- Email: [email protected]
Time-resolved scanned electron beam annealing of ion-implanted polycrystalline silicon
0026-269218411501-0030$5.00/0
Time-resolved scanned electron beam annealing of ion-implanted polycrystalline silicon by E. F. Krimmel* and A. G. K. Lutsch** *Siemens AG, M~Jnchen, West Germany **Rand Afrikaans University, Johannesburg, RSA
Polycrystalline silicon layers of grains with an average diameter of 100 nm and with a thickness of 500 nm grown on an amorphous SiO2 layer are implanted with a dose of 4 x 10 is cm-2 boron ions at an ion energy of 25 keV and subsequently annealed up to maxima of 950°C and/or 300 s with a scanned and line-focussed electron beam of a current density of 1.1 mA/cm 2 at an electron energy of 18 keV. T w o annealing stages and t w o weak reverse ones are observed in contrast to a single annealing stage and a strong single reverse one obtained on phosphorus-or arsenic- implanted polycrystalline silicon layers. A simple model is presented in order to explain the experimental results. The impact of the results on device design for VLSI and solar cells is mentioned.
1.
Introduction
Up to now, very large scale integration (VLSI) is achieved mainly by scaling down the device dimensions without affecting too much the conventional technologies of manufacture. However, we are approaching some limits of these technologies for technical as well as basic physical reasons. Technical limits, for instance the cross-talk between interconnections, may be bypassed by means of artful design. Absolute physical limits such as the tunnelling of electrons through thin insulating layers of the thickness of less than, say, 7 nm are of a quantum mechanical nature and may be bypassed only by introducing new technologies. Scaling-down device dimensions cannot include scaling-down the process times, e.g. the temperature-depending annealing time of radiation damage caused by ion implantation or the redistribution of dopants due to diffusion during such processes. These barriers may arise already in designing 1-Mbit memories and one possible approach to surmounting these difficulties may be in replacing two-dimensional planar structures with three-dimensional ones. In order to utilise the third dimension, multilayer structures of insulating layers alternating with conducting polysilicon layers deposited on single-crystal silicon substrates must exhibit high quality t because active device elements also have to be incorporated into the polysilicon layers. Polycrystalline silicon layers are also of increasing interest in manufacturing solar cells, for economical reasons. The final quality of the grain boundaries after having produced the p-n junction by diffusion or ion implantation is an essential parameter in determining the performance of solar cells. In this connection we report the time-dependent annealing behaviour of ion implanted polycrystalline silicon layers and their properties and compare the experimental result with calculations based on a simple theoretical model. 30
MICROELECTRONICSJOURNAL Vo115 No 1 © 1984Benn ElectronicsPublications Ltd, Luton
(-) 0
Cathode Wehnel
/
O-20k
t
Anode
I
1
OuadruDollens
~""°o~ ~ ~
;;,~ I
%
I el
t I
tI
ObJect plan~__._.~ j;~....... .~,,.,.,,.,~ I
Line focus
ObJect plane
Fig. 1 Electron b e a m annealer with a line-focussed scanned electron beam.
