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Analysis and modeling of arsenic activation and deactivation in silicon

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Analysis and modeling of arsenic activation and deactivation in silicon
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Dokumaci, Haci Omer, 1970-
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vii, 134 leaves : ill. ; 29 cm.

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Antimony ( jstor )
Arsenic ( jstor )
Atoms ( jstor )
Boron ( jstor )
Diffusion coefficient ( jstor )
Dosage ( jstor )
Point defects ( jstor )
Precipitates ( jstor )
Silicon ( jstor )
Simulations ( jstor )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1997.
Bibliography:
Includes bibliographical references (leaves 126-133).
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Typescript.
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Vita.
Statement of Responsibility:
by Haci Omer Dokumaci.

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ANALYSIS AND MODELING OF ARSENIC ACTIVATION
AND DEACTIVATION IN SILICON














By


HACI OMER DOKUMACI

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1997














ACKNOWLEDGEMENTS


I would like to thank my advisor, Dr. Mark E. Law, for his support, guidance, and patience throughout my studies in the University of Florida. His great sense of humor, wide knowledge of processing physics, and excellent teaching abilities make him an ideal professor to work with. I would like to thank Drs. Gijs Bosman, Jerry G. Fossum, and Robert M. Fox for their guidance as members of my doctoral committee. I am grateful to Dr. Kevin S. Jones for coming up with several valuable ideas during the course of this work.

I am very grateful to Viswanath Krishnamoorthy, Sushil Bharatan, Jinning Liu, and Brian Beaudet for their help in the TEM work. I would like to thank James Chamblee and Steve Schein for helping me in my experiments, and Mary Turner for her extensive administrative help.

I was very fortunate to share my time at the university with several nice people: Srinath Krishnan, Chih-Chuan Lin, Jonathan Brodsky, Samir Chaudhry, Stephen Cea, Ming-Yeh Chuang, Susan Earles, David Zweidinger, Doug Weiser, and Glenn Workmann. I was lucky to have two very friendly office-mates: Ahmed Ejaz Nadeem and Hernan Rueda.

This dissertation would have been impossible without the unconditional and unending support of my parents, Osman Dokumaci and Esin Dokumaci, and my sister, Merva Dokumaci. I am very grateful to have been blessed with such a good family.



ii








Finally, I would like to thank all my friends in Gainesville for making this period of my life an enjoyable and meaningful one.


















































111















TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS ............................................................... ii

A B ST R A C T ...................................................................................... ..................... vi

CHAPTERS

I INTRODUCTION ........................................ ......................... 1

1.1 Dopant Activation/Deactivation .......................................................... 3
1.1.1 Electrically Active Dopant Concentration .............................................5
1.1.2 Dopant D iffusion .......................................... ............ ................. 9
1.1.3 Point Defect Injection ......................................... .............. 12
1.1.4 D islocation Loops .................................... ........................................ 16
1.2 Organization........................................................17

H TRANSMISSION ELECTRON MICROSCOPY ANALYSIS OF
EXTENDED DEFECTS IN HEAVILY ARSENIC DOPED, LASER,
AND THERMALLY ANNEALED LAYERS IN SILICON ............................... 20

2.1 Introduction ...............................................................20
2.2 Experim ent ............................................................ 22
2.3 TE M R esults ...................................................................................... 24
2.4 C onclusions ............................................................................................... 33

III HIGH DOSE ARSENIC IMPLANTATION INDUCED TRANSIENT
ENHANCED DIFFUSION............................................................................. 34
3.1 Introduction ................................................................. ....................... 34
3.2 Experim ent ....................................................................................... 36
3.3 Results and Discussion ....................................................... ............... 37
3.4 C onclusions............................................................. ............................ 43

IV INVESTIGATION OF VACANCY POPULATION DURING ARSENIC
ACTIVATION IN SILICON ........................................................ ................ 45
4.1 Experim ental D etails....................................................... .................... 46
4.2 Results and Discussion ...................................................... ............... 48
4.3 Vacancy Population in the Partial Absence of Dislocation Loops ........ 55 4.4 Conclusions......................................................... ............................ 58





iv









V A KINETIC MODEL FOR ARSENIC DEACTIVATION......................... 60

5.1 The Physical Structure of Inactive Arsenic ..................................... 60
5.2 Previous Models for Inactive Arsenic................................. ........ 62
5.3 A Kinetic Model for Extended Defects ............................................ 65
5.4 Sim ulation Results ............................................................................. 72
5.5 Conclusions........................................................79

