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Implant dose uniformity simulation program
Nuclear Instruments and Methods in Physics Research B55 (1991) 253-256 North-Holland
Implant
dose uniformity
simulation
253
program
Nobuo Nagai N&in
Electric Co., Ltd., Ion Equipment
Division, 575 Kuze Tonoshiro-cho,
Minami-ku,
Kyoto, Japan
A two-dimensional implant dose uniformity simulation code consisting of two programs named SCAN and MAP has been developed. The code can take account of the effects of beam sweep waveform, beam sweep frequency, beam size, and wafer rotation speed. The result of the calculations can be plotted in a two-dimensional contour map similar to a wafer uniformity map.
1. Introduction It is very useful to simulate implant dose uniformity on a computer because we can simplify the situation and are able to see the dose distribution as implanted without being disturbed by post-process. Sheet resistivity and Tberrna-wave [l] measurements are the most common techniques to assess the uniformity of the implant dose. But those methods do not measure the implanted ions directly, so the results are influenced by some effects other than from the implanter such as anneal conditions and channeling effects. Besides difficulty in the measurement, an ion implanter itself presents many uncertainties that affect the measurements of dose uniformity. For example, fluctuation on ion beam current, noise on beam sweep waveform, channeling effects due to implant angle (wafer tilt and twist angle) can make a complicated pattern in dose uniformity map [21. To evaluate the essential effects of implanter parameters on implant dose uniformity, a computer simulation program has been developed. The computer code calculates the two-dimensional implant dose distribution over a wafer with given machine parameters such as beam sweep frequencies of x and y directions, a beam sweep waveform, a wafer rotation speed, a wafer tilt angle, and a beam density distribution. With this simulation we can predict the optimal conditions for uniform implantation, on an electrostatically scanned serial implanter with or without wafer rotation.
footprint for every short constant time interval. The program counts the number of footprints left by an ion beam on each mesh. After implant, the counts of the footprint in one mesh show how many times the mesh (small part of a wafer) is exposed to the ion beam. The simulation code consists of two programs. The program 1 names SCAN calculates the beam position at every short time interval and makes a data file containing the footprint counts which is later used by the program 2. The program 2 named MAP calculates the uniformity over the wafer and draws a 2-D contour map. The mesh size must be smaller than the beam size and the uniformity structure which one wants to see on the uniformity map. Using a shorter time interval gives a more precise simulation, but it uses much CPU time. A .desirable time interval is the time in which a beam scans l/2 or l/3 mesh. (The tune interval shown in fig. 1 is too long.) In the program SCAN, a beam is assumed to have a
Wafer \
Mesh
Beam scan area
I
/
2. Description of simulation code The computer code simulates ion implantation on a wafer. To simulate the process by a digital computer, area and time have to be quantized. An implant area is divided into a small rectangular mesh pattern as shown in fig. 1. An ion beam sweeping over the wafer leaves a 0168-583X/91/$03.50
Beam path
footprints
of beam
Fig. 1. Coordinate of simulation and mesh.
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
III. THROUGHPUT
& YIELD
254
N. Nagai / Implant dose uniformity simulation program Wafer ( tilted 45 degree
)
circle indicates the wafer area. The parameters simulation used in this case are as follows: beam scan area: mesh size: time interval: beam:
Fig. 2. Treatment of wafer tilt angle. point cross section, but the actual beam has a size and density distribution. To evaluate the effects of beam spot size, in the program MAP, dose data on the wafer for every mesh is calculated by a weighted average of the footprint counts around the mesh. The weight represents the beam density distribution. The resultant dose uniformity data is plotted as a contour map like a sheet resistivity map with the signs switched. The program SCAN can generate data for MAP if the beam position at any time is known. In the case of an electrostatic-scan implanter (such as a common medium current implanter), the beam position on the wafer is determined by the voltage applied to the scanning electrodes. A tilted wafer is treated as a beam position Y, changed to Y as illustrated in fig. 2. When SCAN simulates the wafer rotational implantation [4], the simulation coordinate system is rotated with the wafer.
3. Result of simulation The implant
result of a simulation for a 45” tilt angle is shown in fig. 3a. In the simulated map, a
of the
150 mm (W) X 150 mm (H); 2 mm square; 6.53 us; Gaussian distribution (both x and y directions), u = 3 mm.
