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Electron beam induced current (EBIC) as a function of the angle of incidence of the electron beam in a scanning electron microscope (SEM)
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Solid-Sfofc Elecfronics Vol. 25, No. 7. pp, 651-653, 1982 Printed in Great Britain.
ELECTRON BEAM INDUCED CURRENT (EBIC) AS A FUNCTION OF THE ANGLE OF INCIDENCE OF THE ELECTRON BEAM IN A SCANNING ELECTRON MICROSCOPE (SEM) A. JAKUBOWICZ Institute of Electron Technology of the Technical University of Wroclaw, Poland (Receiued 31 October 1980;in revised form 15 September 1981) Abstract-The paper presents an analysis of the Electron Beam Induced Current as a function of the angle of incidence of an electron beam. A SEM experiment under steady-state conditions for a silicon diode structure has been performed. Two simple theoretical models have been considered. NOTATION a constant a constant the position of the source for the beam incidence angle 6 the position of the element A& the position of the source for normal incidence 0 = 0 the current the current contribution of the j-element &/Eo[31 the energy of primary electrons the mean energy of backscattered electrons the diffusion length of minority carriers the number of electron-hole pairs for X(0) = 0 the normalized surface recombination velocity Uhd = & the height of the spherical cap (Fig. 4) the thickness of the investigated layer the surface recombination velocity the diffusion velocity l)d= L/T the small element of the source of finite sizes the angle of incidence of the electron beam the lifetime of minority carriers the backscattering coefficient as a function of the angle of incidence of the beam the backscattering coefficient for 6 = 0” 1. INTRODUC’IION
EBIC is widely used for investigations of semiconductors. Among various applications one can distinguish measurements of the diffusion length of minority carriers. In the majority of the studies concerning this problem the normal working mode of the SEM has been used, i.e. the one consisting in scanning the surface of the sample by the electron beam. In a certain number of works the position of the excess carrier source has been changed by altering the accelerating voltage in the SEM[l]. For this purpose the dependence of the penetration depth upon the energy of primary electrons has been used. It seems, however, that also by variation of the electron beam incidence angle one can get controlled changes of the penetration depth. Thus a new technique for minority carriers diffusion length measurement might be developed. For this purpose, however, it is necessary to analyse the behaviour of the excess carrier source when changing the electron beam incidence angle. Such an analysis has to my knowledge never been made. An attempt in this direction has been shown in this paper.
By altering the electron beam incidence angle one changes the effective position and the effective strength of the source. It is rather a complicated task to take into consideration both these effects in a form of an analytical solution. Two simplified models of solving the problem have been presented here. However, it is not the purpose of this paper to elaborate a new method of diffusion length determination. It deals with a simplified geometry which may only answer the question whether it is possible to control the changes of the effective penetration depth and the source strength when changing the beam incidence angle. 2. FXPRRIMENT
This Section presents the results of a SEM experiment in which the EBIC was measured as a function of the electron beam incidence angle. This experiment was performed for a diode structure with a p-n junction parallel to the surface. The configuration of this structure is shown in Fig. 1. The diffusion length of minority carriers in the n type layer was much larger than the size of the excess carrier source. This was to simplify the discussion of experimental results. In order to avoid the influence of any undesirable electrical fields on experimental results, measurements were performed at the side of the substrate with a uniform distribution of donors density. The metal contact and the n+ type layer were removed from a part of the surface by ion beam etching (Ar’ ions of energy 500 eV were used). This was done in order to avoid the influence of the electric field present in d=lSO&m
.‘.‘,‘.‘.‘.‘.’
Fig. 1. The structure used in the experiment. 651
652
A.JAKLBOWICZ Using eqn (1) one obtains:
I(e)
:(8-o”)
Equation (2) is not yet a complete I(e) function because the changes of the source strength have not been taken into account so far. A correction of eqn (2) is possible by considering the angular dependence of the backscattering coefficient. The correction function has the known form: N(0) = No x [I - f? X r(O)]
Fig. 2. Theoretical and experimental results, the accelerating voltage-30 kV, the beam current-l nA, the diffusion length in the n-type layer -50 km; (1) point-source model, (2) source of
finite sizes model, (3) experimental results.
the n+-n junction. Furthermore, ion bombardment makes the surface amorphous. This allows to obtain a uniform surface with a high surface recombination velocity. For theoretical calculations v, = m has been chosen. Measurements were performed with the JSM-35 scanning electron microscope. The accelerating voltage was 30 kV. The small value of the beam current 1 nA ensured low injection conditions. The incidence angle was changed by tilting the sample with respect to the beam. The experimental curve is shown in Fig. 2.
