Noise in field emission diodes

Physica 32 1333-1344

T i m m , G. W . V a n d e r Ziel, A. 1966

NOISE

IN FIELD

EMISSION

DIODES*)

b y G. W. TIMM and A. VAN D E R Z I E L Department of Electrical Engineering University of Minnesota,Minneapolis, Minesota, USA

Synopsis M e a s u r e m e n t s are r e p o r t e d o n noise in field e m i s s i o n v a c u u m diodes. I n some devices t h e n o i s e s p e c t r u m is of t h e t y p e / e q : (la -~- A/]e), w h e r e a s in o t h e r devices is of t h e t y p e /eq ~ (Ia~ + A~/[°~12)2; in m o s t cases ~ is close t o ~. T h e first t y p e of noise c a n b e i n t e r p r e t e d as t h e r e s u l t of t w o i n d e p e n d e n t noise sources, excess noise a n d s h o t noise, s p e c u l a t i o n s are m a d e a b o u t t h e second t y p e of noise. I n m a n y cases t h e excess noise s p e c t r u m is levelling off below 10 cycles. T h e excess noise is i n t e r p r e t e d in t e r m s of w o r k f u n c t i o n f l u c t u a t i o n s g o v e r n e d b y a diffusion of a t o m s o v e r t h e surface. T h i s gives a 1/]t s p e c t r u m a t h i g h frequencies w h e r e a s t h e s p e c t r u m levels off a t low frequencies. T h e e x p e r i m e n t a l t u r n o v e r f r e q u e n c y agrees r o u g h l y w i t h t h e t h e o r e t i c a l predictions. T h e t h e o r y c a n also e x p l a i n t h e t e m p e r a t u r e d e p e n d e n c e of t h e field e m i s s i o n excess noise f o u n d b y K l e i n t .

1. Introduction. The phenomenon of field emission was first reported b y R. W. W o o d in 18971) and was later described b y J. E. L i l i e n f e l d in 19222). In 1928, I{. H. F o w l e r and L. W. N o r d h e i m 3) described the field emission process by a quantum mechanical theory based on a simplified physical model. A convenient alternate form of this relation is 4): Jc(Fc, ~0) = 1.54 × 10-a (F~lry) exp(9.52/9½) exp(--6.36 × IOVgt/Fe) (I) where Jc is the emission current density in A/cm 2, Fc is the field strength at the emitter surface in V/cm and 9 is the work function in electron volts. This relation was verified over a wide range of values of the applied field and the work function by W. P. D y k e and J. K. T r o l a n when the field strength is not limited b y space charge effects s). Noise studies were performed b y K l e i n t and G a s s e 6) at Karl Marx University and by A. L. M o r e h e a d v) at the University of Minnesota. Kleint found 1//noise and shot noise. The 1/] noise increased strongly with increased residual gas pressure; at the lowest obtainable pressures shot noise predominated down to 1 kHz. He attributed the noise to the arrival and the evaporation of impurity atoms from the emitter and obtained a spectrum of the form const/(1 -t- ~o2,2). By assuming a distribution of time constants he could explain the observed 1/[ spectrum. *) Work supported by U.S. Army Electronics Command Contract, Fort Monmouth, New Jersey.

-

-

1333

-

-

1334"

G. W. TIMM AND A. VAN D E R ZIEL

Morehead found spectra of the form 1//~ with ~ close to ~ and with some indication of a leveling off of the spectrum around I0 Hz in some cases. He atrributed the noise to diffusion of impurity atoms over the surface. Diffusion of impurity atoms causes fluctuations in the local work function which reflect themselves in fluctuations in the emission current. It therefore seemed worthwhile to clarify the problem by further experimental work. This paper reports the results of this investigation. 2. E q u i p m e n t and devices. The noise measurements were performed with

the help of existing noise spectrum analyzers for the frequency region 1-100,000 Hz. Standard measuring techniques were used and the noise was represented by an equivalent current generator ~¢~ in parallel with the device under test. This current generator, in turn, is most conveniently expressed in terms of its equivalent saturated diode current Ieq, defined by i 2 = 2qleqA!