VI A COMPARISON OF VARIOUS NUMERICAL METHODS FOR
THE SOLUTION OF THE RATE EQUATIONS IN EXTENDED
DEFECT SIM ULATION............................................................................ 80

6.1 Introduction ..............................................................80
6.2 Rediscretization................................................ 83
6.2.1 Continuous Form for the Rate Equations.............................. ..... 83
6.2.2 Linear Discretization........................................... 87
6.2.3 Logarithmic Discretization ........................................ .......... 88
6.3 Interpolation ............................................................. 90
6.4 Comparison of Numerical Methods ...................................... ....... 92
6.4.1 Comparison of Size Distributions ....................................... ..... 94
6.4.2 Comparison of Active Concentrations ...................................... 99
6.5 Conclusions ........................................ 102

VII AN ARSENIC DEACTIVATION MODEL INCLUDING THE
INTERACTION OF ARSENIC DEACTIVATION WITH
INTERSTITIALS AND DISLOCATION LOOPS ........................................ 104

7.1 Introduction ........................................ 104
7.2 Model for the Inactive Arsenic-Vacancy Complexes .......................... 106
7.3 Model for Dislocation Loops ..................................... 109
7.4 Point Defect Continuity Equations .............................................. 111
7.5 Simulation Parameters ..................................... 112
7.6 Comparison with Experiments ............................ 115
7.7 Conclusions.............................. 120

VIII CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK....... 122

REFERENCES ........................................ 126
BIOGRAPHICAL SKETCH ..................................... 134














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

ANALYSIS AND MODELING OF ARSENIC ACTIVATION AND DEACTIVATION IN SILICON

By

HACI OMER DOKUMACI

May 1997

Chairman: Dr. Mark E. Law
Major Department: Electrical and Computer Engineering

Heavily doped layers are one of the basic components of semiconductor device technology. As device dimensions shrink, higher electrically active dopant concentrations are required to fabricate devices with desirable properties. However, clustering and precipitation limit the obtainable active dopant concentration. Because of its high solubility and low diffusivity, arsenic is the most commonly used dopant for the fabrication of n+ layers in silicon. The electrical activation and deactivation process of arsenic needs to be understood to assess its effects on the electrical properties of devices.

The focus of this thesis is analysis and modeling of phenomena related to electrical activation and deactivation of arsenic. The properties of the dislocation loops formed during arsenic deactivation were investigated with transmission electron microscopy. The loops are confined inside the arsenic layer, suggesting a strong link between loop formation and inactive arsenic. The reduction in buried boron layer diffusivity can be explained by the increase in the number of atoms bound by the loops. Transient enhanced


vi








diffusion after high dose arsenic implantation was quantified using buried boron layers. Dislocation loops were also studied in these samples. The enhancement in boron diffusivity decreases at higher arsenic doses. The effect of arsenic activation on vacancy population was investigated with antimony marker layers. There is not any observable vacancy injection during arsenic activation in the presence of dislocation loops. Small enhancements in antimony diffusion were observed after the loops had dissolved.

An arsenic deactivation model that takes into account the size distribution of inactive arsenic structures was developed in FLOOPS. The model successfully reproduces the initial rapid deactivation of arsenic and the slow deactivation after the first few minutes. Various numerical methods were evaluated for the numerical solution of the rate equations that describe the size evolution of extended defects. The logarithmic rediscretization method was found to be the most accurate and stable technique for reducing the number of rate equations. The inclusion of the interactions between the arsenic-vacancy complexes, interstitials and dislocation loops led to a more general and physical arsenic deactivation model which can account for several experimental trends.





















vii














CHAPTER I
INTRODUCTION


Heavily doped layers are one of the basic components of semiconductor device technology. As semiconductor devices are scaled down to sub-micron dimensions, the design and the development of these regions become increasingly complex. Figure 1.1 illustrates various heavily doped layers in a typical BiCMOS process. The source/drain regions of the MOS transistors are doped with a high concentration of dopants in order to obtain a low sheet resistance. The buried layers below the MOS devices are used to minimize latch-up. For the bipolar transistor, heavy doping is utilized in the emitter to increase the current gain. The heavily doped extrinsic base and buried collector regions reduce the parasitic resistances associated with the bipolar transistor.

