108 Pa) vacuum. The spectrometer was equipped with a fieldelectron microscope for continuous observation of the emission pattern and a dispersive electrostatic energy analyzer with a better resolution of approximately 30 meV [9]. The detection of the emission current at the output of the analyzer was made possible by means of a secondary electron multiplier operated in the counting regime. The selection of the probed emission direction was achieved by means of a special manipulator. The
probed area on the surface (10 nm diameter) of a point was determined by the size of the hole on the screen anode. Measurement and processing of data were controlled by means of a personal computer and a CAMAC interface system using original software. Directly before measurements, the surface of a tip was cleaned by field desorption. For a comparative analysis, a point, after annealing in situ at a temperature of about 8001C for 20 min, was investigated. Annealing was performed by means of current passing through the nickel loop supporting the W-tip.
3. Results and discussion Deformation processing of tungsten resulted in NC samples (Fig. 1) with homogeneous granular
Fig. 1. Microstructure of NC tungsten in TEM: (a) light field with diffraction pattern, (b) dark field.
R.R. Mulyukov et al. / Physica B 324 (2002) 329–335
structure with a mean grain size of about 100 nm [8]. In tips of NC tungsten produced by electrolytic etching such a microstructure was preserved. Fig. 2 shows a field ion image of the surface of NC tungsten with a grain boundary. Such a pattern of the surface was obtained by evaporating about 106 atomic layers of a (1 1 0) plane. During the removal of 43 atomic layers, the atomic structure of the grain boundaries was examined. For further field-emission investigations, a high angle grain boundary was selected (Fig. 2, indicated by an arrow). The analysis of the boundary structure within the tip, performed by means of controlled removal of surface atoms, has shown that its crystalline structure differs from the structure of the grain boundary of those tungsten specimens, not subjected to high plastic deformations. According to our estimations of the field-ion pattern, the width of a boundary is not more than 0.6–0.8 nm. In the non-deformed tungsten this width is 0.3–0.4 nm. The atomically smooth surface of a tip, formed in a field-ion microscope, was then investigated in a field-electron spectrometer. The energy distributions of field-emitted electrons were measured for
Fig. 2. Field ion image of the NC W surface (V ¼ 12:6 kV) with grain boundary (indicated by arrows). Circles 1, 2 indicate portions of the surface for which total energy distributions of field-emitted electrons are given.
331
different emitting sites and the position of each site was controlled by means of the emission pattern. Though the resolution achieved by field-electron microscopy is lower compared to field-ion imaging (by an order of magnitude), comparison of the two emission images allowed to identify the microstructure of areas where electron energy distributions were taken. Three types of total energy distributions of field-emitted electrons depending on the selected emission site on the tip were obtained. Spectra taken from the area containing the grain boundary (Fig. 3) have an additional peak in the low energy region or an inflection in the high energy region. The additional peak increases with increasing anode voltage (Fig. 3a) and the inflection decreases with increasing anode voltage (Fig. 3b). In the case of areas away from the grain boundary the electron energy distributions are similar to the classical one and expected from the Fowler–Nordheim theory (Fig. 4). However, the full-width at half-maximum (FWHM) of this spectrum significantly (by 0.4 eV) exceeds this parameter for the classical spectrum [10] and is 0.58–0.64 eV. As shown before [3,4] annealing of NC samples led to recovery of their physical properties. This recovery correlates with the recovery of the microstructure. In situ annealing of a tip at a temperature of about 8001C for 20 min leads to a partial recovery of electron energy distributions (Fig. 5). Only one peak was observed in the spectrum. After annealing, the FWHM decreased to 0.45–0.60 eV. These significant differences in energy characteristics of field-emitted electrons from NC tungsten and its coarse-grained counterpart have probably been caused by properties of the microstructure. Revealed differences of energy characteristics of electrons emitted from NC metal and electrons emitted from coarse-grained metal can be caused by microstructure features. In particular, we consider an elevated volume fraction of grain boundaries, being in a specific non-equilibrium state. Their effective physical width significantly exceeds the crystallographic width of grain boundaries and is about 10 nm
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Fig. 3. Total energy distributions of field-emitted electrons from NC tungsten at different anode voltages (given in inset) obtained for different areas of the surface of the tip, containing a grain boundary (Fig. 2).
