- Email: [email protected]
Local investigation of the electrical properties of grain boundaries
56
Materials' Science and Engineering, B24 (1994) 56-60
Local investigation of the electrical properties of grain boundaries J. Palm, D. Steinbach and H. Alexander II. Physikalisches Institut, Abteilung fiir Metallphysik, Universitiit zu K6ln, K6ln (Germany)
Abstract We present the recent development of three related techniques for the local investigation of grain boundaries (GBs): grain boundary electron-beam-induced current (GB EBIC), grain boundary light-beam-induced current (GB LBIC) and local grain boundary photoconductance spectroscopy (GB PCS). Two grains which are separated by a common GB are ohmically connected to a current amplifier. In GB EBIC a focused electron beam and in GB LBIC a focused fight beam of
above band gap energy is scanned across the GB. At GBs with a two-dimensional coherent potential barrier a characteristic dark-bright signal is observed which is directly related to the recombination current through the boundary. By applying a small bias, the local attenuation of the potential barrier height as a function of the injection level can be determined. In GB PCS a beam of monochromatic subband gap light is used. By applying a bias, the change in the GB barrier height due to the excitation of carriers into the GB trap states can be detected by the change in the over-barrier current. By varying the light energy, a section of the local distribution of states in the gap can be determined.
1. Introduction We have recently presented the grain boundary (GB) electron-beam-induced current (EBIC) experiment [1, 2] for the characterization of GBs in large-grained polycrystalline (i.e. multicrystalline) silicon for photovoltaic application. In this paper we briefly summarize the principles of this technique and report further developments by replacing the electron beam by a focused light beam in a scanning optical microscope which finally leads to a local spectroscopy of grain boundaries. A GB model for the quantitative description and evaluation of the measured data is given.
in a line perpendicular to the grain boundary results in a characteristic bright-dark current profile (Fig. 1)[1 ]. This GB EBIC signal is due to the electric field of the grain boundary (Fig. 2); minority carriers generated by the electron beam in grain 1 diffuse to the GB and are efficiently drawn into the GB by its attractive field. They recombine with majority carriers trapped in the GB localized states. Holes from both sides of the GB which overcome the barrier at equal rates by thermal excitation refill these traps. The hole current from grain 2 results in a carrier difference between the grains. This will be balanced by the current through the ammeter from grain 1 to grain 2, which is the GB EBIC. We solved the three-dimensional diffusion
2. Experiments
2.1. Material and sample preparation For all experiments samples containing one single GB were cut from wafers of multicrystalline sificon (SILSO and research material from Wacker). They were mechanically polished with diamond paste and alumina down to 0.05 /~m grain size. Ohmic contacts were prepared on the polished surface at least 1 mm away from the GB by scratching InGa dots or by evaporating aluminium dots and subsequent local heating. 2.2. Grain boundary electron-beam-induced current The two grains are ohmically connected to a current amplifier and the sample is placed in a scanning electron microscope with the polished surface normal to the electron beam axis. Scanning the electron beam 0921-5107/94/$7.00 SSDI 0921-5107(93)00526-5
Ohmic I I Contac~
o:-'2.,
. _! \
exp. like rise i :......... I Y = diffusion region ~_~
=generation signalwidth
volume diameter
Fig. 1. Experimental set-up for GB EBIC. © 1994 - Elsevier Sequoia. All rights reserved
J. Palm et aL /
l
Electrical properties of grain boundaries
57
250 ®...~
200 "~ 1 5 0 U H
~ .L_........~
.
£ jcnap "P
ET E
~
m i00 nn 50
grain 1
GB
grain 2
Fig. 2. Currents at the GB (the capture and emission currents refer to the Seager model discussed below).