SlhlPLETHEORETlCALMODELS Two simple theoretical models have been considered in order to describe analytically the shape of the function EBIC = f( 0). 3. TWO
3.1. Point source In the simplest approach the known expression describing the short-circuit EBIC for an ideal pointsource[2] has been used. It has been assumed here that the penetration depth he depends on the angle of incidence as follows (Fig. 3): he=itocosO
n
(1)
(3)
Finally one obtains the current expression:
I(B)=Ax[l-KxX(O)]x[l+(~)e
2w’f,] ‘X
So, when determining the curve f(0), it is necessary to know the function X(“(e).Such function has been given, e.g., by Radzimski[4]: X(O) = X0X exp[B X (I- cos 0)]. The shape of I(0) is shown in Fig. 2. This curve has been calculated, however, using the experimental values of X(O) 141. 3.2. Source of finite sizes Figure 2 (curves 1 and 3) shows that the ideal pointsource model is not sufficient for the problem considered in this paper. Therefore an analysis for a source of finite sizes has been performed. This analysis has been based on assumptions identical with those of [5.6]. For normal incidence the source is a sphere tangent to the surface. It has been assumed that at each point inside the source the generation rate of electron-hole pairs is constant. Figure 4 shows the assumed behaviour of the source when changing the incidence angle of the electron beam. With the increase of 0 the actual source volume decreases. The source also loses its spherical shape. Calculations have been performed by dividing the source into a finite number of small elements AK The total induced current
I
Fig. 3. The ideal point source model, us is the surface recombination velocity and w-the
thickness of the n type layer.
Fig. 4.The model of the source of finite sizes. h, is the position of the element AV,.
653
Electron beam induced current (EBIC) as a function of the angle of incidence is the sum of the individual contributions of each element. In this approach I refer to the special property of EBIC data noted by Hackett [2]. A generation volume of arbitrary shape can be represented as the superposition of ideal point sources. So the total current is the sum:
00 7LY
I(O)=
&
ii.
)
The graphical illustration of eqn (6) for a wide range of incidence angles is shown in Fig. 2. 4. DISCUSSIONAND CONCLUSIONS
Before the discussion of results it seems suitable to analyse briefly eqn (4). One can show that eqn (4) can be simplified for the experimental conditions described earlier -S, 130. h,/L&l: I(e) = A
x [l - 17 X
X 2[e
h, EDSB,L
x(0)] -e
X
[l - e-Z”‘L]-’
X em”“=
-ho ‘OS BIL] ii: const X [ 1 -
K
X X(0)]
Assuming h,/L 4 1 one gets: I(e)=constx
[l-
I&ye)]
xcos
8.
63)
This equation shows that the experimental curve presented in Fig. 2 in normalized current units results at the same time from both factors-the source position [cos e] and the effective source strength [l - I&‘(@]. The comparison of the curves presented in Fig. 2 shows that the point source model is unsufficient for EBIC investigations performed with incidence angle variations. The divergence of experimental and theoretical values is inconsiderable for low angles up to 30 + 40”. For higher angles, however, it significantly increases. The theoretical results obtained by applying the method described in Section 3.2 are in much better agreement with the experimental results. It is worth emphasizing that the approach from Section 3.2 enables to avoid the influence of the surface recombination velocity on the source strength. Each small element AV (less than the diffusion length) is contained entirely in the bulk of the semiconductor and does not touch the surface. Therefore its strength remains uneffected by the surface recombination velocity. The strength of the whole source depends then only on the number of elements AV, which decreases with increase of the angle 8. It is rather a time-consuming task to obtain the complete function I(0) in a wide range of angles. It requires manual adjustment of consecutive angles when using standard scanning electron microscopes. A rough test of a quick determination of the function I(0) has been performed with the three-lenses instrument Stereoscan 180 working in the selected-area diffraction mode. By this means it is possible to obtain the EBIC for an angle
SSE Vol.25.No. 7-H
710
78'
820
Fig. 5. Theoretical curves I(6) and experimental results obtained by rocking the beam about the point of incidence; the angle of the initial tilt of the specimen: 70 degrees, accelerating voltage40 kV, beam current-50 nA. The monotonic character of the experimental curve is disturbed by crystal defects; (1) pointsource model, (2) source of finite sizes model (3) experimental curve.
