The abnormal cathode fall of the glow discharge

P h y s i c a V, n o 9

THE

O c t o b e r 1938

ABNORMAL CATHODE FALL OF THE GLOW DISCHARGE b y M. J. D R U Y V E S T E Y N

Natuurkundig Laboratoriuln der N.V. Philips' Gloeilampenfabrieken, Eindhoven Holland Zusammenfassung E s w i r d d a r a u f h i n g e w i e s e n , d a s s die T h e o r i e y o n v. E n g e 1 u n d S t e e n b e c k, n a c h w e l c h e r die C h a r a k t e r i s t i k des a n o m a l e n K a t h o d e n f a l l e s n u r d u t c h d e n n o r m a l e n K a t h o d e n f a l l u n d die d a z u g e h 6 r i g e S t r o m d i c h t e b e s t i n a m t wird, n i c h t m i t d e n E x p e r i m e n t e n d e s V e r f a s s e r s a n He, Ne, Ar, K r u n d X e i i b e r e i n s t i m m t M i t G r a p h i t - K a t h o d e z e i g t He, bei h 6 h e r e m K a t h o d e n f a l l , e i n e n g r 6 s s e r e n W e f t y o n dV/di, A r a b e r e i n e n k l e i n e r e n W e r t als d e n t h e o r e t i s c h e n (V K a t h o d e n f a l l , i S t r o m d i c h t e ) . A u f die m 6 g l i c h e n U r s a c h e n fiir d i e s e n U n t e r s c h i e d w i r d h i n g e wiesen.

One of the ol~test problems of gas discharges is the cathode faU of the glow discharge. Although a number of experimental and theoretical papers on this subject have appeared, the problem of the characteristic of the abnormal glow discharge (that is the dependence of the cathode fall of the current density) is in my opinion not yet solved. Since the most detailed theory of the abnormal cathode fall is found in the book of v. E n g e 1 and S t e e n b e c k i). I will compare the results of this theory with some experiments. The theory ofv. E n g e l and S t e e n b e c k is assumed to be known to the reader. According to these authors the dependence of the abnormal cathode fall V of the current density i is given by:

V

i

(C i

V

V,~ =/(Bi)

(2)

V,, is the normal cathode fall, i,, the current density belonging to V,,, C a constant (independent of the pressure p). The function / is - -

8 7 5

- -

876

M.J.

DRUYVESTEYN

given b y the authors; it should be the same for all gases and cathode materials. 1~,3 te

a,s

t/~O;600,~,,~1-/.2./3~~5

3).5

V

4,5

,

50~

Ho

--

Ne

d,

d2

Yig. 1

V ~ 0,23

~3

02, i d.~,~A/~,,

Fig, 2 •

(40 ' ~

Q80

o~s7

o75

_ae

tls 1,6 3

Ar

200

dl d,2

d3

024 i

d,SmAIct~

65

1

Fig. 3 g

0.33 ~FO

0,70

1,5

i

2 mA/otr~

Fig. 4 ~,..-0,90

.

, o,~9 0.44 0 , 5 7 ~ ~ 7 6 4OO' ~

gf Fig. 5

1,50

o2

~3

d* i ds,~.e.,"

Fig. 6

Fig. 1-6. Characteristics for t h e 5 noble gases with a g r a p h i t e c a t h o d e a n d different pressures, t h e pressure is i n d i c a t e d in m m Hg. Fig. 4 belongs to a n o t h e r g r a p h i t e c a t h o d e a n d c u r r e n t d e n s i t y scale t h a n t h e o t h e r figures, it shows the inflexion point.

As we could not measure i,, as good as V, V, and i, we will use (2) for the comparison with experiment; B is a constant (but depending on the kind and pressure of the gas). In a tube (diameter 10 cm) two

THE ABNORMAL CATHODE FALL OF THE GLOW DISCHARGE

877

graphite electrodes (surface area 21 cm2) were mounted at a distance of 3 cm. The dependence of the potential difference between the electrodes from the current was measured for a number of pressures for the five noble gases, the anode was always in the F a r a d a y dark space, no anode light being visible. Although this method is no precision method the" difference between cathode fall and tube voltage will probably be less than 10 volts. 1 1 t h ~ ae

25

'

,2

r

#,s

/ Bi

Fig. 7. T h e d a s h e d c u r v e g i v e s t h e t h e o r e t i c a l c h a r a c t e r i s t i c , t h e c u r v e f o r N e is n o t g i v e n , as i t is v e r y n e a r t o t h e t h e o r e t i c a l c u r v e . T h e d o m a i n s f o r H e a n d K r are s h a d e d w i t h h o r i z o n t a l lines, t h o s e for A r a n d X e w i t h v e r t i c a l lines.