problem of two perpendicular surfaces with different finite recombination velocities and evaluated the diffusion lengths of the adjacent grains by analysing the current profiles [1]. By measuring the signal width, i.e. the distance between the two current peaks, the lateral extension of the generation volume and its dependence on the beam voltage can be determined [1]. The GB EBIC peak value which is proportional to the recombination current through the GB has been analysed with respect to its dependence on the beam current, i.e. the excitation level [2] (Fig. 3). The decrease in the slope of the function GB EBIC vs. beam current is related to the decrease in the GB recombination velocity owing to the injection of minority carriers. The detailed balance of capture and emission currents at the GB results in a decrease in the GB charge and hence the GB potential barrier (models for these processes have been given in refs. 3-5, and our modification of a model given by Seager for the GB EBIC is summarized below and has been discussed in detail in ref. 2). The recombination current is only an indirect physical quantity with respect to the GB potential barrier. Therefore in standard EBIC measurements (with a Schottky contact or p-n junction) there is no direct access to the barrier height. However, the GB EBIC experiment can easily be extended to the simultaneous measurement of majority-carrier properties [2]; applying a small bias (much less than kT, 10 ~V to 2 mV) the baseline shifts linearly with U and the shape of the current profile becomes asymmetrical. The maximum relative amplitude increases linearly with increasing U. Figure 4 gives the equivalent circuit for the local current voltage characteristic of the total current and illustrates the processes at the GB during local one-sided excitation under a small bias; along the y axis, which is in the GB plane x = 0, the potential barrier (z or energy axis) is reduced in places close to the electron beam. On application of a bias the majority-carrier current I flows in the x direction perpendicular to the GB. During local excitation at the GB, two paths are open for the current: first through the small area with reduced
200
400
600
800
I000 1 2 0 0
Fig. 3. GB EBIC peak value vs. beam current:
Ib /
pA
, simulated.
e-b~
e-b4
Rd
×=0
Fig. 4. GB with locallyreduced barrier and equivalentcircuit.
barrier ~ b (in the equivalent circuit represented by the resistance Rb), and second through the large unchanged GB with a mean dark barrier ~d (represented by Ro). From the theory of thermionic emission we obtain for the current across a double barrier [6] (for q U ~ kT, where Y is the zero-bias conductance): I = YU
(1)
with Y/F= ( q / k T )A exp[ - ( qdp + ~ )/ k T], F the area, A the pseudo-Richardson constant and ~ the position of the Fermi level in the bulk. We recently showed that the area F b with reduced barrier (P b is equal to the generation volume cross-section. In the quantitative analysis the ohmic resistance of bulk and contacts has to be taken into account. By the measurement of dark resistance and conductance change (evaluated from current increment and bias) finally the local attenuation of the barrier height as a function of beam current can be obtained as shown in Fig. 5 (GBs in SILSO material). 2.3. Grain boundary light-beam-induced current As shown already by Matare' [7] the dark-bright signal can also be obtained by substituting the electron
58
Z Palm et al.
/
Electrical properties ~f grain boundaries
>m0.25[ m
0.2
0.15 .8,--,__
200 400 600 800 I000 1200 Fig. 5. Barrier height vs. beam current:
Ib
/
pA
, simulated.
beam by a focused spot of above-band-gap light. We used a computer-controlled IR microscope with a scanning stage. The light coming from a quartz-halogen source is chopped and passes through a monochromator and the optical system. The current signal is amplified by the lock-in technique and digitized for profile analysis. The excitation geometry is different now; we measured the signal width d for different wavelengths and found a linear relation to the reciprocal absorption coefficient a: d = spot size + constant x a - 1
(2)
From this we can estimate that the maximum signal is achieved when the generation cone touches the GB at a depth of ¼ a-1. Using a monochromatic beam with large penetration depth (2 = 1/~m) most of the carriers are generated deep in the bulk and surface recombination is negligible. Hence the current profiles are purely exponential and the diffusion length can easily be obtained [1]. This method is also applicable to wafers with several GBs, provided that the GBs are GB EBIC active and the grains are larger than a few diffusion lengths. By applying a small bias the same phenomena as shown for the GB EBIC experiment can be observed; minority carriers which are generated by the above-band-gap light diffuse to the GB and the decrease in the GB potential barrier leads to an increase in the majority-carrier current which is observable by the resulting asymmetry of the GB light-beam-induced current (LBIC) profile. Owing to the large difference in excitation level the measured attenuation of the barrier heights are smaller than in GB EBIC ( A ~ ~-60 meV for a photon flux density of 3 × 1017 cm- 2 S- 1). 2.4. Grain boundary photoconductance spectroscopy The local investigation of the electrical properties of GBs with GB EBIC or LBIC demanded for both additional spectroscopic and structural investigations. Our work in the development of GB LBIC under bias directly led to the idea of a local GB spectroscopy; using subband gap light no generation of excess minority
carriers occurs but, if the energy of the photons is suitable for a direct excitation of trapped carriers from the GB into the bands, the change in the GB charge will be measurable as an increase in over-barrier current. As an integral technique this GB photoconductance spectroscopy (PCS) was previously applied to bicrystals [7]. The experimental set-up is identical with the GB LB1C system. Scanning the sample under the focused light beam (2500 nm > 2 > 1100 nm) an increase of overbarrier current (bias, about 2 mV) is detectable when the light spot illuminates the GB provided that there are states in the band gap above the neutral Fermi level at the GB. Measuring the maximum current increment as a function of wavelength a local GB spectrum is obtained, as presented in Fig. 6 for two samples of different casting processes. With the dark resistance and the change in conductance the local barrier height ~ b ( h V ) under monochromatic illumination can be derived. The two spectra show marked differences; in sample A (SILSO) the photoconductance is measurable for energies smaller than 0.7 eV, whereas in sample B (Wacker research material) there is no signal below 0.96 eV.
