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doi:10.1016/j.m

Materials Science in Semiconductor Processing 7 (2004) 13–17

Atomistic simulation of defects evolution in silicon duringannealing after low energy self-ion implantation

Min Yua,*, Ru Huanga, Xing Zhanga, Yangyuan Wanga, Kunihiro Suzukib,Hideki Okab

a Institute of Microelectronics, Peking University, Beijing 100871, PR Chinab Fujistu Laboratories Ltd., Atsugi-shi 243-0197, Japan

Abstract

Defects evolution in silicon during annealing after low energy Si+ implantation is simulated by atomistic method in

this paper. Distribution of implanted dopants and defects is simulated by molecular dynamic method. The experimental

results published by Stolk et al. (J Appl Phys 81 (9) (1991) 6031) are simulated to verify the models and parameters

applied here. The annealing after low energy (5 kev) Si+ implantation is studied by simulation. Although the damage

field is only 10 nm under the surface in this case and thus surface annihilation has important impact on defects

evolution, the experimental results are reproduced by the simulation. The analysis indicates that the Ostwald ripening

can suppress the surface annihilation obviously in the case of low energy implantation.

r 2004 Elsevier Ltd. All rights reserved.

PACS: 67.80 Mg

Keywords: Simulation; Defects; Silicon; Annealing

1. Introduction

Transient-enhanced diffusion (TED) of boron in

silicon occurs in post-implantation annealing [1]. It is

related to the dissolution of Si defects. {3 1 1} defects are

mainly responsible for the TED of boron, as is observed

by TEM. Size of {3 1 1} varies from several nanometers

to hundreds of nanometers. Zig-zag {3 1 1} defects,

which are much stabler than ordinary {3 1 1} defects, are

also observed in the annealing after ultra-low energy

implantation [2]. Whereas {3 1 1} is not the only kind of

defect that contributes to the enhanced diffusion. Many

small silicon precursor clusters exist in the early stage of

annealing. Dislocation loops can also be observed in

some annealed samples. Most small clusters dissolve in

annealing. Whereas larger clusters come into being by

ing author.

ess: yum@ime.pku.edu.cn (M. Yu).

e front matter r 2004 Elsevier Ltd. All rights reserve

ssp.2004.03.003

absorbing free Si interstitial atoms emitted from other

smaller clusters. This mode of evolution is well known as

the Ostwald ripening [3]. On the other hand, surface

annihilation has important impact on defects evolution.

It is especially notable when damage layer is near to the

surface in the case of low energy ion implantation that

has been widely used to form shallow junctions in

integrated circuits.

Several models of Si clusters are published. Rafferty’s

model gives the compact and direct estimation of the

evaporation time of {3 1 1}, with the approximation of

complete sink surface, and describes several experiments

[4,5]. Both analytical model [6] and atomistic model [7]

have been developed to simulate {3 1 1} evolution. The

well developed models can reproduce the annealing of

40 kev Si+ ion implanted silicon, the experimental

results published by Stolk et al. [1]. However, reprodu-

cing the defects evolution in the case of low energy

implantation is not seen although some experimental

d.

ARTICLE IN PRESSM. Yu et al. / Materials Science in Semiconductor Processing 7 (2004) 13–1714

results, such as 5 kev Si+ ion implantation [2], have been

published.

This paper applies the atomistic simulations to the

annealing of low energy implanted silicon. The Mole-

cular Dynamic simulation on implantation and Kinetic

Monte Carlo simulation on anneal are combined to

achieve more reliable calculation. Annealing after 40 kev

Si+ implantation is applied to verify the models and

parameters. The annealing after 5 kev Si+ implantation

is reproduced by the verified models and parameters.

Surface annihilation is discussed. It indicates that the

Ostwald ripening can suppress the surface annihilation.

0 20 40 60 80 1000

20

40

60

80

100

120

140

0

20

40

60

80

100

120

140

Rp(

nm)

Energy (kev)

LEACS TRIM Gibbons data

∆

Rp(

nm)

Fig. 1. The mean projected range and its standard deviation of

Si+ ion implantation into crystal silicon achieved by simulation

and calculation.