The measured characteristics are given in figs. 1-6. In order to be able to compare these curves with formula (2), the current scale for each curve was chosen in such a way that for V ---- 2V~ the characteristics pass through one definite point. For each gas a number of curves is obtained (fig. 7); the deviations from one curve for each gas are caused by errors of measurement as well as by real deviations which, however, will not be discussed here. The dashed curve is the theoretical characteristic, which should be the same for all gases and all pressures. We see that large deviations from theory occur. Especially for V greater than 2V, the value of dV/Bdi (fig. 7) is in He much larger, whereas in Ar it is much less than the theoretical value; the differences between Ne, Kr, Xe and the theoretical curve are only small. In order to see whether the heating of the cathode changed the form of the characteristic at a large current, as the density of the gas

878

M. ]'.

DRUYVESTEYN

will be decreased b y the h o t cathode, the characteristic was also observed with a cathode ray oscillograph. An alternating potential of 200 V (50 periods) was p u t in series with a b a t t e r y of 200 or 300 V. B y means of a resistance in series this potential was connected to the tube. The potential on the tube was (in series with a battery) set on one pair of plates, the potential on the resistande on the other pair of plates of the oscillograph. The form of the characteristic now cannot be altered b y the heating of t h e cathode, as its heat capacity is too large *): The characteristic obtained with increasing current (in the first part of a half cycle) showed within the errors of measurem e n t all the pecularities of the curves of figs. 1-6. The characteristic w i t h decreasing current was shifted so metimes to lower potential differences, probably due to rest ionization 2). At a definite pressure interval the characteristic curves in the a.c. experiment in Ne, Ar and Xe t) showed an inflexion point i.e. for large current density dV/di increased. In this domain curious hystereses occurred (see for instance the drawing fig. 8 and the p h o t o g r a p h fig. 9). The Ar curves of fig. 4 show, just as figs. 8 a n d 9 the increase of dV/di above 1 mA pro cm 2 for a pressure between 0,5 a n d 1,6 ram. The characteristic is m u c h better reproducible with a graphite cathode t h a n with a metal one; the large difference between He and the other gases, which was also observed with a Ni and a Mo cathode, can be seen too in the characteristics measured with a Fe cathode b y G ii nt h e r s c h u 1 z e 3). The inflexion point in the characteristic was also observed in Ne and Ar with a Mo cathode. The large difference between Ar and the gases Ne, K r and Xe for V > 2V,, was, however, not found with a metal cathode. W e will now t r y to answer the question which suppositions of v o n E n g e 1 and S t e e n b e c k account for the difference between experiment and formula (2). The main differences are: the large value of dV/di in He; the inflexion point at large current and the very low value of dV/di for V > 2V,, in Ar with a graphite cathode. As is also pointed out b y v o n E n g e l and S t e e n *) T h e c h a n g e of tile d e n s i t y of t h e g a s c a u s e d b y a t e m p e r a t u r e c h a n g e of t h e c a t h o d e o r of t h e t u b e walls is e l i m i n a t e d b y t h i s m e t h o d . A d i r e c t h e a t i n g of t h e gas b y t h e disc h a r g e c a u s e d e.g. b y collisions of t h e p o s i t i v e ions a g a i n s t g a s a t o m s in t h e C r o o k e s d a r k s p a c e is n o t e l i m i n a t e d . If t h i s d i r e c t h e a t i n g is i m p o r t a n t it h a s to be t a k e n i n t o a c c o u n t in t h e t h e o r y of t h e a b n o r m a l c a t h o d e fall. T h e h y s t e r e s e s d u e to t h i s h e a t i n g a r e in m o s t cases in o p p o s i t e d i r e c t i o n to t h e h y s t e r e s e s d u e to r e s t i o n i z a t i o n . t) K r w a s n o t i n v e s t i g a t e d . I n H e a n i n f l e x i o n p o i n t w a s n e v e r o b s e r v e d .

