Table Of ContentENCYCLOPEDIA OF PHYSICS
EDITED BY
S. FLOGGE
VOLUME XXI
ELECTRON-EMISSION
GAS DISCHARGES I
WITH 378 FIGURES
SPRINGER-VERLAG
BT:RLIN· GOTTINGEN . HEIDELBERG
1956
HANDBUCH DER PHYSIK
HERAUSGEGEBE N VON
S. FLUGGE
BAND XXI
ELEKTRONEN-EMISSION
GASENTLADUNGEN I
M IT 378 FIG U R E N
S P RI N G E R- VE R LA G
BERLIN· GOTTINGEN . HEIDELBERG
1956
ISBN-13: 978-3-642-45846-0 e-ISBN-13: 978-3-642-45844-6
DOl: 10.1007/978-3-642-45844-6
ALLE RECHTE,
INSBESONDERE DAS DER "OBERSETZUNG IN FREMDE SPRACHEN,
VORBEHALTEN
OHNE AUSDR"OCKLICHE GENEHMIGUNG DES VERLAGES
1ST ES AUCH NICHT GESTATTET, DIESES BUCH ODER TEILE DARAUS
AUF PHOTOMECHANISCHEM WEGE (PHOTOKOPIE, MIKROKOPIE) ZU VERVIELFALT IGEN
© BY SPRINGER-VERLAG OHG. BERLIN· GOT TINGEN . HEIDELBERG 1956
Softcover reprint of the hardcover I st edition 1956
Inhaltsverzeichnis.
Seilc
Thermionic Emission. By Professor Dr. VVAYNE B. NOTTINGHAM. Massachusetts Institute
of Technology, Department of Physics, Cambridge/Mass. (USA). (With 62 Figures).
Glossary of symbols
A. Scope and objectives 5
B. Historical highlights . 7
I. General background 7
II. Experiments with clean surfaces 9
III. Experiments with composite surfaces (mainly the discoveries) 11
C. Theory. . . . . . . . . . . . . . . . . . . . . . . . . . 12
I. Statistical mechanics as a basis for emission equations 12
II. The density of an electron atmosphere in an enclosed space 18
III. Field effects with current flow . . . . . . . . . . . . . 22
IY. LAl\GMUIR'S space-charge theory . . . . . . . . . . . . 34
Y. ]r\calized lise of space-charge method for cathode property determination 45
a) Emitter evalllation by accelerating potential methods. . . . . . . 46
b) Emitter evaluation by retarding potential methods ....... 54
c) Emitter evaluation by a combination of retarding and accelerating po-
tential methods . . . . . . . . . . . . . . . . 58
VI. General theory. . . . . . . . . . . . . . . . . . 67
D. Applications of theory to experiments on thermionic emission 97
1. General discussion . . . . . . . . . . . . . 97
II. Emission from single crystals . . . . . . . . 103
III. Modification of electron affinity by polar layers 107
IY. The oxide-coatecl cathode 114
Tables ..................... . 158
Appendix 1: Thermionic constants . . . . . . . . . . 174
Appendix 2: Some useful equations from statistical theory of free electrons 175
Field Emission. By Professor Dr. R. H. GOOD jr. and Professor Dr. ERWIN vV. MULLER,
Department of Physics. Pennsylvania State University, College of Chemistry and
Physics, l'niversity Park, l'ennsyh'ania (USA). (\7V'ith 39 Figures) 176
I. Introcluction. . . . . . 176
II. Theory of field emission. . 181
III. Experimental results . . . 192
IY. Field emission microscopy. 201
Y. Field emission of positive ions 218
References 231
Sekundarelektronen-Emission fester Korper bei Bestrahlung mit Elektronen. Yon
Professor Dr. RUDOLF KOLLATH, II. Physikalisches Institut der Universitat, Mainz
(Deutschl;md). (Mit 5(1 Figlll'cll) ... 232
A. Einfiihrung. . . . 232
B. Energieverteilung der Sekundarelektronen 234
C. Die Anzahl der Sekundarclektronen (Ausbeute) 249
D. vVeitere Eigenschaften von Sekundarelektronen 275
E. Daten tiber die Bewegung langsamer Elektronen in festen Kbrpern. 276
F. Theoretische Ansatze zur Deutung der Sekundaremission 282
Literatur ......................... . 291
VI Inhaltsverzeichnis.