where q is the electron charge and A/ the bandwidth of the spectrum analyzer with which the measurements are performed. The device then gives as much noise as a saturated diode without flicker noise carrying a saturated diode current Ieq. Two types of field emission diodes were used in this experiment. The first type was built in the University of Minnesota Tube Laboratory and depended on electrostatic trapping of the primary and secondary electrons for its operation. In this tube the emitter was enclosed in a capped cylindrical tungsten anode. All support rods and the emitter hairpin were made of tungsten to allow the use of rigorous outgassing techniques necessary for the attainment and maintenance of the ultrahigh vacuum desired for field emission tubes. The second type had an open anode to allow optional viewing of the emission pattern on a luminescent screen. A magnetic field of several kilogauss was normally placed parallel to the line joining the emitter point and the anode to trap the primary and secondary electrons by forcing them to spiral to the anode plates. Of the four tubes of the second type, three were received from the Field Emission Corporation and the other was built at the University of Minnesota. The latter tube used some tantalum support rods because a tantalum to tungsten weld is much easier to perform than a tungsten to tungsten weld. There is some indication that the rigorous outgassing of the tube resulted in the evaporation of a small amount of tantalum onto the tungsten point. The tubes obtained from the Field Emission Corporation were sealed-off tubes provided with a separate region for gettering. The tubes built at the University of Minnesota were provided with a sputter pump so that they

N O I S E IN F I E L D E M I S S I O N D I O D E S

1335

could be permanently pumped after the whole assembly had been rigorously outgassed and sealed off. To ensure that the diodes were actually field emission diodes, the (I-V) characteristic of each tube was measured and log Ia was plotted versus 104/Va, where Va is the applied voltage. In each case a straight line was obtained, which indicated that the current flow was not caused by spurious effects. In the tubes with tungsten emitters, we first flashed the emitter points at temperatures above 2000°C until they were as clean as we could make them. We then measured the noise spectra and also the noise current as a function of tube current for constant frequency. We then contaminated the points and again measured the spectra. In some cases the points were contaminated by the residual gases in the tube and in other cases the points were contaminated by evaporating barium onto the point. We also measured the noise current as a function of time for constant tube current and frequency. We could thus determine the effect of gradual contamination of the point on the noise caused by the residual gases in the tube. At high current levels the current flow in field emission diodes becomes space charge limited and the noise should then be space charge suppressedS). All our measurements were performed for currents far below the space charge limited condition.

3. Results. Figure 1 shows the noise spectra at different current levels for diode A-1 immediately after the point was cleaned by flashing. Except for frequencies below 30 Hz the noise can be represented as Ieq = I~ +

A lit.

(2)

The first term is easily identified as a saturated shot noise term whereas the second term is an excess noise term. As shown in the next section, such a term can be attributed to a noise mechanism governed by diffusion. At 10 Hz there is a slight indication of a levelling off of the spectrum at the highest current. Figure 2 shows similar spectra for diode A-2. A similar behavior is noted, but the leveeing off of the spectra at low frequencies is moire pronounced since measurements were performed down to lower frequencies. It is again seen that the levelling off is more pronounced at the higher current levels. Figure 3 shows the spectra for diode A-3. Here the noise varies as l-t at frequencies above 10 Hz, then the spectrum goes through an intermediate region with a slope of about l-i and finally levels off to shot noise level at the highest frequencies. The noise can now be represented by an equation of the type I e q = [la ½+ A~II"] 2. (3)

1336

G. W.

TIMM

AND

A. VAN

DER

ZIEL

6

io, --

I

I

l

I

£o

,d

,G

#

I

I

I

~r ®

d,o 2

,o'

,d

ore:

l

I

10 2

l

I

104

I0 3

,~,oO,

I0S

l

I

lO l

i 02

I

I

103

I04

I05

Freq. ( H z )

Freq (Hz)

Fig. 2. Noise spectra for F E T A - 2 (with clean tungsten cathode) at 3 current levels.

Fig. l. Noise spectra for F E T A-1 (with clean tungsten cathode) at 3 current levels.

I0e

iOs

I

T

]

I0s

105

lO4

I0 ¢

)'.,,,v I0 3

1.7 ~ A

O,45p.A

'~

iO2

0.7 pA

i0 z - -

101 - -

ioo 1

lo-I lo o

I0 °

1

r

r

i

ioI

io 2

io )

1o4

105

10-1 tOO

101

10~

103

i0 a

10~

Freq. { ~ z ) Freq.

Fig. 3. Noise spectra for F E T A-3 (with clean tungsten cathode) at 4 current levels.

