On relation between the autoemitter top field, anode voltage and cathode geometry
A field emission diode has been made up on the basis of a flat metal anode and pin cathode (of the height a) that is
 mounted on a flat metal plate parallel to the anode. The potential of the field emission diode has been calculated as the
 function of the pin cathode shape, its he...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/88307 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On relation between the autoemitter top field,
 anode voltage and cathode geometry / B.V. Stetsenko, A.I. Shchurenko // Вопросы атомной науки и техники. — 2009. — № 1. — С. 136-138. — Бібліогр.: 8 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860252293583077376 |
|---|---|
| author | Stetsenko, B.V. Shchurenko, A.I. |
| author_facet | Stetsenko, B.V. Shchurenko, A.I. |
| citation_txt | On relation between the autoemitter top field,
 anode voltage and cathode geometry / B.V. Stetsenko, A.I. Shchurenko // Вопросы атомной науки и техники. — 2009. — № 1. — С. 136-138. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | A field emission diode has been made up on the basis of a flat metal anode and pin cathode (of the height a) that is
mounted on a flat metal plate parallel to the anode. The potential of the field emission diode has been calculated as the
function of the pin cathode shape, its height, the anode-cathode potential and the potential value into cathode. It has
been shown that the potential barrier transparency possesses a nonlinear dependence on the anode potential in the
Fowler-Nordheim coordinates, if the cathode height (a) is less than 1000 nm. To obtain a measurable field emission
current, the following condition should be met: Fmid·a>φ, were Fmid is the macroscopic field strength within the anodecathode
spacing, and φ is the pin cathode work function. Therefore, to get the field emission current, either the field
strength should be >10⁶ V/cm, or another field source should be used in addition. For example, the contact electrode
potential between the pin part of the cathode and its base can provide such a field source. An analytic function was
derived for the electric field of a pin cathode located on a flat substrate.
Розрахований потенціал автоемісійного діоду. Показано, що при зменшенні висоти вістря катоду
(<1000 нм) прозорість потенційного бар’єру залежить в координатах Фаулера-Нордгейма нелінійно від анодної
напруги. Необхідною умовою автоемісії є нерівність Fmid·a>φ, де Fmid – величина макроскопічного поля, а φ –
робота виходу катоду. Отже, для одержання автоемісійного струму з вістрів необхідно чи велике середнє поле
між електродами (>10⁶ В/см), чи додаткові до зовнішнього джерела поля. Таке поле може створюватися
контактною різницею потенціалів між підкладкою і вістрям. Одержана аналітична формула для потенціалу
електричного поля.
Рассчитан потенциал автоэмиссионного диода. Показано, что при уменьшении высоты острия катода
(<1000 нм) прозрачность потенциального барьера зависит в координатах Фаулера-Нордгейма нелинейно от
анодного напряжения. Необходимым условием автоэмиссии является неравенство Fmid·a>φ, где Fmid – величина
макроскопического поля, а φ – работа выхода катода. Таким образом, для получения автоэмиссионного тока из
остриев необходимо либо высокое среднее поле между электродами (>10⁶ В/см), либо дополнительные к
внешнему источники поля. Такое поле может создаваться контактной разностью потенциалов между
подложкой и острием. Получена аналитическая формула для потенциала электрического поля.
|
| first_indexed | 2025-12-07T18:44:53Z |
| format | Article |
| fulltext |
ON RELATION BETWEEN THE AUTOEMITTER TOP FIELD,
ANODE VOLTAGE AND CATHODE GEOMETRY
B.V. Stetsenko, A.I. Shchurenko
Institute of Physics, NASU, Kyiv, Ukraine, E-mail: stetsen@iop.kiev.ua
A field emission diode has been made up on the basis of a flat metal anode and pin cathode (of the height a) that is
mounted on a flat metal plate parallel to the anode. The potential of the field emission diode has been calculated as the
function of the pin cathode shape, its height, the anode-cathode potential and the potential value into cathode. It has
been shown that the potential barrier transparency possesses a nonlinear dependence on the anode potential in the
Fowler-Nordheim coordinates, if the cathode height (a) is less than 1000 nm. To obtain a measurable field emission
current, the following condition should be met: Fmid·a>φ, were Fmid is the macroscopic field strength within the anode-
cathode spacing, and φ is the pin cathode work function. Therefore, to get the field emission current, either the field
strength should be >106 V/cm, or another field source should be used in addition. For example, the contact electrode
potential between the pin part of the cathode and its base can provide such a field source. An analytic function was
derived for the electric field of a pin cathode located on a flat substrate.
