S O V I E T P H Y S I C S J O U R N A L 1 0 7

2. In the Penning mixture there is, in addition to "sagging", another process which is quadratic with respect to ne, namely, the breakdown of the metastable atoms of the principal gas by electron impact . The diffusion equations of the column in this mixture, taking account of the direct ionization of the two components (u~n~n e and gznzne), the Penning effect (Upnmn2) , and the breakdown of the metastable atoms by electrons (Bnmne) , have the form

D,~. a2n+/ax ~- + .qn ln e + (bl/b~) ['~+n2ne + "~pn:nm] = O, (4) D m �9 d ~ n m / d X ~ + "Jmntne - - '~pnmn~. - - ~nrnn e = O,

where D m and n m are ~he diffusion coefficient and the concentration of metastable atoms, and b I and bz are the mobilities of the ions of the principal gas and the impurity. Assuming ~ne0 << UpUz0 and D m �9 �9 d Z n m / d x z .-~ - -Dm/A 2 , we obtain the sointion of (4) for n e in the form of (2), but with a different argument of the elliptical sine. Hence, by using the same method of calculation as that in the first case, it can be shown that T e and E z are uniformly increasing func- tions of current.

3. To summarize, on the basis of the study of two particular cases

considered above, it may be said that the role of a small amount of

impurity in maintaining ionization in the column decreases with

growth of the discharge current. As Te(~ ) increases, nz0([) decreases, and nm00) increases more siowly than linearly; therefore as j increases the discharge parameters approach the values characteristic of the discharge in the principal gas. The change in the parameters may

take place in varions ways, depending on the composition of the mix- ture. Thus, for example, the current-voltage characteristic may be positive, negative, or have a max imum in the region of comparatively small currents. The mathemat ica l difficulties do not permit a detailed consideration of these "intermediate conditions", and we are obliged to l imit ourselves to a qualitative analysis which agrees with the results of experimental work for specific gaseous mixtures [ 6 - 8 ] .

In conclusion I wish to express may gratitude to M. V. Konyukov for his constant interest in the work and valuable advice.

REFERENCES

i. K. S. Mustafin and V. I. Protasevich, ZhTF, 82, 1216, 1962. 2. M. A. Cayless, Proc. 4-th Internat. Conf. on Ion. Phenomena

in Gases, Uppsala, 1959, vol. I, 271, 1960, 3. I. Wilhelm, Zs. fur Phys., 151, 361, 1959. 4. Yu. S. Sikorskii, Elements of the Theory of Elliptical Func-

tions [in Russian], ONTI, Moscow and Leningrad, 1935. 5. W. Schotrky, Phys. Zs., 25, 685, 1924. 6. A. A. Zait~v, ZhTF, 18, 949, 1948. 7. W. Verweij, Physica, 25, 980, 1959. 8. H. Alterthum and A. Lompe, Ann. der Phys., 81, 1, 1988.

22 April 1964 Tula Polytechnic Institute

REMARKS ON THE I N F L U E N C E OF A N I S O T R O P I C SPIN W A V E A T T E N U A T I O N ON F E R R O M A G N E T I C R E S O N A N C E S A T U R A T I O N

G. A. Petrakovskii

Izvestiya VUZ. Fizika, No. 6, pp. 169-170, 1965

Schl6mana et al. and Suhl [1, 2] established that the influence of magnet ic tnhomogeneities in ferrites leads to "blurring" of the thresh- old of ferromagnetic resonance saturation. In fact, there is no thresh- old of resonance saturation under these conditions, and one may speak only of a type of non-linear virtual particle parameter, of suscepti- bility • at resonance with microwaves acting on the ferrite. In this short note, we show the possible existence of yet another mechanism of "washed out" threshold of resonance saturation in polycrystalline ferrites.

The proposed mechanism depends on the anisotropy." AH~ of the resonance line-width of the spin waves responsible for the saturation. The anlsotropy appears in the dependence of the spin wave attenuation rate on the magnetizat ion directiOn in the crystal [3]. If the magnetic moments of the separate crystallites do not interact with each other, then one may say they saturate independently. This obviously implies that with an increase of microwave power, a sharp drop in susceptibili- ty will not occur for all crystallites. Actually, after some increase in microwave power, those crystallites saturate first which have a smal - ler AH~ for a given orientation of the field H0, followed by those with much larger values of AH~r Therefore, the anisotropy AHg de- termines the degree of "washing out" of the saturation threshold. We will consider only the simple ease, although in reality the situation is significantly complicated by the magnetic interaction of the crys- tallites. Moreover, we consider the ease of a uni-axial anisotropy AH,~. The re!ation for it can then be written as

where 0 is the polar angle to the magnetizing vector. For an isotropic distribution of crystallites, we have • r for

a volume element , The total s~ceptibi l i ty is

V

where V is the volume of the ferrite specimen. If, at saturated re- sonance, • equals • then for each crystallite

{ ;t~,whereh ~< hkr(O, ~)

t " = �9 hkr(O' ~) whereh ~ hkr (O, ~), (3)

where h is the amplitude of microwave field and hkr the crRical field for saturated resonance.