(Hz)

Fig. 4. Noise spectra for F E T P-2 (with clean tungsten cathode) at 2 current levels.

1337

NOISE IN F I E L D EMISSION DIODES

At the lowest frequencies there is again a levelling off at the highest current levels. Figure 4 shows similar spectra for tube P-2. The spectra are of the form (3) and the levelling off of the spectrum at the lowest frequencies is quite noticeable. This tube is somewhat noisier than the previous ones. Figure 5 shows the noise spectra of diode A-1 at different current levels after the emitter point had been contaminated by residual gases. The spectra are now of the form teq

=

I,~ + B/-~,

(4)

where a increases from a value slightly above 1 to a value close to { with to' -k, ios

I

I

I

I-

1

~-

I

I

--

i06 ~ 0 ~ o

104~ 2.6

0,:32

?,A

I04105 ~

~

I

&

103__

I T = 0.14/~A

o

T

!

= 0.80 p.A

,o

I0o ,o-,

I01

I0~ 1

10z

I

t03 Freq. (Hz)

I

i04

I

105

Fig. 5. N o i s e s p e c t r a f o r F E T A - I ( w i t h t u n g s t e n c a t h o d e c o n t a m i n a t e d b y res i d u a l gases) a t 3 c u r r e n t levels.

1o°

I0°

I

l01

I

!

10z 103 "Freq. (Hz)

Fig. 6. N o i s e s p e c t r a for F E T

I

104

\~ l0 s

A-3 (with

tungsten cathode contaminated by Barium) at 2 current levels.

increasing current. At low frequencies the noise is somewhat larger than for the clean emitter point (Fig. 1). At the lower frequencies there is a slight indication that the spectra level off at the highest current level. Figure 6 shows the noise spectra of diode A-3 after the emitter point has been contaminated by barium. Again the spectrum is now of the form (4) with = ~ 1.2 at the low current level and = ~ 1.4 at the higher current level. There is now little indication of the levelling off of the spectrum at the lowest frequency. Note that the noise is about two orders of magnitude larger than for the uncontaminated point.

1338

G. W. TIMM AND A. VAN DER ZIEL

Figure 7 shows Iea versus Ia for a tube with a clean t u n g s t e n cathode for 200 H z and for 20 kHz. At 200 H z the noise varies as I~ and at 20 k H z the noise varied as Ia except at the highest c u r r e n t levels where the noise seems to go as I~. W e i n t e r p r e t the Ia t e r m as being caused b y shot noise whereas the I~ dependence is a t t r i b u t e d to the excess noise t e r m A/-J.

'°' I

I

I

I

104

"~"IEQOCI~ 200 Nz io 3

103

io 2

102

o

I0 ~

IEQ

I@

~=g~z_~__r_~_~>// 100 I--¢

"'"'IEo o:

\'~-~

100

Ia + I z

20 kHz

10-~ iO-I

I I0 0

; 10I

I 102

103

Ia(/~A)

Fig. 7. Ioq vs. Ia for FET A-2 (with clean tungsten cathode) at 2 frequencies.

I@

102

ro3

ro4

105

Time (Min.)

Fig. 8. /eq vs. time for FET _P-1 at emission current of 0.87 FA, frequency of 3 kc/s, and (A) pressure ~10 -12 torr, (B) pressure somewhat larger.

In view of the fact t h a t the levelling off of the spectra at the lowest frequencies is current d e p e n d e n t , it m u s t be concluded t h a t the I a dependence c a n n o t hold at those frequencies. In addition, the I~s dependence c a n n o t hold for the c o n t a m i n a t e d points in the excess noise region since ~ varies with current. Figure 8 shows Ieq versus time at 3 k H z for t u b e P-1, in which the e m i t t e r is being c o n t a m i n a t e d b y residual gases in the tube. In this set of measurem e n t s the s p u t t e r p u m p was r u n n i n g continuously, so t h a t a more or less c o n s t a n t pressure was obtained. Curve A shows m e a s u r e m e n t s at a residual pressure of a b o u t 10-12 t o r r and curve B shows m e a s u r e m e n t s at a s o m e w h a t

NOISE IN FIELD EMISSION DIODES

1339

larger residual pressure. Both curves show the same general behaviour, in that the noise first rises with time, goes through a maximum and then decreases. As seen in curve B, the noise maximum occurs earlier, as expected for a more rapid contamination. Figure 9 shows the emission patterns for a clean tungsten emitter, for a tungsten emitter that is strongly contaminated with residual gases and for tube P-2. We note the large difference between the latter pattern and the first pattern. This makes it plausible that the emitter point of tube P-2 is contaminated b y impurity atoms that cannot be removed b y flashing. F r o m the history of the processing of this tube it seems likely that the impurity atoms are tantalum atoms evaporated onto the emitter point during the outgassing of the tube.

