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Sodium depletion on glass surfaces during auger analysis
Surface Science 110 (1981) 261-269 North-Holland Publishing Company
261
SODIUM DEPLETION ON GLASS SURFACES DURING AUGER ANALYSIS
*
P.G. WHITKOP E.I. du Pont de Nemours and Co., Savannah River Laboratory, Aiken, South Carolina29808, USA Received 8 may 1981; accepted for publication 30 June 1981
The kinetics of the depletion of sodium on glass surfaces during Auger Electron Spectroscopic analysis is investigated. The decay process is mathematically represented as a sum of two single decaying exponential functions. This behavior may be described by a mechanism that accounts for the neutralization of sodium ions by the electron beam. Sodium ions and neutral sodium atoms are depleted by several known processes.
1. Introduction The analysis of glass surfaces is extremely important in the determination of various corrosion processes acting upon glass-immobilized nuclear waste in underground repositories. In particular, the analysis of various alkali and alkaline earth ions, especially sodium ions, is of great importance to the determination of the mechanism of glass leaching by groundwater. One widely used method of glass surface analysis is Auger Electron Spectroscopy (AES), coupled with argon ion sputter etching [l-4]. This technique is capable of determining glass composition at various depths from the glass surface. Early work using AES on glass demonstrated an inability to detect sodium, although large concentrations were known to be present [5,6]. This was explained by the fact that the electron beam of the Auger analyzer caused a negative charge build-up below the glass surface in the manner first proposed by Lineweaver [7]. The sodium ions migrate away from the surface toward the region of negative charge. Other effects, such as stimulated electron desorption and localized heating, also give rise to the loss of sodium from the glass surface during AES analysis. Electron microprobe studies indicate that the kinetics of the sodium removal process follow an exponential decay, preceded by an incubation period, during which the concentration of sodium ions remains constant [8-lo]. In one AES analysis, however, the portion of the curve following the incubation period was * The information contained in this article was developed during the course of work under Contract No. DE-AC09; 76SROOOOl with the US Department of Energy.
0039-6028/81/0000-0000/$02.50
0 1981 North-Holland
262
P.G. Whitkop / Na depletion on glass surfaces during Auger analysis
represented by the form A [ 1-B ln(t/t,-,)] , in which to is the incubation time, t > to, and A and B are constants [2]. In this study, AES was used to probe the sodium removal process in two types of glass. The experimental evidence suggests that this process is characterized by a sum of two exponential decay curves, each with different decay constants and preexponential factors. These results are interpreted within the context of the mechanism proposed by Lineweaver [7].
2. Experimental
measurements
Measurements were carried out on two types of glass, with compositions shown in table 1. The glass buttons, S/8 inch in diameter by l/8 inch thick, were polished to 600 grit, mounted on a thirty-degree carousel, and placed in the bell jar of a Physical Electronics Model 545 Scanning Auger Microprobe, which is equipped with a cylindrical mirror analyzer. All of the data were obtained at room temperature. The surfaces of the glass buttons, once placed into the spectrometer, received no further treatment. In particular, argon ion bombardment of the glass surface was avoided, since this technique can alter the physical and chemical properties of the
Table 1 Compositions of glasses used in this study Glass
Compound
Weight percent
A
SiO2
52.5
B203
10.0 18.5 4.0 5.0 10.0
Naz 0 Liz0 CaO TiO2 B
SiO2 B203
NazO Liz0 CaO Ti02 Fe203 A1203
Mn02 NiO NazS04 AWSOOa) a) A mixture of CaAIzSQ012
37.3 7.2 15.0 3.0 4.7 7.2 13.4 2.8 3.8 1.8 0.4 2.4
.6 Hz0 and (Ca, Naz, Kz) A12Si10024 . 7 HzO.
P.G. Whitkop/ Na depletion on glasssurfaces during Auger analysis
263
glass surface. With argon ion bombardment, there is a possibility that sodium ions may be reduced to sodium metal, complicating the experimental results obtained with the analyzer beam. A suitable position for analysis was determined with elastically scattered electons. The beam energy and current were adjusted prior to the electron beam shut-down. Once the analyzer beam was turned off, the sample was moved to a new position so that another portion of the sample was analyzed. The moment that the electron beam was reactivated was considered as zero time for kinetic analysis.