3.
Theory
The quantitative description of the measured data is based on models presented previously by Seager [3] and Werner [8]. Since we measure a GB electric field which is attractive for electrons, we can assume that the GB is positively charged and the charge arises predominantly from donor states lying above the equilibrium Fermi level Ev° at the GB. In the GB PCS the positive charge at the GB is reduced by the excitation of holes from GB states above the Fermi level into the valence band. Other processes can be neglected since the excited carriers have to be separated spatially from the GB. Thus a GB PCS signal will only be detectable for photons with energy hv >1Ev ° = ~. + q~d
(3 )
if ~ is the Fermi level in the bulk and ~ j the dark barrier height (Fig. 7). During illumination the resulting charge and hence the barrier height is given by the balance condition between thermal and optical excitation with photon flux density W and thermal recombination (Fig. 7, arrow labelled r). Werner showed how the density of states can be obtained from the measurement of Q(hv) for fixed qs and Q(qJ) for several hv by fitting the measured data to an equation which results from the detailed balance condition. For small changes in the charge (e.g. at room temperature) it can be shown that a relative distribution of states can be evaluated from the derivative of Q with respect to
J. Palm et aL
/
Electrical properties of grain boundaries
59
100.00~
® ® ®®
10.00-
E
Ev÷hV
1.00-
0.100.01 11 O0 12'00 13'00 14'00 15'00 16'00 17'00 18'00 19~00 2.0100
Fig. 7. Werner's model.
wave length (nm)
Fig. 6. GB photoconductance spectrum: current increment vs. wavelength. • SILSO, o Wacker research material.
Nss
(a.u.) 1
0.5
hv for a fixed photon flux density. Figure 8 shows the relative density of states evaluated for the examples presented in Fig. 6. Sample A (SILSO) has a continuum in the gap with small maxima and a tail towards the conduction band; sample B (Wacker research material) shows only a band tail. In the GB EBIC or LBIC experiments, minority carriers are generated by above band gap excitation. Hence the capture and emission processes of both carder types at the GB and the diffusion of the minority carriers to the GB have to be taken into account. In the model of Seager [3] (Fig. 2) all traps are described by the same capture cross-sections. The fraction c of over-barrier hole current captured at the GB depends on the majority-carrier capture cross-section Op and on the number ArT' of unfilled traps. The capture current density Jcapn of electrons is related to the minoritycarrier capture cross-section an, the number NT of filled traps and the density of minority carriers at the GB. This is controlled by the diffusion current density ]difn of electrons to the GB which is described by solving a one-dimensional diffusion problem. We have shown in ref. 2 how the diffusion problem has to be modified for the GB EBIC case of the local one-sided generation by an electron beam. The emission of holes (]emp) is approximated by the capture rate under dark conditions and the emission of electrons can be neglected. The barrier height and the diffusion current (proportional to the GB EBIC for U = 0 ) are calculated as a function of excitation level (or beam current) by requiting detailed balance of all currents. During excitation the GB electric field is responsible for the effective collection of the generated minority carriers. The recombination is limited by LapP since the holes have to overcome the potential barrier. For increasing excitation level the captured electrons lower the positive GB charge. Therefore the barrier decreases and the hole current increases so that the
0.i 0.05
0.01 0.005
0.001
\ 0.7
0.8
0.9
E (ev) Fig. 8. Relative distribution of states for GBs in Silso (curve A) and Wacker research material (curve B).
