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Correction of Auger peak-to-peak height distortions caused by a difference in the values of coordination number of atoms
Vacuum/volume36/numbers 7-9/pages 441 to 443/1986
O042-207X/86S3.00+.O0 Pergamon Journals Ltd
Printed in Great Britain
Correction of Auger peak-to-peak height distortions caused by a difference in the values of coordination number of atoms R S i u d a , A B u k a l u k and M R o z w a d o w s k i , Instytut Matematyki i Fizyki, Akademia Techniczno-Rolnicza. ul
Kaliskiego 7, 85-790 Bydgoszcz, Poland
During the early stages of an overlayer formation the energy of interaction of some substrate and overlayer atoms may change. As a consequence the resultant Auger line may comprise some number of lines, contributions of which change during the overlayer growth. Thus, variability of the line shape may noticeably distort the values of measured Auger peak-to-peak heights. A method has been proposed allowing correction of these distortions.
Introduction In the studies of kinetic processes by Auger electron spectroscopy (AES) recording of many spectra is needed. In such studies the commonly used measure of intensity of Auger lines is Auger peakto-peak height (APPH), since it does not necessitate any moreinvolved and time-consuming treatment of the recorded spectra. However, in the case when the shape of Auger lines changes during the investigated processes, the use of this simplest measure may involve errors too large to be neglected. There is a number of experimental observations which indicate that during formation of very thin layers the shape of both the substrate and the adsorbate Auger line may change x. One of the reasons for the changes of Auger line shape is that such lines may comprise a number of components related to atoms which have either different coordination numbers (CN's) or a different kind of surrounding atoms. For example, in the case of a clean and smooth substrate the substrate atoms can be divided, at least, in two classes--atoms lying in the upmost layer and atoms lying in a deeper region. In general, it seems reasonable to expect that atoms with different energies of interaction may emit Auger electrons revealing some shifts of their kinetic energy. The relative contributions of these shifted components change as the overlayer grows. In such a way they involve variability of the shape of the resultant line. If these shifts are large enough then the effect of variability of the line shape must noticeably disturb the values of the measured APPH's. One of the most important factors in quantitative AES is the inelastic mean free path (IMFP) of electrons. This quantity can be derived from the value of transmission coefficient (sometimes called the attenuation factor) 2-4 of Auger and primary electrons. The latter can be directly obtained from APPH vs 0 relationships, if the model of these relationships is known. However, none of models known at present 2-6 takes into account the effect of variability of the line shape. We are of the opinion that the neglect of the changes of the shape of Auger lines in applied models may be the source of error in determination of I M F P and/or in the detailed interpretation of APPH vs 0 relationships.
The value of distortions of the substrate APPH's depends on a number of parameters, i.e. on the ratio of intensities of surface to bulk components for a clean substrate ( I ° / I ° ) , on the transmission coefficient of electrons (s), on the energy shift between surface and bulk Auger electrons (el), and on the energy shifts between Auger electrons emitted by the adsorbate-covered and uncovered atoms (e~a).Most recently we presented selected APPH vs 0 plots calculated for the case when the overlayer grows in a layer-bylayer (LBL) mode 7. The value of distortions in some cases may reach the value of some tens of per cent.