3. Results and discussion Figs. 1 and 2 show plots of the log, of the sodium peak height (in arbitrary units) versus the analyzer beam bombardment time. Fig. 1 shows the sodium decay characteristics of the surface of Glass A; fig. 2 represents the removal of sodium
1
I
I
.2
.6
I
I
I
1.0 Time rn~n
1.4
1.8
Fig. 1. Plot of log, of peak height versus time for Glass A.
P.G. Whitkop / Na depletion on glass surfaces during Auger analysis
264
r
.2
.6
1.0
1.4
1.6
Time, mm
Fig. 2. Plot of log, of peak height
versus time for Glass B.
from Glass B. The important feature to note is that for each of these curves, there are two distinct linear segments. For the data shown in figs. 1 and 2, the incubation period preceding sodium removal from the glass surface was negligible. During the course of these studies, however, experimental conditions were found in which the incubation period was observable. The presence of the two linear portions in the decay curve is indicative of a mathematical expression of the form Ai = A 1 exp(-Mi)
+ AZ exp(-flti)
.
(1)
The exponents CYand /3 along with coefficients Al and A2 can be determined. The linear segment at longer bombardment times is extrapolated to zero time. For this line segment, the first exponential term is negligible and the contribution is due only to the second term. A least-squares determination of the slope of the extrapolated curve gives a value for /3, and the intercept corresponds to AZ. A 1 and o are determined by subtracting the expression A2 exp(-&i) from the data points Ai in the short time portion of the curve and performing a least-squares analysis on the
P.G. Whitkop/ Na depletion on glasssurfaces during Auger analysis
265
resulting line. Table 2 lists the calculated values of o, 0, A 1, and Aa for the curves in figs. 1 and 2. The overall double exponential behavior exhibited by Glass A and B under several different beam conditions suggests that the sodium ion initially present in the glass must be partially converted to a second species, with simultaneous removal of both forms. Any depletion mechanism which involves only the participation of sodium ion would produce a decay curve following first order kinetic theory. If sodium ion decay proceeded by migration under the influence of the electron beam and electron stimulated desorption, a decay curve obeying first order kinetics would be observed, with an overal depletion rate contant equal to the sum of the rate contants for depletion by migration and electron stimulated desorption. The intercepts A 1 and AZ are a relative measure of the concentrations of the two sodium species that must be present to account for the double exponential decay curve. The data presented in table 2 shows that the relative amounts of sodium species can change under the influence of the electron beam. As beam current density or voltage increase, Az increases while A 1 decreases. This suggests that the electron beam directly participates in the interconversion of sodium species, or secondary beam effects such as samle heating, are important. The temperature rise on the glass surface under electron bombardment can be significant, but the temperature differential between the glass surface bombarded by an electron beam of 0.1 mm diameter, 3 keV and 5 .O PA or 4 keV and 5 .O PA is estimated to be 24’ at the beam center (calculated using the formulas of ref. [ 111) and a value of 0.01 W/cm * “C for the thermal conductivity). The temperature differential between the two beam conditions is not great, yet the coefficients AI and A2 change significantly. This fact suggests that the electron beam is participating in the production of the second species, not secondary effects of the electron beam, such as sample heating. The consecutive reaction mechanism described above identifies two sodium species that must be formed in order to account for the observed double exponential behavior of the sodium decay profile. J.&reweaver [7] has pointed out that two
Table 2 Analyzed data from tigures 1 and 2 a) Glass
Beam voltage OteV)
Beam current (PA)
Q!b) (min-’ )
Db) (min-’ )
Al b, (arbitrary)
AZ b, (arbitrary)
A
3.0 4.0 3.0 4.0
0.16 3.78 5.00 5.00
0.09 0.32 0.65 0.70
0.33 1.30 1.27 1.50
2.53 1.85 2.10 1.80
0.59 1.33 0.68 1.06
B
(0.03) (0.03) (0.04) (0.05)
(0.07) (0.07) (0.06) (0.09)
(0.05) (0.04) (0.04) (0.03)
a) Coefficients A 1 and A* and exponents [Yand p correspond to q. (1) in the text, b, Numbers in parentheses indicate relative errors.