Seite
Photoionization in gases and photoelectric emission from solids. By Professor
Dr. GERHARD L. WEISSLER, Department of Physics, University of Southern Cali-
fornia, Los Angeles, California (USA). (With 92 Figures) 304
A. Photoionization in gases . . 306
I. Historical survey. . . . . . . . . . . . . . 306
II. Experimental methods . . . . . . . . . . . 312
III. Experimental cross sections of photoabsorption and photoionization 320
B. Photoelectric emission from solids . . . . . 341
I. A survey of photoelectric phenomena. 341
II. Selected topics on complex surfaces 370
References 382
Motions of Ions and Electrons. By Professor Dr. WILLIAM P. ALLIS, Research Labora
tory of Electronics, Massachusetts Institute of Technology, Cambridge, Mass. (USA).
(With 15 Figures). . . . . . . 383
Introduction. . . . . . . . . . . 383
I. Electron and ion orbits . . 384
a) Orbits in uniform fields. 384
b) Orbits in inhomogeneous magnetic fields 387
c) Pressure gradients . . 390
II. The LANGEVIN equation. 392
a) Drift. . . . . . 392
b) Diffusion . . . . . . 395
c) Energy and gain. . . 400
III. The BOLTZMANN equation 404
a) The derivative terms . 404
b) The collision integral . 408
c) Motions of electrons . 412
d) The energy distribution. 414
e) Direct current. . . . . 419
IV. BOLTZMANN transport equation. 420
a) General theory 420
b) Constant mean free time 423
c) Constant mean free path 425
d) Polarizable molecules. . 427
V. The FOKKER-PLANCK equation. 429
a) Flow in velocity space . . . 429
b) RUTHERFORD scattering 432
c) MAXWELLian distribution of scatterers 438
d) Stochastic processes 442
General references . . . . . . . . . . . . 444
Formation of Negative Ions. By Professor Dr. LEONARD B. LOEB, Department of Phy-
sics, University of California, Berkeley, California (USA) 445
I. Fundamentals. . . . . . . . . . . . 445
II. Methods of evaluation of hand qa . . . 448
III. Measurement of energy of ion formation 455
IV. Experimental results and interpretation. 456
V. Formation of negative ions by processes other than attachment in the gaseous
phase at low Xjp 463
References 469
The Recombination of Ions. By Professor Dr. LEONARD B. LOEB, Department of Phy-
sics, University of California, Berkeley, California (USA). (With 4 Figures) 471
I. Basic relations. . . . . . . . . . . . . . . . . . . . . . . .. 471
II. The measurement of the coefficient. . . . . . . . . . . . . . .. 477
III. Experimental results and the theories of the recombination coefficient 483
Referen ces 502
I nhaltsverzeichnis. VII
Srite
Ionization in Gases by Electrons in Electric Fields. By Professor Dr. A. vo:-.r ENGEL,
Clarendon Laboratory, Oxford (Great Britain). (\Vith 6<) Figures) 504
_\. Introduction 504
I. Historical notes 504
II. Collisions betwel'n electrons, ions, quanta and atoms 505
III. The problem. . . . . . . . 508
B. Ionization in uniform electric fields 510
I. The electron multiplication 510
I I. The electron a \'alanche . . . 514
III. The classical theory of ionization by collision 515
IY. The methods of measuring ionization coefficients 51<)
Y. The results of the mcasuremt'nts 526
a) The obser\"ed multiplication. . . . . 526
b) The ionization codficients . . . . . 530
YI. Collision theory and ionization coefficient 539
a) Elementary theories . . . . . . . . 539
b) Comparison of the elementary theory with experiment 543
c) Theory of thl' ionization coefficient in monatomic gases. 546
YII. :YIultiplication in the presence of negative ions . . . . . . 550
YIII. :\Iultiplication in tht' presence of positive ions . . . . . . 553
I X. :'II ultiplication by metastablc atoms colliding with traces of a foreign gas 554
X. Future work. . . . . . . . . . . . . . . . . . . . . . 558
C. The non-uniform electric fit'ltl. . . . . . . . . . . . . . . . . 558
I. J\on-uniformity by gcometry and its effect on multiplication. 558
II. :'IIultiplication in space-charge distorted fields 564
III. Future work. . . . . . . . . . . . . . . 570
D. Ionization in combined electric and magnetic fields 570
I. Crossed uniform fields. 570
II. Future work. 571
References 572
Secondary Effects. By Dr. 1'. F. LITTLE, Clarendon Laboratory, Oxford (Great Britain).
