Track etch formation in thin SSNTD in case of variable etch rate ratio

Nuclear Tracks arid Radialiotl Measurelnenls, Vol. 8, Nos. 1 4, pp. t3-16, 1984. Printed in Great Britain.

0191 278X/84 $3.00 + .(X) 1984 Pergamon Press Lid.

TRACK ETCH FORMATION IN THIN SSNTD IN CASE OF VARIABLE ETCH RATE RATIO Almasi G. and B. Kunsch Austrian Research Centre Seibersdorf, A-2444 Seibersdorf, Austria

ABSTRACT Formulae have been derived for the growth of the diameter of the hole produced by through etching with increasing thickness of the removed layers. Perpendicular tracks and a variable etch rate ratio have been assumed. Such calculations seem to be useful for radiography, particle identification and many applications of SSNTD's. Results are presented for alpha particle tracks in CR-39.

KEYWORDS Through etching, variable etch rate ratio, hole parameters, perpendicular beam.

INTRODUCTION The quality of SSNTD's made of CR-39 offers new possibilities to evaluate the track parameters of charged particles in order to identify their type and/or energy (e.g. Tarle and collaborators 1981, Fews and Henshaw 1981). Thick I) detectors are usually used for such purposes. However, in the case of perpendicular tracks the particle range is difficult to evaluate. Here thin detectors have advantages as instead of the track length the hole diameter can readily be measured with high accuracy. If detector stacks are used, the hole diameter is a useful additional parameter to the surface track diameters, the evaluation of which is worthwhile as a better resolution can be obtained for the particle energy and charge number. Therefore we have calculated the hole diameter as a function of the thickness of the removed surface layer for perpendicular tracks and a variable etch rate ratio. Our formulae can also be used to determine the etching conditions for a number of technical applications of SSNTD's e.g. the production of nucleopores.

HOLE FORMATION IN THIN DETECTORS In a previous paper (Somogyi and Almasi, 1979), the thickness hp of the removed layer till the moment of the track perforation has been calculated as well as the hole size as a function of the thickness h of the removed layer for a constant etch rate ratio. Etching from one side for detectors with support layer and from both sides for such without support

i) We use the terms "thin" and "thick" for such detectors, that will be etched through or not under etching.

13

14

(i. ,'\L~
has b e e n treated. For p e r p e n d i c u l a r tracks the hole p a r a m e t e r s have b e e n also g i v e n for a v a r i a b l e etch rate ratio for d e t e c t o r s w i t h support. T h i s a r t i c l e e x t e n d s these c a l c u l a t i o n s to thin d e t e c t o r s w i t h o u t s u p p o r t , w h i c h have g a i n e d p a r t i c u l a r a t t e n t i o n since C R - 3 9 of h i g h q u a l i t y became a v a i l a b l e .

TABLE Formulae

of hole

Xoe)

Xoe)

Xor = Xoe + r e (Xc; r e (Xc; Xoe)

Notations : dr = arcsin

Xoe)

hp (Wl)! io) sing r

hp ( W 2 ) i h ! min{

for f u r t h e r

Lh;

l o - L h}

[ V -I

(Xoe)] ; r e (Xc;

x Xoe) = h - X c S i n @ - / ° e V - l ( x ) xe

dx

R

h - J~o V- I (x) dx;

Xor

notations

sing e

R o) cos6 r

[ v - i ( X o r ) I; 6 e = a r c s i n

lo) =

Xoe)

L h as above

R o) sing r

]

r r (Xor;

! Lh

i o) cos6 r

sing e + r r (Xor;

cos0 e = r r (Xor;

h

if

L h = Xoe + r e (Xc;

cosg e

Xoe)

SSNTD they are valid,

sing e + r r (Xor;

cos~ e = r r (Xor;

d (W 2) = 2r e (Xe; W2

in t h r o u g h - e t c h e d

1 o) cosg r

Xor = Xoe + r e (Xc; r e (Xc;

