Chapter 1 Introduction
1.2 Theory of Field Emission
1.2 Theory of Field Emission
In semiconductor physics, the thermionic-field emission and field emission are both important mechanisms for the transport of electrons over the potential barrier between the metal and the semiconductor. In Schottky barriers on highly-doped silicon crystal, the depletion region is so narrow that the electrons can tunnel through the barrier near the top where the barrier is small enough which is called thermionic-field emission. On the other hand, in a degenerate silicon crystal, the electrons can tunnel through the energy barrier even near the Fermi level which is
called field emission. It can be found that the tunneling in thermionic-field emission process requires electrons with higher energy than in field emission process. The emission of electrons from a surface of conductive material such as metal or semiconductor into a vacuum environment at an extremely high electric field is also a quantum mechanical tunneling phenomenon. The energy diagram of a metal-vacuum system without external electric field is displayed in Fig. 1.1(a). As shown in Fig.
1.1(b), the vacuum level is bent at extremely high electric field and the energy barrier between the surface of metal and the vacuum become so narrow that the electron can tunnel through it easily, even at very low temperature. Here W0 is the energy difference between an electron at rest outside the metal and an electron at rest inside the metal, whereas WF is the energy difference between the Fermi level and the bottom of conduction band. The work function Ф defined as Ф = W0- WF. When an external electric field is applied, the vacuum level is reduced and the energy barrier at the surface of conductive metal or semiconductor becomes thinner. Then an electron having energy “W” has a finite probability of tunneling through the surface barrier.
Fowler and Nordheim derive the famous Fowler-Noedhiem equation (1.1) as below [1.7-1.8]:
where J is the current density (A/cm2), E is the applied electric field (V/cm), Φ is the work function (eV), a = 1.56×10-6, b = -6.831×10-7, y = 3.7947×10-4E1/2/Ф, t2(y)≒1.1 and v(y) can be approximated as [1.9]
(
y)
Typically, the field emission current is measured as a function of the applied voltage V.
Substituting relationships of J = I/α and E = βV into Eq. 1.1, where α is the emitting area and β is the local field enhance factor at the emitting surface, following equation can be obtained
from Eq. 1.5, the slope of a Fowler-Nordhiem (F-N) plot is given by
)
The parameter β can be evaluated from the slope S of the measured F-N plot if the work function Ф is known
)
Emission area α can be subsequently extracted from a rearrangement of Eq. 1.5
⎟⎟
For example, electric field at the surface of a spherical emitter of radius r concentric with a spherical anode (or gate) of radius (r + d) can be represented analytically by
Though a realistic electric field in the emitter tip is more complicated than the equation above, we can multiple Eq. 1.9 by a geometric factor β’ to approximate the real condition.
⎟⎠
Where r is the tip radius of emitter, d is the emitter-anode (gate) distance, β’ is a geometric correction factor [1.9], and F(r,d) is a function of r and d.
For a very sharp conical emitter tip, where d>>r, Etip approached to β’(V/r).
Moreover, for r>>d, Etip approaches to β’(V/d) which is the solution for parallel-plate capacitor and for a diode operation in a small anode-to-cathode spacing.
As the tip radius of the gated field-emission array is very small, Eq. 1.10 can be approximated as:
) ( ' r
Etip =β V (1.11)
Combining E=βV and Eq. 1.11, we can obtain the relationship:
) ( ' r V V
Etip =β =β and β'=βr (1.12)
The tip radius r is usually in the range from a few nm to 50 nm, corresponding to the parameter β’ ranging from 10-1 to 10-2.
Besides, transconductance gm of a field emission device is defined as the change in anode current due to a change in gate voltage [1.10].
ve
m Vg
g Ic
∂
= ∂ (1.13)
Transconductance of a field-emission device is a figure of merit that gives as an indication of the amount of current charge that can be accomplished by a given change in gate voltage. The transconductance can be increased by using multiple tips or by decreasing the cathode-to-gate spacing for a given cathode-to-anode spacing.
1.3 Applications of Vacuum Microelectronics
In past decades, vacuum electronic devices have been developed by reducing the device scale down to micro-size with the improved manufacturing technologies and equipments. Due to the outstanding properties of vacuum microelectronics, there are several potential applications attracting worldwide attention, including field-emission displays (FEDs) [1.11-1.15], microwave amplifiers and generators [1.16-1.18], ultra-fast switches, intense electron/ion sources [1.19-1.20], electron source of scanning electron microscope (SEM) and e-beam lithography, micro-sensors [1.21-1.22], and devices needed to work in hostile environment. Among these applications, FEDs seem most likely to have substantial commercial impact due to the emerging requirement in flat panel display industry.