Fig. 3b is an experimentally obtained sheet resistivity map of a 45” tilt angle implant. The comparison of the simulation and the experiment shows a quite good agreement. But it should be noted that the physical quantity shown in each map is different. Fig. 3a represents the dose uniformity and fig. 3b shows the sheet resistivity. Both maps show the increase of dose from the right bottom to the left top. The pattern is caused by the change in the beam sweep velocity over the wafer [3]. Fig. 4 shows simulation results of a 45 o tilt implant with wafer rotation. The simulation parameters are the same as for fig. 3a. It is shown that the rotational implant for a large tilt angle implant is effective to improve uniformity as reported [4,5]. The simulation shows the uniformity improves from 2.66% to 0.16% for an implant with 1.3 rps wafer rotation. A resonance occurs when the implant time is very short compared with the period of wafer rotation. An example of the resonance pattern is shown in fig. 5a. Fig. 5b is an experimental Therma-wave map. Fig. 5c is derived from fig. 5a using empirical Therma-wave sensitivity. It is shown that the simulation gives fairly good agreement with the experimental result. A resonance occurs at a certain combination of beam scan frequency and wafer rotation speed. Even a ---_ ,J --_-
l-._
/SA ,_ ..- _‘. ,:., _’ \ ./_.A, _.r- _,--4 _/’ ,’ Ye\\ ,// ,,’ ‘.\ ,.” _’ . . . ,’ ,.;- ,A--: _?- ,..c -. /.I_ \ 2’’ __-J” >‘, _...__~..,’ ._.d .’ ,/f / ,~/ _ ( “: / /’ [ __::::;_g, , ,** i \ f 4, ” I __,’ i _&___.‘i, , ,___i--.-; j ,.) -. -.._.---+ .-- ! + /’ i ,_/ _- .-7,. ,rG ,, ,_. ;: ”\ I_/ * ’ .,_f/ / _I-- _F--,-,’.I + iI ,,A’ ;.-,’ ., + ,,’ ., c---‘-~-A% (b) Fig. 3. Uniformity maps of 45 o tilt angle implant. (The wafer twist angle is 300.) (a) A calculated dose uniformity map. The dotted line shows the contour line of a higher dose region and the solid line shows the contour line of a lower dose region. A contour interval is 1% dose. Uniformity is 2.66%. (b) An experimental sheet resistivity map. A higher dose area is indicated by “-” sign. A contour interval is 1% sheet resistitity. Uniformity is 2.67%.
N. Nagai / Implant dose uniformity simulation program
255
Fig. 6. Simulation of beam scan and wafer rotation resonance pattern. Vertical beam scan frequency is 504.16 Hz, and other parameters are the same as for fig. 5a.
Fig. 4. Effect of rotational implant. Simulation parameters are the same as for fig. 3a. Uniformity is 0.16%. Only average lines are shown.
small variation of a parameter can result in a very large in the resonance pattern as shown in figs. 6 and ?I. change
4. Conclusion A two-dimensional simulation code for implant dose uniformity mapping was developed. This simulation code can be used to examine the effects of beam sweep waveform, beam sweep frequency, beam size, and wafer rotation speed and can help us to predict a “good combination” of the beam scan parameters.
Fig. 7. Simulation of beam scan and wafer rotation resonance pattern. Vertical beam scan frequency is 501.38 Hz, and other parameters are the same as for fig. 5a.
References 111 W.L. Smith, A. Rosencwaig, D.L. Willenborg, J. Opsal and M.W. Taylor, Nucl. Instr. and Meth. B21 (1987) 537.
Fig. 5. Simnlation of beam scan and wafer rotation resonance pattern. Implant time: 5 s; wafer rotation speed: 1.0 rps; beam scan frequency: H: 88.85 Hz, V: 502.13 Hz. (a) Simulation. Dose uniformity: 6.53%; contour interval: 5%. (b) An experimental result, Therma-wave (TW) map. TW uniformity: 0.80%; contour interval: 0.5%; TW signal: 609.6 TW units. (c) Simulation. The dose is converted to Therma-wave units. Empirical Therma-wave sensitivity used is as follows: TW = - 1580.61+ 168.063 log,,(dose). TW uniformity: 0.79%; contour interval: 0.5%: TW signal: 604.05 TW units.
III. THROUGHPUT
& YIELD
256
N. Nagai / Implant dose uniformity simulation program
[2] MI. Current, N.L. Turner, T.C. Smith and D. Crane, Nucl. Ins&. and Meth. B6 (1985) 336. [3] M. Sasaki, M. Tanaka, H. Kawakami and H. Kumazaki, Nucl. Instr. and Meth. B37/38 (1989) 469. [4] Y. Tamura, M. Nogami, M. Tanaka, T. Maeda, H.
Kumasaki and S. Tamura, Nucl. Instr. and Meth. B37/38 (1989) 620. [5] S. Oh&i, M. Nagatomo, K. Higashitani, T. Takahashi and T. Hirao, Proc. 31st Semiconductor and Integrated Circuit Technology Symp., Tokyo (Dec. 1986) p. 97, in Japanese.