(0.08) (0.07) (0.07) (0.08)
266
P. G. Whitkop 1 Na depletion on glass surfaces during Auger analysis
types of sodium species are present during the interaction of the glass and the electron beam. These species are sodium ions and neutral sodium atoms, formed by the reduction of sodium ions by the electron beam. The presence of neutral sodium atoms produces the brown discoloration of glasses when they are bombarded with electrons. Although Lineweaver’s mechanism operated at beam voltages between 10 and 27 keV, Dawson has shown that the same mechanism can occur at beam voltages as low as 0.1 keV [ 121. Electron browning is found to occur below the glass surface, but it is not inconceivable that electrons impinging on a glass surface reduce a number of the sodium ions found on the surface. The reduction of surface sodium ions by the electron beam may account for the consecutive reaction mechanism indicated by the double exponential decay described above. No direct evidence for the presence of neutral sodium atoms was obtained. Neutral sodium atoms possess an L2,a W Auger transition at 27 keV [ 131, but this transition was not observed. The complexity of the glass Auger spectrum in this region may have masked the presence of this peak. In terms of a mechanism for the compositional change of sodium during AES analysis of glass, the following scheme is proposed Na’(S,) + e-2
Na’(Sr) ,
Na’(Sr) + e-2
Na’(Sr) + 2 e- ,
Na’(S,) 14: Na’&) Na”(S1)2
@I
,
Na”(S2).
Sr represents the glass surface affected by the electron beam, and Sz represents any area not affected by the beam. In reactions a and b, the beam current density and beam voltage remain constant over time, and these reactions can be represented by a pseudo-first-order equation. Rate constants kr and kz will depend on the beam current density and beam voltage. Constants k3 and k4 represent the total removal rate constants of both Na’ and Na’, respectively. Since Na” is not affected by an accumulation of negative charge beneath the surface, processes such as stimulatedelectron desorption and thermal desorption are probably the dominant removal mechanisms. The rate equations describing the removal of Na’ and Na” are d [Na’]/dt = kz [Na’] - (k, + ka)[Na+] ,
(2)
= kl [Na’] - (kz + k4)[Nao] .
(3)
d[Na’]/dt
Solution of these equations, with k5 = (kz + k4), kg = (kl + k3), and boundary conditions given by [Na’](O) = [Na’] o and [Na’] (0) = 0, produces the following
P.G. Whitkop / Na depletion on glass surfaces during Auger analysis
261
expressions [Na’](t) = ‘:“I]:a”
[(rr - 1) exp(-rr
[NaO](t)= if”:l”’ 1 2
[exp(-r2t) - exp(-rl f)l ,
r1,2=
1(-k,
+k,)+
[(ks
+k6)’ -4(klk2
t) + (1 - rz) exP(-rz t)]
-kgk6)]1’2}/21.
, (5)
(6)
This mechanism predicts the mathematical form that was determined experimentally. The exponent r2 represents the value of fl in eq. (l), and r1 represents cr. Coefficients for the exponentials containing r2 and rr correspond with A2 and AI, respectively. According to table 2, the value of AI decreases with increasing beam current density and beam voltage, while A2 simultaneously increases. Coefficient A 1, therefore, is assigned to the exponential term describing sodium ion decay; AZ represents the coefficient for sodium metal decay. The mechanism of sodium ion depletion by electric field induced migration and electron stimulated desorption (ESD) has been characterized [8,10,14-161. The data described in this work suggests that sodium neutralization may open another sodium depletion channel. Depending upon beam conditions, this channel can account for a significant portion of the overall sodium depletion process. The initial relative concentrations of both sodium species are represented by the coefficients A 1 and AZ. From the data of table 2, where the beam conditions are 4 keV and 3.78 ,uA, the amount of sodium metal, represented by AZ, is 42% of the total amount of sodium in both metallic and ionic forms. Further investigation of table 2 shows that the sodium ion neutralization and decay scheme can depend upon beam voltage alone. This fact can be explained by noting that the rate constant for a two particle reaction can be expressed ask = uu, where k is the rate constant, u is the reaction cross-section and u is the relative velocity of the two particles. Since raising the beam voltage increases the kinetic energy of the electrons in the beam, larger beam voltages