(With 47 Figures) ...... . 574
Introduction. . . . . . . . . . 57+
I. The TOWNSDID discharge 575
a) Introduction 575
b) Physical processes in the discharge. 577
c) l\leasurements in steady discharges. 5<)1
el) ,\nalysis of secondary effects by their time dependence 602
e) :Yleasurements in non-uniform fields . . . . . . . . 61<)
f) The relative importance of various secondary mechanisms. 622
g) Conclusion . . . . . . . . . 633
II. Other discharges . . . . . . . . . . . . . . . . . . . 634
III. Direct measurement of ionization . . . . . . . . . . . 638
a) Secondary electron emission from metals by positive ions 638
b) Secondary electron t'mission by other means 654
c) Ionization in the gas 658
References 662
Sachverzeichnis (Deutsch-Englisch) 664
Subject Index (English-G,'rlll<ln) .. 674
Thermionic Emission.
By
WAYNE B.NOTTINGHAM1•
\Yith (,2 Figures.
Glossary of symbols.
a Thermionic constant, Eq. ('J.j).
it Ratio of radii as defined by Eq. (6n.(,).
ai, {IS Empirical constants of E'1s. (ii.l) and (n.2).
.~ l'niversal thermionic constant, Eqs. (5.2) and (IS,(,) .
. ~ .\rea of conduction specimen, Eq. ((,S.2S) .
.i .".rea of electron emitter as used in E'1. (S2.:;) .
. ~ F FOWLER'S thermionic constant defined by Eq. ((,4.24) .
. ~ R RICHARDSON constant, Eq. (5'1.2) .
. ~ " Constant in general equation as in Eq. (S(LS) .
n Symbol introduced into Eq. (2h.l) to represent barrier properties.
cc"; Grid to emitter capacitance (Sect. S2).
Correction f,[ctor to pore-coI1(\uction equation to include porosity of specimens,
Eq. (('S.2S).
c , Correction factor in Eq. ((,).1»).
c x Capacitance calculated as in Sect. S2.
fJ ])istance between emitter and collector, Eq. (27.4).
fJ (P, H) Transmission O\'cr emission barrier, Eq. (2(J. I).
D(P, H) .\ Yl'rage transmission of electrons from the interior of a solid across a barrier to
tlw outside, Eq. ((,4.22) .
j) . \n abbn'\iation j)IP, 1i) (Sect. (,4).
Electron charge, E'l' ().t).
l'sed as abbre\'iation of I:']) in Eq. (i,·H,).
Electric intensity, Eq. (2,.3).
Electric intcnsity at critical distance xc' Eq. (27.7).
Component of electric intensity, Eq. (23.3) .
.\ cti\·ation energy' dl'1ined by E'1' ((,).t3).
Encrg\' 11'\'('1 or dOl",rs reiatiH' to bottOJll of conduction banel (Sect. 6-1).
Fracti;lll of a :\!.\X\\·ELLidn distribution, Eqs. (33.2) am\ (3-1.1).
:\[a"imum fractiondl distance ffllm an emitter of \'ery high capability to space-
charge minimum, Eq. 111t .. ll.
FL FnOll Ien'l (Fig. 2)
F..(P, I', T) J>robabilit,' of electron absorption by collector depends on momentum, potential
and tl'I1lI','ratnre of l'lllittl'r. Eq. (21,.1).
F(S, (II Function gi\'en in E'I. 1(,11.-1) and computed for Table HI, plotted in Fig. I'J.
F;(S, kT/(o) 'Ldlldated functil)n applied tl) thcon' of electron emission from a cylinder III
a retarding field, Eq. 121),!JI.
F(T'" ["[, II) Ill'iined by E". 11,21,1
Fix) Force function, E'l. (2,.1,).
i(I/',) Function or collector rt'gion potential difference giYen by Eq. (-16.1-1) and Table (,.