diameter

parameter

d (W I) = 2r r (Xor; WI

i. H o l e

see

r r (Xor ; Ro) = h - i o + R o sin@

., -r° V -I

Xor

(x) dx

text

T a b l e i g i v e s the f o r m u l a e for p e r p e n d i c u l a r tracks as for those the d i a m e t e r d and d e p t h h h (i.e. the d i s t a n c e from the o r i g i n a l s u r f a c e ) of the holes are p a r t i c u l a r l y v a l u a b l e p a r a m e t e r s for e v a l u a t i o n . We d i s t i n g u i s h b e t w e e n three p o s s i b l e cases, d e n o t e d by WI, W 2 and W 3 as i l l u s t r a t e d in Fig. la. W I c o r r e s p o n d s to a p a r t i c l e r a t h e R o l a r g e r than the t h i c k n e s s 1 o of the d e t e c t o r . W 2 and W 3 r e p r e s e n t s i t u a t i o n s w h e r e R o < 1 o and the locus of p e r f o r a t i o n P is s i t u a t e d on the l a t e n t t r a c k (W2) or in the b u l k (W3). F i g u r e Ib s k e t c h e s a s i t u a t i o n , w h i c h is t r e a t e d in our c a l c u l a t i o n s : the d i a m e t e r of the hole, w h i c h d e v e l o p s a f t e r p e r f o r a t i o n r e p r e s e n t s a c o n v e n i e n t p a r a m e t e r w h i c h can be m e a s u r e d a d d i t i o n a l l y to the two s u r f a c e t r a c k d i a m e t e r s . W 3 d o e s n t y i e l d such an e t c h t r a c k and is o m i t t e d from our c o n s i d e r a t i o n s as it can be d e s c r i b e d by the w e l l k n o w n f o r m u l a e for the surface track d i a m e t e r s d e r i v e d for t h i c k d e t e c t o r s (e.g. S o m o g y i and c o w o r k e r s , 1977).

W1

s; z/ V[,//'/J

Ill

&

a) Fig.

la, b: Hole

bJ formation

in thin SSNTD.

For d e t a i l s

see text.

T R A C K kIT('H FOR~i,,\ FION IN T H I N SSNTD

In order to make use of the formulae given in Table 1 for particle spectroscopy one can proceed as follows:

13

i d e n t i f i c a t i o n or energy

Having measured the surface diameters D e and D r and the hole diameter d, one calculates a trial R o and an assumed etch rate ratio V(x) D e and D r using the formulae for thick detectors. By x we denote the coordinate along the track.

for

d as g i v e n in Table 1 for W 1 and W 2 is calculated for the same R o and V (x) after the set of the two equations for Xoe and Xor has been solved in a s e l f c o n s i s t e n t way by iteration. Xoe and Xor are the coordinates of the centres of the two spheres, the intersection of which is the contour of the hole. The corresponding radii are denoted by r e and r r . ~ e and ~ are the angles between the plane of the hole and the respective radii r e and r r pointing to the contour of the hole. x c is the critical distance of the latent track and is n o r m a l l y assumed to be zero for p e r p e n d i c u l a r tracks. (Somogyi and coworkers, 1976). We have x c included, however, in our formulae, as for W I they can be modified to hold also for slightly tilted tracks by replacing i o by l o / s i n 0 , 8 being the incident angle. The formulae for d are valid as long as the conditions given in Table i hold, meaning that the contour of the hole did not merge with the etched surface yet. By v a r i a t i o n of R o and V (x) one finally archieves an o p t i m u m fit of the experimental and calculated values of De, D r and d thus identifying the energy (range) and type for the particle. This method gives best results for light particles with low energies because of the strong variation of V (x) in the detector.

RESULTS The a p p l i c a t i o n of the formulae describing the hole formation in thin CR-39 is of importance e.g. for the production of nucleopores. Because of the sensitivity and homogenity of CR-39, n u c l e o p o r e s w i t h well defined, sharp hole contours can be made using ~ particles or protons. Figure 2 shows the e v o l u t i o n of holes in a i00 ~ m thick CR-39 foil, which are due to particles of different ranges R o. The etch rate ratio has been assumed as given by Somogyi and Hunyadi (1979) 2) . Figure 2 shows the strong dependance of d on R o.

50

-

,

-

w

-

m

-

|

•

0

Fig. 2. Hole d i a m e t e r d vs thickness h of removed layer for different CR-39.

2) V (x) = I + exp (-0.034

(Ro-x) + 1.57), R o and x in[ ~ m]

particle ranges R o in

16

G. A I M A S I a n d t 3 . K U N S ( I t

REFERENCES Fews A.P. and D. L. Henshaw (1981). High Resolution Alpha Particle Spectroscopy Using CR-39 Plastic Track Detectors. Bristol Report BSSITL. Somogyi G., R. Scherzer, K. Gabrish and W. Enge (1977). A Spatial Track Formation Model and its Use for Calculating Etch-Pit Parameters of Light Nuclei. Nucl. Instr. and Meth., 147, 11-18. Somogyi G. and I. Hunyadi (1979). Etching Proporties of the CR-39 Polymer Nuclear Track Detectors. Proc. of lOth Int. Conf. on SSNTD, Lyon, 443-451. Somogyi G. and G. Almasi (1979). Etch Pit Formation in Thin Foils and a Conductrometric Study of Hole Parameters. Proc. of lOth Int. Conf. on SSNTD, Lyon, 257-266. Somogyi G., K. Gabrish, R. Scherzer and W. Enge 1976. Revision of the Concept of Registration Threshold in Plastic Track Detectors. Nucl. Instr. and Meth., 134, 129-149. Tarle G., S.P. Ahlen and P.B. Price (1981). Energy Straggling Eliminated as a Limitation to Charge Resolution of Transmission Detectors. Nature 293, 556-560.