A B C Fig. 9. The emission parterns for (A) a clean tungsten emitter, (B) a tungsten emitter contaminated by residual gases, and (C) FET P-2. The fundamental character of a field emission pattern ;:: determined by the crystal structure of the emitter metalg). A tu~gs',_n emitter shows a characteristic pattern readily correlated with the body centered cubic crystal structure, so that the Miller indices of the various crystal surfaces will serve as the system of reference. In most metals the process of wire drawing results in preferred grain orientations along the axis; for the body centered cubic crystals this axis of the emitter point is oriented in the (110) direction. One would expect the darkest areas in an emission pattern to correspond to the crystal faces with the highest work functions. For a tungsten emitter, the E1101 plane is the largest and most densely packed, causing it to have the highest work function. This is in agreement with the large dark area in the middle of our emission pattern. The smaller dark spots correspond to the somewhat less dense and rougher [2111 and [100] planes and the area of intense emission correspond to the very rough E611], [111~ and [310] planes. Because the atoms in the close-packed faces are very tightly bound, one

1340

G.W.

TIMM AND A. VAN DER ZIEL

would expect any impurities on the emitter to accumulate at the edges of these faces or on other less tightly bound faces. The pattern for tube P-2 indicates an accumulation of lower work function material around the [11 I] and [ 100] planes. 4. Interpretation o~ the data. First of all we shall prove that a linear theory of noise generation is adequate in this case. Since the current I a may be written as

I~

=

A e -B

(5)

where A and B m a y fluctuate because the work function ~oand, or, the field strength E at the surface m a y fluctuate. One would expect the fluctuation in B to have the largest effect ; neglecting the fluctuation in A, we thus have M a = - - A e -B ~B ; ~I~ = I~ ~B 2.

(6)

We must now make a rough estimate of M~. Since Ieq ~ 1/El + (///0) ~] ampere at I a ~-- ll~a, where /0 is of the order of 1 Hz, we have at that current oo

=

f

2qleqA/=

2~/3

2q/o sin 2~/3

(7)

0

Substituting for q and putting/0 = 1 Hz, yields 6I~ ~- 10-18 A 2 and hence 6B z ~_ 10-6, so that a linear theory of the noise is quite adequate. For the following it will be assumed that the noise is caused by fluctuations in the local work function at the emitter point. One might assume that these fluctuations occur because impurity atoms of low work function diffuse over the emitter point and that the emission from these impurity atoms depends upon the position of the impurity atoms on the point. Or one might assume t h a t these fluctuations occur because impurity atoms of high work function diffuse over the emitter point and inhibit the emission of electrons by the low-work function planes of the emitter point. This assumption m a y not be fully adequate. It m a y also be that the field strength E at the surface depends on the presence or absence of a foreign atom at the surface. Diffusion of atoms over the emitter point might thus give fluctuations in the local field strength which would influence the noise. A fluctuation of 0.1% on the surface field strength results in a value of 6B 2 of 10.6 , which would be adequate to account for the measured noise. Since the noise in this case is also governed by a diffusion process, the theoretical results will not be materially different from those obtained for the fluctuations in work function caused by diffusion of particles. By assuming that the noise is caused by diffusion of atoms over the surface

NOISE IN F I E L D EMISSION D I O D E S

1341

we have rejected the idea that evaporation of the atoms from the surface gives a major contribution to the noise. The reason for this rejection is that the measurements are performed in a very small time interval. During this time interval relatively few atoms will arrive at or leave the surface. But all the atoms present on the surface will diffuse over the surface in that time and thus contribute to the noise. For that reason it is believed that the diffusion mechanism will be the predominant noise source. We now return to our problem. Fluctuations 6n in the density of particles on the emitting surface give rise to fluctuations in work function 09 89 = - - dn 0n

(8)

and consequently, since I~ = AJc(Fc, 9) where A is the effective emitter area and Jc(Fc, 9) the emitter current density, the fluctuation Ma in current is

