2 Fundamental Theory and Literature Review
2.4 Introduction to Field Emission Theory
The science of field emission began in 1928,[109] when Fowler and Nordheim presented the first quantum mechanical model for describing field induced electron emission from a metallic surface; a model still in use today. In deriving their model, Fowler and Nordheim first assumed that the conduction electrons in the emitting metal are describable as a free-flowing ’electron cloud’ - following Fermi-Dirac statistics -and are bound to the metal by an energy barrier at the surface. Under the influence of a field, these conduction electrons can be induced to tunnel through the barrier into vacuum, producing a field-induced electron emission from the metal surface. The presence of the electric field makes the width of the potential barrier finite and therefore permeable to the electrons. This can be seen in Fig. 2.13 which presents a diagram of the electron potential energy at the surface of a metal. Fowler and Nordheim further assumed that the surface barrier can be approximated with a one dimensional energy function without losing significant accuracy.
Field Emission from Metals
The dashed line in Figure 2.13 shows the shape of the barrier in the absence of an external electric field. The height of the barrier is equal to the work function of the metal, φ, which is defined as the energy required removing an electron from the Fermi level EF of the metal to a rest position just outside the material (the vacuum level). The solid line in Figure 2.13 corresponds to the shape of the barrier in the presence of the external electric field. As can be seen, in addition to the barrier becoming triangular in shape, the height of the barrier in the presence of the electric field E is smaller, with the lowering given by[107]
2
where e is the elementary charge and ε0 is the permittivity of vacuum.
Fig. 2.13 Diagram of potential energy of electrons at the surface of a metal[108].
Fig. 2.14 Diagram of the potential energy of electrons at the surface of an n-type semiconductor with field penetrates into the semiconductor interior.[108]
Knowing the shape of the energy barrier, one can calculate the probability of an electron with a given energy tunneling through the barrier. Integrating the probability function multiplied by an electron supply function in the available range of electron energies leads to an expression for the tunneling current density J as a function of the external electric field E.
The tunneling current density can be expressed by Eq. (4) which is often referred to as the Fowler-Nordheim equation[109]
where y=∆φ/φ with ∆φ given by Eq. (3), h is the Planck's constant, m is the electron mass, and t(y) and v(y) are the Nordheim elliptic functions; to the first approximation t2(y)= 1.1 and v(y) =0.95 - y2. Substituting these approximations in Eq. (4), together with Eq. (3) for y and values for the fundamental constants, one obtains
⎟⎟ ⎠
1/E results in a straight line with the slope proportional to the work function value, φ, to the 3/2 power. Eq. (5) applies strictly to temperature equal to 0oK. However, it can be shown that the error involved in the use of the equation for moderate temperatures (300oK) is negligible.[110]
Field Emission From Semiconductors
To a large degree, the theory for electron emission from semiconductors can be derived parallel to the theory for metals. However, special effects are associated with semiconductors due to the state of their surface and the fact that an external field applied to a semiconductor may penetrate to a significant distance into the interior. For the case when the external electric field penetrates into the interior of an n-type semiconductor and the surface states are neglected, log(J/E2) is shown to be a linear function of 1/E[111]. However, in place of the work
function φ in the Fowler-Nordheim equation one needs to substitute a quantity χ-δ, where χ is the electron affinity defined as the energy required for removing an electron from the bottom of the conduction band of the semiconductor to a rest position in the vacuum, and δ denotes the band bending below the Fermi level. These parameters are illustrated in Fig. 2.14. The linear dependence of log(J/E2) on 1/E is expected only if the density of the current flowing through the sample is much smaller than the current limiting density Jlim =enµnE/ε, where µn is the electron mobility and n is the electron concentration in the bulk of the semiconductor.[112,113] At J≈Jlim, the Fowler-Nordheim character of the relationship J(E) passes into the Ohm's law (if the dependence of electron mobility on the electric field is neglected) which results in the appearance of the saturation region in the emission current vs.
voltage curve.[114] Such saturation regions were observed experimentally for lightly doped n-type semiconductors and for p-type semiconductors.[115,116] Electron emission from semiconductors has been a subject of more recent theoretical considerations which takes into account complications due to electron scattering, surface state density, temperature, and tip curvature.[117-119]
Local Field Enhancement Factor
The Fowler-Nordheim equation predicts that a field of l07 V/cm would be necessary to generate an emission current density of 108A/cm2 from a tungsten tip. However, experimental emission data tends to be on the order of ten to one hundred times greater than the predicted emission current density. Schottky postulated that such an enhancement factor would be due to nanostructures on the tip surface. The geometry of these nanostructures concentrates the applied field locally and so they are locations of high electron concentrations. An example of this effect is shown in Figure 2.15(a). If a voltage is applied across two parallel plates separated by vacuum the field lines will concentrate at small structures, commonly nanometer scale structures.