Implant
dose uniformity
simulation
253
program
Nobuo Nagai N&in
Electric Co., Ltd., Ion Equipment
Division, 575 Kuze Tonoshiro-cho,
Minami-ku,
Kyoto, Japan
A two-dimensional implant dose uniformity simulation code consisting of two programs named SCAN and MAP has been developed. The code can take account of the effects of beam sweep waveform, beam sweep frequency, beam size, and wafer rotation speed. The result of the calculations can be plotted in a two-dimensional contour map similar to a wafer uniformity map.
1. Introduction It is very useful to simulate implant dose uniformity on a computer because we can simplify the situation and are able to see the dose distribution as implanted without being disturbed by post-process. Sheet resistivity and Tberrna-wave [l] measurements are the most common techniques to assess the uniformity of the implant dose. But those methods do not measure the implanted ions directly, so the results are influenced by some effects other than from the implanter such as anneal conditions and channeling effects. Besides difficulty in the measurement, an ion implanter itself presents many uncertainties that affect the measurements of dose uniformity. For example, fluctuation on ion beam current, noise on beam sweep waveform, channeling effects due to implant angle (wafer tilt and twist angle) can make a complicated pattern in dose uniformity map [21. To evaluate the essential effects of implanter parameters on implant dose uniformity, a computer simulation program has been developed. The computer code calculates the two-dimensional implant dose distribution over a wafer with given machine parameters such as beam sweep frequencies of x and y directions, a beam sweep waveform, a wafer rotation speed, a wafer tilt angle, and a beam density distribution. With this simulation we can predict the optimal conditions for uniform implantation, on an electrostatically scanned serial implanter with or without wafer rotation.
footprint for every short constant time interval. The program counts the number of footprints left by an ion beam on each mesh. After implant, the counts of the footprint in one mesh show how many times the mesh (small part of a wafer) is exposed to the ion beam. The simulation code consists of two programs. The program 1 names SCAN calculates the beam position at every short time interval and makes a data file containing the footprint counts which is later used by the program 2. The program 2 named MAP calculates the uniformity over the wafer and draws a 2-D contour map. The mesh size must be smaller than the beam size and the uniformity structure which one wants to see on the uniformity map. Using a shorter time interval gives a more precise simulation, but it uses much CPU time. A .desirable time interval is the time in which a beam scans l/2 or l/3 mesh. (The tune interval shown in fig. 1 is too long.) In the program SCAN, a beam is assumed to have a
Wafer \
Mesh
Beam scan area
I
/
2. Description of simulation code The computer code simulates ion implantation on a wafer. To simulate the process by a digital computer, area and time have to be quantized. An implant area is divided into a small rectangular mesh pattern as shown in fig. 1. An ion beam sweeping over the wafer leaves a 0168-583X/91/$03.50
Beam path
footprints
of beam
Fig. 1. Coordinate of simulation and mesh.
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
III. THROUGHPUT
& YIELD
254
N. Nagai / Implant dose uniformity simulation program Wafer ( tilted 45 degree
)
circle indicates the wafer area. The parameters simulation used in this case are as follows: beam scan area: mesh size: time interval: beam:
Fig. 2. Treatment of wafer tilt angle. point cross section, but the actual beam has a size and density distribution. To evaluate the effects of beam spot size, in the program MAP, dose data on the wafer for every mesh is calculated by a weighted average of the footprint counts around the mesh. The weight represents the beam density distribution. The resultant dose uniformity data is plotted as a contour map like a sheet resistivity map with the signs switched. The program SCAN can generate data for MAP if the beam position at any time is known. In the case of an electrostatic-scan implanter (such as a common medium current implanter), the beam position on the wafer is determined by the voltage applied to the scanning electrodes. A tilted wafer is treated as a beam position Y, changed to Y as illustrated in fig. 2. When SCAN simulates the wafer rotational implantation [4], the simulation coordinate system is rotated with the wafer.
3. Result of simulation The implant
result of a simulation for a 45” tilt angle is shown in fig. 3a. In the simulated map, a
of the
150 mm (W) X 150 mm (H); 2 mm square; 6.53 us; Gaussian distribution (both x and y directions), u = 3 mm.
