RU2529452C1 - Method of non-contact determination of amplification of local electric field and work function in nano or microstructural emitters - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: dark characteristic of tunnel emission current is measured with increase of voltage on the anode and the value of voltage V_∞ is determined, the measured surface of the emitter is eradiated with a laser beam of ultraviolet or visible band with a fixed value of optical power and wavelength λ₁, the value of tunnel photoemissive current at increase of voltage on the anode is measured, and the value of voltage V_∞λ1 is fixed, the value of work function A and value of amplification of local electric field β In a spatial area of the emitter irradiation from the given relation are determined, or the measured surface of the emitter is eradiated additionally with a laser beam at another wavelength λ₂ of ultraviolet or visual band with maximum difference with reference to the first wavelength, the value of voltage V_∞λ2 is determined, and also the value of amplification of a local electric field in a spatial area of the emitter irradiation and value of the work function A from the given relation are determined.

EFFECT: possibility for determination of local electric field at simultaneous determination of work function of electrons from the emitter.

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Description

The invention relates to vacuum microelectronics and can be used to create vacuum devices for microwave microelectronics with cold field emission of the emitter, in matrix vacuum displays and visualizers.

Known optical method of determining the work function of the emitter based on the measurement of the optical spectrum transmission or reflection under irradiation emitter optical radiation in the ultraviolet and visible region of the spectrum and measurement of a sharp (by several orders of magnitude) reduce the absorption coefficient of the wavelength, determining the wavelength λ _c, the appropriate boundary transmittance ( "red" boundary of the photoelectric effect), and determining the work function of A ratio A = h · c / λ _c or A (eV) = 1240 / λ _c (nm); where: h is the Planck constant, c is the speed of light (Ukhanov Yu.I. Optical properties of semiconductors. M: Nauka. 1977. P.368; Zolotarev VM, Morozov VN, Smirnova EV Optical permanent natural and technical environments. Reference book. L .: Chemistry. 1984. P.216). However, this method allows you to determine the work function of the metals, provided that the geometrical dimensions of the emitter are larger than the probe optical beam. In optical spectrometers, the probe beam has typical dimensions of the order of cm in cross section; therefore, the use of this method for real microemitters is a difficult experimental problem. In addition, the method does not allow determining the locality of the field associated with a sharp spatial change in the topography of the surface of the emitter.

A known method for determining the work function of the emitter of a vacuum photodiode when it is irradiated with optical radiation with a tunable wavelength and measuring the value of the photocurrent. In the spectral region corresponding to a sharp decrease in the photocurrent with increasing wavelength, the red border of the photoelectric effect is determined, which corresponds to the boundary of the occurrence of zero photocurrent. This value of the wavelength corresponds to the condition when the photon energy hν is equal to the work function of output A (Lebedeva V.V. Experimental optics. M: Publishing House of Moscow State University. S.352). The wavelength of electromagnetic radiation of light λ is related to the frequency by the ratio λ = c / ν, therefore, the ratio for determining the work function A (eV) = 1240 / λ _g (nm). Since the value of the work function for known metals lies in the range from 2 to 6 eV (Zi S. Physics of semiconductor devices. M: Mir, 1984. 456 pp.), To determine the work function, for example, for tungsten with a value A = 5 eV requires radiation with a wavelength less than or equal to 248 nm, i.e. tunable radiation in the far UV region. When irradiating a vacuum photocathode, a quartz window is required to transmit such UV radiation. In addition, if it is a vacuum microdiode, then technical difficulties arise in the spatial irradiation of such emitters. The method also does not allow to determine the value of the local electrostatic field gain at the emitter.

There is a method of determining the work function of the emitter of a vacuum diode in the study of thermionic emission (Petrin AB About thermofield emission from metal tips // Plasma Physics. 2010, v. 36, No. 7, p.671-679). The method consists in measuring the current-voltage characteristic at a fixed cathode temperature and setting the current density value corresponding to the saturation region of the I – V characteristic and calculating A using the well-known Richardson-Deschmann relation. However, this method is only suitable for emitters with thermionic emission. In addition, the Richardson-Deschmann formula includes a thermionic constant, which depends on the probability of tunneling determined by the width of the potential barrier.