Fi'l',) .\ function applied tl) the collcctor space defined lJy F'ls US.,I) '11\(\ (31).5).
p Cllllllllc1il)ll pel' unit ;iIl"'. 1,'1 (1,).2;».
1;", Tr'lnscllndllcLlllCl' I"I' Illlltll'll-conlltiCLl1lcc) defilll'l\ by E'l. (S2.S).
(; .\ullfl'\·iatcll rlll'lll of I, Ix) as in Eq. (27.1t).
(; I S) Electron f1"" in a n·taniin.g ri"ld between cylinders, Eq. (26.11), and Tables 2 alll\ 10.
1 This \\ork was SlIpp"rtl'd in part I,y the Signal Corps; the Office of Scientific Research,
.\ir Hesearch and lle\Ti"pnll'nt Clllllmand; the Office of !\Ca\'al Research; the Research
LalJoratory of Electmnics and th" I kp"rtnll'nt of Physics of the :\Iassachusetts Institlltc of
Techno)og\·.
H.llIdbuch tier PJl\·~il.;, Br!. XXI.
2 WAYNE B. NOTTINGHAM: Thermionic Emission.
G(x) Geometrical function relating E to Y,;, Eq. (27.3).
G' Empirical value of constant of Eq. (79.1).
GE-218 Special form of General Electric tungsten wire (Sect. 70).
h PLANCK'S constant, Eq. (15.1).
Extention in phase space per quantum state (Sect. 15).
i Emission current as in Eq. (82.8).
/ Electron current density, Eqs. (5.1) and (5.2).
"Random" electron current density in a cavity, Eqs. (18.2) and (18.4).
Current density at the surface of a cavity. Same as /00' Eq. (18.1).
Constant of the SCHOTTKY Equation, Eq. (27.11).
Current density at zero field as in Eqs. (27.14) and (40.1).
Current density defined by Eqs. (18.5) and (26.10).
Minimum current density with zero field at emitter computed by Eq. (46.12).
Maximum possible current density flowing across a diode with zero field at the
collector, Eq. (43.2).
Maximum current density given by Eqs. (46.11) or (58.2).
Current density computed by Eq. (52.4).
Current density under critical condition of zero field at the collector, Eq. (43.1).
Current density with zero field at the emitter and the critical temperature e,
Eq. (47.1).
BOLTZMANN'S constant, Eq. (5.1).
A number defined by Eq. (64.14).
The LANGMUIR-CHILD constant, Eq. (38.3).
Average free flight distance in a pore, Eq. (65.17).
Free flight distance in a semiconductor, Eq. (65.6).
Free flight distance at some low temperature To, Eq. (65.6).
Thickness of a test specimen for pore conduction in a high field, Eq. (66.3).
Designation of straight lines in Figs. 11 and 12.
m Electron mass, Eq. (5.1).
Average dipole moment per atom, Eq. (73.2).
Dipole moment per atom at very low surface concentration.
Proportionality constant defined by Eq. (82.3).
Electron mobility in a pore, Eq. (65.4).
Mobility of electrons in a pore over temperature range II, Eq. (65.18).
Electron mobility in a semiconducting solid, Eq. (65.3).
Concentration of free electrons, Eqs. (5.1) and (22.1).
n Term index in summation of Eqs. (62.3) and (62.5).
Number of atoms per unit area, Eq. (73.2).
Concentration of electrons in cavity space, Eq. (18.3).
Donor concentration used in Sect. 64.
Adsorbed atoms per unit area in a monolayer, Eq. (75.1).
Electron concentration at cavity center of Fig. 3.
Maximum possible electron density at the center of a cavity, Eq. (24.4).
Concentration of electrons at emitting surface of cavity, Eq. (24.8).
A numerical constant defined by Eqs. (38.8) or. (46.4).
Number of electrons that can cross a solid boundary out of a cavity per second
per unit area per unit range in energy, Eq. (17.2).
Number of electrons that can cross a solid boundary into a cavity per second per
unit area per unit range in energy, Eq. (17.1).
N(fix) Number of electrons crossing unit area per second per unit range in fix, Eq. (16.1).
P Momentum of an electron, Eq. (26.2).
Px' Py' pz Momentum component along x, y, z direction.
Px
Average momentum component, Eq. (33.3).
p~ Momentum component in the x direction of an electron at the limiting part of the
barrier, Eq. (26.4).