Fig. 3b is an experimentally obtained sheet resistivity map of a 45” tilt angle implant. The comparison of the simulation and the experiment shows a quite good agreement. But it should be noted that the physical quantity shown in each map is different. Fig. 3a represents the dose uniformity and fig. 3b shows the sheet resistivity. Both maps show the increase of dose from the right bottom to the left top. The pattern is caused by the change in the beam sweep velocity over the wafer [3]. Fig. 4 shows simulation results of a 45 o tilt implant with wafer rotation. The simulation parameters are the same as for fig. 3a. It is shown that the rotational implant for a large tilt angle implant is effective to improve uniformity as reported [4,5]. The simulation shows the uniformity improves from 2.66% to 0.16% for an implant with 1.3 rps wafer rotation. A resonance occurs when the implant time is very short compared with the period of wafer rotation. An example of the resonance pattern is shown in fig. 5a. Fig. 5b is an experimental Therma-wave map. Fig. 5c is derived from fig. 5a using empirical Therma-wave sensitivity. It is shown that the simulation gives fairly good agreement with the experimental result. A resonance occurs at a certain combination of beam scan frequency and wafer rotation speed. Even a ---_ ,J --_-
l-._
/SA ,_ ..- _‘. ,:., _’ \ ./_.A, _.r- _,--4 _/’ ,’ Ye\\ ,// ,,’ ‘.\ ,.” _’ . . . ,’ ,.;- ,A--: _?- ,..c -. /.I_ \ 2’’ __-J” >‘, _...__~..,’ ._.d .’ ,/f / ,~/ _ ( “: / /’ [ __::::;_g, , ,** i \ f 4, ” I __,’ i _&___.‘i, , ,___i--.-; j ,.) -. -.._.---+ .-- ! + /’ i ,_/ _- .-7,. ,rG ,, ,_. ;: ”\ I_/ * ’ .,_f/ / _I-- _F--,-,’.I + iI ,,A’ ;.-,’ ., + ,,’ ., c---‘-~-A% (b) Fig. 3. Uniformity maps of 45 o tilt angle implant. (The wafer twist angle is 300.) (a) A calculated dose uniformity map. The dotted line shows the contour line of a higher dose region and the solid line shows the contour line of a lower dose region. A contour interval is 1% dose. Uniformity is 2.66%. (b) An experimental sheet resistivity map. A higher dose area is indicated by “-” sign. A contour interval is 1% sheet resistitity. Uniformity is 2.67%.
N. Nagai / Implant dose uniformity simulation program
255
Fig. 6. Simulation of beam scan and wafer rotation resonance pattern. Vertical beam scan frequency is 504.16 Hz, and other parameters are the same as for fig. 5a.
Fig. 4. Effect of rotational implant. Simulation parameters are the same as for fig. 3a. Uniformity is 0.16%. Only average lines are shown.
small variation of a parameter can result in a very large in the resonance pattern as shown in figs. 6 and ?I. change
4. Conclusion A two-dimensional simulation code for implant dose uniformity mapping was developed. This simulation code can be used to examine the effects of beam sweep waveform, beam sweep frequency, beam size, and wafer rotation speed and can help us to predict a “good combination” of the beam scan parameters.
Fig. 7. Simulation of beam scan and wafer rotation resonance pattern. Vertical beam scan frequency is 501.38 Hz, and other parameters are the same as for fig. 5a.
References 111 W.L. Smith, A. Rosencwaig, D.L. Willenborg, J. Opsal and M.W. Taylor, Nucl. Instr. and Meth. B21 (1987) 537.
Fig. 5. Simnlation of beam scan and wafer rotation resonance pattern. Implant time: 5 s; wafer rotation speed: 1.0 rps; beam scan frequency: H: 88.85 Hz, V: 502.13 Hz. (a) Simulation. Dose uniformity: 6.53%; contour interval: 5%. (b) An experimental result, Therma-wave (TW) map. TW uniformity: 0.80%; contour interval: 0.5%; TW signal: 609.6 TW units. (c) Simulation. The dose is converted to Therma-wave units. Empirical Therma-wave sensitivity used is as follows: TW = - 1580.61+ 168.063 log,,(dose). TW uniformity: 0.79%; contour interval: 0.5%: TW signal: 604.05 TW units.
III. THROUGHPUT
& YIELD
256
N. Nagai / Implant dose uniformity simulation program
[2] MI. Current, N.L. Turner, T.C. Smith and D. Crane, Nucl. Ins&. and Meth. B6 (1985) 336. [3] M. Sasaki, M. Tanaka, H. Kawakami and H. Kumazaki, Nucl. Instr. and Meth. B37/38 (1989) 469. [4] Y. Tamura, M. Nogami, M. Tanaka, T. Maeda, H.
Kumasaki and S. Tamura, Nucl. Instr. and Meth. B37/38 (1989) 620. [5] S. Oh&i, M. Nagatomo, K. Higashitani, T. Takahashi and T. Hirao, Proc. 31st Semiconductor and Integrated Circuit Technology Symp., Tokyo (Dec. 1986) p. 97, in Japanese.