(a) (b)
E
Fig. 2.15 (a) Local Field Enhancement due to nanostructure and (b) Model for local field enhancement.
Fig. 2.16 (a)Simulation of the equipotential lines of the electrostatic field for tubes of 1 mm height and 2 nm radius, for distances between tubes of 4, 1, and 0.5 mm;
along with the corresponding changes of the field enhancement factor ß and emitter density (b), and current density (c) as a function of the distance[120].
The apparent enhancement of the applied field is represented by the ß coefficient, which has been dubbed the “local field enhancement factor”. The local field enhancement can be considered a product of the nanoscale protrusion from the metal surface. The local field enhancement can be similarly produced by other nanostructures. The factor is related to the tip radius, r, and the height, h, of the material and field enhancement can be expressed as (6):
V
E = β
(6) To incorporate the local field enhancement factor and the constants into the previous equations, the substitution suggested by equation (6) is made. The simplified Fowler-Nordheim equation becomes: Along with the I-V curve, a “Fowler-Nordheim plot” is generally shown for a material.Its linearity clearly illustrates whether or not the non-linear I-V curve can be represented by field emission. If the field emission data is properly described by the Fowler-Nordheim equation, the plot shows a straight line with a projected y-axis intercept of B and slope of A.
Screening Effect
The Fowler-Nordheim equation has predicted the field emission behavior for a film or a single emitter (which also include a single emitter in the gated device). However in normal cases, the field emission current does not achieve the predicted value since nanostructures are usually synthesized with massive amount. In fact, for high density films, screening effect reduces the field enhancement that account for the decreased emission current. For films of medium density, there is an ideal compromise between the emitter density and the inter-emitter distance, which is sufficiently large to avoid screening effects. A better control of density and morphology (and hence of the β factors) of the films is thus clearly required for future applications.
In the previous reports[120,121], a predicted inter-emitter distance of about 2 times the height of the CNTs optimizes the emitted current per unit area. Simulation of an ideal density of 2.5x107emitters/cm2, or equivalently to 625 emitters per 50x50 mm2 pixel was obtained.
Introduction to Field Emission Device (Display)
The application of field emission is basically the electron source which may be applied into vacuum tubes, magnetrons, electron guns in TEM or SEM, cold-cathode pressure sensors and displays. Here we focus on the application of display technology which nowadays called field emission display (FED).
Fig. 2.17(a) shows the structure of one form of a FED based on emission of electrons from sharp-tipped cones. The cones are small, and each pixel contains hundreds or thousands of them. Instead of thermo-ionic emission, electrons are released in the high electric field that occurs close to the microscopic tips. The field at the tips is determined by the microscopic geometric and the difference in the voltage between the gate and cathode. After emission, the electrons are accelerated towards a phosphor coated on an optically transparent anode on the opposite substrate. The anode voltage is limited by breakdown between spacers. Since the FED needs no magnetic coils to change the trajectory of the electrons, there’s no need for such a dimension like traditional CRT is. Fig. 2.17(b) demonstrates the dimension difference between a CRT and a FED.
Table 1. shows the power efficiency of the state-of-the-art display technologies which reveals the potential advantage of FED. To date, FEDs are still serious competitors to LCDs and concentrate their most important advantages, such as small thickness (less than 1cm), low power consumption (comparable and even less than LCDs), together with such important feature as high luminance efficiency (>5lm/W), high brightness (300-600cd/m2), perfect linear grayscale, wide view angles, and CRT image quality. At the same time, FEDs have no problems with color convergence and x-rays and magnetic irradiation, which is typical for the conventional CRTs. The FEDs do not require polarizers or backlighting and cannot contain black (dead) pixels, as in the LCD case.
(a) (b)
Fig. 2.17 (a) Schematic diagram of a field emission cell (b) comparison between traditional CRT (left) and FED (right) modules.
Table 1. Power efficiency of current display technologies.
Chapter 3 Experimental Details
3.1 Fabrication of Metal-Insulator-Silicon Structure
In order to achieve practical application, fabrication of the triode structure (or gated device) is a necessary step prior to the deposition of nanomaterials. Properties of high current density, controllability of emission current, can therefore be attained. Thanks to modern semiconductor technologies, fabricating the triode structure has become facile. There are several ways to fabricate a gated structure and there are vast structures with the same idea have been invented. In this thesis, we fabricate the very original circular triode structure, which was once used to fabricate a Spindt-type structure, to study its characteristics.
