2.1 Field Emission and Fowler-Nordheim Theory Field emission is a phenomenon that describes the tunneling of an electron from the surface of a solid into vacuum, due to the application
Trang 1Chapter 2 Physics of Field Emission
In this chapter, the physics behind field emission will be reviewed in details The definition of field emission phenomenon and the origin of Fowler-Nordheim theory,
an evaluation approach for field emission, will be presented in section 2.1 Section 2.2 will focus on the discussion of field emission from semiconductors The parameters influencing the field emission properties will be covered in the last section
2.1 Field Emission and Fowler-Nordheim Theory
Field emission is a phenomenon that describes the tunneling of an electron from
the surface of a solid into vacuum, due to the application of a strong electric field
(typically E > 109 V m-1) [1] More specifically, it is a quantum effect when under a sufficiently high external electric field, electrons near the Fermi level can tunnel through the energy barrier and escape to the vacuum level [2] It is an alternative way to extract electrons from solid surface and it is a special case of thermionic emission When compared to traditional thermionic emission, this is a preferred mechanism for certain applications such as flat panel display because no heating is required and the emission current is almost solely controlled by the external field The mechanism of field emission is schematically illustrated in Fig 2.1
Trang 2Fig 2.1 Schematic potential
on the energy barrier for electrons at a metal surface
E vac represents the vacuum level,
The Fowler-Nordheim (F
Nordheim as well as some other researchers in order to
between the emission current density and the elect
surface [3-6] The derivation of F
physics such as density of states, Fermi
thermionic emission
approximation employed at the early stage [3, 7], the F
) (
2 3
y t h
F e J
φ π
0
3
4
1
πε φ
F e
where m e represents the electron mass
barrier height of the emitter
otential energy diagram illustrating the effect of an external electric field
on the energy barrier for electrons at a metal surface, with consideration of an image potential
represents the vacuum level, E F refers to the Fermi level, and Ø is the work function of
the metal
Nordheim (F-N) theory was developed by R H Fowler and L W some other researchers in order to describe the relationship between the emission current density and the electric field applied on the metal
6] The derivation of F-N equation is built on the basic semiconductor density of states, Fermi-Dirac distribution, tunneling phenomenon
Considering the Wentzel-Kramers-Brillouin (WKB) approximation employed at the early stage [3, 7], the F-N equation can be written as:
3
2 8 exp
2 / 3
y heF
υ φ π
represents the electron mass, h is the Planck’s constant, Ø
barrier height of the emitters, F is the local field, ε 0 is the permittivity of free space,
energy diagram illustrating the effect of an external electric field
, with consideration of an image potential
is the work function of
Fowler and L W describe the relationship ric field applied on the metal
is built on the basic semiconductor tribution, tunneling phenomenon and
louin (WKB)
N equation can be written as:
(2.1)
(2.2)
is the emission
is the permittivity of free space,
Trang 3and t(y) and υ(y) are the Nordheim elliptic functions including image potential
corrections For a triangle-shaped potential barrier used in Fowler and Nordheim’s work, this F-N equation can be simplified by using the approximation of t2(y)≈1.1 and υ(y)≈0.95 [8] Finally, the F-N equation can be obtained:
−
=
E
B E
A
J
β
φ β
φ
2 exp (2.3)
where Ø represents the emission barrier height of the emitters (eV), β refers to the field enhancement factor, E is the applied field, α is assigned to the area where electron emission takes place, and the universal constants A = 1.54×10-6 A eV V-2 and B =
6.83×103 eV-3/2 V µm-1
The typical FE characteristic plots are shown in Fig 2.2 The plot of ln(J/E2)
versus 1/E (so called F-N plot) displayed in the inset comprised a linear region,
emphasizing the quantum tunneling electron emission mechanism The slope of the
linear region of the F-N plot is a function of both β and Ø, which can be expressed as
below by transformation of the Eq (2.3):
β
φ3 / 2 3 10 83
−
=
This equation is the most commonly used format in FE studies and it is utilized
as a standard calculation formula in order to evaluate the FE properties of different samples all through this dissertation The F-N equation used to be exclusively applied
on FE from bulk metals, but recently it is abundantly used in FE studies of other materials, such as semiconductors [9-13]
Trang 4Fig 2.2 The electron emission current density versus applied field (J-E) characteristics of the
specimen The corresponding Fowler–Nordheim (F-N) plot is shown in the inset
2.2 Field Emission from Semiconductors
Field emission was once considered to be an exclusive phenomenon of metals,
however, semiconductors were later found to exhibit similar properties and the emission current could be approximated by the same method that Fowler and Nordheim used as well [14] In contrast with metals, the external electrical field would penetrate into semiconductors and result in the band bending near the semiconductor surface as illustrated in Fig 2.3 This bending would lead to lowered emission barrier height for electrons so as to enhance the FE performance of the semiconductors
0
2
4
6
8
-14 -12 -10 -8 -6 -4 -2 0
2)
1/E
Trang 5Fig 2.3 Energy band bending near the surface of a semiconductor induced by the external
electrical field E c represents the conduction band minimum,
the valence band maximum,
The FE process for semiconductors is much more complicated as compared to that for traditional bulk metals For instance, it was found that for some semiconductor materials, the F
slopes at low and high electrical field This deviation might
effects, overheating of the emitter tips
conduction band of semiconductors
also be strongly affected by the temperature owing to their temperature
nature [10, 18, 19] The doping type and concentration
band structures of the semiconductors, resulting in varied emission barrier height thus diverse FE performance
semiconductors, in some cases electrons tunnel from conduction band, some eject from valence band while emission from the donor level within the bandgap is also
Energy band bending near the surface of a semiconductor induced by the external
represents the conduction band minimum, E F refers to the Fermi level,
the valence band maximum, V 0 donates the original emission barrier height, and
barrier height with band bending
The FE process for semiconductors is much more complicated as compared to that for traditional bulk metals For instance, it was found that for some
r materials, the F-N plots comprise linear relationships with different slopes at low and high electrical field This deviation might be due to the
effects, overheating of the emitter tips, or the low concentration of the carriers in the