Method of correction of the substrate APPH's We now give an example how to correct experimentally obtained substrate APPH vs 0 plots, in order to determine the true value of the transmission coefficient s and undisturbed APPH vs 0 functions. As an example we take some arbitrarily chosen but realizable set of parameters listed at the end of the previous section, i.e. 1 ° / l ° = 1 . 6 , s=0.4, e ~ = - e ~ , = 0 . 4 . F , where ~s-sE~ - E b, e] = E a - E s and E~, E b and E a are energies of components related to surface, bulk and adsorbate-covered substrate atoms, respectively. We also assume that all the components reveal Lorentzian shape with a common F W H M equal to F. The additional assumption is that the second and further monolayers of an overlayer do not influence the energy of the substrate atoms. Calculations performed under the above assumptions for the LBL mode of growth lead to the relationship denoted ABCD in Figure la, and to ABCD in Figure lb. A E / A E o in Figure lb is the relative width of the resultant substrate Auger line (AE0 is the line width of a clean substrate). In order to determine quantitatively normalized APPH (NAPPH) functions we adjust predictions of the Gallon model 5 in the form given in 6. We have: k
h~=l-(1-s)
~
Oi s i - 1 ,
(1)
i=1
where hi is NAPPH, s is the transmission coefficient, 0~ is the coverage of the ith monolayer of the overlayer and k is the number 441
R Siuda, A Bukaluk and M R o z w a d o w s k i : Correction of Auger peak-to-peak height distortions
The question arises, however, as to whether the introduced correction factor can be applied when other than LBL modes of growth are observed. With the aim of answering this question we performed calculations for two modes of growth like the V o l m e r - W e b e r one. In the first case we assumed that two monolayers grow simultaneously (01 = 02) and in the second one that three monolayers grow simultaneously (01 =02 =03). The obtained relationships for N A P P H are given as curves A C D and AD, respectively (Figure la). The relative widths for these cases are shown in Figure lb. If one plots the ratio of h ks to h ks as a function of A E / A E o, the c o m m o n curve for both cases shown in Figure 2 may be obtained. Moreover, this curve is the same as obtained for the LBL case. Therefore, one can see that A E / A E o may be an important and convenient parameter in the correction procedure, since it allows one to give a simple relation:
1 .8
D D'
\
s
hk = x
S
(6)
" hk"
1.3
1.2 0
1
~
2
3C
3
Figure 1. (a) The dependences of the normalized Auger peak-to-peak heights (NAPPH) on the total coverage 0 (0 = E0.), for different modes of growth. Curve ABCD is the distorted plot for the layer-by-layer (LBL) mode of growth, obtained on the basis of calculations performed under assumptions specified in the text. Curve AB'C'D' is the corrected plot of the LBL mechanism of growth obtained by the use of relation (1). Curves ACD and AD are the distorted plots corresponding to a Volmer-Weber type mechanism of growth, in the case when 01=02 (ACD) and 0~=02=0 a (AD). AC'D' and AD' are the corrected plots for such mechanisms of growth. (b) The dependences of the relative Auger line width A E / A E o on the coverage 0. AE 0 is Auger line width of clean substrate and AE is the line width for a given 0. The denotations of curves are the same as in Figure la. of monolayers existing in the overlayer. Introducing a correction factor, the value of which depends on 0~, we can write: *h~ = x ( O x ) ' h
~ =x(01) • [1-(1-s)01],
(2)
where *h~ is the measured N A P P H and x(O 0 is the correction factor. F o r 01 = 1 we have: *h~l ~ = x(1)" s, whereafter for 0~ = 1 and 0 < 0 2 4
(3) 1 we obtain:
*h i = x ( 1 ) • [1 - ( 1 - s ) ( 1 + 02s)].
(4)
Thus, using the values of *h~l ) and of the slope of the function at the points where the second monolayer grows (given as ct2 = x(1)' (1-s)s), we can determine the true value of s: s = 1 -- ~2/*h~Sl) .
(5)
We are thus able to determine the true value ofs based on the plot of disturbed values of N A P P H as a function of coverage for the LBL mode of growth. Since for known structure of the overlayer (i.e. for a given 0~, i = 1, 2 . . . . k) the N A P P H values in (1) depend on the value of s only, then it is possible to draw the undisturbed plot of N A P P H vs 0, i.e. A B ' C ' D ' in Figure la. 442
1.1
.7
.8 -4 E .9
7.0
z~ E o
Figure 2. The dependence of the correction factor x on the relative line width AE/AE o.
So, if one knows x ( A E / A E o ) determined from the LBL mode of growth, then one can determine the corrected N A P P H vs 0 relationships for other modes of growth, based on the measured values of A P P H and the measured values of the relative line width.
Conclusions We have applied the method of correction of measured A P P H ' s of the substrate line during early stages of the overlayer growth to the case when E b = E , g : E s. This is not the only possibility. Therefore, it is essential to decide when the presented method of correction is valid. The basic assumptions of the method are that the second and further monolayers of the overlayer do not change the shape of the line and that one and only one value of correction factor may be ascribed to the particular value of the line width. F o r any substrate-adsorbate system both the assumptions may be checked in the LBL experiment by observation of the line width. If they appear to be valid, then the method can be applied to any other mechanism of growth, independently of the values of E s, E b and E,.