balance is maintained. For higher excitations the diffusion gradient from the generation volume to the GB decreases so that the GB is less effective, i.e. the recombination velocity decreases. With decreasing GB barrier the recombination rate is governed by the minority-carrier capture cross-section. These processes can be observed with GB EBIC measuring both the GB EBIC peak value ( U-- 0) and the barrier height, and the measured data can be well described by simulations with this model (full curves in Figs. 3 and 5). The fitted parameters of these calculations are the minority-carrier capture cross-section On and the fraction c of over-barrier hole current captured at GB states [2, 3]. If the majority-carrier capture crosssection is known (e.g. from admittance measurements) the total number of traps can be determined. We obtained, for the SILSO GB, ~0 -- 0.3 __0.02 eV, o, = (0.85 - - 0 . 0 5 ) X 10 -16 cm 2, c = 0 . 0 2 +0.005, O'p~---"10 -13 cm 2 and N O~ 1012 cm -2.
4. Conclusion
We presented three techniques for the local investigation of the electrical properties of GB and showed
60
J. Palm et al.
/
Electrical properties of grain boundaries
briefly how the measured data can be quantitatively described and evaluated. We are now working on the application to the characterization of GBs in different materials and on the correlation with structural analysis (TEM). T h e G B PCS will be experimentally improved (low temperatures and spectral range) and should be first applied to GBs intentionally contaminated with process-relevant impurities such as Fe, Cu, C and O. T h e measured differences between GBs of different cast processes (Figs. 6 and 8) have to be further investigated in order to decide whether G B structure or process-induced contaminations are responsible for them.
References t J. Palm and H. Alexander, J. Phys. (Paris) Ili, Colloq. C6, 1 (1991) 101. 2 J. Palm, J. Appl. Phys., 74 (1993) 1169. 3 C.H. Seager, J. Appl. Phys., 52 ( 1981 ) 3960. 4 Y. Marfaing and J. L. Maurice, in J. H. Werner, H. J. M611er and H, P. Strunk (eds.), Polycrystalline Semiconductors 11, in Springer Proc. Phys., 35 (1991 ) 205. 5 C. H~i$1er, G. Pensl, M. Schulz, A. Voigt and H. P. Strunk, Phys. Status Solidi A, 137 (1993) 50. 6 G.E. Pike and C. H. Seager, J. Appl. Phys., 50 (1979) 3414. 7 H. F. Matare', Defect Electronics in Semiconductors, Wiley-lnterscience, New York, 1971, p. 349. 8 J. H. Werner, W. Jantsch, K. H. Fr6hner and H. J. Queisser, in G. E. Pike, C. H. Seager and J. Leamy (eds.), Grain Boundaries in Semiconductors, Elsevier, Amsterdam, 1982, p. 415.
Materials' Science and Engineering, B24 (1994) 56-60
Local investigation of the electrical properties of grain boundaries J. Palm, D. Steinbach and H. Alexander II. Physikalisches Institut, Abteilung fiir Metallphysik, Universitiit zu K6ln, K6ln (Germany)
Abstract We present the recent development of three related techniques for the local investigation of grain boundaries (GBs): grain boundary electron-beam-induced current (GB EBIC), grain boundary light-beam-induced current (GB LBIC) and local grain boundary photoconductance spectroscopy (GB PCS). Two grains which are separated by a common GB are ohmically connected to a current amplifier. In GB EBIC a focused electron beam and in GB LBIC a focused fight beam of
above band gap energy is scanned across the GB. At GBs with a two-dimensional coherent potential barrier a characteristic dark-bright signal is observed which is directly related to the recombination current through the boundary. By applying a small bias, the local attenuation of the potential barrier height as a function of the injection level can be determined. In GB PCS a beam of monochromatic subband gap light is used. By applying a bias, the change in the GB barrier height due to the excitation of carriers into the GB trap states can be detected by the change in the over-barrier current. By varying the light energy, a section of the local distribution of states in the gap can be determined.