on band of semiconductors [15-17] FE properties of semiconductors could also be strongly affected by the temperature owing to their temperature
nature [10, 18, 19] The doping type and concentration of carriers would influence the
of the semiconductors, resulting in varied emission barrier height thus diverse FE performances [20, 21] Furthermore, the origin of FE is not fixed for semiconductors, in some cases electrons tunnel from conduction band, some eject
band while emission from the donor level within the bandgap is also
Energy band bending near the surface of a semiconductor induced by the external
refers to the Fermi level, E v is
donates the original emission barrier height, and V is the
The FE process for semiconductors is much more complicated as compared to that for traditional bulk metals For instance, it was found that for some
N plots comprise linear relationships with different
the space charge the low concentration of the carriers in the 17] FE properties of semiconductors could also be strongly affected by the temperature owing to their temperature-dependent
would influence the
of the semiconductors, resulting in varied emission barrier heights and
[20, 21] Furthermore, the origin of FE is not fixed for semiconductors, in some cases electrons tunnel from conduction band, some eject
band while emission from the donor level within the bandgap is also
Trang 6possible [22, 23]
With the development of synthesis methods, nanosized semiconductors, such as nanowires and nanoparticles can be produced The dimension decrease of the materials would induce quantum effects such as discretization of energy band, which would confine the electron motion and change the width of the bandgap [24] The FE cold cathode can be fabricated with multilayer semiconductor thin film structures as well and these films can be produced thinner than 10 nm with the sophisticated technology [25, 26] In this case, the substrate is usually critical important because it acts as a primary electron source during emission process Deposited with ultrathin films, the FE cathode can be dramatically modified in the electronic structures hence leading to significantly promoted FE characteristics [27] By utilizing multilayer ultrathin film structures as FE cold cathode, the effective emission barrier can be controlled by monitoring the space charge value on the surface [28]
2.3 Influencing Parameters of Field Emission
Based on the above review of the F-N theory and the literature on FE from semiconductors, it is obvious that the FE properties of materials are essentially affected by a few parameters
First, FE is a tunneling phenomenon of electrons from the surface of a condensed matter to vacuum, thus excellent vacuum is a basic requirement for reliable and stable
Trang 7FE performance Generally, a base pressure of below 1 × 10-8 Torr is required for the
FE test [29] If the operation pressure is too high, work function of the emitter may be changed due to the gas adsorbed onto the emitter surface Additionally, the emitted electrons may cause ionization of the residual gas molecules, thus leading to increased bombardment at the cathode [3, 30] However, currently FE can also be operated at much higher pressures where in some cases, the electron emission phenomena occurred over a low applied voltage [31-34]
Second, the anode-cathode distance is also a parameter influencing the FE performances of emitters Threshold voltage, defined as the anode voltage where an emission current of 10-9 A was observed, is an essential index to evaluate the FE properties of emitters [35] The lower the threshold voltage, the lower the applied field is needed for the commencement of FE phenomenon, thus a lower power is required for this kind of electronic devices to work Low power for device operation
is the ultimate goal for device manufacturing Some researchers have investigated the relationship between the varied anode-cathode spacing and the threshold field Results showed that with varied anode-cathode distances, the threshold voltage shifted accordingly [35, 36] With the increase of anode-cathode spacing, the threshold voltage increased as well With the further increase of the applied voltage, large current density could be obtained
Third, the surface morphology affects the emitter’s performance as well Generally, it is much more difficult for a smooth surface to emit electrons than for a
Trang 8sharp geometry in that the applied electric field tends to concentrate on the sharp point thus resulting in a much larger local field at the emitter tips [37, 38] The local electric field with respect to the applied electric field is donated as the field enhancement factor β, which can be roughly estimated by the ratio h/r, where h is the projection height and r is the radius of the emitter tip [39] As such, shapes like nanowires, nanotubes and nanocones have aroused more and more interest among FE researchers since they have sharp emission tips [40-46] However, there is a problem with these structures that if they are too densed, the local electric fields of the neighboring emitters will interact such that the field gets weaken This phenomenon is called screening effect [47] To avoid this effect, these emitters should possess an optimum adjacent distance, which has been worked out to be twice the height of the emitters [48]
In addition, the work function of the emitter also plays a crucial role in influencing its FE properties According to the F-N equation shown in Eq (2.10), the
emission barrier height Ø is one of the parameters affecting the emission current J However, during calculation, the value of Ø is usually assumed to be similar to the
work function value Lower work function means lower barrier height for the quantum tunneling phenomenon As such, reducing the work function of the emitter is one approach to improve its FE properties There have been considerable studies showing that with low work function materials coated on the emitters, their threshold voltage can be significantly reduced [49-52] The underlying mechanism is that the
Trang 9coated materials have reacted and formed a Schottky contact with the emitters, thus resulting in the modification of the band structures so as to lower the barrier height for the quantum tunneling
Last but not the least, one of the most important parameters that affect emitter’s
FE properties is the lifetime The commercial use of FE devices should ensure stable emission current for a long time As the emitters are working in ultra-high vacuum environment and the emitter tips always bare high electron emitting current or elevated local temperature, corrosion or damage may happen to the emitter tips thus affecting the lifetime of the emitters [53] Therefore, one primary issue about FE devices is to improve the corrosion resistance of the emitters One of the methods, i.e., coating the emitters with materials of high chemical or thermal stability has been proposed and has shown promising results [54-58]
Trang 10References
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