LJpx Average gain in momentum as in Eq. (65.1).
P, Radial component of momentum, Eq. (60.1).
Prs Same as P, at the surface of the emitter, Eq. (60.1).
Prj Limiting value of initial radial momentum at the emitter for arrival at a potential
point V. negative, Eq. (60.3).
Pel Limiting value of tangential momentum at the emitter for arrival at a potential
point V. negative, Eq. (60.3).
Pe Tangential component of momentum, Eq. (60.1).
Pes Same as Pe but at the surface of the emitter, Eq. (60.1).
Glossary of symbols. 3
.\bbrcviation for contact difference in potential, Eq. (38.10).
Contact difference in potential at 0° K by extrapolation according to Eq. (38.10)
(usually not the true value).
PT Contact difference in potential (a function of temperature). Eq. (27.1).
P('1'~) Probability integral. Eq. (34.(».
l' Radius of emitter, Eqs. (26.5) and (27.5).
l' Radius between that of the emitter and the collector, Eq. (60.2).
r, Radius of emitter in Eq. (6u.2U).
H Hadius of l'ollector, Eqs. (26.5) and (27.5), or radius at potential minimum as in
Eq. (6(1.3).
Cdlector radius as used in Sect. 67 .
. \ dimensionless measure of applied voltage defined by Eq. (56.1).
-'u Dimensionless measure of applied voltage for zero field at collector, Eq. (Si.1).
<; Retarding potential in dimensionless units, Eqs. (26.8) and (50.5).
Sa Slope of line in Fig. 11.
Sb Slope of line in Fig. 12.
,5' Dimensionless change in potential with zero field at collector as reference, Eq. (57.1).
'~9 )Iaximum value of collector potential change in dimensionless units (Fig. 14).
SII \'alue of S' when cllfrent ratio is expressed as 1/2, Eq. (58.13).
So' Slope given by Eq. (52.S) and illustrated in Fig. 13.
T Temperature on Keh'in scale (sec also V1-).
Ta .\ctivation temperature (Sect. 75).
To :--latching temperature for relating thermionic constants, Eq. (50.5).
To .\ low temperature at which a free flight distance Iso is known, Eq. (65J».
~J T Increase in temperature above the critical value e, Eq. (4U.2).
u2 Current ratio as in Eq. (57.3).
lfi'1i :--Iaximum current ratio between space·charge limits, Eq. (57.4).
['2 Current ratio definl'd by Eq. (58.3) .
V,I .\ verage speed of electrons of low concentration, Eq. (65.6).
.\pplied potential, Eq. (27.1).
v" .-\pplied voltage for cUITent density 1M (Sect. 47).
v' . \ pplied voltage for current density 1 L (Sect. 47).
v** \'oltage computed from observables as in Eq. (47.5).
(/1 .\pplied voltage for a calculated current, Eq. (52.1).
vi Defined by Eq. (52.2).
Defined by Eq. (52.3).
Observable applied voltage, Eq. (52.5) .
. \pplied voltage for zero gradient at the collector (Sect. 57) .
.\ pplied voltage at critical condition of zero field at the emitter, Eq. (49.7).
Observable potential difference over temperature difference of L1 Vl' with zero net
current (Sect. 86).
J." I nternal potential due to surface charges as in Sect. 86.
J' "agnitude of true retarding potential in the space between the emitter and collector
in Eqs. (26.5) and (2(,.(,).
Potential with respect to the space·charge minimum of Fig. 3, see Eq. (22.1) .
.\ constant depending on tube geometry and temperature. See Sect. 9 and Eq. (27.11).
Potential difference between emitter and collector as in Eq. (27.11) or potential
across the collector space as in Eq. (32.1).
Lowest temperature of range expressed in electron-volts, Eq. (49.1) and (11.3).
Highest temperature of range expressed in electron-volts, Eq. (49.1) and (11.3).
\'oltage drop over an average pore distance of ip, Eq. (66.2).
Retarding potential difference bptween surface of emitter anel surface of collector,
Eq. (42.1).
J's Potential llifference in emitter space as in Eq. (32.1) in Fig. 7.
V Difference in potential between center of cavity and its houndary just lJutsi,le the
s
conducting surface a, ill Sect. 24.
The electron volt equivalent of the energy liT, Eq. (46.9).