can increase the rate constants for the reactions described by eqs. (a) and (b). Differentiating eq. (5), setting it equal to zero and solving for t, gives an equation for the time at which the sodium metal concentration is maximum. Substituting this expression back into eq. (5) shows that the maximum amount of sodium metal produced in the neutralization and decay scheme depends upon the relative magnitudes of the rate constants. Since rate constants kl and k2 depend upon the kinetic energy of the electrons, the intercepts A 1 and A2 should vary when beam voltage is changed. The exact mechanism of the depletion of neutral sodium atoms is not clear from these experiments. Several possibilities include ESD, thermal desorptidn and momentum transfer. Momentum transfer is unlikely because of the extremely small mass of the electron relative to the sodium atom. ESD may occur by several mechanisms [ 171. These include desorption of ground state or excited state neutral sodi-
268
P. G. Whitkop INa depletion on glass surfaces during Auger analysis
urn atoms or desorption of positive sodium ions formed from neutral atoms. This possibility is suggested by eq. (b) of the kinetic scheme. The Auger process can easily account for the formation of sodium ions from neutral atoms. Thermal desorption is possible due to the high temperatures to which the glass may be heated. With the conditions cited previously, the temperature rise of the glass under the influence of a 4 keV, 5 I.IA and 0.1 mm diameter electron beam is on the order of 100°C. This is sufficient temperature rise to account for a thermal desorption process. The double exponential behavior of sodium depletion found in this study appears to be a more general expression of earlier results. In particular, Varshneya, Cooper and Cable [8] reported that potassium, under the influence on an electron microprobe beam, decayed by a process described by the general form [K] = A exp(-at) f B, where A, B and D are constants. During Auger analysis, proper beam conditions can be chosen where one of the two exponential constants becomes small enough so that the corresponding exponential term approaches unity. This reduces the double exponential expression to one which is identical to that described in ref. [S].
4. Conclusion The interaction of an electron beam from an AES analyzer with a glass surface causes sodium to deplete in a manner that can be described by the sum of two exponential decay components. The proposed mechanism that gives rise to this behavior is the neutralization of surface sodium ions by the electron beam. Neutralization is followed by removal of sodium ions and neutral atoms by migration, simulated electron desorption, and localized heating. Kinetic analysis of this mechanism shows that the predicted mathematical form matches the form found experimentally.
The author wishes to thank J.R. Price for his assistance in obtaining data.
the Auger
References [I] C.G. Pantano, Jr., D.B. Dove and G.Y. Onoda, Jr., J. Non-Crystalline Solids 19 (1975) 41.
[2] C.G. Pantano, Jr., D.B. Dove and G.Y. Onoda, Jr., J. Vacuum Sci. Technol. 13 (1976) 414. [3] D.L. Maim, M.J. Vasile, F.J. Padden, D.B. Dove and C.G. Pantano, Jr., J. Vacuum Sci. Technol. 15 (1978) 35. 141 R.A. ChappeIl and C.T.H. Stoddart, Phys. Chem. Glasses 15 (1974) 130.
F. G. Whitkop / Nu ~ep~et~~non glas surfaces during Auger analysis [S] [6] [7] [8] [9]
269
8. Goldstein and DE. Carlson, J. Am. Ceram. Sot. 55 (1972) 51. C.G. Pantano, Jr., A.E. Clark and L.L. Hench, J. Am. Ceram. Sot. 57 (1974) 412. J.L. Lineweaver, J. Appl. Phys. 34 (1963) 1786. A.K. Varshneya, A.R. Cooper and M. Cable, J. Appl. Phys. 37 (1966) 2199. R.G. Gossink, H. Von Doveren and J.A.T. Verhoeven, J. Non-Crystalline Solids 37 (1980) 111. [lo] L.F. Vassamillet and V.E. Caldwell, J. Appl. Phys. 40 (1969) 1637. [ll] G.S. Almasi, J. Blair, R.E.0~~eandR.J. Schwartz, J. App~.Phys. 36 (1965) 1848. [12] P.H. Dawson, Nuovo Ciiento Suppl. 5 (1967) 612. [ 13J A.P. Janssen, R. Schoonmaker, J.A.D. Matthew and A. Chambers, Solid State Commun. 14 (1974) 1263. [ 141 M.P. Borom and R.E. Hanneman, J. Appl. Phys. 38 (1967) 2406. [ 151 R.G. Gossink and T.P.A. Lommen, Appl. Phys. Letters 34 (1979) 444. [16] Fumio Ohuchi, Ph.D. Dissertation, University of Florida, Gainesville, Florida (1981). f17] Theodore E. Madey and John T. Yates, Jr., J. Vacuum Sci. Technol. 8 (1971) 525.