Acknowledgement This work was partly supported by PR-3 project.
R Siuda, A Bukaluk and M Rozwadowski: Correction of Auger peak-to-peak height distortions
References 1 S S Chao, E -A Knabbe and R W Voock, Surface Sci, 100, 581 (1980); S S Chao, R W Vook and Y Namba, J Vac Sci Technol, 18, 695 (1981); Y Namba, R W Vook and S S Chao, Surface Sci, 109, 320 (1981); Y Namba and R W Vook, Thin Solid Films, 82, 165 (1981); R W Vook and Y Namba, Appl Surface Sci, 11]12, 400 (1982); R Siuda, Surface Sci, 123, L667 (1982); G Kaindl, T -C Chiang and T Mandel, Phys Rev B, 28, 3612 (1983); M Y Zhou, R H Milne, M A Karolewski, D C Frost and K A R Mitchel, Surface Sci, 139, El81 (1984). 2 j p Biberian and G A Somorjai, Appl Surface Sci, 2, 352 (1979). 3 M P Scab, Surface Sci, 32, 703 (1972).
4 F Londry and A J Slavin, J Vac Sci Technol A, 1, 44 (1983). T E Gallon, Surface Sci, 17, 486 (1969); D C Jackson, T E Gallon and A Chambers, Surface Sci, 36, 381 (1973); M L Tarng and G K Wehner, Jappl Phys, 44, 1534 (1973); C C Chang, in Characterization of Solid Surface, (Edited by P F Kane and G B Larrabee), Plenum, New York (1974); R Memeo, F Ciccacci, C Mariani and S Ossicini, Thin Solid Films, 109, 159 (1983); F C M J M van Delft, A D van Langeveld and B E Nieuwenhuys, Thin Solid Films, 123, 333 (1985). 6 R Siuda, Surface Sci, 140, 472 (1984). 7R Siuda, A Bukaluk and M Rozwadowski, Acta Univ Wratislav, No 937, 131 (1986).
443
O042-207X/86S3.00+.O0 Pergamon Journals Ltd
Printed in Great Britain
Correction of Auger peak-to-peak height distortions caused by a difference in the values of coordination number of atoms R S i u d a , A B u k a l u k and M R o z w a d o w s k i , Instytut Matematyki i Fizyki, Akademia Techniczno-Rolnicza. ul
Kaliskiego 7, 85-790 Bydgoszcz, Poland
During the early stages of an overlayer formation the energy of interaction of some substrate and overlayer atoms may change. As a consequence the resultant Auger line may comprise some number of lines, contributions of which change during the overlayer growth. Thus, variability of the line shape may noticeably distort the values of measured Auger peak-to-peak heights. A method has been proposed allowing correction of these distortions.
Introduction In the studies of kinetic processes by Auger electron spectroscopy (AES) recording of many spectra is needed. In such studies the commonly used measure of intensity of Auger lines is Auger peakto-peak height (APPH), since it does not necessitate any moreinvolved and time-consuming treatment of the recorded spectra. However, in the case when the shape of Auger lines changes during the investigated processes, the use of this simplest measure may involve errors too large to be neglected. There is a number of experimental observations which indicate that during formation of very thin layers the shape of both the substrate and the adsorbate Auger line may change x. One of the reasons for the changes of Auger line shape is that such lines may comprise a number of components related to atoms which have either different coordination numbers (CN's) or a different kind of surrounding atoms. For example, in the case of a clean and smooth substrate the substrate atoms can be divided, at least, in two classes--atoms lying in the upmost layer and atoms lying in a deeper region. In general, it seems reasonable to expect that atoms with different energies of interaction may emit Auger electrons revealing some shifts of their kinetic energy. The relative contributions of these shifted components change as the overlayer grows. In such a way they involve variability of the shape of the resultant line. If these shifts are large enough then the effect of variability of the line shape must noticeably disturb the values of the measured APPH's. One of the most important factors in quantitative AES is the inelastic mean free path (IMFP) of electrons. This quantity can be derived from the value of transmission coefficient (sometimes called the attenuation factor) 2-4 of Auger and primary electrons. The latter can be directly obtained from APPH vs 0 relationships, if the model of these relationships is known. However, none of models known at present 2-6 takes into account the effect of variability of the line shape. We are of the opinion that the neglect of the changes of the shape of Auger lines in applied models may be the source of error in determination of I M F P and/or in the detailed interpretation of APPH vs 0 relationships.