31
~me-resolved scanned electron beam annealingof ion-implanted polycrystalline silicon continued from page 31
2. Experiments According to the present trend, devices are processed at the lowest possible temperatures. H e n c e undoped, fine-grained polycrystalline silicon layers were grown to a thickness of 500 nm by low pressure chemical vapor deposition (CVD) at 620°C on 50 nm thick SiO2 surface layers of 20 ohm cm p-(100)-silicon wafers. 2 T h e polysilicon layers exhibited a (110) texture. These polysilicon layers of grains with average diameter of 100 nm, were implanted with a dose of 4 x 10 ~5cm -2 boron ions at an ion energy o f 25 keV (Rp = 79.5 nm, A Rp = 36.6 nm). T h e surface layer of the polysilicon, with a thickness of approximately 120 nm becomes heavily damaged due to the high implantation dose. The implanted wafers were subdivided into chips o f 0.8 × 0.8 cm 2. These chips were mounted on to a graphite holder with four pyramidal points supporting the specimen in order to reduce heat loss by thermal contact between specimen and graphite holder. This procedure ensures a sufficiently uniform ~ t e m p e r a t u r e distribution over the entire chip. The specimens to be annealed were irradiated with a scanned and line-focussed electron beam at a current density of 1.1 mA/cm 2 and an electron energy of 18 keV. In o r d e r to eliminate effects like the generation of slip lines, an electron beam annealer with a line focus 3 was used in this work and not the conventional type with a point focus. TM T h e electron beam annealer 3 (Fig. 1) evacuated by a turbomolccular pump down to 10-3 Pa consists of an electron gun with a point cathode of tungsten and a spheric Wehnelt cylinder for long focal length, a magnetic quadrupole lens acting as a cylindrical lens or an electrostatic three-electrode cylindrical lens in order to focus the electron beam on the specimen surface into a line of 2 x 0.1 cm 2 area. A magnetic scanner, which can be linearly operated with scan frequencies up to approximately 1.5 kHz, is mounted between the cylindrical lens and the specimen. High thermomechanical stresses generating slip lines are safely avoided 3 by scanning the line focus with frequencies above, say, 500 Hz. No damage to the oxide layer is observed after annealing the specimen. The annealing occurs in thermodynamic equilibrium in contrast to short pulse irradiation. Beam current and electron energy can be adjusted with high precision leading to reproducible processes. The temperature of the specimen can be kept within 2°C as measured with a filament pyrometer. T h e electron beam irradiation was stopped when the specimen reached the temperature preset on the filament pyrometer. The maximum annealing time was 300 s and the maximum annealing temperature 950°C. The temperature of the specimen rises almost linearly up to 850°C in 5 s 4 and reaches the constant maximum value of approximately 950°C after an irradiation time of 10 s. Thus the annealing is a solid phase process and is limited to temperatures of practical interest. T h e annealed specimens are characterised by the sheet resistance Rs. Hall measurements supplied some additional information about the Hall mobility, /ZH, and the sheet concentration of the electrically active dopants C,, but were not worked out quantitatively because the inhomogenous distribution of the dopants needs special analysis not included in conventional van der Pauw measurements. This will be presented elsewhere. T h e results obtained by the measurement of the sheet resistance R, are compared with the results of phosphorus or arsenic-implanted specimens obtained in earlier work. 4 T h e specimens were irradiated on the front side because it was shown ~ that there is no difference in the results whether irradiating the front side or the back. The temperature difference between front side and back is balanced out after approximately 25 ms s due to the high velocity o f the thermal wave generated at the instantaneously irradiated spot. 3. Experimental results T h e measured sheet resistance Rs of the annealed specimens is plotted against the irradiation time t (Fig. 2). The sheet resistance Rs remains very high up to a temperature of approximately 700°C at the chosen rate of temperature rise. Above 700°C (after the irradiation time of 3 s) 32
i~ I I I I //
I O
aP
d~
/ / / ,~ f , p f
I I /
I
/ /
d
/
/ f
,/
,-
I
lb
2b
~
1
.0
btcoa.i~ TtMEt
I
~s~
I
,It
Fig. 2 Sheet resistance Rs(ohm/I-q) of boron-, arsenic- and phosphorus-implanted specimens versus the annealing time t(s.); polysilicon(500 nm) on SiO2 (50 rim). Implantation • boron 4.10'Jcm -~, 25 keV; A arsenic 2.1015 cm -2, ll0 keV; phosphorus 2.1015 cm-2, 50 keV; annealing: electron beam 1.1 mA/cm2, 18 keV, 500 Hz; * value of boron after 300 s anneal.