2. Atomistic model and simulation method

Kinetic Monte Carlo (KMC) method has been

successfully applied to the annealing simulation [8].

We have developed an annealing simulator named

AMAS based on the KMC. The model implemented

in the simulator is explained in Ref. [9]. In this paper,

AMAS is used to simulate dissipation of defects.

Only defects in silicon are considered in the model.

Single particles are defined in the model to describe

individual point defects, such as single dopant atom, Si

intersitital atom and vacancy. Cluster model is defined

to describe all extended defects that contain two or more

single particles. Clusters result from the gathering of

single particles. Clusters grow up by absorbing free

single particles and evaporate by emitting single

particles. The rate of cluster absorbing is mainly

controlled by the concentration of free single particles

around the cluster. And the rate of cluster emitting is

determined by its dissipation energy.

The dissipation energy of Si clusters has been studied

through experiments. Cowern et al. derive the value

from the boron marker experiments [10]. His result

shows that the dissipation energy oscillates around

about 3.5 ev when clusters’ size is less than 10 atoms and

keeps at about 3.7 ev when clusters’ size ranges from 10

to 200 atoms. Rafferty carries out the direct observation

of {3 1 1} dissipation [4] and takes the activation energy

of {3 1 1} to be 3.57 ev by analyzing the experimental

data. The two results agree with each other roughly. In

our model, the dissipation energy of Si clusters is taken

to be 3.5 ev according to the published data. Although

the dependence of dissipation energy on size is not

considered in this model, the effect of clusters size is

included in the simulator. Larger clusters have more

chances to capture free single particles due to its larger

surface area.

The published experimental data of dissipation time is

related to {3 1 1} defects. No experimental data of small

Si clusters are published due to the limitation of

experiment’s capability. This paper calculates the area

density of clustered Si without distinguishing cluster

size. In fact, the simulation shows that only large

clusters remain after the early period of annealing. Thus

the simulation gives out the results that can be compared

with the experimental data.

It has been in debate whether the surface of silicon

wafer is a good sink for free interstitials during

annealing. On one hand it seems difficult to understand

the cluster formation in annealing for 1 kev Si+

implantation by assuming the perfect surface sink,

because the surface is only 30 A from the damage field

in this case [2]. On the other hand the annealing after

40 kev Si+ implantation can be explained with the

assumption of perfect annihilation at surface [4]. The

latest experiment [5] shows that the dissipation time of

clusters varies linearly with depth confirming that the

surface recombination is the controlling parameter. We

hereby apply the complete sink surface model in the

following simulation.

The initial distribution of Si interstitials and vacancies

generated by ion implantation are key parameters for

annealing simulation. The molecular dynamic (MD)

implantation simulator LEACS [11] developed by us is

used to provide the distribution of defects after

implantation. In this simulator, the mean radius of

single electron is the only fitting parameter embedded in

the electronic stopping model, as is proposed by Cai

et al. [12]. The value of 1.217 A, which is published for

the phosphorus implantation into silicon [12], is adopted

for Si+ ion implantation into silicon after verification.

3. Results and discussion

3.1. Si+ ion implantation

To verify the validity of using 1.217 A as the mean

radius of single electron for Si+ ion implantation,

simulations are performed by using LEACS and the

famous simulator TRIM. The results are plotted in Fig.

1 as well as the data from Gibbons [13]. Mean projected

ARTICLE IN PRESS

100 101 102 103 104 1051011

1012

1013

1014

1015

705 oC 670 oC

Inte

rstit

ials

in c

lust

ers

(cm

-2)

Annealing time (s)

815 oC738 oC

Fig. 3. Simulation results of Si clusters dissipation in the

annealing after Si+ 40 kev 5� 1013 cm�2 implantation. Symbols

show the experimental results.

100 101 102 103 1041011

1012

1013

1014

1015

Inte

rstit

ials

in c

lust

ers

(cm

-2)

Annealing time (S)

Si+ 5kev 1x1014cm-2

Si+ 5kev 3x1014cm-2

750 oC annealing

Fig. 4. Simulation results of Si clusters dissipation in the 750�C

annealing after Si+ 5 kev 3� 1014 and 1� 1014 cm�2 implanta-

tion. Symbols show the experimental results. The underestima-

tion of the dissipation time after 2000 s for higher dose is due to

that abnormal zig-zag {3 1 1} defects domains in the late period

of annealing [2].