1.4 Field Emission Displays
Owing to the requirement of displays with excellent image qualities and large image size, the development of flat-panel displays (FPDs) is one of the most important industries in the world now. Based on the operation physics of display devices, the flat panel displays generally can be categorized into two types:
self-emissive and non-emissive types. The non-emissive type can not produce luminous light by itself, which should combine with other lighting elements for displaying images, such as active matrix-liquid crystal displays (AMLCD) which need a back light module. In contrast, the self-emissive type can produce graphic vision by itself, and there are many technologies announced worldwide, including plasma display panel (PDP), organic light Emission display (OLED), light emission diode (LED), polymer light emitting diode (PLED), electro-luminescence display (EL display), vacuum fluorescent display (VFD), Flat cathode-ray tube (CRT), and field
emission display (FED). Among these display technologies, FEDs were considered to be one of the most promising technologies that will be the major display technique in the near future due to its outstanding performance.
The idea of the field-emission display was first proposed and described in U.S.
patent 3,500,102 issued in 1970 by Crost, Shoulders, and Zinn. However, the first monochrome prototype was demonstrated in Japan Display until 1986 by a group from LETI [1.23] and the first color display (6 inch) was demonstrated in 1993 by Pixel/LETI [1.24]. To know the history of field-emission displays better, more relative events of field-emission displays were listed in Table 1.2.
The operation of FED is similar to that of CRT, in which phosphor is excited by a stream of electrons traveling through a vacuum. In contrast with CRT which employed electron guns, FED is matrix-addressed by an array of emitters where electrons emitted to a phosphor anode plate that is located in close proximity (0.2-2 mm) to the cathode plate. It can provide an image with high resolution and avoid the distortion of image caused by external electric or magnetic field. The figures of field-emission displays and traditional CRTs shown in Fig. 1.2 illustrate the differences between these two displays schematically. The advantages of field-emission displays over other flat panel displays are higher brightness, better viewing angle, lower power consumption, less radiation, and larger operating range of temperature. The comparison of the characteristics for several flat-panel displays is listed in Table 1.3.
Generally, the field-emission displays could be classified into two main categories based on the operation configuration: diode and triode structures. As shown in Fig. 1.3(a), the field emission current is emitted from the cathode to the anode in the diode configuration, and the emission current is controlled by the voltage applied on the anode electrode. It has the merit of simple structure as compared with the
triode structure. However, the driving voltage required to show a grayscale is high so that it is costly and complex for the design of driving circuit. By comparison, the triode configuration, shown in Fig. 1.3(b), utilizes an extraction gate proximity to the emitter array so as to extract electrons from the cathode with a relative lower driving voltage. The emission current density from the cathodes to the anode is controlled by the voltage biased to the gate electrode. The electrons on the tip of emitters are extracted by the electric field induced from the gate voltage and parts of them are attracted by the electric field induced from the anode voltage. In the triode configuration, a much lower driving voltage is required to realize a grayscale than the diode structure. In addition, the field emission device with a triode structure has the merits of luminous efficiency, emission stability, and uniformity over large areas compared with diode one [1.25].
1.4.1 Technologies of Field Emission Displays
Fundamentally, FEDs are constructed by using three elemental technologies:
micro-fabrication technology for the emitter arrays, optoelectronic technology for the anode plates, and vacuum technology for the packaging. Among these technologies, the performance of FEDs is determined by the technology of the cathode plates by which the electrons are generated. So far, researchers have put their attention to the development of new cathode structures for more robust in manufacture and application, such as Spindt-type field emitters, silicon tip field emitters, metal-insulator-metal (MIM), ballistic-electron surface-emitting device (BSD), ferroelectric emitters, and planar field emitters including surface conduction electron emitter (SCE) and edge field emitters. Besides, new cathode materials, such as diamond, diamond-like carbon, and carbon nanotubes, had been intensively studied for their potential as attractive electron sources. Many companies like Samsung of
Korea, ITRI of Taiwan, NEC of Japan, etc. have taken a lot of resources to research and develop the technology of field-emission display, and many amazing achievements had been announced in publications.
