E Dobroèka, P Novák, D Búc
The pres ence of re sid ual stresses in the near sur face re gion of bulk ma te ri als and in thin films is a gen eral prob lem of var i ous tech nol o gies. Among a num ber of meth ods de vel-oped for stress anal y sis, X-ray dif frac tion meth ods are of spe cial im por tance due to their ca pa bil ity to an a lyze the depth vari a tion of the re sid ual stresses. Since the first stress de ter mi na tion by X-ray dif frac tion in the 1930s a large va-ri ety of mea sur ing meth ods and eval u
more » ... eth ods and eval u a tion pro ce dures were de vel oped. While the stan dard sin 2 y method can be eas ily used for bulk ma te ri als, it is not ap pli ca ble for thin films, where steep stress gra di ent per pen dic u lar to the sample sur face can be pres ent. In this case the meth ods based on graz ing in ci dence (GI) setup are more ap pro pri ate. The con stant (and usu ally small) an gle of in ci dence a, that is a char ac ter is tic fea ture of GI X-ray dif frac tion, en sures that the in for ma tion depth does not change dur ing the mea sure-ment. The GI method of stress de ter mi na tion is clas si fied as mul ti ple {hkl} mode in com par i son with the sin 2 y method, that uses only one set of {hkl} planes while the angle of sam ple in cli na tion c var ies. The GI method is based on the fact that all dif frac tion vec tors con trib ut ing to the GI dif frac tion pat tern make dif fer ent an gles with the sur face nor mal of the sam ple and pro vide suf fi cient set of data for stress eval u a tion. How ever, this method of stress mea sure-ment fails if the an a lyzed layer is strongly tex tured. In this case the ori en ta tion of the dif frac tion vec tors is sharply local ized and the num ber of dif frac tions reg is tered in the mea sure ment per formed at con stant a and c (usu ally c = 0°) may be in suf fi cient for the eval u a tion of the stress state. In the pre sented con tri bu tion a mod i fied method com-bin ing mul ti ple {hkl} and mul ti ple c modes of stress measure ments is out lined. Mea sur ing at c ¹ 0° can sig nif i cantly in crease the num ber of ac ces si ble dif frac tions. The an a-lyzed film is sup posed to have a fi bre tex ture with the texture axis par al lel to the sur face nor mal. The most prob a ble val ues of an gles y be tween the dif frac tion vec tors and the di rec tion are cal cu lated from sin gle crys tal data. In or der to mea sure the dif frac tion with Bragg an gle q at se lected angle of in ci dence a, the tilt ing an gle c and the ro ta tion an gle w of the goniometer have to be cal cu lated ac cord ing to re la-tions cos cos cos sin sin sin cos 2 2 2 2 2 c y y q a a q =-+ and sin sin cos w a c =. Due to ro ta tional sym me try of the tex ture there is no spe cific re stric tion for the az i muthal an gle j. The de scribed method was used for eval u a tion of bi-axial stress in ZnO lay ers de pos ited on (111) GaP sub-strates. The stress mea sure ments were per formed on as de pos ited sam ples and re peated af ter an neal ing at 300 °C for 1 hour in N 2 at mo sphere. The de tails of sam ple prep a ration are given else where [1]. The lay ers ex hibit strong fi bre tex ture with [001] axis per pen dic u lar to sam ple sur face, the 002 pole fig ure is shown in Fig. 1. Due to this tex ture, only three dif frac tions (002, 103 and 203) with suf fi cient in ten-si ties can be used for stress eval u a tion, when the dif frac tion pat tern is re corded in stan dard GI setup with a = 1.5° and c = 0°. How ever, polycrystalline hex ag o nal ZnO pro vides 20 dif frac tions in the range 2q < 122° (for Cu K a ra di a tion) with rel a tive in ten si ties above 1%, 17 of them are ac ces si-ble by an ap pro pri ate choice of an gles c and w for a constant an gle of in ci dence a = 1.5°. Ten stron gest dif frac tions were mea sured for dif fer ent val ues of y around the ideal an gle cor re spond ing to sin gle crys tal data. Fig ure 1. 3D Pole fig ure 002 of ZnO layer mea sured within the an gu lar range c = 0°-30°.