THE ABNORMAL CATHODE FALL OF THE GLOW DISCHARGE

879

b e c k t h e i r t h e o r y is b a s e d on s e v e r a l r a t h e r r o u g h s i m p l i f i c a t i o n s ,

i

Fig. 8 and 9. Characteristics o b t a i n e d with a c a t h o d e r a y oscillograph in Ar, voltage in vertical direction, c u r r e n t in horizontal direction. Fig. 8 was o b t a i n e d with a g r a p h i t e c a t h o d e and 1,6 mm Ar, the m a x i m u m curr e n t d e n s i t y being 4 mA pro cm2. The arrows indicate the direction in which the curve is passed. In fig. 9 a Mo c a t h o d e and 0,9 m m Ar were used, the m a x i m u m c u r r e n t d e n s i t y was resp. 4; 2,7 and 2 mA per cm2. Only the left curve slaows the inflexion point. a p r i o r i t h e s u p p o s i t i o n s m o s t o p e n t o d o u b t s e e m to b e : 1) T h o u g h in t h e C r o o k e s d a r k s p a c e t h e e l e c t r i c f i e l d is b y n o w a y c o n s t a n t , a n u m b e r of f o r m u l a e is u s e d w h i c h a r e o n l y c o r r e c t in a c o n s t a n t f i e l d : for i n s t a n c e t h e v e l o c i t y of t h e p o s i t i v e i o n s is c a l c u l a t e d w i t h a m o b i l i t y f o r m u l a ; for t h e i o n i z a t i o n b y e l e c t r o n s t h e T o w n s e n d f o r m u l a (~) is u s e d , t h e n u m b e r of i o n i z a t i o n s p r o e l e c t r o n is s u p p o s e d t o d e p e n d o n l y on t h e f i e l d s t r e n g t h , m o r e p a r t i c u l a r l y t h e i o n i z a t i o n in t h e n e g a t i v e glow, w h e r e t h e e l e c t r i c field is a l m o s t zero, is w h o l l y n e g l e c t e d . 2) T'he p o s i t i v e i o n s d o n o t i o n i z e t h e g a s (~ = 0) ; t h e p r o b a b i l i t y t h a t a p o s i t i v e i o n l i b e r a t e s a n e l e c t r o n f r o m t h e c a t h o d e (y) is supposed to be constant. T h e l o w v a l u e of dV/di for a l a r g e c u r r e n t in A r w i t h a g r a p h i t e c a t h o d e c a n b e e x p l a i n e d b y t h e i o n i z a t i o n b y t h e p o s i t i v e i o n s (~) ; f r o m W o 1 f ' s m e a s u r e m e n t s 4) i t is s e e n t h a t t h e p r o b a b i l i t y f o r t h i s i o n i z a t i o n is p r o b a b l y l a r g e e n o u g h t o e x p l a i n t h i s effect *). I n H e t h i s p r o b a b i l i t y is m u c h less t h a n in A t . T h e g r e a t l u m i n o s i t y of t h e f i r s t c a t h o d e l a y e r in A r a b o v e 400 V p o i n t s in t h e s a m e direction. *) with with with

A ~-mechanism will have a greater influence on the characteristic with a cathode a small y than with a cathode with a large y. In this way we can understand that a carbon cathode (small y) the difference between Ar and Ne is much larger than a metal cathode.

880

M.J.

DRUYVESTEYI~"