0Jc 09 ~n

Ma = A - 09

0n

(9)

But according to the theory of field emission, Jc(Fc, 9) is given b y (1), and hence 0Jc0~_-

J c ~ - v4.76 + ~-1 + 9.54 Fe )< 1079½ _~"

(io)

Consequently, making a spectral analysis: V 4.76 1 9.54 × 1079½7 2 ( 09 '~ Sea(/) = I2 [- 9 t -~- --9 -+Fo _l \ ~ n / Sn(/)

(11)

where Sn(/) is the spectral density of the density fluctuations 8n, 9 is in volts and Fc is in volts/cm. The solution of the problem thus depends only upon finding Sn(/). We n o w represent the emitting face on the emitter point b y a circular patch of radius a in an infinite plane. Impurity atoms diffuse over the infinite plane, and when they are within the circular patch they influence the emission current. If N is the total number of impurity atoms on the emitting patch and N its average value, if ~ is the average density : ~a2~;

var N -= _~(1 -- 4)

(12)

where ,~ is the probability that an available impurity site on the patch is occupied b y an impurity atom. According to BurgesslO), V a n V l i e t and C h e n e t t e 11) a 2 berl (A/u) keil (A/u) -~- beil (A/u) kerl (A/u) S2v(~o) = 8 var N --D --u

(:3)

1342

G. W.

TIMM

AND

A. VAN

DER

ZIEL

where u = o)a2/D, and berl, beil, kerl and keil are the Kelvin functions of order 1. Consequently, s.(~)

-

(~a2)2

-

~

D •

z(~

-

~).

berl (~/u) keil (~/u) + bell (~/u) kerl (~/u) --U

(14)

The low-frequency limit of this spectrum is Sn(¢O - +

0)

:~n X(1 - - 2) In (coa2/D)

--

(14a)

and the high-frequency asymptote of this spectrum is of the form

Sn(cO) --

8

~

D

2(1 -- 2)

C

(om2/D) ~

(14b)

where C is a constant that does not depend on ~, a, D, or 2. The turnover frequency/1 occurs approximately at eD In (coaZ/D) ----- 1, or coa2/D ~ e, or / = / a = 2~a2. (14c) This gives a turnover frequency of about 1 Hz if D = 2 × 10-12 cm2/s and a ---- 10-6 cm (100 ~mgstrSm). This is roughly the turnover frequency found at large currents. Because of the uncertainty in the values of D and a, this can be considered reasonable agreement. The diffusion constant for surface diffusion can be written as D = 7vd 2 e--qEa/kT

(15)

where 7 is a constant of the order 1, v the vibration frequency of the lattice (of the order 1018/s), and d the lattice spacing (of the order of a few ~ngstrSm) and Ea is the activation energy in electron volts of the diffusion process. A value of Ea of about 0.6 electron volts gives the required diffusion constant of about 10-12cm2/s. Since Sn(cO) varies as D~ at high frequencies, one would expect the excess field emission noise term to increase rather strongly with increasing temperature. This agrees with experimental data obtained by K l e i n t 6 ) . As a matter of fact, taking Kleint's data for a Ba-covered surface at 295°K and 410°K, gives an activation energy of the diffusion process slightly above 0.5 eV. Having explained the /-~ spectrum and the temperature dependence of the noise, we now turn to the current dependence of the turnover frequency observed at low frequencies. According to K l e i n t 6) an increase in field strength results in a more pronounced step-type structure of the surface.

NOISE IN FIELD EMISSION DIODES

1343

This will have the tendency to cut up the emitting surfaces into smaller active patches. This corresponds to a decrease in the patch radius, and according to (14c) this results in an increase in the cutoff frequency. The difficulty with this explanation is, that a dependence of a on the field strength would result in a deviation from the I~ dependence of the excess noise, which is not observed. Our conclusion is therefore that we have at present no satisfactory explanation of the current dependence of the turnover frequency. We can also give a qualitative explanation of the dependence of the noise on the concentration of impurity atoms on the surface. According to (11) and (14b) the significant part of $I~(/) is in the factor D½ ( c~9 "~2 ~t(l -- 4). an ] n a s

(16)