1. Introduction We have recently presented the grain boundary (GB) electron-beam-induced current (EBIC) experiment [1, 2] for the characterization of GBs in large-grained polycrystalline (i.e. multicrystalline) silicon for photovoltaic application. In this paper we briefly summarize the principles of this technique and report further developments by replacing the electron beam by a focused light beam in a scanning optical microscope which finally leads to a local spectroscopy of grain boundaries. A GB model for the quantitative description and evaluation of the measured data is given.
in a line perpendicular to the grain boundary results in a characteristic bright-dark current profile (Fig. 1)[1 ]. This GB EBIC signal is due to the electric field of the grain boundary (Fig. 2); minority carriers generated by the electron beam in grain 1 diffuse to the GB and are efficiently drawn into the GB by its attractive field. They recombine with majority carriers trapped in the GB localized states. Holes from both sides of the GB which overcome the barrier at equal rates by thermal excitation refill these traps. The hole current from grain 2 results in a carrier difference between the grains. This will be balanced by the current through the ammeter from grain 1 to grain 2, which is the GB EBIC. We solved the three-dimensional diffusion
2. Experiments
2.1. Material and sample preparation For all experiments samples containing one single GB were cut from wafers of multicrystalline sificon (SILSO and research material from Wacker). They were mechanically polished with diamond paste and alumina down to 0.05 /~m grain size. Ohmic contacts were prepared on the polished surface at least 1 mm away from the GB by scratching InGa dots or by evaporating aluminium dots and subsequent local heating. 2.2. Grain boundary electron-beam-induced current The two grains are ohmically connected to a current amplifier and the sample is placed in a scanning electron microscope with the polished surface normal to the electron beam axis. Scanning the electron beam 0921-5107/94/$7.00 SSDI 0921-5107(93)00526-5
Ohmic I I Contac~
o:-'2.,
. _! \
exp. like rise i :......... I Y = diffusion region ~_~
=generation signalwidth
volume diameter
Fig. 1. Experimental set-up for GB EBIC. © 1994 - Elsevier Sequoia. All rights reserved
J. Palm et aL /
l
Electrical properties of grain boundaries
57
250 ®...~
200 "~ 1 5 0 U H
~ .L_........~
.
£ jcnap "P
ET E
~
m i00 nn 50
grain 1
GB
grain 2
Fig. 2. Currents at the GB (the capture and emission currents refer to the Seager model discussed below).
problem of two perpendicular surfaces with different finite recombination velocities and evaluated the diffusion lengths of the adjacent grains by analysing the current profiles [1]. By measuring the signal width, i.e. the distance between the two current peaks, the lateral extension of the generation volume and its dependence on the beam voltage can be determined [1]. The GB EBIC peak value which is proportional to the recombination current through the GB has been analysed with respect to its dependence on the beam current, i.e. the excitation level [2] (Fig. 3). The decrease in the slope of the function GB EBIC vs. beam current is related to the decrease in the GB recombination velocity owing to the injection of minority carriers. The detailed balance of capture and emission currents at the GB results in a decrease in the GB charge and hence the GB potential barrier (models for these processes have been given in refs. 3-5, and our modification of a model given by Seager for the GB EBIC is summarized below and has been discussed in detail in ref. 2). The recombination current is only an indirect physical quantity with respect to the GB potential barrier. Therefore in standard EBIC measurements (with a Schottky contact or p-n junction) there is no direct access to the barrier height. However, the GB EBIC experiment can easily be extended to the simultaneous measurement of majority-carrier properties [2]; applying a small bias (much less than kT, 10 ~V to 2 mV) the baseline shifts linearly with U and the shape of the current profile becomes asymmetrical. The maximum relative amplitude increases linearly with increasing U. Figure 4 gives the equivalent circuit for the local current voltage characteristic of the total current and illustrates the processes at the GB during local one-sided excitation under a small bias; along the y axis, which is in the GB plane x = 0, the potential barrier (z or energy axis) is reduced in places close to the electron beam. On application of a bias the majority-carrier current I flows in the x direction perpendicular to the GB. During local excitation at the GB, two paths are open for the current: first through the small area with reduced
200
400
600
800
I000 1 2 0 0
Fig. 3. GB EBIC peak value vs. beam current:
Ib /
pA
, simulated.
e-b~
e-b4
Rd
×=0
Fig. 4. GB with locallyreduced barrier and equivalentcircuit.