PACS:85.45.Db;85.45.Fd
1. INTRODUCTION
The field value of autoemission cathodes has not been
measured. Calculated estimations are rather rough. In the
case of metals, the field is in a linear dependence on the
anode voltage [1]. For semiconductor cathodes, these
estimations are complicated with the voltage drop inside
the cathode [2], which results in non-linearity of current-
voltage characteristics [3, 4] and, as a consequence, in
nonlinear field dependence on the voltage [5, 6].
Currently investigated are the systems of metallic and
semiconductor cathodes with micrometer and sub-
micrometer sizes [7]. Thereof, estimation of the field for
these systems seems to be topical.
This work is devoted to the dependence of the
external field on linear dimensions, shape of cathodes and
potential drop on them.
2. THE DIRICHLET TASK
FOR THE LAPLACE EQUATION
The electrostatic field potential inside a closed
domain is expressed via known potential values at its
boundary with the following formula:
S
S S
S dS
dn
MNdGNUMU ⋅⋅= ∫
),()()( , (1)
where U(M) is the potential in internal points of the
region, US(N) – potential values at the boundary, G(N,M)
– Green’s function of the Laplace operator for the S
region.
Let us consider the electrodes by the way of two parallel
metallic planes with the cathode shaped as a pin of the
height a. The potential between electrodes can be
expressed by the following sum
, )()(0)( MUEMUMU += zFMU mid ⋅=)(0 .(2)
136 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2009. № 1.
Series: Plasma Physics (15), p. 136-138.
Here, U0(M) is the potential between metallic planes, the
field of which is Fmid; UE(M) – potential of the pin
cathode itself that enhances the field near its top. The
potential U0(M) at the pin surface SN is U0(N). If the
cathode potential UC = 0 (metallic cathode), and the anode
one UA<0, then
S
S S
S dS
dn
MSdGNUMUE
N
N
⋅⋅= ∫
),()()( , (3)
where at the pin surface , and in the
rest parts of the surface S
)(0)( NUNU
NS −=
A, SC, US(N) = 0.
Fig. 1. The scheme of an autoelectronic emitter (pin with
rounded top) on a metallic plane. The internal surface of
the autoelectronic diode is S = SA + SC + SN
Let us introduce relative coordinates z
aξ = and
r
aη = . The potential and integral are expressed in
dimensionless coordinates normalized by the pin height.
Derivates of with respect to dimension
coordinates are equal to the product of derivates with
respect to dimensionless coordinates and a. In the case of
a metallic electrode,
)(MUE
ξξ =)(f within the interval 0< ξ <1.
At the surface of a semiconductor cathode, the
potential is not equal to zero. In the absence of contact
voltages between the pin and metallic base, it is the most
probable that
ξξξ ≤≤⋅ )(fk , (4)
where k < 1. When the contact potential takes place, f(ξ)
is added with its value normalized by the expression
Fmid·a. It means that with decreasing the height of the
semiconductor cathode the potential near its surface in
vacuum can be considerably changed even for
equilibrium bend of bands. Thus, the formula (3)
describes the part of the potential that creates the field of
a high strength near the autoemitter top. From the
physical viewpoint, this field is created by charges on the
pin charges of the opposite sign on flat parts of the
cathode band anode, the amount of which being equal to
that on the top. In the considered by us system of flat
electrodes, when removing the anode to the distance
considerably exceeding the pin length, the charges on the
flat part of the cathode surface are a mirror image of pin
charges in the cathode plane. It is obvious that the
autoemission field is mainly created by charges located on
the cathode pin part. Its value is in proportion to the
voltage drop along the pin length, which is created by the
uniform field existing between the electrodes. Besides,
the voltage of the uniform field along the cathode length
should exceed the work function. Only in this case after
the turning point from the vacuum side there will be free
electron states accepting carriers tunneling from the states
of solid.
137
3. CALCULATION OF POTENTIALS
AND BARRIER TRANSPARENCE
FOR SOME CATHODE SHAPES
The potential barrier transparence was calculated
using the formula from the work [8]. The pin shape on
Fig.2, express by when the function equal 0:
( ) ),,,,,,(, gbazrutqzFzruc mid δ⋅+⋅= . (5)
The function is the potential of the charges on
the axis z between dots
),( zrut
aaead <<<< ς0 which the
linear density ( ) ςςρ ⋅+= gp ( ( ) 1=aeρ ). The potential
is equal to:
( ) ( ) ( ) ς
ςς
ςρ d
zrRzrR
gpbazrut
ae
ad
⋅⎥
⎦
⎤
⎢
⎣
⎡
−⋅= ∫ ,,2
1
,,1
1),,,,,,( , (6)
( ) 22 )(,,1 ςς −+= zrzrR , ( ) 22 )(,,2 ςς ++= zrzrR .