the sheet resistance Rs decreases in a fraction of a second to a value which is already very close to the calculated one (30 ohm/["l). 8 T h e sheet resistance R,, however, starts to increase by prolonging the irradiation time t as observed in annealing phosphorus or arsenic-implanted specimens 4 (Fig. 2), but it decreases again after an irradiation time of 20 s and reaches an absolute m i n i m u m after a time of approximately 35 s. The resistance increases in turn only slightly by the factor of 1.4 during continuing annealing. This two-stage annealing separated by a reverse one obtained on boron implanted specimens is different from the one-stage annealing with a final increase of the sheet resistance by the factor of about 10, obtained on arsenic or phosphorus-implanted specimens, 4 and will be treated elsewhere. It might be attributed to differences in the re-ordering and diffusion processes. The main electrical activation of the implanted boron atoms is achieved in the first annealing stage but the main re-ordering of the damaged crystal lattice in the second one. T h e final weak increase o f the resistance is attributed to the partial outdiffusion of boron into the grain boundaries. 33
)3me-resolved scanned electron beam annealing of ion-implanted polycrystalline silicon continued from page 33
4. Theoretical model and discussion In o r d e r to determine theoretically the change of the resistance Rs of the polysilicon layer after the annealing of 300 s, a simple one-dimensional diffusion model is assumed with grain boundaries acting as inexhaustible sinks for diffusing boron atoms. All crystallites shall have the same length of 10 -5 cm and the origin of the distance measuring the crystal length is put in the grain boundary. As it turns out later, the crystallite may be treated as semi-infinite along the x-axis (Fig. 3). Space charge effects might be neglected due to the high concentration of the implanted dopants. T h e activation energy E and diffusion constant Do can be determined using:
D = D o exp [ - E / ( k T ) ]
............................................
(1)
from known plotted values, 6 E = 3.84 eV; Do = 53.6 cmZ/s with D(90(PC) = 9.4 x 10 -16 cmZ/s. I f we name the trapping rate of boron atoms in the grain boundary 'a', the differential equation for diffusion: 8C/8t = D ~ C / S x 2
............................................
(2)
............................................
(3)
has to be solved under the condition:
DSC/ x = a(C - Co)
at x = 0 where Co is the constant original doping concentration inside the crystaUite and c, the doping concentration at the grain boundary. T h e general solution is: C(x)/Co = err [x(4Dt) -v'] + exp [ax/D + aZt/D] erfc [x(4Dt) -v2 +
(aZtlD)V']...
(4)
H o w e v e r , the diffusion along the grain boundary may be 1000 times larger than in the bulk of the crystallite. 7 The second term in eqn. (4) does not give a significant contribution and the problem can be treated with the simple approximation: C(x)/Co = erf[x(4Dt) -v~]
............................................
(5)
T h e average normalised sheet resistance can be determined from: X
Rs(X)/R~o = f
4d O
X
(1/eft(X) d X / f O
dX, with lim R d R ~ = 1
(6)
X~e
where R~o is the minimum sheet resistance measured experimentally (97 ohm/Q) and X = x(4Dt) -trz is the normalised length of the crystallite assuming that the sheet resistance changes almost linearly with 1/C in the doping range to be considered. 8 Equation (6) was evaluated numerically for the diffusion coefficient D = 9.4 x 10-t6 cm2/s and the process time t -- 300 s. T h e normalised sheet resistance RdR~o is plotted against the normalised crystal depth X = x(4Dt)-v' in Fig. 4. The two diagrams of Figs. 3 and 4 show that crystallites with a normalised length o f X > 5 can be treated as semi-infinite. The sheet resistance of a crystal of length 100 nm increases by a factor of 1.36 due to the outdiffusion of the boron into the grain boundary. T h e same result is obtained experimentally. T h e contribution of the potential barrier of the grain boundary is small compared with the change of the sheet resistance due to outdiffusion. The potential barrier Va can be calculated from: VB = eQZ/(8~ eoC)
............................................
(7)
where Q = 3 × 10 ~2 cm -2 is t h e trap density in the grain boundary, e = 1.6x I0-~9C the e l e m e n t a r y charge, ~ = 11.6 the dielectric constant of silicon, ~o = 8.9× 10 -t4 Fcm -1 the vacuum permittivity and C = 4× 10 z° cm-3 the carrier density in the doped layer. 9 T h e potential barrier turns out to be VB = 10-3V. Only thermionic emission will contribute 34
1,0
_~
f
o.6
~ 0.6 0.2
1.~"
2.~
,.~
~
~.'~
0~sr~l. t.l~-m x Fig. 3 Normalised dopant concentration C/Co calculated using eqn. (5) versus crystal length x. The grain boundary is at x = 0 and the grain extends to x > 0.