With increasing impurity atom concentration ~9/~n is first practically independent of ~ but decreases appreciable if ~ approaches nearly full coverage. The factor 4(1 -- 4) goes through a maximum for 2 ---- ½. Equation (16) thus increases first with increasing value of ~, passes through a maximum, decreases again and reaches a new limiting value when a new surface equilibrium condition has been attained. The difficulty with this interpretation is that it does not explain the sharp peak in Ieq observed in fig. 8. A possible explanation might be that either D depends on the impurity concentration or that a depends on the impurity concentration. The latter could be attributed to the fact that at a given field strength the step-type surface structure becomes most pronounced for a particular range of surface impurity concentration. Another possible explanation would be clustering of the atoms for a particular range of the surface impurity concentration. The explanation of the large increase in the noise caused by evaporation of barium atoms onto the point might be that ~q~/~n is much larger in this case than for residual gas contamination. We have at present no satisfactory explanation for the spectra 1//~' with a < {. Since a apparently approaches { for large currents, it seems that the effect is restricted to lower values of the surface field strength. It could perhaps be caused b y a distribution of time constants, but it is at present not clear how this distribution arises nor why it is eliminated at larger field strengths. We have at present no satisfactory explanation of the spectra of the form (2). One would almost be tempted to attribute it to a correlation between shot noise and excess noise. But how can such a correlation come about ? We observed the effect in a tube in which the emitting point was contaminated with tantalum and in a tube that was later used for barium contamination studies. It is not unlikely, even for an apparently clean point, that

1344

NOISE I N F I E L D E M I S S I O N D I O D E S

there would be some isolated barium atoms on the emitting point in the latter tube. Both tubes would thus have low work function atoms on tungsten. These low work function atoms would act as emission centers. Since these atoms diffuse over the surface and can locate at different atomic planes on the surface, the rate of emission of these atoms would be modulated b y a random diffusion process. It is not unlikely, therefore, t h a t in this case the excess noise and the shot noise could be correlated. We intend to work out this model in greater detail. In surfaces th at are contaminated by high work function atoms, this effect does not occur, for here the impurity atoms will inhibit the electron emission in their vicinity. Hence t hey do not act as emission centers in the proper sense of the word and the excess noise and the shot noise should be independent. The question has sometimes been posed whether an absolutely clean metal point will show shot noise down to the lowest frequencies. The answer must be t h at this will probably not be the case. For even if an absolutely clean metal point could be obtained, which is highly unlikely, metal atoms would diffuse over the emitter point and still cause local fluctuations in work function and, or, field strength and these would show up as excess noise. A c k n o w l e d g m e n t . The authors are indebted to Mr. E. E. M a r t i n of the Field Emission Corporation, McMinnville, Oregon for providing some of the field emission tubes used in this research and for giving practical advice on the construction o f field emission tubes. T h e y also want to t hank Dr. K. M. v a n V l i e t of thi~ D e pa r t m e nt for helpful discussions on the theory of field emission noise. Received 10-1-66 REFERENCES 1) W o o d , R. W., Phys. Rev. 5 (1897) 1. 2) L i l i e n f e l d , J. E., Phys. Zs. 23 (1922) 506. 3) F o w l e r , R. H. and N o r d h e i m , L. W., Proc. roy. Soc. (London) 119 (1928) 173. N o r d h e i m , L. W., Proc. roy. Soc. (London) 121 (1928) 626. 4) M a r t i n , E. E. and others, Research on Field Emission Cathodes, Wright Air Development Division Technical Report, 59-20, 3 (1960). 5) D y k e , W. P. and T r o l a n , J. K., Phys. Rev. 8 9 (1953) 799. 6) K l e i n t , Ch. and G a s s e , H. J., Z. Naturforsch. 15a (1960) 87. K l e i n t , Ch., Ann. Physik 10 (1963) 295. K l e i n t , Ch., Ann. Physik 10 (1963) 309. 7) M o r e h e a d , A. L., Flicker Noise in Field Emission Tubes, M. S. Thesis, University of Minesota (1960) unpublished. 8) P u s h p a v a t i , P. J. and V a n d e r Ziel, A., I E E E Transactions on Electron Devices ED 12 (1965) 395. 9) D y k e , W. P. and D o l a n , W. W., Field Emission, in Advances in Electronics and Electron Physics 8 (1956) 90. 10) B u r g e s s , R. E., ]?roe. Phys. Soe. (London) 6 6 B (1953) 334. 11) V a n V l i e t , K. M. and C h e n e t t e , E. R., Physiea 31 (1965) 985.