Electron-volt equivalent of minimum temperature for space-charge minimum of Vr
as in Eq. U;2.7).
Electron volt equivalent of To in Eq. (65.6).
Characteristic temperature expressed in electron volts defined by Eq. (47.12).
Critical temperatures expressed in electron volt equivalent, Eq. (53.1).
Electron-volt equivalent of the critical temperature e and given by e/l1 (,I 10 (Sect. 47).
])istance hetween plane conducting surfaces (Sect. 21, Figs. 1, 2, 3, anrl 7).
1*
4 WAYNE B. NOTTINGHAM: Thermionic Emission.
Separation of surface charges, Eq. (73.1) (Fig. 34).
Potential energy difference shown in Fig. 2-Electron affinity of a solid, Eq. (17.4).
Electron affinity modified by an externally applied potential, Eq. (27.10).
Integration variable, Eqs. (26.11) and (60.4).
Distance variable as in Sect. 27.
Characteristic unit distance of space-charge theory, Eqs. (35.1)' (35.2) and (38.9).
Escape distance as in Fig. 5 and Eq. (27.6).
Distance from potential minimum to collector Fig. 7 and Eq. (38.2).
Distance from emitter to control grid of idealized triode.
Location of mirror-image surface with respect to an arbitrary reference as in
Eq. (27.8).
Maximum value of distance from emitter to space-charge minimum, Eq. (46.10).
Integration variable, Eqs. (26.12) and (34.3).
Ratio of distances as in Eqs. (24.2) and (43.4).
Ratio of electron concentrations as in Eq. (24.11) or currents as in Eqs. (43.4)
and (51.2).
Arbitrary ratio of currents as in Eq. (52.4).
Arbitrary choices of z, Eq. (53.1).
Current ratio defined by Eq. (58.7).
(drpjdVT) or the temperature coefficient of work-function with temperature expressed
in its electron-volt equivalent, Eq. (65.21).
y Proportionality constant of Eq. (80.2).
,) Distance from potential minimum to surface at which 1J!s is infinite, Eqs. (24.1)
and (43.1).
Kinetic energy when potential energy is zero.
Energy, Eq. (15.1).
Permitivity of free space, Eq. (22.1).
Kinetic energy associated with motion in the positive x direction, Eq. (16.2).
p;j2m or kinetic energy over an image barrier as in Eq. (63.2).
Kinetic energy associated with the x direction of motion in the cavity of Fig. 2.
Kinetic energy associated with electron motion in the semiconductor illustrated in
Fig. 27.
Average kinetic energy of an electron, Eqs. (63.1) and (63.2).
Difference in energy between bottom of conduction band in the semiconductor and
that of the metal in Fig. 27.
e
Temperature critical for zero field at either the collector or emitter with space charge
(Sect. 31).
{} Fraction of surface covered by adsorbed atoms.
(jp Coefficient of thermal emf (thermoelectric power) defined by Eq. (86.5) for a pore in
a semiconducting structure.
Coefficient of thermal emf (thermoelectric power) defined by Eq. (86.3) for semi
conducting solid.
). Approximately half of the characteristic pore length lp, Eq. (66.1).
fl FERMI level measured relative to bottom of conduction band as in Eqs. (16.1) and
(64.1).
A measure of donor concentration and temperature as in Eq. (64.9).
FERMI level in the metal illustrated in Fig. 27.
FERMI level in a semiconductor illustrated in Fig. 27.
FERMI level in cavity (see Fig. 2).
FERMI level in solid (see Fig. 2).
Change in the FERMI level with temperature relati"e to its value at T = 00 K as used
in Eq. (81.4).
Change in FERMI le"el with a temperature change of Ll VT as in Eq. (86.2).
~umber of electrons per unit volume.
Electron concentration at space-charge minimum, Eq. (35.3).
Temperature exponent in Eq. (50.8).
Integration variable representing energy in dimensionless units as in Figs. 23 and 24
and Eqs. (62.3) and (62.7).
Conductivity as in Eq. (65.2).
Surface charge per unit area, Eq. (73.1).
Conductivity over range I of Fig. 37.
Conductivity over range II of Fig. 37.
Pore conductivity over temperature range II, Eq. (65.19).
Change in applied potential in dimensionless units, Eq. (58.5).