M. Yu et al. / Materials Science in Semiconductor Processing 7 (2004) 13–17 15

range Rp and standard deviation DRp are shown in the

figure. The results of LEACS agree with that of TRIM

and Gibbons’ data. It shows that the value of 1.217 A is

valid in simulating Si+ implantation, at least when

energy is less than 80 kev. Considering that 40 and 5 kev

Si+ implantations are concerned here, the value is good

enough.

The 40 and 5 kev Si+ implantation into (1 0 0) crystal

silicon wafer with 7� tilting angle is simulated. The

distribution of Si interstitial and vacancies is achieved.

The concentration of total interstitials and vacancies are

plotted in Fig. 2. In all cases, the peak concentrations

are far below the value of 5� 1022 cm�3, the atom

density of crystal silicon. Thus no amorphorization

occurs. For 5 kev implantation, the peak concentration

of total damage of higher dose (3� 1014 cm�2) implan-

tation is about 3 times that of lower dose (1� 1014 cm�2)

implantation, which agrees with the ratio of dose and

can be explained by considering that no amorphoriza-

tion occurs. On the other hand, the peak concentration

for 5 kev 1� 1014 cm�2 is about 3.3 times that for 40 kev

5� 1013 cm�2. Although the energy of the later is higher,

that ratio is bigger than the corresponding ratio of dose.

That is mainly due to that the 40 kev implantation

induces a much wider spread of defects than 5 kev

implantation as is shown in Fig. 2.

3.2. Dissipation of Si clusters

The annealing after 40 kev Si+ implantation is

simulated firstly. The experimental results are from

Ref. [1], which are achieved by observing the annealed

samples with transmission electron microscopy (TEM),

counting the number of {3 1 1} extended defects within

an area and thus estimating the area density of

interstitials stored in {3 1 1} defects. The experimental

results have been explained [4] and simulated [6,7]. Thus

it is applied to verify the models and parameters in this

paper. The simulation results are shown in Fig. 3. The

area density of clustered Si interstitials extracted from

0 20 40 60 80 100 120 1401018

1019

1020

1021

Con

cent

ratio

n (c

m-3

)

Depth (nm)

Si+ 5kev 1x1014cm-2

Si+ 40kev 5x1013cm-2

Si+ 5kev 3x1014cm-2

Fig. 2. Simulation results of concentration of total damage

caused by 5 and 40 kev Si+ ion implantation.

simulation is compared with the experiment. The

simulation results agree with the experiment at all four

annealing temperatures.

In Fig. 3, it is noticed that the area density is about

2� 1014 cm�2 before 1 s, which is much higher than

5� 1013 cm�2 assumed by ‘‘+1’’ model [4,6]. In this

paper, the initial distribution of defects comes from the

MD implantation simulation. So the assumption of

‘‘+1’’ model is not needed. On the other hand, the

experimental data shows that the area density can reach

1� 1014 cm�2 in the annealing at 670�C and 705�C.

Thus it is reasonable to believe that the amount of

clustered interstitials is underestimated by ‘‘+1’’ model.

The verified model is applied to simulate 750�C

annealing of 5 kev Si+ implantation. The simulation

results are shown in Fig. 4. The experimental results are

from Ref. [2]. It shows that the model again reproduces

the experimental data of two doses. It indicates that the

ARTICLE IN PRESSM. Yu et al. / Materials Science in Semiconductor Processing 7 (2004) 13–1716

model can explain the dissipation of clusters in the case

of low energy implantation. The simulation shows the

initial area density at 1 s is about 2� 1014 cm�2 for lower

dose and 6� 1014 cm�2 for higher dose, which are also

higher than the estimation of ‘‘+1’’ model agreeing with

above discussion.