As device dimensions shrink, the absolute value of the threshold voltage of short-channel MOS transistors decreases. One way to reduce this effect is to fabricate shallower source/drain junctions. The resulting increase in the source/ drain sheet resistance should be countered by increasing the electrically active dopant concentration. As the device dimension is reduced, the metal/silicon contact resistance also increases due to the reduction in the area of the contact. The contact resistance can be decreased by utilizing higher active dopant concentrations. However, the active dopant concentration does not increase indefinitely as the




I






2







NMOS PMOS Bipolar





+ P Well P+ N Well P + n+

N Well
P
p n n n






Figure 1.1 A cross-section of the active layers in a typical BiCMOS process.


dopant concentration is increased, because it is limited by the precipitation and clustering processes. These processes determine the electrical activation/ deactivation behavior of dopants. They need to be understood in order to obtain lower sheet and contact resistances and to assess their effects on other electrical properties of the devices.

Arsenic is the most commonly used dopant in the fabrication of n-type layers because of its high electrical activation and low diffusivity, making it a suitable candidate for shallow junction technology. In this chapter, a review of literature on dopant activation/deactivation in silicon will be provided with an emphasis on arsenic. Some of the phenomena related to activation/deactivation and their effects on silicon devices will be discussed. The reasons of why a further understanding








and modeling of arsenic activation/deactivation processes is needed will be explained. Finally, the organization of this dissertation will be given.



1.1 Dopant Activation/Deactivation



Semiconductor technology relies on the ability to fabricate two types of electrically different layers: n-type and p-type. These layers are obtained by doping the semiconductor with electrically active donor or acceptor atoms. An electrically active dopant atom provides a free carrier to the conduction or valence band. When a dopant atom occupies a substitutional site, it creates an energy level that is very close to one of the bands, making it electrically active.

There are several ways of introducing dopant atoms into the semiconductor lattice. Ion-implantation is the most widely used technology for this purpose because of its excellent controllability and reproducibility which are required by today's integrated circuit technology.

During ion-implantation into silicon, the dopant atoms are accelerated to a certain energy and targeted to the silicon substrate. They penetrate through the surface, colliding with many host atoms before losing all their energy and coming to rest. These collisions disturb the crystalline nature of silicon and create disorder in the lattice in the form of point defects and amorphous zones. Most of the implanted dopant atoms do not occupy substitutional sites in such a disordered state. In order to transfer the dopants to substitutional sites and activate them, the substrate is subjected to a temperature treatment at several hundreds degrees Celsius.





4










o





1020




700 800 900 1000 1100
T (C)

Figure 1.2 The temperature dependence of the equilibrium active concentration of arsenic [1].


The electrically active dopant concentration in high concentration layers is determined by the activation/deactivation processes during thermal anneal. Generally speaking, it is a function of the anneal temperature and time, the dopant, the chemical dopant concentration, and the state of the surface layer just after the ion-implantation (amorphous or non-amorphous). Under equilibrium conditions, the active concentration of dopant atoms in silicon, such as arsenic and boron, has been found to exhibit an Arrhenius dependence on temperature. For example, Figure 1.2 shows the equilibrium active concentration of arsenic as a function of temperature [1]. Today's integrated circuit processing conditions usually keep the silicon-dopant system away from equilibrium. Therefore, it is not simply possible to accurately model the active dopant concentration just as a function of temperature.





5


The following sections will describe various phenomena which are related to dopant activation/deactivation in silicon.



1.1.1 Electrically Active Dopant Concentration



When the ion-implantation damage exceeds a certain level, an amorphous layer is formed. Dopants in amorphous layers can be electrically activated up to a concentration many times higher than their equilibrium activation levels. During thermal annealing, arsenic has been observed to activate up to 5x1020 cm-3 at 5600C [2] even though the equilibrium active concentration of arsenic at 7000C is around lx1020 cm-3 (Figure 1.2). The carrier concentration increases until the amorphous layer crystallizes completely. Further annealing causes arsenic to deactivate rapidly [2,3]. Non-equilibrium activation is also observed for boron [4,5] and antimony [6] in amorphized layers. In the case of boron, a preamorphization step is done since impractical high doses of boron are necessary to get an amorphous layer during boron implantation.