261
SODIUM DEPLETION ON GLASS SURFACES DURING AUGER ANALYSIS
*
P.G. WHITKOP E.I. du Pont de Nemours and Co., Savannah River Laboratory, Aiken, South Carolina29808, USA Received 8 may 1981; accepted for publication 30 June 1981
The kinetics of the depletion of sodium on glass surfaces during Auger Electron Spectroscopic analysis is investigated. The decay process is mathematically represented as a sum of two single decaying exponential functions. This behavior may be described by a mechanism that accounts for the neutralization of sodium ions by the electron beam. Sodium ions and neutral sodium atoms are depleted by several known processes.
1. Introduction The analysis of glass surfaces is extremely important in the determination of various corrosion processes acting upon glass-immobilized nuclear waste in underground repositories. In particular, the analysis of various alkali and alkaline earth ions, especially sodium ions, is of great importance to the determination of the mechanism of glass leaching by groundwater. One widely used method of glass surface analysis is Auger Electron Spectroscopy (AES), coupled with argon ion sputter etching [l-4]. This technique is capable of determining glass composition at various depths from the glass surface. Early work using AES on glass demonstrated an inability to detect sodium, although large concentrations were known to be present [5,6]. This was explained by the fact that the electron beam of the Auger analyzer caused a negative charge build-up below the glass surface in the manner first proposed by Lineweaver [7]. The sodium ions migrate away from the surface toward the region of negative charge. Other effects, such as stimulated electron desorption and localized heating, also give rise to the loss of sodium from the glass surface during AES analysis. Electron microprobe studies indicate that the kinetics of the sodium removal process follow an exponential decay, preceded by an incubation period, during which the concentration of sodium ions remains constant [8-lo]. In one AES analysis, however, the portion of the curve following the incubation period was * The information contained in this article was developed during the course of work under Contract No. DE-AC09; 76SROOOOl with the US Department of Energy.
0039-6028/81/0000-0000/$02.50
0 1981 North-Holland
262
P.G. Whitkop / Na depletion on glass surfaces during Auger analysis
represented by the form A [ 1-B ln(t/t,-,)] , in which to is the incubation time, t > to, and A and B are constants [2]. In this study, AES was used to probe the sodium removal process in two types of glass. The experimental evidence suggests that this process is characterized by a sum of two exponential decay curves, each with different decay constants and preexponential factors. These results are interpreted within the context of the mechanism proposed by Lineweaver [7].
2. Experimental
measurements
Measurements were carried out on two types of glass, with compositions shown in table 1. The glass buttons, S/8 inch in diameter by l/8 inch thick, were polished to 600 grit, mounted on a thirty-degree carousel, and placed in the bell jar of a Physical Electronics Model 545 Scanning Auger Microprobe, which is equipped with a cylindrical mirror analyzer. All of the data were obtained at room temperature. The surfaces of the glass buttons, once placed into the spectrometer, received no further treatment. In particular, argon ion bombardment of the glass surface was avoided, since this technique can alter the physical and chemical properties of the
Table 1 Compositions of glasses used in this study Glass
Compound
Weight percent
A
SiO2
52.5
B203
10.0 18.5 4.0 5.0 10.0
Naz 0 Liz0 CaO TiO2 B
SiO2 B203
NazO Liz0 CaO Ti02 Fe203 A1203
Mn02 NiO NazS04 AWSOOa) a) A mixture of CaAIzSQ012
37.3 7.2 15.0 3.0 4.7 7.2 13.4 2.8 3.8 1.8 0.4 2.4
.6 Hz0 and (Ca, Naz, Kz) A12Si10024 . 7 HzO.