The value of distortions of the substrate APPH's depends on a number of parameters, i.e. on the ratio of intensities of surface to bulk components for a clean substrate ( I ° / I ° ) , on the transmission coefficient of electrons (s), on the energy shift between surface and bulk Auger electrons (el), and on the energy shifts between Auger electrons emitted by the adsorbate-covered and uncovered atoms (e~a).Most recently we presented selected APPH vs 0 plots calculated for the case when the overlayer grows in a layer-bylayer (LBL) mode 7. The value of distortions in some cases may reach the value of some tens of per cent.
Method of correction of the substrate APPH's We now give an example how to correct experimentally obtained substrate APPH vs 0 plots, in order to determine the true value of the transmission coefficient s and undisturbed APPH vs 0 functions. As an example we take some arbitrarily chosen but realizable set of parameters listed at the end of the previous section, i.e. 1 ° / l ° = 1 . 6 , s=0.4, e ~ = - e ~ , = 0 . 4 . F , where ~s-sE~ - E b, e] = E a - E s and E~, E b and E a are energies of components related to surface, bulk and adsorbate-covered substrate atoms, respectively. We also assume that all the components reveal Lorentzian shape with a common F W H M equal to F. The additional assumption is that the second and further monolayers of an overlayer do not influence the energy of the substrate atoms. Calculations performed under the above assumptions for the LBL mode of growth lead to the relationship denoted ABCD in Figure la, and to ABCD in Figure lb. A E / A E o in Figure lb is the relative width of the resultant substrate Auger line (AE0 is the line width of a clean substrate). In order to determine quantitatively normalized APPH (NAPPH) functions we adjust predictions of the Gallon model 5 in the form given in 6. We have: k
h~=l-(1-s)
~
Oi s i - 1 ,
(1)
i=1
where hi is NAPPH, s is the transmission coefficient, 0~ is the coverage of the ith monolayer of the overlayer and k is the number 441
R Siuda, A Bukaluk and M R o z w a d o w s k i : Correction of Auger peak-to-peak height distortions
The question arises, however, as to whether the introduced correction factor can be applied when other than LBL modes of growth are observed. With the aim of answering this question we performed calculations for two modes of growth like the V o l m e r - W e b e r one. In the first case we assumed that two monolayers grow simultaneously (01 = 02) and in the second one that three monolayers grow simultaneously (01 =02 =03). The obtained relationships for N A P P H are given as curves A C D and AD, respectively (Figure la). The relative widths for these cases are shown in Figure lb. If one plots the ratio of h ks to h ks as a function of A E / A E o, the c o m m o n curve for both cases shown in Figure 2 may be obtained. Moreover, this curve is the same as obtained for the LBL case. Therefore, one can see that A E / A E o may be an important and convenient parameter in the correction procedure, since it allows one to give a simple relation:
1 .8
D D'
\
s
hk = x
S
(6)
" hk"
1.3
1.2 0
1
~
2
3C
3
Figure 1. (a) The dependences of the normalized Auger peak-to-peak heights (NAPPH) on the total coverage 0 (0 = E0.), for different modes of growth. Curve ABCD is the distorted plot for the layer-by-layer (LBL) mode of growth, obtained on the basis of calculations performed under assumptions specified in the text. Curve AB'C'D' is the corrected plot of the LBL mechanism of growth obtained by the use of relation (1). Curves ACD and AD are the distorted plots corresponding to a Volmer-Weber type mechanism of growth, in the case when 01=02 (ACD) and 0~=02=0 a (AD). AC'D' and AD' are the corrected plots for such mechanisms of growth. (b) The dependences of the relative Auger line width A E / A E o on the coverage 0. AE 0 is Auger line width of clean substrate and AE is the line width for a given 0. The denotations of curves are the same as in Figure la. of monolayers existing in the overlayer. Introducing a correction factor, the value of which depends on 0~, we can write: *h~ = x ( O x ) ' h
~ =x(01) • [1-(1-s)01],
(2)
where *h~ is the measured N A P P H and x(O 0 is the correction factor. F o r 01 = 1 we have: *h~l ~ = x(1)" s, whereafter for 0~ = 1 and 0 < 0 2 4
(3) 1 we obtain:
*h i = x ( 1 ) • [1 - ( 1 - s ) ( 1 + 02s)].