However, it is noticed that the simulation under-

estimates the dissipation time for 3� 1014 cm�2 implan-

tation in the late period of annealing. It has been

observed in the experiment [2], for 3� 1014 cm�2

implantation, only zig-zag {3 1 1} extended defects

survive after 2� 103–1.7� 105 s anneals whereas ordin-

ary {3 1 1} defects dominate after short anneals (20–

600 s). The size of zig-zag defects is quite larger than

ordinary defects. It indicates that zig-zag {3 1 1} is

stabler than ordinary {3 1 1}. Thus larger dissipation

energy values are necessary for zig-zag defects modeling.

We test the model that let dissipation energy increase

with the size of defects. Although such model can

reproduce the dissipation time for 5 kev implantation, it

tends to overestimate that for 40 kev implantation where

no zig-zag {3 1 1} defects are observed. So it seems that

special model of zig-zag {3 1 1} defects is needed.

3.3. Surface annihilation in annealing

The free single particles emitted from clusters diffuse

to surface and get annihilated there. In later period of

annealing, when most vacancies disappear, surface

annihilation is the main method in which Si interstitials

are annealed out of silicon bulk [8]. The speed of surface

annihilation of interstitials in annealing after 5 kev

1� 1014 cm�2 Si+ implantation is extracted from the

simulation and illustrated in Fig. 5. The surface

annihilation speed is the number of particles that get

annihilated at surface per unit area in unit time. As is

seen, the surface annihilation speed decreases fast and

steadily from 1 s to 500 s. The ratio of the surface

annihilation speed at 1 s to that at 500 s is about 100.

100 101 102 103 1010

1011

1012

1013

1014

sur

face

ann

ihila

tion

(cm

-2s-1

)

Annealing time (s)

Si+ 5kev 1⋅ 1014cm-2 + 750 oC

Fig. 5. Speed of surface annihilation of Si interstitials in the

annealing at 750�C after Si+ 5kev 1� 1014 cm�2 implantation.

Fig. 6. Atomic images of defects from the simulation of Si+ 5

kev 1� 1014 cm�2 implantation and annealing at 750�C for (a)

1 s (b) 50 s (c) 500 s. The black ball is an interstitial Si atom and

the white circle is a vacancy. The Z-axis is the direction of

depth. The size of atoms is enlarged in the image to achieve

proper visual effect.

Whereas the corresponding ratio of total clustered Si

interstitials is about 10, as is shown in Fig. 4. Thus the

fast decrease of surface annihilation speed can not be

explained by the decrease of clustered interstitials only.

ARTICLE IN PRESSM. Yu et al. / Materials Science in Semiconductor Processing 7 (2004) 13–17 17

The analysis on simulation shows that the number of Si

clusters at 1 s to that at 500 s is about 100 and the size of

clusters becomes larger. Thus the large decrease of

surface annihilation speed can be related to the decrease

of cluster numbers in the coarsening process. It is

because the number of free interstitials is controlled by

the emission of clusters. The corresponding atomic

images of defect evolution are shown in Fig. 6. The

annealing at 750�C for 1, 50 and 500 s for Si+ 5 kev

1� 1014 cm�2 are shown here. It should be noticed,

although the damage layer is only about 10 nm under

the surface, the implantation defects do not annihilate

quickly at surface. Instead, Ostwald ripening process

still dominates. Interstitials are stored in clusters and

emitted gradually within the coarsening process of

clusters.

It has been expected that shallow junctions can be

achieved by decreasing the implantation energy of

boron, where the enhanced diffusion of boron will be

suppressed by the surface annihilation of interstitials.

This paper, however, shows that surface annihilation

can be largely suppressed by the Ostwald ripening

process. It can partly explain why the enhanced

diffusion is still obvious for low energy boron implanta-

tion. Thus the evolution of extended defects must be

considered carefully in the shallow junction formation.

4. Conclusion

The Molecular Dynamic simulation on implantation

and Kinetic Monte Carlo simulation on anneal are

performed. The dissipation of clusters in annealing is

successfully reproduced for both 40 and 5 kev implanta-

tion. The annealing for 5 kev implantation, where

damage layer is near the surface, can still be described by

the model. The analysis shows that surface annihilation

is suppressed by the growing up of extended defects.

Acknowledgements

This work is supported by the Natural

Science Foundation of China (project No. 60206004)

and the State Key Fundamental Research Project

(G2000036501).

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