Fig. 4. Total energy distributions of field-emitted electrons from NC tungsten at different anode voltages (given in inset) obtained for area 2 (Fig. 2) away from the grain boundary.
Fig. 5. Total energy distributions of field-emitted electrons at different anode voltages (given in inset) for the annealed point at 8001C in vacuum.
[11–13]. The NC material can be characterized by two ‘‘phases’’: granular and grain boundary. The first phase has the characteristics of a conventional monocrystalline or coarse-grained
material. The characteristics of the second phase have different fixed values. For interpreting the experimental data, let us do the following. Following Ref. [5] let us write the
R.R. Mulyukov et al. / Physica B 324 (2002) 329–335
experimentally measured total energy distributions of field-emitted electrons in the form j ð1Þ N ¼ Sf ðx; yÞ; e ðexpðxÞÞy e eF ; x¼ ; 1 þ expðxÞ kT pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 8p 2mjZð e3 E =jÞ y¼ kT ; 2ehE
f ðx; yÞ ¼
ð2Þ
where j is the emission current density, e is the elementary charge, S is the efficient area of emission, eF is the Fermi energy, k is the Boltzmann’s constant, T is the absolute temperature, h is the Planck’s constant, m is the electron mass, j is the localpwork ffiffiffiffiffiffiffiffi function, E is the electric field strength, Zð e3 E =jÞ is a slowly varying function [10]. Then while analyzing emission from areas containing grain boundaries, one should take into account that it comprises the emission from the grain body N0 and from the grain boundary area Ngb : It is assumed that the grain boundary phase has a different work function and Fermi level values: N ¼ N0 þ Ngb jgb j0 ¼ S0 f0 ðx; yÞ þ Sgb fgb ðx b; cyÞ e e j0 ¼ S0 ½f0 ðx; yÞ þ afgb ðx b; cyÞ; e pffiffiffiffiffiffiffi jgb jgb Sgb DeF a¼ ; cE pffiffiffiffiffiffi : ; b¼ j0 S 0 kT j0
333
This is reflected in the spectrum in the form of emission from different Fermi levels. Thus, a formal assumption for different Fermi level values of grain and grain boundary phases is made for simplification of the description. More detailed reasons for the simplification is cited in the end of this paper. Conduction electrons, which can be emitted, are in a potential pit with Coulomb interaction with positive ion cover: jP ¼ e2 n1=3 :
ð5Þ
jP is the full work function while removing an electron, n is the concentration of conduction electrons or ions. The Fermi energy is given by 2=3 h2 3 eF ¼ n ð6Þ 2m 8p and the emission work function can be written as j ¼ jP eF :
ð7Þ
We assume that the change in the value jP ; eF and j is connected with the change in the concentration n in one of the crystallographic directions. Then Dn 2 Dn ; DeF ¼ eF ; n 3 n 1 Dn Dj ¼ j þ eF : 3 n
DjP ¼ jP ð3Þ ð4Þ
For determining DeF ¼ ðeF Þgb ðeF Þ0 and jgb ¼ j0 þ Dj let us take the following model. Certainly it is known that the presence of electric contact between grain and grain boundary phases leads to leveling their Fermi levels. But contact potentials between spots [14] corresponding to the exit of grain and grain boundary phases on the surface of emission appear on the surface. The value of contact potential is equal to the difference of work functions or the difference of Fermi levels calculated from the energy of a free electron at rest in vacuum. Electrons pick up transverse energy with respect to the direction of emission comparable with the contact potential.
ð8Þ
Not considering the physics in question let us study expression (3) for assumptions with respect to the numerical values for j; eF ; Dn: It turned out, that distributions (3) can be formally obtained similar to the experimental ones if j eF > 0; Dno0; from which it results that DeF o0; Djo0; bo0; co1 (Fig. 6). This is in accordance with smaller values of the concentration n and of the work function for the grain boundary phase. In the case of a smaller contribution to the emission from this phase (a ¼ 0:3) one obtains a distribution with an additional peak in the low energy region (Fig. 6a) by numerical modeling. When the contributions from both phases are comparable (a ¼ 0:9) the calculated distribution has an inflection on the high energy side (Fig. 6b).
