822 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



Using eq. (1) 



d = I ^^^ ~ ^^2 I ,^s 



(tan2 0^ ^ tan2 ^2-2 tan Bi tan 02 cos (^2 - ^1))* 



For a given replica film the intrinsic resolution d varies simply as the sine 

 of the azimuth of the hne of intersection. For example, if da = 30°, d varies 

 from J/o down to zero. But observable resolution is closely connected with 

 contrast, as is indicated by eq. (7). One could not hope to observe good 

 resolution if present, unless the thickness difference were at least two or 

 three times the minimum perceptible thickness difference. In micrographs, 

 because of the greater contrast characteristic of the azimuth j8 c^ 90°, the 

 resolution always appears best in the vicinity of the plane of incidence of 

 the atom beam. The average thickness in the direction of the electron beam 

 is /, = ta cos Ba and hence: 



<i = /, tan 0a I sin /3 I (8) 



For Ba = 30°, sin /3 = 1, f/ = 0.577 J,. If an attempt is made to improve 

 resolution by decreasing Ba, contrast is again reduced. It may be concluded 

 that the observable intrinsic resolution of an incidence-shaded replica film is 

 not less than half the average thickness tg . 



b) Diffusion and Combined Shading 

 With pure diffusion shading, 



d = tn [sin^ Bi + sin^ B2 - 2 sin Bi sin B2 cos (^2 - ^1)]* (9) 



Figure 2(b) illustrates this case for <pi = <P2 -\- tt. From eq. (4), for a = 



0, I /el - /. 



, since tn = ta cos Ba ~ . Study of these 



11. ^0 



— dinrp /._ = /,_ rr»<!, ft- 



COS Bi COS 02 



two equations, for resolution and contrast respectively, shows that resolu- 

 tion is highly dependent on the relation of the local directions Wi and W2 to 

 the incident electron beam: Values of d observable from a contrast stand- 

 point frequently exceed te, and are less than ^te only when the two inter- 

 secting planes are fairly steep (0i and 02 > 60°) and are not too far apart 

 in azimuth (^2 ^^ <P\)- Hence the above conclusion also applies to pure diffu- 

 sion shading, and consequently to combined shewing such as thai of a silica 

 replicdf except possibly for special situations on steep slopes. 



c) Shadow-edges 



Shadow-edges are always due to the atoms that stick where they first 

 strike, even though, as in the case of sihca, part of the condensing material 

 diffuses over the surface. Figure 17 illustrates the formation of a shadow- 