(4)
Thus, using the values of *h~l ) and of the slope of the function at the points where the second monolayer grows (given as ct2 = x(1)' (1-s)s), we can determine the true value of s: s = 1 -- ~2/*h~Sl) .
(5)
We are thus able to determine the true value ofs based on the plot of disturbed values of N A P P H as a function of coverage for the LBL mode of growth. Since for known structure of the overlayer (i.e. for a given 0~, i = 1, 2 . . . . k) the N A P P H values in (1) depend on the value of s only, then it is possible to draw the undisturbed plot of N A P P H vs 0, i.e. A B ' C ' D ' in Figure la. 442
1.1
.7
.8 -4 E .9
7.0
z~ E o
Figure 2. The dependence of the correction factor x on the relative line width AE/AE o.
So, if one knows x ( A E / A E o ) determined from the LBL mode of growth, then one can determine the corrected N A P P H vs 0 relationships for other modes of growth, based on the measured values of A P P H and the measured values of the relative line width.
Conclusions We have applied the method of correction of measured A P P H ' s of the substrate line during early stages of the overlayer growth to the case when E b = E , g : E s. This is not the only possibility. Therefore, it is essential to decide when the presented method of correction is valid. The basic assumptions of the method are that the second and further monolayers of the overlayer do not change the shape of the line and that one and only one value of correction factor may be ascribed to the particular value of the line width. F o r any substrate-adsorbate system both the assumptions may be checked in the LBL experiment by observation of the line width. If they appear to be valid, then the method can be applied to any other mechanism of growth, independently of the values of E s, E b and E,.
Acknowledgement This work was partly supported by PR-3 project.
R Siuda, A Bukaluk and M Rozwadowski: Correction of Auger peak-to-peak height distortions
References 1 S S Chao, E -A Knabbe and R W Voock, Surface Sci, 100, 581 (1980); S S Chao, R W Vook and Y Namba, J Vac Sci Technol, 18, 695 (1981); Y Namba, R W Vook and S S Chao, Surface Sci, 109, 320 (1981); Y Namba and R W Vook, Thin Solid Films, 82, 165 (1981); R W Vook and Y Namba, Appl Surface Sci, 11]12, 400 (1982); R Siuda, Surface Sci, 123, L667 (1982); G Kaindl, T -C Chiang and T Mandel, Phys Rev B, 28, 3612 (1983); M Y Zhou, R H Milne, M A Karolewski, D C Frost and K A R Mitchel, Surface Sci, 139, El81 (1984). 2 j p Biberian and G A Somorjai, Appl Surface Sci, 2, 352 (1979). 3 M P Scab, Surface Sci, 32, 703 (1972).
4 F Londry and A J Slavin, J Vac Sci Technol A, 1, 44 (1983). T E Gallon, Surface Sci, 17, 486 (1969); D C Jackson, T E Gallon and A Chambers, Surface Sci, 36, 381 (1973); M L Tarng and G K Wehner, Jappl Phys, 44, 1534 (1973); C C Chang, in Characterization of Solid Surface, (Edited by P F Kane and G B Larrabee), Plenum, New York (1974); R Memeo, F Ciccacci, C Mariani and S Ossicini, Thin Solid Films, 109, 159 (1983); F C M J M van Delft, A D van Langeveld and B E Nieuwenhuys, Thin Solid Films, 123, 333 (1985). 6 R Siuda, Surface Sci, 140, 472 (1984). 7R Siuda, A Bukaluk and M Rozwadowski, Acta Univ Wratislav, No 937, 131 (1986).
443