Although I cannot explain the other deviations from theory, they are probably connected with the more serious difficulties mentioned under 1). It seems probable that the ionization in the negative glow may not be neglected, the number of ions formed in this glow that reach the cathode, can not be evaluated at present *). On the other hand the number of ionizations in the Crookes dark space for one electron leaving the cathode can be estimated roughly in several ways ~); this number is for the normal glow in He and Ne less than 5, in Ar between 10 and 20, and in Xe about 100; in the abnormal discharge these numbers are still less. The number of ionizations, especially in He and Ne, is so low that it seems probable that the number of ions reaching the cathode that were formed in the negative glow may not be neglected s). However, I do not see how the difference between He and Ne can be explained in this way **). *) T h e c u r i o u s e f f e c t d i s c o v e r e d b y G i i n t h e r s c h u l z e (Z. P h y s . 4 0 , 414, 1926; 6 1 , 1 a n d 581~ 1930. P e n n i n g, Z. P h y s . 7 0 , 782, 1931) c a n p r o b a l b y be e x p l a i n e d w i t h t h e i o n i z a t i o n in t h e n e g a t i v e glow. T h i s a u t h o r f o u n d a s h a r p m i n i m u m in t h e v o l t a g e b e t w e e n the e l e c t r o d e s as a f u n c t i o r / o f t h e i r d i s t a n c e , if t h e a n o d e is p l a c e d a b o u t in t h e m i d d l e of t h e n e g a t i v e g l o w in a n a b n o r m a l g l o w d i s c h a r g e i n H e a n d s o m e o t h e r g a s e s . L e t us a s s u m e t h a t a p o t e n t i a l m a x i m u m e x i s t s in t h e n e g a t i v e g l o w a t a d i s t a n c e of e.g. t/5 of its l e n g t h , c o u n t i n g f r o m t h e l i m i t b e t w e e n C r o o k e s d a r k s p a c e a n d n e g a t i v e glow. T h e i o n s f o r m e d in t h e first f i f t h p a r t of t h e g l o w will r e a c h t h e c a t h o d e , t h e o t h e r i o n s will d i f f u s e t o t h e t u b e w a l l a n d t h e a n o d e . If n o w we p u t t h e a n o d e in t h e m i d d l e of t h e n e g a t i v e g l o w a n e g a t i v e a n o d e fall w i t h a s p a c e c h a r g e s h e a t h b e f o r e t h e a n o d e will be f o r m e d (L a n g m u i r, Gen. El. R e v . ,°7, 762, 1924; t h i s s p a c e c h a r g e s h e a t h w a s p r o b a b l y o b s e r v e d in Ne, P h y s i c a 4, n o t e 1, p. 675, 1937) A n u m b e r of e l e c t r o n s will b e r e p e l l e d b y t h i s a n o d e fall, t h e p o s i t i v e s p a c e c h a r g e in t h e n e g a t i v e g l o w will d e c r e a s e a n d t h e p o t e n t i a l m a x i m u m will be s h i f t e d s o m e w h a t in t h e d i r e c t i o n of t h e a n o d e (e.g. to 0,3 of t h e l e n g t h of t h e n e g a t i v e glow), so t h a t t h e n u m b e r of ions, r e a c h i n g t h e c a t h o d e will i n c r e a s e a n d t h e c a t h o d e fall will d e c r e a s e . A f t e r t h i s a r t i c l e w a s w r i t t e n , a p a p e r of F i s c h e r a p p e a r e d (Z. P h y s . I 1 0 , 197, 1938) w h e r e t h i s effect of G i i n t l l e r s c l l u l z e w a s a t t r i b u t e d t o t h e c o o l i n g of t h e g a s b y t h e cold a n o d e . I t h i n k t o o t h a t t h i s c o o l i n g m a y b e i m p o r t a n t . t) T h e n u m b e r of i o n i z a t i o n s in t h e C r o o k e s d a r k s p a c e c a n be f o u n d r o u g h l y , e i t h e r b y a n i n t e g r a t i o n of t h e r e s u l t s of S m i t h o n t h e e l e m e n t a r y p r o c e s s of i o n i z a t i o n b y e l e c t r o n s ( P h y s . R e v . 36, 1293, 1930), or b y u s i n g a n c~ f o r m n l a of T o w n s e n d, in t h i s d •

~ladX

l a s t case t h e t e r m A in i = *0e~ m a y n o t be n e g l e c t e d in Ne (x is zero a t t h e c a t h o d e a n d x = d a t t h e l i m i t of t h e n e g a t i v e glow). **) T h e s t e e p c h a r a c t e r i s t i c in H e m a y b e a n a l o g o u s to t h e s h a r p rise of t h e P a s c h e n c u r v e in H e a t a p r e s s u r e b e l o w t h e m i n i m u m s p a r k i n g p o t e n t i a l . A n o t h e r d i f f e r e n c e b e t w e e n H e a n d t h e o t h e r n o b l e gases is t h e f a c t t h a t m o l e c u l e s are o n l y f o u n d in a H e d i s c h a r g e .

T H E ABNORMAL CATHODE FALL OF T H E GLOW DISCHARGE

881

t

The inflexion point at large current density may be connected with the decrease of the ionization probability b y electrons at a high velocity. I do not think that these experiments permit an extension of ~r. E n g e l and S t e e n b e c k ' s theory; for such an extension measurements of the ionic and electronic current in the Crookes dark space are wanted. Received September 9th, 1938.

Eindhoven, 28th July 1938.

REFERENCES 1) A. y o n E n g e l and l~. S t e e n b e c k , Elektrische Gasentladungen If, p. 68-80, 1934. 2) H. G a w e h n a n d G. V a l l e , Ann. Physik20, 601, 1934; 23,381, 1935. H.J. R e i c h and W. A. D e p p , J. appl. Phys. 9, 421, 1938. M.J. D r u y v e s t e y n , Z. Phys. 57, 292, 1929. 3) A. G f i n t h e r s c h u l z e , Z. Phys. 49,358, 1928. 4) F. Wolf. Z. Phys. 74, 575, 1932; Ann. Physik 23, 627, 1935. 5) A. K e i t h B r e w e r and J. W. V ~ e s t h a v e r , J. appl. Phys. B, 779, 1937. A spectroscopicobservationin Ne (Physica I, 427, 1934) agreeswith the conclusionof the first part of this paper, namely that some electrons reach he negative glow with an energy, belonging to almost the whole cathode fall. Physica V

56*