4
~2
2
~ N~.I ~
4 5 I.J~~ ~ c~r~r~c X
6
Fig. 4 Normalised sheet resistance Rs/Rso versus normalised crystal length X = x(4Dt) -v2. 35
"lime-resolved scannedelectronbeam annealingof ion-implanted polycrystalline silicon continuedfrompage35
to the carrier transport across the grain boundary since tunnelling can be neglected at such low barrier heights. Hence, the conductivity across the grain boundary is trB = xe2C(2 m*kT)-V' exp[-eVB/(kT)]
..............................
(8)
where m* is the effective mass of the holes and x the length of the crystallite. The numerical value of the sheet resistance
R,a = (trB. d)-'
............................................
(9)
turns out to be approximately R s ~ 5 ohm/l:] where d = 1.1 × 10-5 cm is the thickness of the implanted layer. The good agreement between the experimental results and the theoretically obtained values indicates that the contribution of the resistance of the grain boundary is small compared with the resistance of the crystallite and hence can be neglected. The resistance change is mainly due to outdiffusion of boron.
5.
Conclusions
Electron beam annealed boron-, arsenic- or phosphorus-implanted specimens show that the re-ordering process in boron-implanted specimens is due to atomic diffusion of boron into the grain boundaries at activation energies well known to be valid for ordinary diffusion. The enhanced reverse annealing observed on arsenic or phosphorus-implanted specimens indicates a process controlled by much lower activation energies which must be attributed to migration of complexes. It must be emphasised, that these experiments were performed to show the diffusion effects of electrically active dopants in a pronounced way. In order to obtain the bulk material value 8 of the electrical activation of dopants, a large extent of solid- or liquid-phase recrystallisation of such fine-grained CVD-polycrystalline silicon layers has to be achieved prior to ion implantation or after ion implantation during annealing in a furnace or by laser or electron beam irradiation. The reverse annealing peak observed on boron implanted specimens might be attributed to the beginning of the well known weak re-ordering processes of the polycrystalline structure of the polysilicon layer. This peak, of course, is too small to be seen on the arsenic or phosphorus implanted specimens. There is a fundamental impact of these results on device design. We may state that the reduced reaction of boron in fine-grained polysilicon on long lasting high-temperature annealing compared with the reactions of arsenic or phosphorus and the decreasing difference in hole and electron drift velocity (approximately 107 cm/s at electric field strengths of 105 V/cm) with decreasing channel length of MOS transistors 10should lend more weight to the application of ion implanted p-channel MOS transistors in polysilicon layers of VLSI devices than was the case before. Solar cell grade polysilicon often turns out to be n-type if no additional purification is carried out for reasons of economy. The relatively high thermal stability of the boron doping offers such material a good chance for application in solar cell manufacture. 6.
Acknowledgments
The authors wish to thank the Siemens technology group for preparing the polysilicon layers, H. Glawischnig and J. Hoepfner for ion implantation and Mrs H. Fellner and K. Eden for assistance in carrying out the measurements. The authors thank the Research Grants Division of the CSIR for financial support. 7.
References
[1] Krimmel, E. F., Lamatsch, H. and Runge, H., Proc. Syrup.Laser and Electron Beam Processingof Electronic Materials, Los Angeles, 14-19 Oct. 1970, ECS 80-1,161 (1980). 36
[2] Oppolzer, H., Falckenberg, R. and Doering, E., J. Microscopy, 118, 97 (1980). [3] Kdmmel, E. F., Phys. Stat. Sol., (a) 70, K63 (1982). [4] Krimmel, E. E , Lutsch, A. G. K. and Doering, E., Phys. Star. Sol., (a) 71,451 (1982). [5] Wondrak, W., Diplomarbeit, Universit~it Frankfurt/Main (1981). [6] Tuck, B., Introduction to diffusion in semiconductors, IEE Monograph Ser., 16, Peregrinus, Stevenage (1974). [7] Holloway, P. H., J. Vac. Sci. Techn., 21, 19 (1982). [8] Dearnaly, G., Freeman, J. H., Nelson, R. S. and Stephen, J., Ion Implantation, North-Holland, Amsterdam (1973). [9] Seto, J. Y. W., J. Appl. Phys., 46, 5247 (1975). [10] Nelson, D. F. and Cooper, Jnr., J. A., Workshop on the Physics of Submicron Structures, Urbana, Illinois, 28-30 June (1982). [11] McMahon, R. A., Ahmed, H. and Cullis, A. G., Appl. Phys. Letters, 37, 1016 (1980).