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Fig. 6. Energy-distribution function N versus x at y ¼ 0:2; b ¼ 8; c ¼ 0:9 for (a) a ¼ 0:3 and (b) a ¼ 0:9:
Fig. 7. Energy-distribution function N versus x at (1) y ¼ 0:22; a ¼ 0:1; d ¼ 0:2; (2) y ¼ 0:21; a ¼ 0:2; d ¼ 0:5 and (3) y ¼ 0:20; a ¼ 0:3; d ¼ 1:
Increasing field strength corresponds to a relatively small decrease in y; an increasing a-value and larger values of the factor d ¼ j0 =eS0 : Numerical modeling also shows that by increasing the field E the left maximum becomes more distinct (Fig. 7) and the right inflection decreases. This behavior agrees with the experimental observations. Thus, our numerical modeling suggests decreasing values of concentration n; Fermi energy and work function
for the grain boundary phase, which is compatible with present experimental data. Let us explain how different Fermi levels and different work functions can affect the total energy distributions of field-emitted electrons. Let us apply the concept from the theory of spots for work function of a non-homogeneous electron emitter [14]. Following our analysis grain and grain boundary phases of NC metals have different Fermi’s energies. The presence of electric contacts with each other leads to violation of charge neutrality of these areas, leveling their electrochemical potentials (Fermi levels) and appearance of contact potentials between spots corresponding to the exit of areas on the surface of emission. The value of contact potential is equal to the difference of work functions or the difference of Fermi levels calculated from the energy of a free electron at rest in vacuum. The electric field of the contact potential or the field above spots can be calculated for our case as Ep101 V/106 cmE105 V/cm. In the case of field emission the external field exceeds this value and emission occurs from separate areas with different work function that is reflected in the spectra. The field close to the spots has a normal component near the metal surface and a tangential one at some distance. Electrons pick up transverse energy with respect to the direction of emission compar-
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able with the contact potential. This is reflected in the spectrum in the form of emission from different Fermi’s levels. Decoding of spectra requires knowledge of the apparatus functions of a definite device and seems to be sufficiently informational.
4. Conclusions It has been shown that energy distributions of fieldemitted electrons from NC tungsten differ from those of coarse-grained metal. In the case of emission from the surface areas, a grain boundary in an additional peak in the low energy region or in an inflection in the high energy region is observed, respectively. On the basis of the theoretical analysis it can be concluded that due to the formation of NC structures (by means of severe plastic shear straining under quasi-hydrostatic pressure) paths of currents with low work function at grain boundaries occur in the metal. It is possible that, this is caused by the change due to deformation of packing density in definite crystallographic directions. The investigations performed offer the challenge in searching materials in which this effect is most distinct. This would open new routes for creation of matrices being highly efficient field emitters.
Acknowledgements This work was supported by the Complex Program of RAS (grant ‘‘Structure and properties of NC materials’’).