To calculate the amplification of the local electrostatic field at nano- or microstructural field-emission emitters, due to the local spatial surface gradient, it is necessary to measure the 3D microrelief of the emitter surface. A known method for determining the surface microrelief based on atomic force microscopy (Method and atomic force microscope for imaging surfaces with atomic resolution. BR 605251, 1987-07-28, BINNING GERD KARL). However, the probe elastic cantilever (cantilever) of an atomic force microscope (AFM) cannot always measure the three-dimensional surface of the emitter. The same problems arise for the metal tip probe of a tunneling microscope (VL Mironov. Fundamentals of scanning probe microscopy. Nizhny Novgorod. 2004. 110 pp.) When measuring the complex relief of the 3D surface of a conducting microemitter.

A known method for determining the micro- and nanorelief of the surface of the emitter (A.N. Obraztsov et al. The role of the curvature of atomic layers in field emission of electrons from graphite-like nanostructured carbon. Letters JETP, 1999, V.69, B.5, P.381-386) . Using various projections, it is possible to determine the complex surface of the emitter using an electron microscope (Gouldstein J. et al. Scanning electron microscopy and X-ray microanalysis. M .: Mir. S.304), but the establishment of a 3D microrelief of the surface of the emitter only allows one to estimate the increase in the local electrostatic field based on calculated models of electrostatics. In addition, these methods do not allow to determine the work function in the emitter.

A known method for determining the work function of the emitter of a vacuum diode with field emission (Muller EW // J. Appl. Phys. 1955. V. 26. P. 732; Obraztsov AN, Volkov AP, Pavlovsky I.YU. Mechanism cold emission of electrons from carbon materials // JETP Letters. 1998. V.68. B.1. S.56-60), which consists in measuring the field emission current J of a vacuum diode with increasing accelerating voltage V at the anode, the construction of the obtained current-voltage characteristics diode coordinates lg (I / F ²⁾ and 1 / F, determination of the work function of the inclination a graph of this relationship where F = β ∙ V / Z tension the electrostatic field with the influence of the surface gradient, and Z - emitter-anode spacing. However, this method assumes that the amplification value of the local electrostatic field β, the so-called form factor, is known in advance value corresponding to an increase in electrostatic field strength due to the spatial gradient of the surface shape of the emitter.

The objective of the invention is the ability to determine the local electrostatic field created by the spatial micro- and nano-inhomogeneities of the emitter with the simultaneous determination of the work of electron output from the emitter with a spatial resolution in the range of 300-1000 nm, determined by the wavelength of the probe optical UV or visible beam.

The problem is solved in that in the method of non-contact determination of the local electrostatic field gain and work function in nano- or microstructural emitters, according to the invention, the dark dependence of the tunneling emission current is measured with increasing voltage at the anode and the voltage value V _∞ tending to the field emission voltage is determined , which is controlled by an exponential increase of 3-5 orders of magnitude of the tunneling field emission current, the measured surface of the emitter laser is irradiated th beam of ultraviolet or visible range with a fixed value of optical power and wavelength λ _1, the value measured photoemission tunneling current when the voltage increases at the anode and the fixed voltage value V _{∞ λ1,} tending to photoemission breakdown voltage, which is controlled by an exponential increase 3-5 orders of the tunneling photoemissive current, determine the value of the work function A and the value of the amplification of the local electrostatic field β in the spatial region of irradiation em EPA ratio of

β ^1/2 = 2.77 · 10 ³ (hс / λ ₁ ) · z ^1/2 / [(V _∞ ) ^1/2 - V _{∞ λ1} ) ^1/2 ] (1)

A = hс / (λ ₁ [1- (V _{∞ λ1} / V _∞ ) ^1/2 ]) (2)

or additionally irradiate the measured surface of the emitter with a laser beam at a different wavelength λ _{2 of the} ultraviolet or visible range with a maximum difference with respect to the first wavelength, determine the voltage V _∞λ2 , tending to the voltage of the photoemission breakdown, which is controlled by an exponential increase of 3-5 orders of magnitude tunnel photoemission current and determine the value of the amplification of the local electrostatic field in the spatial region of the irradiation of the emitter and the value of the work function A from the ratio

β ^1/2 = 2.77 · 10 ³ z ^1/2 (hс / λ ₁ - h s / λ ₂ ) · / [(V _{∞ λ2} ) ^1/2 - V _{∞ λ1} ) ^1/2 ] (3)

A = (h s / λ ₁ - h s / λ ₂ ) / [1- (V _{∞ λ1} / V _{∞ λ2} ) ^1/2 ] (4)

where: β is the form factor-value corresponding to the enhancement of the local intensity of the electrostatic field in nano- or microstructural emitters, due to the spatial gradient of the shape of the surface of the emitter irradiated with a light beam;

z is the distance between the emitter and the anode in cm;