The higher activation effect is totally reversed when the sample is not amorphized by the implant. There are several reports indicating that active boron concentration remains much below its equilibrium activation level after ionimplantation and a low temperature anneal [7-9]. As shown in Figure 1.3, the tail of the boron profile undergoes an enhanced diffusion due to ion-implant damage. The peak is immobile, because boron at the peak region is either in the form of clusters or precipitates which can not diffuse through the lattice. The suppressed activation





6





Equilibrium active concentration Immobile peak


O Implanted profile
Annealed
profile Active concentration profile









Depth

Figure 1.3 Representative boron profiles after ion-implantation and diffusion. The profile is not completely electrically active although the peak concentration is much below the equilibrium active concentration.


of boron at the peak has been attributed to the large supersaturation of interstitials just after ion-implantation [9-11]. If boron atoms are assumed to form clusters through a reaction with silicon interstitials, a high supersaturation of interstitials will increase the rate of formation of boron clusters, thus decreasing the electrically active boron concentration. Precipitation has been another explanation for boron deactivation in implanted samples [7].

Arsenic and phosphorus have been shown to exhibit a phenomenon called reverse annealing [12-14] (Figure 1.4). After being annealed at 6500C, high concentration arsenic samples have been subsequently annealed at 7500C [12].





7





6500C 7500C














Equilibrium active concentration


Time


Figure 1.4 Illustration showing the reverse annealing phenomenon in arsenic and phosphorus doped samples.


Although the carrier concentration at the end of the 6500C anneal is above the equilibrium active concentration of arsenic at 7500C, it still increases at the beginning of the 7500C anneal to a maximum. Normally, one would expect a faster rate of deactivation upon increasing the temperature, since the electrically active concentration is above the equilibrium value at that temperature. This phenomenon has been claimed to be a solid proof that the electrically inactive dopant is in the form of precipitates rather than a cluster.

In terms of activation/deactivation, arsenic has been the most studied dopant in silicon because of its peculiar properties. Various studies [15-17] have reported incomplete arsenic deactivation for concentrations below the equilibrium activation





8


level. The deactivation is observed both at the tail and the peak of the profiles. It was suggested that inactive arsenic is in the form of arsenic-point defect pairs [15]. Another explanation has recently been given: Although the electrically active arsenic concentration is below its equilibrium value and no deactivation is expected, significant deactivation will still take place if the free energy of formation of very small inactive arsenic clusters is small enough [18]. The electrically active arsenic concentration is also dependent on the rate of ramp-down at the end of a thermal anneal. A slower ramp-down rate has been observed to increase the arsenic sheet resistance by 30% [19]. In a BiCMOS process, it was demonstrated that the sheet resistance of arsenic doped polysilicon increases upon doubling the ramp-down time [20]. It was also shown in the same study that a subsequent 15 second RTA step significantly reduces n+ silicon and polysilicon sheet resistances and the poly/mono silicon contact resistance by dissolving the precipitates formed during ramp-down.

Laser annealing is another way of activating dopants in semiconductors. Although it is not widely used by industry, it has proved to be a very useful research tool. During laser annealing, a laser beam is directed to the silicon surface, melting the surface layer to a depth which is dependent on the incident laser power. The melt layer regrows very rapidly, incorporating nearly all of the dopant atoms onto substitutional sites. Therefore, up to a certain concentration, dopants can be totally activated with laser annealing. For example, phosphorus has been shown to activate up to a concentration of 5x1021 cm-3 and arsenic up to 3x1021 cm-3 [21]. Laser annealing also wipes out implantation damage and prevents the formation of extended defects like dislocation loops and stacking faults.





9


Because of this macroscopically clean state of silicon just after laser annealing, laser annealing and subsequent thermal annealing have been used numerous times to investigate the deactivation kinetics of dopants [3,5,6,12,13,2123]. Subsequent thermal annealing deactivates dopants at temperatures as low as 3000C [12]. Since laser annealing activates all of the dopants, there is no uncertainty concerning the initial activation conditions. In one of the studies, boxshaped profiles have been created by repeated laser pulse annealing [23]. This allows one to interpret the electrical measurements as characteristic of a single doping concentration. This is not possible with simple thermal annealing since the dopant concentration is a function of depth in that case.