barrier ~ b (in the equivalent circuit represented by the resistance Rb), and second through the large unchanged GB with a mean dark barrier ~d (represented by Ro). From the theory of thermionic emission we obtain for the current across a double barrier [6] (for q U ~ kT, where Y is the zero-bias conductance): I = YU
(1)
with Y/F= ( q / k T )A exp[ - ( qdp + ~ )/ k T], F the area, A the pseudo-Richardson constant and ~ the position of the Fermi level in the bulk. We recently showed that the area F b with reduced barrier (P b is equal to the generation volume cross-section. In the quantitative analysis the ohmic resistance of bulk and contacts has to be taken into account. By the measurement of dark resistance and conductance change (evaluated from current increment and bias) finally the local attenuation of the barrier height as a function of beam current can be obtained as shown in Fig. 5 (GBs in SILSO material). 2.3. Grain boundary light-beam-induced current As shown already by Matare' [7] the dark-bright signal can also be obtained by substituting the electron
58
Z Palm et al.
/
Electrical properties ~f grain boundaries
>m0.25[ m
0.2
0.15 .8,--,__
200 400 600 800 I000 1200 Fig. 5. Barrier height vs. beam current:
Ib
/
pA
, simulated.
beam by a focused spot of above-band-gap light. We used a computer-controlled IR microscope with a scanning stage. The light coming from a quartz-halogen source is chopped and passes through a monochromator and the optical system. The current signal is amplified by the lock-in technique and digitized for profile analysis. The excitation geometry is different now; we measured the signal width d for different wavelengths and found a linear relation to the reciprocal absorption coefficient a: d = spot size + constant x a - 1
(2)
From this we can estimate that the maximum signal is achieved when the generation cone touches the GB at a depth of ¼ a-1. Using a monochromatic beam with large penetration depth (2 = 1/~m) most of the carriers are generated deep in the bulk and surface recombination is negligible. Hence the current profiles are purely exponential and the diffusion length can easily be obtained [1]. This method is also applicable to wafers with several GBs, provided that the GBs are GB EBIC active and the grains are larger than a few diffusion lengths. By applying a small bias the same phenomena as shown for the GB EBIC experiment can be observed; minority carriers which are generated by the above-band-gap light diffuse to the GB and the decrease in the GB potential barrier leads to an increase in the majority-carrier current which is observable by the resulting asymmetry of the GB light-beam-induced current (LBIC) profile. Owing to the large difference in excitation level the measured attenuation of the barrier heights are smaller than in GB EBIC ( A ~ ~-60 meV for a photon flux density of 3 × 1017 cm- 2 S- 1). 2.4. Grain boundary photoconductance spectroscopy The local investigation of the electrical properties of GBs with GB EBIC or LBIC demanded for both additional spectroscopic and structural investigations. Our work in the development of GB LBIC under bias directly led to the idea of a local GB spectroscopy; using subband gap light no generation of excess minority
carriers occurs but, if the energy of the photons is suitable for a direct excitation of trapped carriers from the GB into the bands, the change in the GB charge will be measurable as an increase in over-barrier current. As an integral technique this GB photoconductance spectroscopy (PCS) was previously applied to bicrystals [7]. The experimental set-up is identical with the GB LB1C system. Scanning the sample under the focused light beam (2500 nm > 2 > 1100 nm) an increase of overbarrier current (bias, about 2 mV) is detectable when the light spot illuminates the GB provided that there are states in the band gap above the neutral Fermi level at the GB. Measuring the maximum current increment as a function of wavelength a local GB spectrum is obtained, as presented in Fig. 6 for two samples of different casting processes. With the dark resistance and the change in conductance the local barrier height ~ b ( h V ) under monochromatic illumination can be derived. The two spectra show marked differences; in sample A (SILSO) the photoconductance is measurable for energies smaller than 0.7 eV, whereas in sample B (Wacker research material) there is no signal below 0.96 eV.
3.