A is the electron work function from the emitter in eV;

V _∞ - voltage in volts, tending to the field emission voltage, which is controlled by an exponential increase of 3-5 orders of magnitude of the tunnel field emission current;

V _∞λ1 is the voltage in volts, tending to the photoemission breakdown voltage, which is controlled by an exponential increase of 3-5 orders of magnitude of the tunneling photoemissive photocurrent when the emitter is irradiated with optical radiation with photon energy hc / λ ₁ ;

hc / λ ₁ = hν ₁ is the photon energy in eV absorbed by the emitter electron due to the single-photon photoelectric effect;

V _∞λ2 is the voltage in volts, tending to the photoemission breakdown voltage, which is controlled by an exponential increase of 3-5 orders of magnitude of the tunneling photoemission current when the emitter is irradiated with optical radiation with photon energy hν _2, respectively, with wavelength λ ₂ = s / ν ₂ ;

ν is the radiation frequency of the optical range;

c is the speed of light;

h is Planck's constant.

The invention is illustrated by drawings.

Figure 1 presents a block diagram of an experimental setup for implementing the proposed method based on measuring the current-voltage characteristics of a vacuum microdiode with carbon emitters with a nanoscale structure in strong electrostatic fields when the emitter surface is irradiated with laser or LED optical radiation of UV or visible range.

Figure 2 shows the calculated dependence of the change in the height of the potential emitter-vacuum barrier on the field strength when the electron exit from the emitter is 5 eV.

Figure 3 shows the experimental dependence of the tunneling photoemissive current under laser irradiation with a wavelength of λ = 473 nm (photon energy 2.62 eV) of a carbon nanoscale emitter (B) and dark field emission current (C) on the change in the accelerating voltage at the anode of the vacuum microdiode at an emitter distance anode Z = 1 micron.

Figure 4 shows the dependence of the tunneling photoemissive current upon laser irradiation of a carbon nanoscale emitter at a wavelength of a red-He-Ne laser with λ = 633 nm (photon energy 1.96 eV) (D) and dark field emission current (G) in the absence of optical irradiation of the emitter from a change in the accelerating voltage at the anode of the vacuum microdiode at a distance of the emitter anode of 1 micron.

The positions in the drawings indicate:

1 - power supply unit for lasers or LEDs;

2 - solid-state microlaser, semiconductor laser or LED with a spectral maximum wavelength from near UV to IR

3 - focusing optical system;

4 - voltmeter;

5 - stabilized tunable source of constant voltage;

6 - a vacuum microdiode with a carbon spatially periodic emitter of a nanoscale structure with micro blades, each of which has a tip edge with a length of 200 nm and a thickness of 20 nm, while the distance between the planes of the blade and the anode is from 1 to 3 microns;

7 - limiting resistance;

8 - measuring resistance;

10 - microvolmeter.

The method is as follows.

Using a stabilized power source 5, the minimum (close to zero) positive voltage is applied to the anode of the vacuum microdiode 6, the emitter of which is connected to zero potential through the limiting 7 and measuring resistance 8. When the positive potential increases, at block 5, the corresponding voltage is fixed with 4 and the threshold of the field emission current is measured with a microvolmeter 10, the voltage at the anode of the microdiode is increased and its exponentially increasing value is fixed at which the field emission current increases by at least three to five orders of magnitude and tends to to breakdown value. The power source of the laser 1 is turned on and coherent laser or LED optical radiation is excited in the laser 2. Using the optical system 3, the emitter surface of the microdiode is irradiated with a laser beam with a UV or visible wavelength, provided that the energy of the corresponding photons is less than the expected work function of the diagnosed emitter. (The typical value for any metal and alloy of emitters lies in the range of 6–2 eV.) Increase the positive potential at block 5 from zero to the value corresponding to the appearance of the tunneling photocurrent, and fix the threshold for the photoemission current with a microvolmeter 9, increase the voltage at the anode of the microdiode and fix its exponentially increasing value at which the photoemission current increases by at least three to five orders of magnitude and tends to the breakdown value, and using the working formula (3) and (4) determine the value of A and the work function value of the local field intensity in the spatial region of the emitter radiation.