1.4.1.1 Cathode Structures
1.4.1.1.1 Spindt-Type Field Emitters
The original idea for the development of microfabricated field emitter array (FEA) came from Ken Shoulders and Dubley Buck at Massachusetts Institute of Technology (MIT) in the 1950s [1.26] but it was realized 40 years later beyond the reach of technology. The basic concepts were brought by Shoulders to the Stanford Research Institute (SRI) to develop the microfabricated vacuum integrated circuits [1.27] and he also proposed a thin display tube base on matrix-addressed arrays of microfabricated field emitters, the field-emission displays (FEDs) [1.28]. As part of Shoulder’s program, Capp Spindt proposed a smart method to form the arrays of miniature metal field emitter cones in microsize cavities with an surrounded extraction gate [1.29]. The cathodes of Spindt field emitter arrays are fabricated by forming metal cones on the conducting cathode electrodes as electron emitters by using thin film deposition processes. The metal cone is surrounded by an accelerating grid electrode (gate) which is insulated from the conducting cathode electrode by a dielectric layer. The cathode array features like a source of electrons with a positive voltage bias applied to the surrounding gate electrode. The micrographs of Spindt field emitter arrays taken by SEM are shown in Fig. 1.4 [1.27]. Although the Spindt type field emitter array provide a method to realize sharp metal tips with extraction gate electrode, it still has some drawbacks of needing huge metal depositing equipment, complex processes, requirement of high driving voltage, and reliability issues.
1.4.1.1.2 Silicon Tip Field Emitters
Sharp silicon tips of field emitter array are fabricated from crystalline silicon wafer by using oxidation processes to obtain silicon tips with small radius [1.30]. The processing steps of forming the silicon tips can be realized via standard semiconductor processes. According to some researches, the emission current from silicon tips can reach as high as 10 µA/tip [1.31]. Furthermore, crystalline silicon is a good material for the investigation of field emission array because of its great electronic, crystalline, mechanical properties, and availability. With well-developed techniques and equipments for fabrication, the apex radii of fabricated silicon tips can be bellow 10 nm with small deviation. One of the methods to form silicon tips is utilizing the orientation-dependant etching (ODE) which can form a convex pyramids structure [1.32-1.33]. Another way of fabricating silicon tips array is the oxidation sharpening process which is also the most used method in creating sharp tips on silicon wafers [1.34]. However, the array of silicon tips still has the problem of local failure due to high emission current density. Local heating at the silicon tips due to high emission current passing through can result in a local evaporation of silicon tips to reduce its sharpness and, therefore, cause a gradual degradation in emission current.
Moreover, the requirement of driving voltage is still too high for the applications of field-emission devices due to its high work function.
1.4.1.1.3 Metal-Insulator-Metal Emitters (MIM)
Metal-insulator-metal cathodes are a kind of thin film tunneling device proposed by Mead in early 1960s and has been studied by many researchers [1.35-1.40]. Due to the stack structure, the buried cathode of MIM devices is less contamination and the electrons tunnel through interfacial Schottky barriers instead of surface barriers. This
device consists of a thin insulating film (e.g. Al2O3) sandwiched between two metal electrodes, as shown in Fig. 1.5(a). The ultra-narrow insulating film allows the tunneling trough of electrons when a moderate electric field is applied across the layer.
The energy diagram in Fig. 1.5(b) shows that the tunneling electrons are injected from the negative electrode (the emitter) through the insulating layer into the positive electrode (the gate) as hot electrons and are detected as diode current Ib. Part of the electrons have sufficient kinetic energy to overcome the surface energy of the Au and emit into the vacuum, which are collected as an emission current Ie. However, most of the tunneling electrons lose their kinetic energies while they pass through the structure due to scattering events in both the insulator and the gate metal. It is important to notice that the MIM structure requires a very precise control over the thickness of film to even atomic scale and the roughness of film is also very critical which can cause a very significant fluctuations in emission current and emission uniformity.
1.4.1.1.4 Ballistic Election Surface-Emitter Device (BSD)
In 1998, a novel cold-cathode technology based on a nanocrystallized polysilicon (NPS) layer was reported by the authors [1.41]. The electron emission characteristics strongly suggest that electrons injected into the NPS layer are transported quasi-ballistically [1.42]. It showed various excellent characteristics as compared with conventional FEDs [1.43] and it was termed a ballistic electron surface-emitting display (BSD). The device structure is schematically illustrated in Fig. 1.6. A non-doped polysilicon layer formed by a plasma-enhanced chemical vapor deposition (PECVD) technique was anodized in a solution of HF and ethanol under the illumination of tungsten lamp in order to form the NPS layer. After anodization, thin SiO2 layers on the surface of Si nanocrystallites were created by an electrochemical oxidation (ECO) technique. It was also shown that the BSD had excellent thermal
stability and a frit sealed model was fabricated [1.44-1.45]. However, the oxide charging effect results in the degradation of device performance, and damage of thin oxide layer often takes place while the current density is large.