Theory
The quantitative description of the measured data is based on models presented previously by Seager [3] and Werner [8]. Since we measure a GB electric field which is attractive for electrons, we can assume that the GB is positively charged and the charge arises predominantly from donor states lying above the equilibrium Fermi level Ev° at the GB. In the GB PCS the positive charge at the GB is reduced by the excitation of holes from GB states above the Fermi level into the valence band. Other processes can be neglected since the excited carriers have to be separated spatially from the GB. Thus a GB PCS signal will only be detectable for photons with energy hv >1Ev ° = ~. + q~d
(3 )
if ~ is the Fermi level in the bulk and ~ j the dark barrier height (Fig. 7). During illumination the resulting charge and hence the barrier height is given by the balance condition between thermal and optical excitation with photon flux density W and thermal recombination (Fig. 7, arrow labelled r). Werner showed how the density of states can be obtained from the measurement of Q(hv) for fixed qs and Q(qJ) for several hv by fitting the measured data to an equation which results from the detailed balance condition. For small changes in the charge (e.g. at room temperature) it can be shown that a relative distribution of states can be evaluated from the derivative of Q with respect to
J. Palm et aL
/
Electrical properties of grain boundaries
59
100.00~
® ® ®®
10.00-
E
Ev÷hV
1.00-
0.100.01 11 O0 12'00 13'00 14'00 15'00 16'00 17'00 18'00 19~00 2.0100
Fig. 7. Werner's model.
wave length (nm)
Fig. 6. GB photoconductance spectrum: current increment vs. wavelength. • SILSO, o Wacker research material.
Nss
(a.u.) 1
0.5
hv for a fixed photon flux density. Figure 8 shows the relative density of states evaluated for the examples presented in Fig. 6. Sample A (SILSO) has a continuum in the gap with small maxima and a tail towards the conduction band; sample B (Wacker research material) shows only a band tail. In the GB EBIC or LBIC experiments, minority carriers are generated by above band gap excitation. Hence the capture and emission processes of both carder types at the GB and the diffusion of the minority carriers to the GB have to be taken into account. In the model of Seager [3] (Fig. 2) all traps are described by the same capture cross-sections. The fraction c of over-barrier hole current captured at the GB depends on the majority-carrier capture cross-section Op and on the number ArT' of unfilled traps. The capture current density Jcapn of electrons is related to the minoritycarrier capture cross-section an, the number NT of filled traps and the density of minority carriers at the GB. This is controlled by the diffusion current density ]difn of electrons to the GB which is described by solving a one-dimensional diffusion problem. We have shown in ref. 2 how the diffusion problem has to be modified for the GB EBIC case of the local one-sided generation by an electron beam. The emission of holes (]emp) is approximated by the capture rate under dark conditions and the emission of electrons can be neglected. The barrier height and the diffusion current (proportional to the GB EBIC for U = 0 ) are calculated as a function of excitation level (or beam current) by requiting detailed balance of all currents. During excitation the GB electric field is responsible for the effective collection of the generated minority carriers. The recombination is limited by LapP since the holes have to overcome the potential barrier. For increasing excitation level the captured electrons lower the positive GB charge. Therefore the barrier decreases and the hole current increases so that the
0.i 0.05
0.01 0.005
0.001
\ 0.7
0.8
0.9
E (ev) Fig. 8. Relative distribution of states for GBs in Silso (curve A) and Wacker research material (curve B).
balance is maintained. For higher excitations the diffusion gradient from the generation volume to the GB decreases so that the GB is less effective, i.e. the recombination velocity decreases. With decreasing GB barrier the recombination rate is governed by the minority-carrier capture cross-section. These processes can be observed with GB EBIC measuring both the GB EBIC peak value ( U-- 0) and the barrier height, and the measured data can be well described by simulations with this model (full curves in Figs. 3 and 5). The fitted parameters of these calculations are the minority-carrier capture cross-section On and the fraction c of over-barrier hole current captured at GB states [2, 3]. If the majority-carrier capture crosssection is known (e.g. from admittance measurements) the total number of traps can be determined. We obtained, for the SILSO GB, ~0 -- 0.3 __0.02 eV, o, = (0.85 - - 0 . 0 5 ) X 10 -16 cm 2, c = 0 . 0 2 +0.005, O'p~---"10 -13 cm 2 and N O~ 1012 cm -2.
4. Conclusion
We presented three techniques for the local investigation of the electrical properties of GB and showed
60
J. Palm et al.
/
Electrical properties of grain boundaries
briefly how the measured data can be quantitatively described and evaluated. We are now working on the application to the characterization of GBs in different materials and on the correlation with structural analysis (TEM). T h e G B PCS will be experimentally improved (low temperatures and spectral range) and should be first applied to GBs intentionally contaminated with process-relevant impurities such as Fe, Cu, C and O. T h e measured differences between GBs of different cast processes (Figs. 6 and 8) have to be further investigated in order to decide whether G B structure or process-induced contaminations are responsible for them.
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