P.G. Whitkop/ Na depletion on glasssurfaces during Auger analysis
263
glass surface. With argon ion bombardment, there is a possibility that sodium ions may be reduced to sodium metal, complicating the experimental results obtained with the analyzer beam. A suitable position for analysis was determined with elastically scattered electons. The beam energy and current were adjusted prior to the electron beam shut-down. Once the analyzer beam was turned off, the sample was moved to a new position so that another portion of the sample was analyzed. The moment that the electron beam was reactivated was considered as zero time for kinetic analysis.
3. Results and discussion Figs. 1 and 2 show plots of the log, of the sodium peak height (in arbitrary units) versus the analyzer beam bombardment time. Fig. 1 shows the sodium decay characteristics of the surface of Glass A; fig. 2 represents the removal of sodium
1
I
I
.2
.6
I
I
I
1.0 Time rn~n
1.4
1.8
Fig. 1. Plot of log, of peak height versus time for Glass A.
P.G. Whitkop / Na depletion on glass surfaces during Auger analysis
264
r
.2
.6
1.0
1.4
1.6
Time, mm
Fig. 2. Plot of log, of peak height
versus time for Glass B.
from Glass B. The important feature to note is that for each of these curves, there are two distinct linear segments. For the data shown in figs. 1 and 2, the incubation period preceding sodium removal from the glass surface was negligible. During the course of these studies, however, experimental conditions were found in which the incubation period was observable. The presence of the two linear portions in the decay curve is indicative of a mathematical expression of the form Ai = A 1 exp(-Mi)
+ AZ exp(-flti)
.
(1)
The exponents CYand /3 along with coefficients Al and A2 can be determined. The linear segment at longer bombardment times is extrapolated to zero time. For this line segment, the first exponential term is negligible and the contribution is due only to the second term. A least-squares determination of the slope of the extrapolated curve gives a value for /3, and the intercept corresponds to AZ. A 1 and o are determined by subtracting the expression A2 exp(-&i) from the data points Ai in the short time portion of the curve and performing a least-squares analysis on the
P.G. Whitkop/ Na depletion on glasssurfaces during Auger analysis
265
resulting line. Table 2 lists the calculated values of o, 0, A 1, and Aa for the curves in figs. 1 and 2. The overall double exponential behavior exhibited by Glass A and B under several different beam conditions suggests that the sodium ion initially present in the glass must be partially converted to a second species, with simultaneous removal of both forms. Any depletion mechanism which involves only the participation of sodium ion would produce a decay curve following first order kinetic theory. If sodium ion decay proceeded by migration under the influence of the electron beam and electron stimulated desorption, a decay curve obeying first order kinetics would be observed, with an overal depletion rate contant equal to the sum of the rate contants for depletion by migration and electron stimulated desorption. The intercepts A 1 and AZ are a relative measure of the concentrations of the two sodium species that must be present to account for the double exponential decay curve. The data presented in table 2 shows that the relative amounts of sodium species can change under the influence of the electron beam. As beam current density or voltage increase, Az increases while A 1 decreases. This suggests that the electron beam directly participates in the interconversion of sodium species, or secondary beam effects such as samle heating, are important. The temperature rise on the glass surface under electron bombardment can be significant, but the temperature differential between the glass surface bombarded by an electron beam of 0.1 mm diameter, 3 keV and 5 .O PA or 4 keV and 5 .O PA is estimated to be 24’ at the beam center (calculated using the formulas of ref. [ 111) and a value of 0.01 W/cm * “C for the thermal conductivity). The temperature differential between the two beam conditions is not great, yet the coefficients AI and A2 change significantly. This fact suggests that the electron beam is participating in the production of the second species, not secondary effects of the electron beam, such as sample heating. The consecutive reaction mechanism described above identifies two sodium species that must be formed in order to account for the observed double exponential behavior of the sodium decay profile. J.&reweaver [7] has pointed out that two
Table 2 Analyzed data from tigures 1 and 2 a) Glass
Beam voltage OteV)
Beam current (PA)
Q!b) (min-’ )
Db) (min-’ )
Al b, (arbitrary)
AZ b, (arbitrary)
A
3.0 4.0 3.0 4.0
0.16 3.78 5.00 5.00
0.09 0.32 0.65 0.70
0.33 1.30 1.27 1.50
2.53 1.85 2.10 1.80
0.59 1.33 0.68 1.06
B
(0.03) (0.03) (0.04) (0.05)
(0.07) (0.07) (0.06) (0.09)
(0.05) (0.04) (0.04) (0.03)
a) Coefficients A 1 and A* and exponents [Yand p correspond to q. (1) in the text, b, Numbers in parentheses indicate relative errors.