1.4.1.1.5 Ferroeletric Emitters
About 40 years ago, it has been observed that electrons emitted from the surfaces of ferroelectric materials during polarization reversal [1.46-1.47]. It was recognized that the polarization induces macroscopic charge separation on the two opposite surfaces of ferroelectric samples. As shown in Fig. 1.7, the screening charges are developed to compensate the net charges. A fast reversal (about sub-microseconds) of the polarization results a large electric field that ejects the electrons from the negative charged surface. By contrast, no external extraction field is required to overcome the surface work function to obtain electrons emission from ferroelectric emitters [1.48].
The emission depends on the polarization fields within the ferroelectric material and only excitation energies such as electrical, optical, thermal or mechanical energies are required to overcome the coercive fields. Ferroelectric emission is thus a transient unipolar effect generated from non-equilibrium charged ferroelectric surface.
Ferroelectric cathodes have very robust surfaces that may be exposed to air and operated in poor vacuum conditions (up to 10-2 torr) or even in plasma. However, many issues in ferroelectric emissions such as polarization fatigue during multiple fast switching, emission current stability, and domain structure aging are still needed to be overcome before those envisioned devices could be realized.
1.4.1.1.6 Planar (Lateral) Field Emitters
Planar field emitters, small in device size, had the merits of design versatility and low operation voltage, and therefore showed a potential in vacuum microelectronics,
especially, for high frequency application. Besides, owing to the simplicity in device structure and operation in low voltage, the planar also attract much interest in the application of field emission displays, such as surface conduction electron emitter (SCE) and edge field emitters.
Surface Conduction Electron Emitters (SCE)
Surface conduction emission is the phenomenon that electrons are emitted from a cathode when electric current flows through the cathode in parallel with the cathode surface [1.49]. It has attracted a great deal of attention since a 10-inch full color display incorporated a thin film PdO cathode based on the surface conduction emission mechanism was built by the researchers at Canon in Japan [1.50]. The device structure with two ultrafine PdO film as cathode and gate electrodes from top view is demonstrated in Fig. 1.8(a). The forming process of the gap between cathode and gate electrodes is to apply a voltage between two electrodes so that an electric current with high density flows through the PdO film in parallel with the surface. The thin film generates Joule heating when the electric current passing through and cause a fissure of nano scale between two electrodes. The fissure where be spatially discontinuous but electric continuous which causes field emissions because of high fields established across the cracks along the surface. The emitted electrons can be collected by the anode spaced apart from the surface of cathode after multiple scatterings on the cathode, as shown in Fig. 1.8(b). Due to the nanosize of the gap between cathodes and gates, the driving voltage can be greatly suppressed to several decades volt. The uniformity of emission current from device to device is also good resulting from the uniform PdO film. However, the emission current from cathode to anode is still low due to the fact that most of the emitted electrons are collected by the gate electrode merely 10 nm apart from the cathode.
Thin Film Edge Emitters
In contrast to SCE formed by thick film techniques, the thin film edge emitters were fabricated mainly based on the thin film deposition process. Similar to the device structure of SCE, the emitter and collector electrodes were posited in the same horizon between which a submicron gap was created. So far, many techniques such as electron beam lithography (EBL), focus ion beam (FIB), and chemical mechanical polish (CMP) [1.51-1.53], were employed to form a small spacing across electrodes.
Nevertheless, the throughput is poor and there is a lack of scalability for large area.
1.4.1.2 Cathode Materials
Fabricating field emission cathodes with low operation voltage, high emission current, excellent stability and good reliability is crucial to commercialize the field emission display. According to the F-N equation, the performance of emission devices could be improved with novel cathode materials in terms of aspects: the work function φ of the cathode material must be as low as possible and the field-enhancement factor β and emission area α should be as large as possible.
1.4.1.2.1 Diamond and Diamond-Like Carbon (DLC)
Diamond is one of the main crystalline allotropes of carbon, which is formed in an sp3 tetrahedral bonded cubic structure. Due to its negative work function, diamond possesses a very small barrier for its electrons to leave the surface and emit into the
Diamond is one of the main crystalline allotropes of carbon, which is formed in an sp3 tetrahedral bonded cubic structure. Due to its negative work function, diamond possesses a very small barrier for its electrons to leave the surface and emit into the