This integral are evaluated by a primitive functions (the
final express so bulky unfortunatly) The cathode (1)
repeats the shape of an elongated spheroid with the height
a, base radius b (b < a), and top radius of curvature da.
The shape of the cathode changes in dependence on the
system parameters (Fig. 2). However, for the same values
of a, b, da, the field value near the cathode top is
practically unchanged.
Fig. 3 illustrates the shapes of the cathode potential
(1) and potential barrier (2) for an electron with account
of the Shottky effect (3) as well as for the linear potential
(2), the field of which is equal to that near the top Fmax.
This field is used in the Fowler-Nordheim formula. It is
seen from the figure that the far turning point for the real
potential is more removed from the cathode top than that
used in the Fowler-Nordheim formula.
Account of the real potential results in essential
departure of the voltage-current characteristic (Fig. 4)
from the straight-line dependence in the Fowler-
Nordheim coordinates (5). Differences grow with
decreasing the cathode height (curves 4 to 1).
-0,4 -0,2 0,0 0,2 0,4
0,0
0,2
0,4
0,6
0,8
1,0
z,
c
m
r, cm
1
2
3
Fig. 2. Shapes of cathode pins with the radius of
curvature for the top 4.5·10-4 in units of the cathode
length. (1) stands for the ellipsoidal and covering it
curves when g = 1; (2) – g = 0.6, (3) – g = -1
Fig. 3. The potential of the field near the surface of
the ellipsoidal cathode. The dimensions of the cathode:
a = 500 nm, b = 50 nm and da = 2.5 nm
The transparence of the potential barrier for the
cathode with the height а = 300 nm decreases more than
one order when changing the voltage on it from 0 to
-1.5 V.
0,1 0,2
-15
-10
-5
0
lg
D
105F-1
mid, (V/cm)-1
5
1 2 3
4
Fig. 4. The transparence of the potential barrier for
various emitter heights a: (1) 1000 , (2) 500, (3) 250,
(4)150 nm. The radius of the cathode base b = 0.1 a.
(5) – transparence of the triangle potential barrier
Transfer of electrons from the solid cathode into
vacuum requires the turning point to be located at the
distance no more than several nanometers. Besides, the
0,0 0,5 1,0 1,5 2,0 2,5 3,0
-4
-2
0
2
4
u, В
x, нм
1
2
3
It is possible that the light sensitivity non-limited by its
threshold from the side of low frequencies is a result of
rectifying the light wave field by the autocathode.
following condition should take place: ϕ≥⋅aFmid ,
where ϕ is the work function for the pin cathode. This
condition is realized when vacuum has free states with the
energy corresponding to that of the Fermi level in the
cathode. Thus, to obtain electron emission, the voltage
drop at the height of the cathode top should be higher than
its work function. The potential difference compared with
this value can be obtained at the cost of the contact
potential difference between the flat and pin cathode
parts.
REFERENCES
1. M.I. Yelinson, G.F. Vasilyev. Autoelectronic emission.
Moscow: “GIFML”, 1958 (in Russian).
2. N.D. Morgulis. Peculiarities of autoelectronic emission
from semiconductors //Journal of Technical Physics.
1947, v. 17, N 9, p. 983 (in Russian). 4. CONCLUSIONS
3. L. Apker, E. Taft. Field emission from CdS // Phys.
Rev. 1952. v.88 , p.1037.
The following conclusions may be done:
4. P.G. Borzyak, A.F. Yatsenko, L.S. Miroshnichenko.
Photo-field-emission from high-resistance silicon and
germanium// Phys. Stat. Sol. 1966, v.14, N 2, p.403.
1. When decreasing the cathode pin height a, the
transparency of the potential barrier depends non-
linearly on the anode voltage in the Fowler-Nordheim
coordinates; some departures are noticeable when
a < 1000 nm;
5. B.P. Bundza, B.V. Stetsenko. Distribution of the
potential in an autophotocathode and a model of its
function//Izvestiya of AS of USSR. Ser. “Fizika”. 1976,
v. 40, N 8, p. 1589 (in Russian).