Figure 3.1 shows a detail flow chart for fabricating a triode structure. We design a MIS structure and fabricate it by standard semiconductor process technologies. Starting substrate is a polished n-type, (100) oriented wafer with resistivity of 4~6 Ω-cm. The selection of Pt as the electrode has several reasons. First is due to the high melting point that makes it hard to be vaporized and be more resistant to ion-bombardment in the later MPCVD process. Second, the inertia of Pt makes difficult to form compounds. Third, the most important, Pt is relatively hard for the VLS process of carbon that could disturb the selective growth of the nanomaterials. In fact, doped poly silicon has been used to fabricate the structure because of its simplicity in the process steps, but it shows poor resistance that makes it etched away.
Therefore, compare with poly silicon, Pt has the fourth advantage, which is good electron conductivity. However, these advantages make the device much complex and require additional steps to fabricate, including several photolithography alignments and lift-off process since Pt is not suitable for reactive ion etching.
All processes for fabricating MIS structure here are supported by National Nano Device Lab and Nano Facility Center, NCTU. The list below shows the model for the fabrication processes.
Photolithography G-line Stepper, ASM PAS2500/10 Stepper Horizontal furnace and LPCVD ASM/LB45 Furnace System
Oxide etcher TEL, TE-5000
Sputtering system ULVAC EBX-10C Dual E-Gun Evaporation System
Clean bench SANTD CLARA PLASTICS Model 1100B
Vertical furnace ASM Vertical Furnace system
Table 2 Facilities for fabricating the FED device.
1. 6” n-type (100) Si wafer
2. Deposit wet oxide (5800Ǻ) by furnace
3. Photoresist mask by photolithograhy
4. Etch of SiO2 (5800Ǻ) by oxide etcher
5. Deposit Chromium (200Ǻ) by E-Gun evaporator
6. Removal of photoresist by lift-off process
7. Photoresist mask by photolithography
8. Deposit Titanium (500Ǻ) and Platinum (1500Ǻ) by E-Gun evaporator
9. Remove photoresist by lift-off process
10. Selective growth of Carbon nanotips by BAMPCVD
Si SiO2 PR Cr
Pt Ti Nanotips
Fig. 3.1 Fabrication procedure of a MIS structure.
(a)
(a) (b)
(c) (d)
(e)
Fig. 3.2 SEM images of the triode structure (a) a 50 x 50 array (b) close-view of the array (c) cross-section view (d) an individual hole.
Silicon or silicon coated with catalyst
Deposition of carbon nanomaterials Pretreatment with H2
plasma
Fabrication of the gated structure
SEM, TEM Raman, XRD I-V
Characterization of the film and nanostructure
Fig. 3.3 Flow chart of experimental procedure.
3.2 Deposition of Carbon Nanomaterials by Bias-assisted Microwave Plasma Chemical Vapor Deposition
Figure 3.3 show approximately the experimental procedure. In most conditions we use two step pretreatments, which include wet cleaning and H2 plasma treatment. The substrates are first cleaned with organic solvents and washed with de-ionized water with ultrasonic. Pure nitrogen gas is then introduced to dry the substrate before loading into the CVD chamber.
The chamber is evacuated to a pressure of ~10-2 Torr with a rotary pump. To begin the H2
pretreatment process, the reactant gas hydrogen is then introduced into the chamber at a rate of 200 sccm to a setting pressure of 15Torr. The microwave power of 400W is applied and the plasma is obtained. The plasma's horizontal position is adjusted by the plunger to fully immerse the sample in the plasma. The reflected power is minimized to < 10 W with the assistance of a three-stub tuner.
After the hydrogen plasma pretreatment, the reactive gases are introduced into the system by directly changing the mass flow meter. The reactive gases used in deposition are a mixture of CH4 and H2. In order to verified the new material we discovered here, several parameters are introduced which include H2 plasma pretreatment time, methane concentration, growth time, and applied bias.
Figure 3.4 schematically depicts the layout of the Bias-assisted MPCVD system. A quartz tube is vertically attached to a rectangular waveguide used as deposition chamber. The microwave from a magnetron source (model IMG 2502-S, IDX Tokyo, Japan) is supplied to the quartz tube through an isolator, three-stub tuner, and a power meter. Then the microwave power is coupled to the quartz tube through an aluminum waveguide with a hole drilled through from top to bottom face.
Aluminum tubes extend out from both holes; the tube extensions are water-cooled as well. A sliding short circuit is then attached at the end of the waveguide. The lower position of the quartz tube is connected a stainless steel multi-port chamber equipped with a rotary pump.
The substrates are positioned in the middle of the quartz tube waveguide intersection and held vertically by a substrate holder which is 20mm in diameter, made of molybdenum. Under the holder, attached a tantalum wire which is connected to the bias system; it was used as the lower electrode in the bias treatment stage. A quartz protector under the holder to protect the plasma not attracted to the tantalum wire attached to the molybdenum. The upper electrode, a molybdenum plate of 20mm in diameter which is placed 35 mm above the substrate, also attached to a tantalum wire. The controlled amount of the source gases was introduced into the chamber by mass flow controllers (model 647B, MKS instrument, Inc., USA) from the upper end of the quartz tube. A small window was cut in the waveguide at the center of the plasma cavity, allowing direct observation of the plasma.
