2 Fundamental Theory and Literature Review
2.2 Methods for Synthesizing Carbon Materials
Arc discharge is the first and the effective way to produce single-wall carbon nanotubes (SWNTs) and multi-wall carbon nanotubes (MWNTs).[84-86] The arc discharge equipment contains a stainless steal vacuum chamber with about 500 torr pressure filled with Helium.
Two separated graphite electrode are biased with high current density (50~150A) to about 25~40V. Arc is then induced, and the graphite target is vaporized. Products are deposited on cathode or chamber which includes fullerence, tubes, nano particles and amorphous carbon, etc. Impurities are one of its disadvantages, which need further purifications. Figure 2.8 shows schematic diagram of typical arc discharge equipment.[87]
Laser Ablation
Smalley et al.[88,89] discovered that single-wall carbon nanotubes can be produced by laser ablation with good quality and efficiency, which draws a lot of attention. A carbon target is evaporated by high power continuous CO2 laser or pulse Nd:YAG laser source. The evaporated species are carried out by Argon or Helium to the water-cooled copper finger or copper wire; single-wall nanotubes are then formed. One specialty is that no amorphous carbon is formed on nanotubes. It has to be noted that, fullerence and multi-wall nanotubes can also be obtained by this method. Fig. 2.9[90] shows schematic diagram of laser ablation equipment.
Fig. 2.8 Schematic diagram of arc discharge equipment (Krätschmer-Huffmann).
Fig. 2.9 Oven laser-vaporization apparatus[90].
Chemical Vapor Deposition (CVD)
Chemical vapor deposition includes thermal CVD, Hot filament CVD, microwave plasma CVD, etc. Catalysts are normally used for the growth of carbon related material.
Typically chemical vapor deposition are used for the production of carbon fibers.[91,92] It is not until 1993 that Yacaman et. al.[93] successfully use chemical vapor deposition to deposit carbon nanotubes. And till 1997 microwave plasma enhanced chemical vapor deposition is used to deposit carbon nanofibers and carbon nanotubes.[94,95] Hydrocarbon gases are usually mixed with hydrogen (or ammonia) to be the reaction gas.[96] Products may be carbon nanotubes, amorphous carbon, carbon fiber, or even carbon nano tips, which are correlated to growth temperature, flow rate, reaction gas, growth time, bias, and catalyst. Compare with the methods above, CVD has the advantage of low process temperature, relative good uniformity, convenience, large area growth, and easy for in-situ doping.[97]
Bias Assisted Microwave Plasma Chemical Vapor Deposition (MPCVD)
Microwave plasma chemical vapor deposition is one of the important facilities for thin film deposition, micro manufacturing, and surface treatment.[98] By the advantage of high ion density, high degree of dissociation, high reactivity, and low process temperature, a lot of kinds of substrates are capable of fabrication under low temperature with deposition and etching, which is meaningful for LSI process, microelectronic device, optoelectronic device, polymer, and thin film sensor.
By applying electric field, the reaction gas breakdown to induce electrons and ions. With electromagnetic field obtained by microwave or RF power, more electrons and ions are generated by colliding with the un-dissociated gas. Stable plasma is reached when the generation rate and consumption rate are equal for all species. Unlike traditional thermal plasma, temperature of electrons, ions, and neutral particles in low temperature plasma induced by discharge are not identical. The temperature of electron is about 1000oK, while the
ions and neutral ones are below 500oK. Therefore, low temperature plasma is a non-equilibrium plasma with not only few ions, electrons, but also excite state, transient state, and free radicals. By manipulating these high energy species, reaction which is hard for steady state species are attainable.
Take diatomic plasma for example, the procedure may appear as followed:
(Ⅰ)Ionization
A
2+ e
−→ A
2++ 2 e
−(Ⅱ)Dissociative ionization
A
2+ e
−→ A
++ A + 2 e
−(Ⅲ)Attachment
A
2+ e
−→ A
2−(Ⅳ)Detachment
A
2−+ e
−→ A
2+ 2 e
−(Ⅴ)Recombination
A
2++ e
−→ A
2(Ⅵ)Atom recombination
2 A
•→ A
2*any polyatomic molecule is substituent for mentioned above.
(•) stands for free radical.
Basically, microwave plasma chemical vapor deposition does not need any electrode or even heater. But in this thesis, bias plays an important role in the growth of nanomaterials, and also an essential term.
When a DC bias is added on to the substrate, before the ions pass through the plasma sheath area, the movement of the ions do not effect by the collision between the ions, comparatively and statistically. Also means the ions can strike the substrate directly and vertically by the applied field.[99]
2.3 Growth Mechanism for Nanomaterials
Due to huge amount compound and various atomic bonding of carbon, plenty of kinds of methods are used for the growth of carbon related nanomaterials. Each method has its advantages, disadvantages, distinguishing feature, and a range for suitable use. Most of them have been successfully synthesize carbon nanotubes.
The model used for describing the growth of nanomaterials still is an issue because of the difficulty for observation under such extremely small scale. Even though, several mechanisms are brought up to characterize the behavior for the growth. Here we discuss some growth models which are considered to be the major mechanism for nanosize material.
Growth mechanism of various kind of bottom-up nanosize materials are generally considered to be three models: Vapor-Solid (VS) model, Vapor-Liquid-Solid (VLS) model, and recently, Solution-Liquid-Solid (SLS) model. Some modifications[100] have also been published which will not be discussed here.
Vapor-Solid (VS) Model
Figure 2.10 shows an approximately growth model of vapor-solid growth mechanism.
The diagram takes the growth of GaN for example. Epitaxial growth can be achieved without catalyst or liquid phase. The sum of thermodynamic surface energy and heat of fusion become the driving force for VS growth. The growth rate of VS is dominated by the rate of atoms or molecules diffusion and rearrangement. Compare with the growth mechanism with catalyst, the VS mechanism has a lower growth rate.
Vapor-Liquid-Solid (VLS) Model
The mechanism[101] was first introduced in the 1960s to explain the growth of silicon whiskers or tubular structures[102]. In this model, growth occurs by precipitation from a
supersaturated liquid-metal-alloy droplet located at the top of whisker, into which silicon atoms are preferentially absorbed from the vapor phase. The similarity between the growth of carbon nanotubes and the VLS model has also been pointed out by Saito et al[103-104] on the basis of their experimental findings for multi-walled nanotube growth in a purely carbon environment (Fig. 2.11). Solid carbon sublimates before it melts at ambient pressure, and therefore these investigators suggested that some other disordered carbon form with high fluidity, possibly induced by ion irradiation, should replace the liquid droplet.
Solid-Liquid-Solid (SLS) Model
Figure 2.12[105] shows diagram of solution-liquid-solid growth mechanism which takes
Ⅲ-Ⅴ materials for example. No catalyst is used for solution-phase synthesis. The materials are produced as polycrystalline fibers or near-single-crystal whiskers having width of 10 to 150 nanometers and length of up to several micrometers[106]. This mechanism shows that process analogous to vapor-liquid-solid growth operated at low temperatures, while requirement of a catalyst that melts below the solvent boiling point to be its potential limitation.
Fig. 2.10 Schematic diagram of vapor-solid (VS) growth model.
Fig. 2.11 Schematic diagram of VLS growth mechanism for nanotubes.[103]
Fig. 2.12 Schematic depiction of SLS growth mechanism.[105]
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
Fig. 3.2 SEM images of the triode structure (a) a 50 x 50 array (b) close-view of the