range up to more than ten degrees. The output signal variations are very small for low angles. Therefore the sample should be initially tilted . The angle of the initial tilt should be selected so as to get a measurable slope of the I(0) curve. This method makes it possible to obtain EBIC information from areas down to approx. 10pm across, naturally when neglecting the influence of the diffusion length on the resolution power. The size of this area depends on the total angle through which the beam is rocked and on the “working distance”. Figure 5 shows the comparison of theoretical characteristics I(0) and experimental results obtained by applying the method described above. In the case of monocrystals angular measurements may be disturbed by diffraction effects. These effects may appear when the nearsurface region of the crystal has a sufficiently high crystallographic perfection. Real surfaces, however, are usually deformed to a high extent. In order to avoid diffraction effects in the experiment the sample described in Section 2 was bombarded with ions. The results of this paper show that it is possible to control the effective penetration depth and source strength when the beam incidence angle changes. It seems that angular EBIC measurements may become useful for diffusion length determination. Such a method would show some advantages. It would be quick and non-destructive. The essential disadvantage of this technique is the small range of variations of the effective penetration depth of the beam, which would reduce the accuracy of high diffusion length measurements. Therefore only short diffusion lengths could be measured. So this technique may be of value when used with a geometry which takes into consideration the real distribution of generated electron-hole pairs, for example with the geometry of Wu and Wittry [l]. UEPXRENCES 1. C. J. Wu and D. B. Wittry, .I. Appl. Phys. 49(5), 2827(1978). 2. W. H. Hackett, Jr., .I. Appl. Phys. 43, 1649(1972). 3. E. J. Sternglass, Phys. Reo. 95, 345, (1954). 4. Z. Radzimski, Doctoral thesis. Technical University of Wroclaw. Institute of Electron Technology, Poland (1976). 5. F. Berz, H. K. Kuiken, Solid-St. Electron. 19,437, (1976). 6. J. F. Bresse, Proc. 5th Ann. Symp. p. 105. IITRI, Chicago, (1972).
Solid-Sfofc Elecfronics Vol. 25, No. 7. pp, 651-653, 1982 Printed in Great Britain.
ELECTRON BEAM INDUCED CURRENT (EBIC) AS A FUNCTION OF THE ANGLE OF INCIDENCE OF THE ELECTRON BEAM IN A SCANNING ELECTRON MICROSCOPE (SEM) A. JAKUBOWICZ Institute of Electron Technology of the Technical University of Wroclaw, Poland (Receiued 31 October 1980;in revised form 15 September 1981) Abstract-The paper presents an analysis of the Electron Beam Induced Current as a function of the angle of incidence of an electron beam. A SEM experiment under steady-state conditions for a silicon diode structure has been performed. Two simple theoretical models have been considered. NOTATION a constant a constant the position of the source for the beam incidence angle 6 the position of the element A& the position of the source for normal incidence 0 = 0 the current the current contribution of the j-element &/Eo[31 the energy of primary electrons the mean energy of backscattered electrons the diffusion length of minority carriers the number of electron-hole pairs for X(0) = 0 the normalized surface recombination velocity Uhd = & the height of the spherical cap (Fig. 4) the thickness of the investigated layer the surface recombination velocity the diffusion velocity l)d= L/T the small element of the source of finite sizes the angle of incidence of the electron beam the lifetime of minority carriers the backscattering coefficient as a function of the angle of incidence of the beam the backscattering coefficient for 6 = 0” 1. INTRODUC’IION
EBIC is widely used for investigations of semiconductors. Among various applications one can distinguish measurements of the diffusion length of minority carriers. In the majority of the studies concerning this problem the normal working mode of the SEM has been used, i.e. the one consisting in scanning the surface of the sample by the electron beam. In a certain number of works the position of the excess carrier source has been changed by altering the accelerating voltage in the SEM[l]. For this purpose the dependence of the penetration depth upon the energy of primary electrons has been used. It seems, however, that also by variation of the electron beam incidence angle one can get controlled changes of the penetration depth. Thus a new technique for minority carriers diffusion length measurement might be developed. For this purpose, however, it is necessary to analyse the behaviour of the excess carrier source when changing the electron beam incidence angle. Such an analysis has to my knowledge never been made. An attempt in this direction has been shown in this paper.