37
Time-resolved scanned electron beam annealing of ion-implanted polycrystalline silicon by E. F. Krimmel* and A. G. K. Lutsch** *Siemens AG, M~Jnchen, West Germany **Rand Afrikaans University, Johannesburg, RSA
Polycrystalline silicon layers of grains with an average diameter of 100 nm and with a thickness of 500 nm grown on an amorphous SiO2 layer are implanted with a dose of 4 x 10 is cm-2 boron ions at an ion energy of 25 keV and subsequently annealed up to maxima of 950°C and/or 300 s with a scanned and line-focussed electron beam of a current density of 1.1 mA/cm 2 at an electron energy of 18 keV. T w o annealing stages and t w o weak reverse ones are observed in contrast to a single annealing stage and a strong single reverse one obtained on phosphorus-or arsenic- implanted polycrystalline silicon layers. A simple model is presented in order to explain the experimental results. The impact of the results on device design for VLSI and solar cells is mentioned.
1.
Introduction
Up to now, very large scale integration (VLSI) is achieved mainly by scaling down the device dimensions without affecting too much the conventional technologies of manufacture. However, we are approaching some limits of these technologies for technical as well as basic physical reasons. Technical limits, for instance the cross-talk between interconnections, may be bypassed by means of artful design. Absolute physical limits such as the tunnelling of electrons through thin insulating layers of the thickness of less than, say, 7 nm are of a quantum mechanical nature and may be bypassed only by introducing new technologies. Scaling-down device dimensions cannot include scaling-down the process times, e.g. the temperature-depending annealing time of radiation damage caused by ion implantation or the redistribution of dopants due to diffusion during such processes. These barriers may arise already in designing 1-Mbit memories and one possible approach to surmounting these difficulties may be in replacing two-dimensional planar structures with three-dimensional ones. In order to utilise the third dimension, multilayer structures of insulating layers alternating with conducting polysilicon layers deposited on single-crystal silicon substrates must exhibit high quality t because active device elements also have to be incorporated into the polysilicon layers. Polycrystalline silicon layers are also of increasing interest in manufacturing solar cells, for economical reasons. The final quality of the grain boundaries after having produced the p-n junction by diffusion or ion implantation is an essential parameter in determining the performance of solar cells. In this connection we report the time-dependent annealing behaviour of ion implanted polycrystalline silicon layers and their properties and compare the experimental result with calculations based on a simple theoretical model. 30
MICROELECTRONICSJOURNAL Vo115 No 1 © 1984Benn ElectronicsPublications Ltd, Luton
(-) 0
Cathode Wehnel
/
O-20k
t
Anode
I
1
OuadruDollens
~""°o~ ~ ~
;;,~ I
%
I el
t I
tI
ObJect plan~__._.~ j;~....... .~,,.,.,,.,~ I
Line focus
ObJect plane
Fig. 1 Electron b e a m annealer with a line-focussed scanned electron beam.