Similarly, measurements are carried out when the emitter is irradiated with laser radiation with a different wavelength, and in order to increase the accuracy of the measurement method, the wavelengths of the probe radiation are selected with the maximum difference from the UV and visible and near infrared ranges.

The method for determining the work function and the local electrostatic field in nano- or microstructural field-emission emitters is based on the tunneling photoeffect discovered by the authors at photon energies significantly lower than the work function of the electron from the emitter, which can be observed when a strong electrostatic field is formed in the emitter-anode electrode gap . The physical mechanism of the tunneling photoelectric effect discovered by the authors in strong electrostatic fields consists in the possibility of controlling the probability of tunneling of nonequilibrium photoelectrons resulting from the absorption of photons with energy hν through the potential metal-vacuum barrier with a decrease in its height and width using a strong electrostatic field when the Schottky effect is taken into account ( Zi S. Physics of Semiconductor Devices (Moscow: Mir. 1984. P.456). Using the proposed model to assess the effect of strong electrostatic fields with a strength of 10 ⁷ -10 ⁸ V / cm showed that the height and width of the potential barrier can be effectively controlled, reducing them several times with increasing field strength up to the mode of field emission electron breakdown. Using a modified Fowler-Nordheim field emission model taking into account the Fermi level change for nonequilibrium photoelectrons (Fowler RH, Nordheim L. Electron Emission in Intense Electric Fields // Proc. Roy. Soc. Lond. 1928. A119. P. 173-181), a relation can be obtained that determines the energy distance from the Fermi level to the top of the potential barrier at photon energy hν

Δφ = А- hν- (е ³ βU / Z) ^1/2 , (5)

where e is the electron charge; β is the form factor of local amplification of the field strength; U is the potential difference of the external field at the gap Z emitter-anode.

Expression (5) allows one to determine and experimentally verify those field strengths E = U / Z and form factor β corresponding to the tunneling probability of nonequilibrium photoelectrons or equilibrium field emission electrons tending to 1, which corresponds to the field emission condition, and in the case of optical irradiation of the emitter with photon energy hν photoemission breakdown. Corresponding calculations of the change in the height of the potential barrier during the work of the electron exit from the emitter equal to 5 eV from the field strength value were carried out and are presented in FIG. 2.

It is possible to determine the work function of the electrons exit from the emitter and the form factor of strengthening the local electrostatic field strength when the emitter is irradiated at the same wavelength, but in this case it is necessary to measure the dark field emission current-voltage characteristics, then we can obtain the relationships for determining the work function of the electrons from the emitter and the forms -factor of local amplification of field strength from relations (1) and (2). If we measure the field strength in V / cm, the emitter-anode distance in cm, and the electron work function A in (eV), then using relation (5), we can obtain numerical relations that allow one to determine the work function and the local gain electrostatic field strength, provided that the tunneling probability tends to 1.

Then, for the field emission current, the relation

A = 3.6 10 ^-4 (β V _∞ / z) ^1/2 …………………… .. (6)

When the emitter is irradiated with laser or LED radiation with photon energy hν, we obtain the relation

A-hν ₁ = 3.6 10 ^-4 (β V _{∞ λ1} / z) ^1/2 …………………. (7),

where: V _∞ is the voltage in volts corresponding to the breakdown voltage of the field emission current when the tunneling probability tends to 1.

V _{∞ λ1} is the voltage in volts corresponding to the breakdown voltage of the tunneling photoemissive current, when the tunneling probability tends to 1, which occurs when the emitter is irradiated with optical radiation with photon energy hν ₁ = hc / λ ₁ .

Using relation (7) for two UV and visible wavelengths, one can obtain working formulas for determining the work function of electrons from the emitter and the form factor of local field strength amplification, i.e. relations (3) and (4).

The results of testing this method were experimentally tested on the basis of measuring the current-voltage characteristics when irradiating a carbon nanoscale emitter with laser radiation with red -633 nm and blue λ = 473 nm radiation wavelength and dark field emission characteristics are presented in Figs. 3 and 4.