2. To obtain a measurable autoemission current, it is
necessary for the voltage drop along the pin part of the
cathode to exceed the work function value
ϕ≥⋅aFmid ;
6. B.P. Bundza, B.V. Stetsenko. On relation between the
field and voltage near the top of a semiconductor
emitter // Journal of Technical Physics. 1980, v. 50,
N 10, p. 2136 (in Russian). 3. A field with the autoemission value can be obtained
at the cost of a contact potential difference in the
heterojunction emitter-substrate, if its value is higher
than the work function one. It allows to understand the
nature of light sensitivity inherent to autoelectronic and
low-field emission;
7. A.A. Dadykin, A.G. Naumovets, Yu.N. Kozyrev. Field
electronic emission from Ge-Si nanostructures with
quantum dots// ZhETF Letter. 2002, v.5, N 76, р. 550.
8. L.D. Landau, Ye.M. Lifshits. Quantum mechanics
(non-relativistic theory). Moscow: “Fizmatgiz”, 1963
(in Russian). 4. Numeric estimations for the external field value in
dependence of the voltage drop on the cathode are
adduced; Article received 22.09.08
Revised version 15.10.08 5. Analytic formula for the electric field potential has
been obtained.
О СООТНОШЕНИИ МЕЖДУ ПОЛЕМ У ВЕРШИНЫ АВТОЭМИТТЕРА, АНОДНЫМ
НАПРЯЖЕНИЕМ И ГЕОМЕТРИЕЙ КАТОДА
Б.В. Стеценко, А.И. Щуренко
Рассчитан потенциал автоэмиссионного диода. Показано, что при уменьшении высоты острия катода
(<1000 нм) прозрачность потенциального барьера зависит в координатах Фаулера-Нордгейма нелинейно от
анодного напряжения. Необходимым условием автоэмиссии является неравенство Fmid·a>φ, где Fmid – величина
макроскопического поля, а φ – работа выхода катода. Таким образом, для получения автоэмиссионного тока из
остриев необходимо либо высокое среднее поле между электродами (>106 В/см), либо дополнительные к
внешнему источники поля. Такое поле может создаваться контактной разностью потенциалов между
подложкой и острием. Получена аналитическая формула для потенциала электрического поля.
ПРО СПІВВІДНОШЕННЯ МІЖ ПОЛЕМ БІЛЯ ВЕРШИНИ АВТОЕМІТЕРА, АНОДНОЮ
НАПРУГОЮ І ГЕОМЕТРІЄЮ КАТОДУ
Б.В. Стеценко, А.І. Щуренко
Розрахований потенціал автоемісійного діоду. Показано, що при зменшенні висоти вістря катоду
(<1000 нм) прозорість потенційного бар’єру залежить в координатах Фаулера-Нордгейма нелінійно від анодної
напруги. Необхідною умовою автоемісії є нерівність Fmid·a>φ, де Fmid – величина макроскопічного поля, а φ –
робота виходу катоду. Отже, для одержання автоемісійного струму з вістрів необхідно чи велике середнє поле
між електродами (>106 В/см), чи додаткові до зовнішнього джерела поля. Таке поле може створюватися
контактною різницею потенціалів між підкладкою і вістрям. Одержана аналітична формула для потенціалу
електричного поля.
138
1. When decreasing the cathode pin height a, the transparency of the potential barrier depends non-linearly on the anode voltage in the Fowler-Nordheim coordinates; some departures are noticeable when a < 1000 nm;
2. To obtain a measurable autoemission current, it is necessary for the voltage drop along the pin part of the cathode to exceed the work function value ;
3. A field with the autoemission value can be obtained at the cost of a contact potential difference in the heterojunction emitter-substrate, if its value is higher than the work function one. It allows to understand the nature of light sensitivity inherent to autoelectronic and low-field emission;
Рассчитан потенциал автоэмиссионного диода. Показано, что при уменьшении высоты острия катода (<1000 нм) прозрачность потенциального барьера зависит в координатах Фаулера-Нордгейма нелинейно от анодного напряжения. Необходимым условием автоэмиссии является неравенство Fmid∙a>φ, где Fmid – величина макроскопического поля, а φ – работа выхода катода. Таким образом, для получения автоэмиссионного тока из остриев необходимо либо высокое среднее поле между электродами (>106 В/см), либо дополнительные к внешнему источники поля. Такое поле может создаваться контактной разностью потенциалов между подложкой и острием. Получена аналитическая формула для потенциала электрического поля.
Розрахований потенціал автоемісійного діоду. Показано, що при зменшенні висоти вістря катоду (<1000 нм) прозорість потенційного бар’єру залежить в координатах Фаулера-Нордгейма нелінійно від анодної напруги. Необхідною умовою автоемісії є нерівність Fmid·a>φ, де Fmid – величина макроскопічного поля, а φ – робота виходу катоду. Отже, для одержання автоемісійного струму з вістрів необхідно чи велике середнє поле між електродами (>106 В/см), чи додаткові до зовнішнього джерела поля. Таке поле може створюватися контактною різницею потенціалів між підкладкою і вістрям. Одержана аналітична формула для потенціалу електричного поля.