(0.08) (0.07) (0.07) (0.08)
266
P. G. Whitkop 1 Na depletion on glass surfaces during Auger analysis
types of sodium species are present during the interaction of the glass and the electron beam. These species are sodium ions and neutral sodium atoms, formed by the reduction of sodium ions by the electron beam. The presence of neutral sodium atoms produces the brown discoloration of glasses when they are bombarded with electrons. Although Lineweaver’s mechanism operated at beam voltages between 10 and 27 keV, Dawson has shown that the same mechanism can occur at beam voltages as low as 0.1 keV [ 121. Electron browning is found to occur below the glass surface, but it is not inconceivable that electrons impinging on a glass surface reduce a number of the sodium ions found on the surface. The reduction of surface sodium ions by the electron beam may account for the consecutive reaction mechanism indicated by the double exponential decay described above. No direct evidence for the presence of neutral sodium atoms was obtained. Neutral sodium atoms possess an L2,a W Auger transition at 27 keV [ 131, but this transition was not observed. The complexity of the glass Auger spectrum in this region may have masked the presence of this peak. In terms of a mechanism for the compositional change of sodium during AES analysis of glass, the following scheme is proposed Na’(S,) + e-2
Na’(Sr) ,
Na’(Sr) + e-2
Na’(Sr) + 2 e- ,
Na’(S,) 14: Na’&) Na”(S1)2
@I
,
Na”(S2).
Sr represents the glass surface affected by the electron beam, and Sz represents any area not affected by the beam. In reactions a and b, the beam current density and beam voltage remain constant over time, and these reactions can be represented by a pseudo-first-order equation. Rate constants kr and kz will depend on the beam current density and beam voltage. Constants k3 and k4 represent the total removal rate constants of both Na’ and Na’, respectively. Since Na” is not affected by an accumulation of negative charge beneath the surface, processes such as stimulatedelectron desorption and thermal desorption are probably the dominant removal mechanisms. The rate equations describing the removal of Na’ and Na” are d [Na’]/dt = kz [Na’] - (k, + ka)[Na+] ,
(2)
= kl [Na’] - (kz + k4)[Nao] .
(3)
d[Na’]/dt
Solution of these equations, with k5 = (kz + k4), kg = (kl + k3), and boundary conditions given by [Na’](O) = [Na’] o and [Na’] (0) = 0, produces the following
P.G. Whitkop / Na depletion on glass surfaces during Auger analysis
261
expressions [Na’](t) = ‘:“I]:a”
[(rr - 1) exp(-rr
[NaO](t)= if”:l”’ 1 2
[exp(-r2t) - exp(-rl f)l ,
r1,2=
1(-k,
+k,)+
[(ks
+k6)’ -4(klk2
t) + (1 - rz) exP(-rz t)]
-kgk6)]1’2}/21.