In this thesis, nanomaterials including CNTs and carbon nanotips are synthesized with various catalyst and growth parameters. The optimized parameters are listed in Table 3.
Carbon nanotubes Carbon nanotips
Catalyst Fe Cr Ni, Ni/Au Cr Catalyst free
Microwave power 400 W
Operating Pressure 15 Torr
H2 treatment 15 min 30min None (annealed)
15 min
Gases H2/CH4=40/10 H2/CH4=30/10
Bias None 150V
Growth time 15min 30min
Substrate temperature ~700℃
Table 3 Growth conditions for carbon nanomaterials.
Fig. 3.4 Schematic diagram of the bias assisted microwave plasma chemical vapor deposition system.
3.3 Analysis Instruments
Scanning Electron Microscopy (SEM)
Scanning electron microscopy is used to observe the surface morphology of wide range kinds of objects. It has the advantage of rather easy sample preparation, high image resolution, large depth of field, and high magnification. A common SEM contains an electron gun to generate electron beams, which will be accelerated under 0.4-40kV voltage. By deflecting the incident beams with the focusing coils, a two dimensional image can be obtained by detect the reflected secondary electrons and the backscatter electrons.
The model we use most here is field emission type SEM JEOL-6500. Accelerating voltage is 15kV with current of 10µA. Working distance is 10mm under 9.63x10-5Pa.
Transmission Electron Microscopy (TEM)
In a typical TEM a static beam of electrons at 100-400kV accelerating voltage illuminate a region of an electron transparent specimen which is immersed in the objective lens of the microscope. The transmitted and diffracted electrons are recombined by the objective lens to form a diffraction pattern in the back focal plane of that lens and a magnified image of the sample in its image plane. A number of intermediate lenses are used to project either the image or the diffraction patter onto a fluorescent screen for observation. The screen is usually lifted and the image formed on photographic film for recording purposes.
The TEM used for the study is filament type Philips Tecnai-20 equipped with CCD camera for high resolution image.
Raman Spectroscopy
While photons illuminate a molecule or a crystal, they react with the atoms accompany with momentum change or energy exchange. By collecting the scatter photons, we can obtain a sequence of spectrum, including Raman scattering (inelastic scattering) and Reyleigh scattering (elastic scattering). The photon of Raman scattering can be classified into two kinds, Stoke side which photons loss energy or the molecules gains energy, and anti-Stoke side,
which photons gains energy or molecules loss energy. Generally, Stoke side is used to characterize the material. As Raman spectrum provides information of crystallinity and bonding, it has become the most direct and convenient way to identify carbon related materials. The Raman spectrum peak of C-C and C=C bond in crystalline graphite are 1380 (D0peak) and 1580 cm-1(G-peak), respectively, as shown in figure 3.5. The ratio of D-peak intensity (ID) and G-peak intensity (IG), ID/IG is commonly used for characterizing the degree of graphitization for carbon materials. In a series of test of samples, lower the ratio indicates a better graphitization.[122-124]
The instrument we use is a Renishaw Raman microscope, Model 2000, equipment settings are shown in figure 3.6. The source we use is He-Ne laser with wavelength of 632.82nm and power of 200mW. The spectral slit width is 0.4cm-1.
Field Emission Measurement
A display needs ~0.1 mA/cm2 current density assuming an anode voltage of ~2 kV. The turn-on and threshold field for 10µA/cm2 and 10mA/cm2, respectively have been used as the parameters to characterize various emitter.[125] Fig. 3.7 shows the setup of a field emission measurement facility. To ensure the precision of the gap between the cathode and anode, spacers which are soda-lime glasses with thickness of 150µm are directly attached onto the sample. The anode is an ITO conductive glass with thickness of ~1mm. The length of the field emission area is defined as the distance between the two spacers and the width is the width of the sample itself. High voltage source (Keithley-237) is connected to the anode and cathode by physical contact. The experiment is carried out in a vacuum chamber with pressure of
A display needs ~0.1 mA/cm2 current density assuming an anode voltage of ~2 kV. The turn-on and threshold field for 10µA/cm2 and 10mA/cm2, respectively have been used as the parameters to characterize various emitter.[125] Fig. 3.7 shows the setup of a field emission measurement facility. To ensure the precision of the gap between the cathode and anode, spacers which are soda-lime glasses with thickness of 150µm are directly attached onto the sample. The anode is an ITO conductive glass with thickness of ~1mm. The length of the field emission area is defined as the distance between the two spacers and the width is the width of the sample itself. High voltage source (Keithley-237) is connected to the anode and cathode by physical contact. The experiment is carried out in a vacuum chamber with pressure of