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References [1] I.D. Morokhov, L.I. Trusov, V.I. Lapovok, Physical Phenomena in Ultra-fine Environments, Nauka, Moscow, 1984 (in Russian). [2] R. Birringer, H. Gleiter, in: R.W. Cahn (Ed.), Encyclopedia of Materials, Sci. and Eng. Suppl. 1, Pergamon Press, Oxford, 1988, p. 339. [3] R.Z. Valiev, A.V. Korznikov, R.R. Mulyukov, Mater. Sci. Eng. A168 (1993) 141. [4] R.R. Mulyukov, M.D. Starostenkov, Acta Metallur. Sin. (English Letters) 13 (1) (2000) 301. [5] L.R. Zubairov, R.R. Mulyukov, R.Sh. Musalimov, Yu.M. Yumaguzin, Proc. on The Structure and Properties of Nanocrystalline Materials, Ekaterinburg, 1999, UD RAS, ISBN 5-7691-0954-8, pp. 275–278. [6] L.R. Zubairov, E.A. Litvinov, R.R. Mulyukov, R.Sh. Musalimov, Yu.M. Yumaguzin, Doklady Phys. 45 (5) (2000) 198. [7] R.R. Mulyukov, Yu.M. Yumaguzin, V.A. Ivchenko, L.R. Zubairov, JETP Lett. 72 (5) (2000) 257. [8] N.I. Noskova, E.G. Volkova, R.R. Mulyukov, A.V. Korznikov, L.R. Zubairov, Proceedings of the International Conference on Current Status of Theory and Practice of Superplasticity in Materials, Ufa, 2000, pp. 167–173. [9] R.Z. Bakhtizin, V.M. Lobanov, Yu.M. Yumaguzin, Apparatus Tech. Exp. 4 (1987) 247 (in Russian). [10] A. Modinos Field, Thermionic and Secondary Electron Emission Spectroscopy, University of Salford, Salford, Plenum Press, New York, 1984. [11] R.Z. Valiev, R.R. Mulyukov, V.V. Ovchinnikov, Philos. Mag. Lett. 62 (4) (1990) 253. [12] R.Z. Valiev, R.R. Mulyukov, V.V. Ovchinnikov, V.A. Shabashov, Scr. Met. Mat. 25 (1991) 2717. [13] R.R. Mulyukov, Metal. Sci. Heat Treat. (8) (1998) 34 (in Russian). [14] C. Herring, M.H. Nickols, Rev. Mod. Phys. 21 (1949) 165.
Characteristics of field emission from nanocrystalline metals R.R. Mulyukova, E.A. Litvinovb, L.R. Zubairova,*, Yu.M. Yumaguzinc, V.A. Ivchenkob a
Institute for Metals Superplasticity Problems, Russian Academy of Sciences, Khalturin Str. 39, Ufa 450001, Russia b Institute of Electrophysics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia c Bashkir State University, Frunze Str. 32, Ufa 450074, Russia Received 19 March 2002; received in revised form 1 July 2002
Abstract Nanocrystalline (NC) samples of tungsten have been investigated by transmission electron microscopy, field ion microscopy and field electron energy spectroscopy. It has been shown that energy distributions of field-emitted electrons from NC tungsten differ significantly from energy distributions of coarse-grained metal. Theoretical analysis shows that the revealed differences are caused by work function changes and Fermi’s level shifts due to formation of NC structure in the metal. r 2002 Elsevier Science B.V. All rights reserved. PACS: 61.46; 79.70 Keywords: Field electron emission; Nanocrystalline tungsten; Total energy distribution
1. Introduction Recent interest in nanocrystalline (NC) materials [1–4] with a mean grain size of about 10– 100 nm is due to the fact that their physical properties significantly differ from properties of usual coarse-grained materials. This opens new potentials for processing materials with prespecified properties. A large volume fraction of grain boundaries within NC metals and their special, non-equilibrium states play a significant *Corresponding author. Tel.: +7-3472-253710; fax: +73472-253759. E-mail address: [email protected] (L.R. Zubairov).
role in the formation of its specific properties. The specific behavior of physical properties from NC materials allows one to await the features of the electronic structure from these materials. The method of field electron energy spectroscopy was first applied for the investigation of NC nickel in Ref. [5]. Qualitative and quantitative changes in energy distributions, resulting from NC structure formation, were revealed. Two types of distributions for different areas of an emitting surface of a tip were observed. However, the lack of experimental data on the actually probed area of the microstructure (from grain body or from vicinity of grain boundaries) delayed the analysis of the results of this work.