, (5)
(6)
This mechanism predicts the mathematical form that was determined experimentally. The exponent r2 represents the value of fl in eq. (l), and r1 represents cr. Coefficients for the exponentials containing r2 and rr correspond with A2 and AI, respectively. According to table 2, the value of AI decreases with increasing beam current density and beam voltage, while A2 simultaneously increases. Coefficient A 1, therefore, is assigned to the exponential term describing sodium ion decay; AZ represents the coefficient for sodium metal decay. The mechanism of sodium ion depletion by electric field induced migration and electron stimulated desorption (ESD) has been characterized [8,10,14-161. The data described in this work suggests that sodium neutralization may open another sodium depletion channel. Depending upon beam conditions, this channel can account for a significant portion of the overall sodium depletion process. The initial relative concentrations of both sodium species are represented by the coefficients A 1 and AZ. From the data of table 2, where the beam conditions are 4 keV and 3.78 ,uA, the amount of sodium metal, represented by AZ, is 42% of the total amount of sodium in both metallic and ionic forms. Further investigation of table 2 shows that the sodium ion neutralization and decay scheme can depend upon beam voltage alone. This fact can be explained by noting that the rate constant for a two particle reaction can be expressed ask = uu, where k is the rate constant, u is the reaction cross-section and u is the relative velocity of the two particles. Since raising the beam voltage increases the kinetic energy of the electrons in the beam, larger beam voltages can increase the rate constants for the reactions described by eqs. (a) and (b). Differentiating eq. (5), setting it equal to zero and solving for t, gives an equation for the time at which the sodium metal concentration is maximum. Substituting this expression back into eq. (5) shows that the maximum amount of sodium metal produced in the neutralization and decay scheme depends upon the relative magnitudes of the rate constants. Since rate constants kl and k2 depend upon the kinetic energy of the electrons, the intercepts A 1 and A2 should vary when beam voltage is changed. The exact mechanism of the depletion of neutral sodium atoms is not clear from these experiments. Several possibilities include ESD, thermal desorptidn and momentum transfer. Momentum transfer is unlikely because of the extremely small mass of the electron relative to the sodium atom. ESD may occur by several mechanisms [ 171. These include desorption of ground state or excited state neutral sodi-
268
P. G. Whitkop INa depletion on glass surfaces during Auger analysis
urn atoms or desorption of positive sodium ions formed from neutral atoms. This possibility is suggested by eq. (b) of the kinetic scheme. The Auger process can easily account for the formation of sodium ions from neutral atoms. Thermal desorption is possible due to the high temperatures to which the glass may be heated. With the conditions cited previously, the temperature rise of the glass under the influence of a 4 keV, 5 I.IA and 0.1 mm diameter electron beam is on the order of 100°C. This is sufficient temperature rise to account for a thermal desorption process. The double exponential behavior of sodium depletion found in this study appears to be a more general expression of earlier results. In particular, Varshneya, Cooper and Cable [8] reported that potassium, under the influence on an electron microprobe beam, decayed by a process described by the general form [K] = A exp(-at) f B, where A, B and D are constants. During Auger analysis, proper beam conditions can be chosen where one of the two exponential constants becomes small enough so that the corresponding exponential term approaches unity. This reduces the double exponential expression to one which is identical to that described in ref. [S].
4. Conclusion The interaction of an electron beam from an AES analyzer with a glass surface causes sodium to deplete in a manner that can be described by the sum of two exponential decay components. The proposed mechanism that gives rise to this behavior is the neutralization of surface sodium ions by the electron beam. Neutralization is followed by removal of sodium ions and neutral atoms by migration, simulated electron desorption, and localized heating. Kinetic analysis of this mechanism shows that the predicted mathematical form matches the form found experimentally.
The author wishes to thank J.R. Price for his assistance in obtaining data.
the Auger
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269
8. Goldstein and DE. Carlson, J. Am. Ceram. Sot. 55 (1972) 51. C.G. Pantano, Jr., A.E. Clark and L.L. Hench, J. Am. Ceram. Sot. 57 (1974) 412. J.L. Lineweaver, J. Appl. Phys. 34 (1963) 1786. A.K. Varshneya, A.R. Cooper and M. Cable, J. Appl. Phys. 37 (1966) 2199. R.G. Gossink, H. Von Doveren and J.A.T. Verhoeven, J. Non-Crystalline Solids 37 (1980) 111. [lo] L.F. Vassamillet and V.E. Caldwell, J. Appl. Phys. 40 (1969) 1637. [ll] G.S. Almasi, J. Blair, R.E.0~~eandR.J. Schwartz, J. App~.Phys. 36 (1965) 1848. [12] P.H. Dawson, Nuovo Ciiento Suppl. 5 (1967) 612. [ 13J A.P. Janssen, R. Schoonmaker, J.A.D. Matthew and A. Chambers, Solid State Commun. 14 (1974) 1263. [ 141 M.P. Borom and R.E. Hanneman, J. Appl. Phys. 38 (1967) 2406. [ 151 R.G. Gossink and T.P.A. Lommen, Appl. Phys. Letters 34 (1979) 444. [16] Fumio Ohuchi, Ph.D. Dissertation, University of Florida, Gainesville, Florida (1981). f17] Theodore E. Madey and John T. Yates, Jr., J. Vacuum Sci. Technol. 8 (1971) 525.