Using the experimental results presented in Figure 3, in accordance with the working formula (4), boundary stresses were found corresponding to a sharp increase in the tunneling photoemissive current upon irradiation of the same spatial space in the microdiode emitter, which allowed us to determine the value of the form factor β, those. amplification of the local electrostatic field strength equal to 89, while the value of the electron work function from the carbon emitter determined from formula (3) is 4.97 eV. The value of the work function of the electron exit from carbon, presented in the Zi monograph recognized by the scientific community (Zi S. Physics of semiconductor devices. M: Mir, 1984. 456 p.), A = 5 eV. The accuracy of determining β and A by the proposed method will be maximum when determining the voltage corresponding to the breakdown condition for field emission current and photoemission current under optical irradiation. In the experimental implementation of the method, the voltage value is measured corresponding to the increase in the emission current of the microdiode by three orders of magnitude compared to the threshold value. Estimates of the error in determining the work function and the increase in the local field on the emitter due to the micro- and nanorelief of its surface in accordance with the working formula (1-4), using relation (1) and the exponential dependence of the tunneling current on the field strength, the emitter anode showed that it does not exceeds 5% due to the very high steepness of the volt-ampere characteristic of the tunneling emission near the breakdown condition defined by relation (1). The proposed method makes it possible to measure the value of the local electrostatic field on a microemitter with a spatial resolution determined by the size of the optical beam on the emitter. The minimum size of the focused laser beam is determined by the diffraction limit equal to 1.22 λ / NA, where NA≤1, therefore, for UV and visible radiation, this size is limited by the wavelength of the probe radiation, i.e. 300-1000 nm.

Claims (1)

The method of non-contact determination of the local electrostatic field gain and work function in nano- or microstructural emitters, characterized in that they measure the dark dependence of the tunneling emission current with increasing voltage at the anode and determine the voltage value V _∞ , tending to the field emission voltage, which is controlled by an exponential increase 3-5 orders of magnitude tunneling field emission current, irradiate the measured surface of the emitter with a laser beam of ultraviolet or imogo range with a fixed value of optical power and wavelength λ _1, the value measured photoemission tunneling current when the voltage increases at the anode and the fixed voltage value V _{∞ λ1,} tending to photoemission breakdown voltage, which is controlled according to an exponential increase of 3-5 orders of magnitude of the tunneling current photoemission , determine the value of the work function A and the amplification value of the local electrostatic field β in the spatial region of the emitter irradiation from the relation
β ^1/2 = 2.77 · 10 ³ (hс / λ ₁ ) · z ^1/2 / [(V _∞ ) ^1/2 - V _{∞ λ1} ) ^1/2 ] (1)
A = hс / (λ ₁ [1- (V _{∞ λ1} / V _∞ ) ^1/2 ]) (2)
or additionally irradiate the measured surface of the emitter with a laser beam at a different wavelength λ _{2 of the} ultraviolet or visible range with a maximum difference with respect to the first wavelength, determine the voltage V _∞λ2 , tending to the voltage of the photoemission breakdown, which is controlled by an exponential increase of 3-5 orders of magnitude tunnel photoemission current, and determine the value of the amplification of the local electrostatic field in the spatial region of the irradiation of the emitter and the value of the work function A and ratio
β ^1/2 = 2.77 · 10 ³ z ^1/2 (hс / λ ₁ - h s / λ ₂ ) · / [(V _{∞ λ2} ) ^1/2 - V _{∞ λ1} ) ^1/2 ] (3)
A = (h s / λ ₁ - h s / λ ₂ ) / [1- (V _{∞ λ1} / V _{∞ λ2} ) ^1/2 ] (4)
where: β is the form factor-value corresponding to the enhancement of the local intensity of the electrostatic field in nano- or microstructural emitters, due to the spatial gradient of the shape of the surface of the emitter irradiated with a light beam;
z is the distance between the emitter and the anode in cm;
A is the electron work function from the emitter in eV;
V _∞ - voltage in volts, tending to the field emission voltage, which is controlled by an exponential increase of 3-5 orders of magnitude of the tunnel field emission current;
V _∞λ1 is the voltage in volts, tending to the photoemission breakdown voltage, which is controlled by an exponential increase of 3-5 orders of magnitude of the tunneling photoemissive photocurrent when the emitter is irradiated with optical radiation with photon energy hc / λ ₁ ;
hc / λ ₁ = hν ₁ is the photon energy in eV absorbed by the emitter electron due to the single-photon photoelectric effect;
V _∞λ2 is the voltage in volts, tending to the photoemission breakdown voltage, which is controlled by an exponential increase of 3-5 orders of magnitude of the tunneling photoemission current when the emitter is irradiated with optical radiation with photon energy hν _2, respectively, with wavelength λ ₂ = s / ν ₂ ;
ν is the radiation frequency of the optical range;
c is the speed of light;
h is Planck's constant.

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