31
~me-resolved scanned electron beam annealingof ion-implanted polycrystalline silicon continued from page 31
2. Experiments According to the present trend, devices are processed at the lowest possible temperatures. H e n c e undoped, fine-grained polycrystalline silicon layers were grown to a thickness of 500 nm by low pressure chemical vapor deposition (CVD) at 620°C on 50 nm thick SiO2 surface layers of 20 ohm cm p-(100)-silicon wafers. 2 T h e polysilicon layers exhibited a (110) texture. These polysilicon layers of grains with average diameter of 100 nm, were implanted with a dose of 4 x 10 ~5cm -2 boron ions at an ion energy o f 25 keV (Rp = 79.5 nm, A Rp = 36.6 nm). T h e surface layer of the polysilicon, with a thickness of approximately 120 nm becomes heavily damaged due to the high implantation dose. The implanted wafers were subdivided into chips o f 0.8 × 0.8 cm 2. These chips were mounted on to a graphite holder with four pyramidal points supporting the specimen in order to reduce heat loss by thermal contact between specimen and graphite holder. This procedure ensures a sufficiently uniform ~ t e m p e r a t u r e distribution over the entire chip. The specimens to be annealed were irradiated with a scanned and line-focussed electron beam at a current density of 1.1 mA/cm 2 and an electron energy of 18 keV. In o r d e r to eliminate effects like the generation of slip lines, an electron beam annealer with a line focus 3 was used in this work and not the conventional type with a point focus. TM T h e electron beam annealer 3 (Fig. 1) evacuated by a turbomolccular pump down to 10-3 Pa consists of an electron gun with a point cathode of tungsten and a spheric Wehnelt cylinder for long focal length, a magnetic quadrupole lens acting as a cylindrical lens or an electrostatic three-electrode cylindrical lens in order to focus the electron beam on the specimen surface into a line of 2 x 0.1 cm 2 area. A magnetic scanner, which can be linearly operated with scan frequencies up to approximately 1.5 kHz, is mounted between the cylindrical lens and the specimen. High thermomechanical stresses generating slip lines are safely avoided 3 by scanning the line focus with frequencies above, say, 500 Hz. No damage to the oxide layer is observed after annealing the specimen. The annealing occurs in thermodynamic equilibrium in contrast to short pulse irradiation. Beam current and electron energy can be adjusted with high precision leading to reproducible processes. The temperature of the specimen can be kept within 2°C as measured with a filament pyrometer. T h e electron beam irradiation was stopped when the specimen reached the temperature preset on the filament pyrometer. The maximum annealing time was 300 s and the maximum annealing temperature 950°C. The temperature of the specimen rises almost linearly up to 850°C in 5 s 4 and reaches the constant maximum value of approximately 950°C after an irradiation time of 10 s. Thus the annealing is a solid phase process and is limited to temperatures of practical interest. T h e annealed specimens are characterised by the sheet resistance Rs. Hall measurements supplied some additional information about the Hall mobility, /ZH, and the sheet concentration of the electrically active dopants C,, but were not worked out quantitatively because the inhomogenous distribution of the dopants needs special analysis not included in conventional van der Pauw measurements. This will be presented elsewhere. T h e results obtained by the measurement of the sheet resistance R, are compared with the results of phosphorus or arsenic-implanted specimens obtained in earlier work. 4 T h e specimens were irradiated on the front side because it was shown ~ that there is no difference in the results whether irradiating the front side or the back. The temperature difference between front side and back is balanced out after approximately 25 ms s due to the high velocity o f the thermal wave generated at the instantaneously irradiated spot. 3. Experimental results T h e measured sheet resistance Rs of the annealed specimens is plotted against the irradiation time t (Fig. 2). The sheet resistance Rs remains very high up to a temperature of approximately 700°C at the chosen rate of temperature rise. Above 700°C (after the irradiation time of 3 s) 32
i~ I I I I //
I O
aP
d~
/ / / ,~ f , p f
I I /
I
/ /
d
/
/ f
,/
,-
I
lb
2b
~
1
.0
btcoa.i~ TtMEt
I
~s~
I
,It
Fig. 2 Sheet resistance Rs(ohm/I-q) of boron-, arsenic- and phosphorus-implanted specimens versus the annealing time t(s.); polysilicon(500 nm) on SiO2 (50 rim). Implantation • boron 4.10'Jcm -~, 25 keV; A arsenic 2.1015 cm -2, ll0 keV; phosphorus 2.1015 cm-2, 50 keV; annealing: electron beam 1.1 mA/cm2, 18 keV, 500 Hz; * value of boron after 300 s anneal.