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 4 1 9 - 9
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R.R. Mulyukov et al. / Physica B 324 (2002) 329–335
2. Experimental procedure In the present work transmission electron microscopy, field ion and field electron emission methods [6,7] were used to study features of microstructure and electronic structure of the NC tungsten (purity of 99.99%). The NC structure was obtained by high plastic deformations up to the true logarithmic strain e ¼ 7 by means of torsion under quasihydrostatic pressure on a Bridgemen anvil. The microstructure of the NC sample was studied using a transmission electron microscope JEM-2000EX [8]. Samples selected for investigations of the microstructure in a field-ion microscope were produced from NC tungsten in the form of point emitters with a radius of curvature, B30–50 nm, by means of electrolytic etching. The tip was spot welded to a nickel loop. The field-ion microscope was equipped with a microchannel ion–electron converter, which intensified the brightness of surface micropatterns by a factor of 104. Liquid nitrogen was used as a coolant (T ¼ 78 K). Spectroscopically pure neon was used as imaging gas. The field emitter tips, prepared for investigations using field-emission methods, had an atomically smooth surface, which was close to semi-spherical. The surface was prepared in situ by field evaporation. A controlled removal of atomic layers from the sample surface was carried out until a grain boundary appeared on a field ion image. The tip with grain boundaries at the apex was installed in a field-electron spectrometer to study the features of the electronic structure of the material. Experimental studies were conducted under conditions of ultra-high (o108 Pa) vacuum. The spectrometer was equipped with a fieldelectron microscope for continuous observation of the emission pattern and a dispersive electrostatic energy analyzer with a better resolution of approximately 30 meV [9]. The detection of the emission current at the output of the analyzer was made possible by means of a secondary electron multiplier operated in the counting regime. The selection of the probed emission direction was achieved by means of a special manipulator. The
probed area on the surface (10 nm diameter) of a point was determined by the size of the hole on the screen anode. Measurement and processing of data were controlled by means of a personal computer and a CAMAC interface system using original software. Directly before measurements, the surface of a tip was cleaned by field desorption. For a comparative analysis, a point, after annealing in situ at a temperature of about 8001C for 20 min, was investigated. Annealing was performed by means of current passing through the nickel loop supporting the W-tip.
3. Results and discussion Deformation processing of tungsten resulted in NC samples (Fig. 1) with homogeneous granular
Fig. 1. Microstructure of NC tungsten in TEM: (a) light field with diffraction pattern, (b) dark field.
R.R. Mulyukov et al. / Physica B 324 (2002) 329–335
structure with a mean grain size of about 100 nm [8]. In tips of NC tungsten produced by electrolytic etching such a microstructure was preserved. Fig. 2 shows a field ion image of the surface of NC tungsten with a grain boundary. Such a pattern of the surface was obtained by evaporating about 106 atomic layers of a (1 1 0) plane. During the removal of 43 atomic layers, the atomic structure of the grain boundaries was examined. For further field-emission investigations, a high angle grain boundary was selected (Fig. 2, indicated by an arrow). The analysis of the boundary structure within the tip, performed by means of controlled removal of surface atoms, has shown that its crystalline structure differs from the structure of the grain boundary of those tungsten specimens, not subjected to high plastic deformations. According to our estimations of the field-ion pattern, the width of a boundary is not more than 0.6–0.8 nm. In the non-deformed tungsten this width is 0.3–0.4 nm. The atomically smooth surface of a tip, formed in a field-ion microscope, was then investigated in a field-electron spectrometer. The energy distributions of field-emitted electrons were measured for
Fig. 2. Field ion image of the NC W surface (V ¼ 12:6 kV) with grain boundary (indicated by arrows). Circles 1, 2 indicate portions of the surface for which total energy distributions of field-emitted electrons are given.