..@ .-] ,

:PI'+"~ i J ! Carrying out the integration in Eq. (2), and taking into account

that

hkr = AHo V aH~ h/-/~ + 4 ~ - s C4)

we find

where

h~ - - , ko---~o y ~ ,

108

~; = ~; ~-~---~ r +

AH~ + AH~ 1 / ~ AH~ + 2 1 / ' ~ x t arcsln hUx ~ ~"AH~

- 2 nl x (5)

I Z V E S T I Y A V U Z . F I Z I K A

In Fig. ! the dependence of X" on the excitation level is indicated. calculated for the case AH~ = ZXl-l~ using Eq. 5. The antsorsopy of the spin-wave line-width also leads to a =washed out" threshold satttra- tton parameter for spin-waves in a longitudinal microwave magnetic field [4].

RE FERE NCE S

1. E. SchlOmann, I. J. Green, and V. Milano, L Appl. Phys., 31, 386 S, 1960.

2. H. Suhl, J. App1. Phys., 30, 1961, 1959. 3. G. A. Petrakovskii, Izv. vuzov SSSR, Fizika, no. 6, 29, 1962. 4. G. A. Petrakovskii, Doctoral dissertation, Tomsk, 1963.

// h2--h~ il 2 I/-~-"~K arcsln " I / ' ~ 21 May 1964 Kuznetsov Siberian Institute of Technical Physics

THE TWO-PROBE METHOD OF MEASURING THE LIFETIMES OF CURRENT CAR- RIERS IN SEMICONDUCTING FILMS

V. L. Kon'kov

Izvestiya VUZ. Fizika, No. 6, pp. 170-172. 1965

Measurement of the lifetimes of minority current carriers in mmi- conducting films by the photoconductivity method consists, in the f~st place, of determining their change in conductivity upon illumination.

L' i~, I , ' ~ , / ~

1

t~ L* g,

x=

The conductivity of semiconducting films is most conveniently mea- sured by the probe method. In order to eliminate the effect on the results of the contact resistance between the probe and the film, a four- probe method is generally used [1], but to determine the conductivity changes during illumination it is better to use a two-probe method. However. in order to avoid the change in resistivity between the probe and the film upon illumination, not the whole film, but only that part of it between the probes, need be illuminared.

We place the probes carrying the current as shown in the figure and illuminate a part of the film 2a I in length, which is less than the dis- tance between the probes, 2l~. We assume that the film is thin and that the beam of light passes through the whole thickness of the film with- out significant reduction in intemtty. The conductivity of the film in the absence of light is regarded as known and designated by o, the conductivity during illumination being designated o t. We maintain the current in the probes constant and measure the potential difference between the probes with and without illumination. F~m the data given and the recurs of these measuremenu we find the change in conductivity of the film upon illumination, Ao = o I - o.

With the constant-cu~ent measurements and the potential scheme given above, the fields satisfy the Laplace equation and the following conditions,

A2~ l (x, y, z)= O,

O~-Ix~.-a, = OJ'dlx=a,;(~t--'~)x~a'==O'ox

o,, o o~, / = o . ~ = ~ l " ~ x - Ox l~=~, ' Ox ~.=o O,

0 ~ = 0 ; O~l = Oy y-~o dz z=o,a O,

Or z_o=--~-~,(x--lO~(y);OO~ z=a=O , (1)

where 6(x) is the delta function, for the probes are regarded in the limit as point ones. Bearing in mind the symmetry of the problem, it is sufficient to determine 01 and ~z.

To integrate (I) we put [1]

~s(r)=U(r)+ V(r), v2U=q; v~V=--q (2) and require that the functions U and V should satisfy the boundary con- dltiom

OU OU I d~XL.a,,a=O' ~yly=T# =o' ~z ,-0 =--'~-~(x--ll)~(y),

~zlz=e =0 , (?x-U--V)x_m=0 ,

) I a v ov -- =0, =0, =0. (3)

Equation (I) for ~z will be satisfied for any value of q, but in order to simplify Eq. (2) as much as possible we will regard q as constant and