the sheet resistance Rs decreases in a fraction of a second to a value which is already very close to the calculated one (30 ohm/["l). 8 T h e sheet resistance R,, however, starts to increase by prolonging the irradiation time t as observed in annealing phosphorus or arsenic-implanted specimens 4 (Fig. 2), but it decreases again after an irradiation time of 20 s and reaches an absolute m i n i m u m after a time of approximately 35 s. The resistance increases in turn only slightly by the factor of 1.4 during continuing annealing. This two-stage annealing separated by a reverse one obtained on boron implanted specimens is different from the one-stage annealing with a final increase of the sheet resistance by the factor of about 10, obtained on arsenic or phosphorus-implanted specimens, 4 and will be treated elsewhere. It might be attributed to differences in the re-ordering and diffusion processes. The main electrical activation of the implanted boron atoms is achieved in the first annealing stage but the main re-ordering of the damaged crystal lattice in the second one. T h e final weak increase o f the resistance is attributed to the partial outdiffusion of boron into the grain boundaries. 33
)3me-resolved scanned electron beam annealing of ion-implanted polycrystalline silicon continued from page 33
4. Theoretical model and discussion In o r d e r to determine theoretically the change of the resistance Rs of the polysilicon layer after the annealing of 300 s, a simple one-dimensional diffusion model is assumed with grain boundaries acting as inexhaustible sinks for diffusing boron atoms. All crystallites shall have the same length of 10 -5 cm and the origin of the distance measuring the crystal length is put in the grain boundary. As it turns out later, the crystallite may be treated as semi-infinite along the x-axis (Fig. 3). Space charge effects might be neglected due to the high concentration of the implanted dopants. T h e activation energy E and diffusion constant Do can be determined using:
D = D o exp [ - E / ( k T ) ]
............................................
(1)
from known plotted values, 6 E = 3.84 eV; Do = 53.6 cmZ/s with D(90(PC) = 9.4 x 10 -16 cmZ/s. I f we name the trapping rate of boron atoms in the grain boundary 'a', the differential equation for diffusion: 8C/8t = D ~ C / S x 2
............................................
(2)
............................................
(3)
has to be solved under the condition:
DSC/ x = a(C - Co)
at x = 0 where Co is the constant original doping concentration inside the crystaUite and c, the doping concentration at the grain boundary. T h e general solution is: C(x)/Co = err [x(4Dt) -v'] + exp [ax/D + aZt/D] erfc [x(4Dt) -v2 +
(aZtlD)V']...
(4)
H o w e v e r , the diffusion along the grain boundary may be 1000 times larger than in the bulk of the crystallite. 7 The second term in eqn. (4) does not give a significant contribution and the problem can be treated with the simple approximation: C(x)/Co = erf[x(4Dt) -v~]
............................................
(5)
T h e average normalised sheet resistance can be determined from: X
Rs(X)/R~o = f
4d O
X
(1/eft(X) d X / f O
dX, with lim R d R ~ = 1
(6)
X~e
where R~o is the minimum sheet resistance measured experimentally (97 ohm/Q) and X = x(4Dt) -trz is the normalised length of the crystallite assuming that the sheet resistance changes almost linearly with 1/C in the doping range to be considered. 8 Equation (6) was evaluated numerically for the diffusion coefficient D = 9.4 x 10-t6 cm2/s and the process time t -- 300 s. T h e normalised sheet resistance RdR~o is plotted against the normalised crystal depth X = x(4Dt)-v' in Fig. 4. The two diagrams of Figs. 3 and 4 show that crystallites with a normalised length o f X > 5 can be treated as semi-infinite. The sheet resistance of a crystal of length 100 nm increases by a factor of 1.36 due to the outdiffusion of the boron into the grain boundary. T h e same result is obtained experimentally. T h e contribution of the potential barrier of the grain boundary is small compared with the change of the sheet resistance due to outdiffusion. The potential barrier Va can be calculated from: VB = eQZ/(8~ eoC)
............................................
(7)
where Q = 3 × 10 ~2 cm -2 is t h e trap density in the grain boundary, e = 1.6x I0-~9C the e l e m e n t a r y charge, ~ = 11.6 the dielectric constant of silicon, ~o = 8.9× 10 -t4 Fcm -1 the vacuum permittivity and C = 4× 10 z° cm-3 the carrier density in the doped layer. 9 T h e potential barrier turns out to be VB = 10-3V. Only thermionic emission will contribute 34
1,0
_~
f
o.6
~ 0.6 0.2
1.~"
2.~
,.~
~
~.'~
0~sr~l. t.l~-m x Fig. 3 Normalised dopant concentration C/Co calculated using eqn. (5) versus crystal length x. The grain boundary is at x = 0 and the grain extends to x > 0.
4
~2
2
~ N~.I ~
4 5 I.J~~ ~ c~r~r~c X
6
Fig. 4 Normalised sheet resistance Rs/Rso versus normalised crystal length X = x(4Dt) -v2. 35
"lime-resolved scannedelectronbeam annealingof ion-implanted polycrystalline silicon continuedfrompage35
to the carrier transport across the grain boundary since tunnelling can be neglected at such low barrier heights. Hence, the conductivity across the grain boundary is trB = xe2C(2 m*kT)-V' exp[-eVB/(kT)]
..............................