331
different emitting sites and the position of each site was controlled by means of the emission pattern. Though the resolution achieved by field-electron microscopy is lower compared to field-ion imaging (by an order of magnitude), comparison of the two emission images allowed to identify the microstructure of areas where electron energy distributions were taken. Three types of total energy distributions of field-emitted electrons depending on the selected emission site on the tip were obtained. Spectra taken from the area containing the grain boundary (Fig. 3) have an additional peak in the low energy region or an inflection in the high energy region. The additional peak increases with increasing anode voltage (Fig. 3a) and the inflection decreases with increasing anode voltage (Fig. 3b). In the case of areas away from the grain boundary the electron energy distributions are similar to the classical one and expected from the Fowler–Nordheim theory (Fig. 4). However, the full-width at half-maximum (FWHM) of this spectrum significantly (by 0.4 eV) exceeds this parameter for the classical spectrum [10] and is 0.58–0.64 eV. As shown before [3,4] annealing of NC samples led to recovery of their physical properties. This recovery correlates with the recovery of the microstructure. In situ annealing of a tip at a temperature of about 8001C for 20 min leads to a partial recovery of electron energy distributions (Fig. 5). Only one peak was observed in the spectrum. After annealing, the FWHM decreased to 0.45–0.60 eV. These significant differences in energy characteristics of field-emitted electrons from NC tungsten and its coarse-grained counterpart have probably been caused by properties of the microstructure. Revealed differences of energy characteristics of electrons emitted from NC metal and electrons emitted from coarse-grained metal can be caused by microstructure features. In particular, we consider an elevated volume fraction of grain boundaries, being in a specific non-equilibrium state. Their effective physical width significantly exceeds the crystallographic width of grain boundaries and is about 10 nm
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Fig. 3. Total energy distributions of field-emitted electrons from NC tungsten at different anode voltages (given in inset) obtained for different areas of the surface of the tip, containing a grain boundary (Fig. 2).
Fig. 4. Total energy distributions of field-emitted electrons from NC tungsten at different anode voltages (given in inset) obtained for area 2 (Fig. 2) away from the grain boundary.
Fig. 5. Total energy distributions of field-emitted electrons at different anode voltages (given in inset) for the annealed point at 8001C in vacuum.
[11–13]. The NC material can be characterized by two ‘‘phases’’: granular and grain boundary. The first phase has the characteristics of a conventional monocrystalline or coarse-grained
material. The characteristics of the second phase have different fixed values. For interpreting the experimental data, let us do the following. Following Ref. [5] let us write the
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experimentally measured total energy distributions of field-emitted electrons in the form j ð1Þ N ¼ Sf ðx; yÞ; e ðexpðxÞÞy e eF ; x¼ ; 1 þ expðxÞ kT pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 8p 2mjZð e3 E =jÞ y¼ kT ; 2ehE
f ðx; yÞ ¼
ð2Þ
where j is the emission current density, e is the elementary charge, S is the efficient area of emission, eF is the Fermi energy, k is the Boltzmann’s constant, T is the absolute temperature, h is the Planck’s constant, m is the electron mass, j is the localpwork ffiffiffiffiffiffiffiffi function, E is the electric field strength, Zð e3 E =jÞ is a slowly varying function [10]. Then while analyzing emission from areas containing grain boundaries, one should take into account that it comprises the emission from the grain body N0 and from the grain boundary area Ngb : It is assumed that the grain boundary phase has a different work function and Fermi level values: N ¼ N0 þ Ngb jgb j0 ¼ S0 f0 ðx; yÞ þ Sgb fgb ðx b; cyÞ e e j0 ¼ S0 ½f0 ðx; yÞ þ afgb ðx b; cyÞ; e pffiffiffiffiffiffiffi jgb jgb Sgb DeF a¼ ; cE pffiffiffiffiffiffi : ; b¼ j0 S 0 kT j0
333
This is reflected in the spectrum in the form of emission from different Fermi levels. Thus, a formal assumption for different Fermi level values of grain and grain boundary phases is made for simplification of the description. More detailed reasons for the simplification is cited in the end of this paper. Conduction electrons, which can be emitted, are in a potential pit with Coulomb interaction with positive ion cover: jP ¼ e2 n1=3 :
ð5Þ
jP is the full work function while removing an electron, n is the concentration of conduction electrons or ions. The Fermi energy is given by 2=3 h2 3 eF ¼ n ð6Þ 2m 8p and the emission work function can be written as j ¼ jP eF :
ð7Þ
We assume that the change in the value jP ; eF and j is connected with the change in the concentration n in one of the crystallographic directions. Then Dn 2 Dn ; DeF ¼ eF ; n 3 n 1 Dn Dj ¼ j þ eF : 3 n
DjP ¼ jP ð3Þ ð4Þ
For determining DeF ¼ ðeF Þgb ðeF Þ0 and jgb ¼ j0 þ Dj let us take the following model. Certainly it is known that the presence of electric contact between grain and grain boundary phases leads to leveling their Fermi levels. But contact potentials between spots [14] corresponding to the exit of grain and grain boundary phases on the surface of emission appear on the surface. The value of contact potential is equal to the difference of work functions or the difference of Fermi levels calculated from the energy of a free electron at rest in vacuum. Electrons pick up transverse energy with respect to the direction of emission comparable with the contact potential.