By altering the electron beam incidence angle one changes the effective position and the effective strength of the source. It is rather a complicated task to take into consideration both these effects in a form of an analytical solution. Two simplified models of solving the problem have been presented here. However, it is not the purpose of this paper to elaborate a new method of diffusion length determination. It deals with a simplified geometry which may only answer the question whether it is possible to control the changes of the effective penetration depth and the source strength when changing the beam incidence angle. 2. FXPRRIMENT
This Section presents the results of a SEM experiment in which the EBIC was measured as a function of the electron beam incidence angle. This experiment was performed for a diode structure with a p-n junction parallel to the surface. The configuration of this structure is shown in Fig. 1. The diffusion length of minority carriers in the n type layer was much larger than the size of the excess carrier source. This was to simplify the discussion of experimental results. In order to avoid the influence of any undesirable electrical fields on experimental results, measurements were performed at the side of the substrate with a uniform distribution of donors density. The metal contact and the n+ type layer were removed from a part of the surface by ion beam etching (Ar’ ions of energy 500 eV were used). This was done in order to avoid the influence of the electric field present in d=lSO&m
.‘.‘,‘.‘.‘.‘.’
Fig. 1. The structure used in the experiment. 651
652
A.JAKLBOWICZ Using eqn (1) one obtains:
I(e)
:(8-o”)
Equation (2) is not yet a complete I(e) function because the changes of the source strength have not been taken into account so far. A correction of eqn (2) is possible by considering the angular dependence of the backscattering coefficient. The correction function has the known form: N(0) = No x [I - f? X r(O)]
Fig. 2. Theoretical and experimental results, the accelerating voltage-30 kV, the beam current-l nA, the diffusion length in the n-type layer -50 km; (1) point-source model, (2) source of
finite sizes model, (3) experimental results.
the n+-n junction. Furthermore, ion bombardment makes the surface amorphous. This allows to obtain a uniform surface with a high surface recombination velocity. For theoretical calculations v, = m has been chosen. Measurements were performed with the JSM-35 scanning electron microscope. The accelerating voltage was 30 kV. The small value of the beam current 1 nA ensured low injection conditions. The incidence angle was changed by tilting the sample with respect to the beam. The experimental curve is shown in Fig. 2.
SlhlPLETHEORETlCALMODELS Two simple theoretical models have been considered in order to describe analytically the shape of the function EBIC = f( 0). 3. TWO
3.1. Point source In the simplest approach the known expression describing the short-circuit EBIC for an ideal pointsource[2] has been used. It has been assumed here that the penetration depth he depends on the angle of incidence as follows (Fig. 3): he=itocosO
n
(1)
(3)
Finally one obtains the current expression:
I(B)=Ax[l-KxX(O)]x[l+(~)e
2w’f,] ‘X
So, when determining the curve f(0), it is necessary to know the function X(“(e).Such function has been given, e.g., by Radzimski[4]: X(O) = X0X exp[B X (I- cos 0)]. The shape of I(0) is shown in Fig. 2. This curve has been calculated, however, using the experimental values of X(O) 141. 3.2. Source of finite sizes Figure 2 (curves 1 and 3) shows that the ideal pointsource model is not sufficient for the problem considered in this paper. Therefore an analysis for a source of finite sizes has been performed. This analysis has been based on assumptions identical with those of [5.6]. For normal incidence the source is a sphere tangent to the surface. It has been assumed that at each point inside the source the generation rate of electron-hole pairs is constant. Figure 4 shows the assumed behaviour of the source when changing the incidence angle of the electron beam. With the increase of 0 the actual source volume decreases. The source also loses its spherical shape. Calculations have been performed by dividing the source into a finite number of small elements AK The total induced current
I
Fig. 3. The ideal point source model, us is the surface recombination velocity and w-the
thickness of the n type layer.
Fig. 4.The model of the source of finite sizes. h, is the position of the element AV,.
653
Electron beam induced current (EBIC) as a function of the angle of incidence is the sum of the individual contributions of each element. In this approach I refer to the special property of EBIC data noted by Hackett [2]. A generation volume of arbitrary shape can be represented as the superposition of ideal point sources. So the total current is the sum:
00 7LY
I(O)=
&
ii.