(8)
where m* is the effective mass of the holes and x the length of the crystallite. The numerical value of the sheet resistance
R,a = (trB. d)-'
............................................
(9)
turns out to be approximately R s ~ 5 ohm/l:] where d = 1.1 × 10-5 cm is the thickness of the implanted layer. The good agreement between the experimental results and the theoretically obtained values indicates that the contribution of the resistance of the grain boundary is small compared with the resistance of the crystallite and hence can be neglected. The resistance change is mainly due to outdiffusion of boron.
5.
Conclusions
Electron beam annealed boron-, arsenic- or phosphorus-implanted specimens show that the re-ordering process in boron-implanted specimens is due to atomic diffusion of boron into the grain boundaries at activation energies well known to be valid for ordinary diffusion. The enhanced reverse annealing observed on arsenic or phosphorus-implanted specimens indicates a process controlled by much lower activation energies which must be attributed to migration of complexes. It must be emphasised, that these experiments were performed to show the diffusion effects of electrically active dopants in a pronounced way. In order to obtain the bulk material value 8 of the electrical activation of dopants, a large extent of solid- or liquid-phase recrystallisation of such fine-grained CVD-polycrystalline silicon layers has to be achieved prior to ion implantation or after ion implantation during annealing in a furnace or by laser or electron beam irradiation. The reverse annealing peak observed on boron implanted specimens might be attributed to the beginning of the well known weak re-ordering processes of the polycrystalline structure of the polysilicon layer. This peak, of course, is too small to be seen on the arsenic or phosphorus implanted specimens. There is a fundamental impact of these results on device design. We may state that the reduced reaction of boron in fine-grained polysilicon on long lasting high-temperature annealing compared with the reactions of arsenic or phosphorus and the decreasing difference in hole and electron drift velocity (approximately 107 cm/s at electric field strengths of 105 V/cm) with decreasing channel length of MOS transistors 10should lend more weight to the application of ion implanted p-channel MOS transistors in polysilicon layers of VLSI devices than was the case before. Solar cell grade polysilicon often turns out to be n-type if no additional purification is carried out for reasons of economy. The relatively high thermal stability of the boron doping offers such material a good chance for application in solar cell manufacture. 6.
Acknowledgments
The authors wish to thank the Siemens technology group for preparing the polysilicon layers, H. Glawischnig and J. Hoepfner for ion implantation and Mrs H. Fellner and K. Eden for assistance in carrying out the measurements. The authors thank the Research Grants Division of the CSIR for financial support. 7.
References
[1] Krimmel, E. F., Lamatsch, H. and Runge, H., Proc. Syrup.Laser and Electron Beam Processingof Electronic Materials, Los Angeles, 14-19 Oct. 1970, ECS 80-1,161 (1980). 36
[2] Oppolzer, H., Falckenberg, R. and Doering, E., J. Microscopy, 118, 97 (1980). [3] Kdmmel, E. F., Phys. Stat. Sol., (a) 70, K63 (1982). [4] Krimmel, E. E , Lutsch, A. G. K. and Doering, E., Phys. Star. Sol., (a) 71,451 (1982). [5] Wondrak, W., Diplomarbeit, Universit~it Frankfurt/Main (1981). [6] Tuck, B., Introduction to diffusion in semiconductors, IEE Monograph Ser., 16, Peregrinus, Stevenage (1974). [7] Holloway, P. H., J. Vac. Sci. Techn., 21, 19 (1982). [8] Dearnaly, G., Freeman, J. H., Nelson, R. S. and Stephen, J., Ion Implantation, North-Holland, Amsterdam (1973). [9] Seto, J. Y. W., J. Appl. Phys., 46, 5247 (1975). [10] Nelson, D. F. and Cooper, Jnr., J. A., Workshop on the Physics of Submicron Structures, Urbana, Illinois, 28-30 June (1982). [11] McMahon, R. A., Ahmed, H. and Cullis, A. G., Appl. Phys. Letters, 37, 1016 (1980).
37