ð8Þ
Not considering the physics in question let us study expression (3) for assumptions with respect to the numerical values for j; eF ; Dn: It turned out, that distributions (3) can be formally obtained similar to the experimental ones if j eF > 0; Dno0; from which it results that DeF o0; Djo0; bo0; co1 (Fig. 6). This is in accordance with smaller values of the concentration n and of the work function for the grain boundary phase. In the case of a smaller contribution to the emission from this phase (a ¼ 0:3) one obtains a distribution with an additional peak in the low energy region (Fig. 6a) by numerical modeling. When the contributions from both phases are comparable (a ¼ 0:9) the calculated distribution has an inflection on the high energy side (Fig. 6b).
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Fig. 6. Energy-distribution function N versus x at y ¼ 0:2; b ¼ 8; c ¼ 0:9 for (a) a ¼ 0:3 and (b) a ¼ 0:9:
Fig. 7. Energy-distribution function N versus x at (1) y ¼ 0:22; a ¼ 0:1; d ¼ 0:2; (2) y ¼ 0:21; a ¼ 0:2; d ¼ 0:5 and (3) y ¼ 0:20; a ¼ 0:3; d ¼ 1:
Increasing field strength corresponds to a relatively small decrease in y; an increasing a-value and larger values of the factor d ¼ j0 =eS0 : Numerical modeling also shows that by increasing the field E the left maximum becomes more distinct (Fig. 7) and the right inflection decreases. This behavior agrees with the experimental observations. Thus, our numerical modeling suggests decreasing values of concentration n; Fermi energy and work function
for the grain boundary phase, which is compatible with present experimental data. Let us explain how different Fermi levels and different work functions can affect the total energy distributions of field-emitted electrons. Let us apply the concept from the theory of spots for work function of a non-homogeneous electron emitter [14]. Following our analysis grain and grain boundary phases of NC metals have different Fermi’s energies. The presence of electric contacts with each other leads to violation of charge neutrality of these areas, leveling their electrochemical potentials (Fermi levels) and appearance of contact potentials between spots corresponding to the exit of areas on the surface of emission. The value of contact potential is equal to the difference of work functions or the difference of Fermi levels calculated from the energy of a free electron at rest in vacuum. The electric field of the contact potential or the field above spots can be calculated for our case as Ep101 V/106 cmE105 V/cm. In the case of field emission the external field exceeds this value and emission occurs from separate areas with different work function that is reflected in the spectra. The field close to the spots has a normal component near the metal surface and a tangential one at some distance. Electrons pick up transverse energy with respect to the direction of emission compar-
R.R. Mulyukov et al. / Physica B 324 (2002) 329–335
able with the contact potential. This is reflected in the spectrum in the form of emission from different Fermi’s levels. Decoding of spectra requires knowledge of the apparatus functions of a definite device and seems to be sufficiently informational.
4. Conclusions It has been shown that energy distributions of fieldemitted electrons from NC tungsten differ from those of coarse-grained metal. In the case of emission from the surface areas, a grain boundary in an additional peak in the low energy region or in an inflection in the high energy region is observed, respectively. On the basis of the theoretical analysis it can be concluded that due to the formation of NC structures (by means of severe plastic shear straining under quasi-hydrostatic pressure) paths of currents with low work function at grain boundaries occur in the metal. It is possible that, this is caused by the change due to deformation of packing density in definite crystallographic directions. The investigations performed offer the challenge in searching materials in which this effect is most distinct. This would open new routes for creation of matrices being highly efficient field emitters.
Acknowledgements This work was supported by the Complex Program of RAS (grant ‘‘Structure and properties of NC materials’’).
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