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| id | nasplib_isofts_kiev_ua-123456789-88307 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:44:53Z |
| publishDate | 2009 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Stetsenko, B.V. Shchurenko, A.I. 2015-11-11T19:49:46Z 2015-11-11T19:49:46Z 2009 On relation between the autoemitter top field,
 anode voltage and cathode geometry / B.V. Stetsenko, A.I. Shchurenko // Вопросы атомной науки и техники. — 2009. — № 1. — С. 136-138. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS:85.45.Db;85.45.Fd https://nasplib.isofts.kiev.ua/handle/123456789/88307 A field emission diode has been made up on the basis of a flat metal anode and pin cathode (of the height a) that is
 mounted on a flat metal plate parallel to the anode. The potential of the field emission diode has been calculated as the
 function of the pin cathode shape, its height, the anode-cathode potential and the potential value into cathode. It has
 been shown that the potential barrier transparency possesses a nonlinear dependence on the anode potential in the
 Fowler-Nordheim coordinates, if the cathode height (a) is less than 1000 nm. To obtain a measurable field emission
 current, the following condition should be met: Fmid·a>φ, were Fmid is the macroscopic field strength within the anodecathode
 spacing, and φ is the pin cathode work function. Therefore, to get the field emission current, either the field
 strength should be >10⁶ V/cm, or another field source should be used in addition. For example, the contact electrode
 potential between the pin part of the cathode and its base can provide such a field source. An analytic function was
 derived for the electric field of a pin cathode located on a flat substrate. Розрахований потенціал автоемісійного діоду. Показано, що при зменшенні висоти вістря катоду
 (<1000 нм) прозорість потенційного бар’єру залежить в координатах Фаулера-Нордгейма нелінійно від анодної
 напруги. Необхідною умовою автоемісії є нерівність Fmid·a>φ, де Fmid – величина макроскопічного поля, а φ –
 робота виходу катоду. Отже, для одержання автоемісійного струму з вістрів необхідно чи велике середнє поле
 між електродами (>10⁶ В/см), чи додаткові до зовнішнього джерела поля. Таке поле може створюватися
 контактною різницею потенціалів між підкладкою і вістрям. Одержана аналітична формула для потенціалу
 електричного поля. Рассчитан потенциал автоэмиссионного диода. Показано, что при уменьшении высоты острия катода
 (<1000 нм) прозрачность потенциального барьера зависит в координатах Фаулера-Нордгейма нелинейно от
 анодного напряжения. Необходимым условием автоэмиссии является неравенство Fmid·a>φ, где Fmid – величина
 макроскопического поля, а φ – работа выхода катода. Таким образом, для получения автоэмиссионного тока из
 остриев необходимо либо высокое среднее поле между электродами (>10⁶ В/см), либо дополнительные к
 внешнему источники поля. Такое поле может создаваться контактной разностью потенциалов между
 подложкой и острием. Получена аналитическая формула для потенциала электрического поля. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Низкотемпературная плазма и плазменные технологии On relation between the autoemitter top field, anode voltage and cathode geometry Про співвідношення між полем біля вершини автоемітера, анодною напругою і геометрією катоду О соотношении между полем у вершины автоэмиттера, анодным напряжением и геометрией катода Article published earlier |
| spellingShingle | On relation between the autoemitter top field, anode voltage and cathode geometry Stetsenko, B.V. Shchurenko, A.I. Низкотемпературная плазма и плазменные технологии |
| title | On relation between the autoemitter top field, anode voltage and cathode geometry |
| title_alt | Про співвідношення між полем біля вершини автоемітера, анодною напругою і геометрією катоду О соотношении между полем у вершины автоэмиттера, анодным напряжением и геометрией катода |
| title_full | On relation between the autoemitter top field, anode voltage and cathode geometry |
| title_fullStr | On relation between the autoemitter top field, anode voltage and cathode geometry |
| title_full_unstemmed | On relation between the autoemitter top field, anode voltage and cathode geometry |
| title_short | On relation between the autoemitter top field, anode voltage and cathode geometry |
| title_sort | on relation between the autoemitter top field, anode voltage and cathode geometry |
| topic | Низкотемпературная плазма и плазменные технологии |
| topic_facet | Низкотемпературная плазма и плазменные технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/88307 |
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