)
The graphical illustration of eqn (6) for a wide range of incidence angles is shown in Fig. 2. 4. DISCUSSIONAND CONCLUSIONS
Before the discussion of results it seems suitable to analyse briefly eqn (4). One can show that eqn (4) can be simplified for the experimental conditions described earlier -S, 130. h,/L&l: I(e) = A
x [l - 17 X
X 2[e
h, EDSB,L
x(0)] -e
X
[l - e-Z”‘L]-’
X em”“=
-ho ‘OS BIL] ii: const X [ 1 -
K
X X(0)]
Assuming h,/L 4 1 one gets: I(e)=constx
[l-
I&ye)]
xcos
8.
63)
This equation shows that the experimental curve presented in Fig. 2 in normalized current units results at the same time from both factors-the source position [cos e] and the effective source strength [l - I&‘(@]. The comparison of the curves presented in Fig. 2 shows that the point source model is unsufficient for EBIC investigations performed with incidence angle variations. The divergence of experimental and theoretical values is inconsiderable for low angles up to 30 + 40”. For higher angles, however, it significantly increases. The theoretical results obtained by applying the method described in Section 3.2 are in much better agreement with the experimental results. It is worth emphasizing that the approach from Section 3.2 enables to avoid the influence of the surface recombination velocity on the source strength. Each small element AV (less than the diffusion length) is contained entirely in the bulk of the semiconductor and does not touch the surface. Therefore its strength remains uneffected by the surface recombination velocity. The strength of the whole source depends then only on the number of elements AV, which decreases with increase of the angle 8. It is rather a time-consuming task to obtain the complete function I(0) in a wide range of angles. It requires manual adjustment of consecutive angles when using standard scanning electron microscopes. A rough test of a quick determination of the function I(0) has been performed with the three-lenses instrument Stereoscan 180 working in the selected-area diffraction mode. By this means it is possible to obtain the EBIC for an angle
SSE Vol.25.No. 7-H
710
78'
820
Fig. 5. Theoretical curves I(6) and experimental results obtained by rocking the beam about the point of incidence; the angle of the initial tilt of the specimen: 70 degrees, accelerating voltage40 kV, beam current-50 nA. The monotonic character of the experimental curve is disturbed by crystal defects; (1) pointsource model, (2) source of finite sizes model (3) experimental curve.
range up to more than ten degrees. The output signal variations are very small for low angles. Therefore the sample should be initially tilted . The angle of the initial tilt should be selected so as to get a measurable slope of the I(0) curve. This method makes it possible to obtain EBIC information from areas down to approx. 10pm across, naturally when neglecting the influence of the diffusion length on the resolution power. The size of this area depends on the total angle through which the beam is rocked and on the “working distance”. Figure 5 shows the comparison of theoretical characteristics I(0) and experimental results obtained by applying the method described above. In the case of monocrystals angular measurements may be disturbed by diffraction effects. These effects may appear when the nearsurface region of the crystal has a sufficiently high crystallographic perfection. Real surfaces, however, are usually deformed to a high extent. In order to avoid diffraction effects in the experiment the sample described in Section 2 was bombarded with ions. The results of this paper show that it is possible to control the effective penetration depth and source strength when the beam incidence angle changes. It seems that angular EBIC measurements may become useful for diffusion length determination. Such a method would show some advantages. It would be quick and non-destructive. The essential disadvantage of this technique is the small range of variations of the effective penetration depth of the beam, which would reduce the accuracy of high diffusion length measurements. Therefore only short diffusion lengths could be measured. So this technique may be of value when used with a geometry which takes into consideration the real distribution of generated electron-hole pairs, for example with the geometry of Wu and Wittry [l]. UEPXRENCES 1. C. J. Wu and D. B. Wittry, .I. Appl. Phys. 49(5), 2827(1978). 2. W. H. Hackett, Jr., .I. Appl. Phys. 43, 1649(1972). 3. E. J. Sternglass, Phys. Reo. 95, 345, (1954). 4. Z. Radzimski, Doctoral thesis. Technical University of Wroclaw. Institute of Electron Technology, Poland (1976). 5. F. Berz, H. K. Kuiken, Solid-St. Electron. 19,437, (1976). 6. J. F. Bresse, Proc. 5th Ann. Symp. p. 105. IITRI, Chicago, (1972).