1.1.2 Dopant Diffusion



Substitutional dopants in silicon, such as arsenic, phosphorus and boron, are believed to diffuse via interactions with point defects: interstitials and vacancies [24]. These point defects can exist in various charge states. A chemical reaction between the substitutional dopant and point defects can be envisioned that converts the immobile substitutional dopant to a mobile dopant-defect pair. For a donor atom, this reaction can be written as:




A+ + Xc A+Xc 1-1





10


where A+ represents the substitutional donor atom, Xc represents a point defect with charge c. Since the point defects are charged, their concentration will depend on free carrier concentrations. For example, the concentration of negatively charged point defects with respect to their intrinsic values is given by [24]:




S n- I 1-2 (Cx-) ni




where Cx-, denotes the concentration of X-c defects, (Cx-c)' their concentration in intrinsic silicon, n the electron and ni the intrinsic electron concentration. This equation has been written under the assumptions that the environment is inert and the reactions between point defects and electrons are so fast that they may be considered in chemical equilibrium.

The diffusivity of a dopant is proportional to the concentration of the mobile dopant-defect pairs. Since the number of dopant-defect pairs is proportional to the number of point defects and the number of point defects depend on the free carrier concentration, the diffusivity depends on the free carrier concentration under extrinsic conditions. Actually, if the dopant-defect reactions and the defects are in equilibrium, the diffusivity for a donor atom can be written as:




D = Do+D (- +D (ni)... 1-3





11


where DO is the diffusivity due to uncharged point defects, D_ due to negatively charged defects, etc. At high concentrations and under the condition of charge neutrality, for a single dopant:



n = CA 1-4




where C A is the active dopant concentration. So, ultimately the diffusivity depends on the active dopant concentration under extrinsic conditions.

In so-called isoconcentration studies, the dopant under study is diffused in a region which is homogeneously doped with either another dopant or an isotope of the same dopant at a much higher concentration. This way, the carrier concentration is controlled independently of the diffusing species. The isoconcentration experiments have shown that arsenic [25], phosphorus [26], and antimony [27,28] diffusion are enhanced with increasing electron concentration. Also, boron [29,30] diffusivity is observed to increase with hole concentration.

Recent isoconcentration study by Larsen et al. [31] has revealed an even stronger dependence of arsenic and antimony diffusion on donor concentration than that expressed by Equations 1-3 and 1-4. The diffusivities of arsenic and antimony have been found to be proportional to the third to fifth power of the background phosphorus donor concentration for phosphorus concentrations greater than 2x1020 cm-3. At the highest donor concentrations, the diffusion coefficients are identical for arsenic, antimony and tin, although these dopants have different diffusivities at lower electron concentrations.





12


All the results mentioned above indicate that dopant diffusivities get increasingly sensitive to the amount of electrically active dopant concentration as the concentration is increased. Therefore, high concentration dopant diffusion is tightly coupled to the dopant activation/deactivation phenomena which determine the electrically active dopant concentration. From a modeling point of view, even small errors in the prediction of the electrically active dopant concentrations can result in a big error in dopant diffusivities and make the diffusion simulations unreliable. This point may become more and more important in the future as the IC technology requires higher carrier concentrations and therefore higher temperatures in the sub-micron regime.



1.1.3 Point Defect Injection



A recent study by Rousseau et al. [32] confirmed the interaction between point defects and dopant activation/deactivation (Figure 1.5). Boron buried layers were used as markers of interstitial supersaturation in the bulk. These layers were obtained by first growing a boron doped silicon epi-layer on silicon and then growing an undoped silicon layer on top of it. Arsenic was implanted and the wafers were laser annealed. The laser annealing achieved full electrical activation of arsenic and a flat arsenic concentration, and destroyed the implant damage by melting the surface layer. For control purposes, another wafer was doped with germanium in exactly the same way. Germanium is similar to arsenic in size and mass. Next, the wafers were annealed at 7500C in an inert ambient for 15s and 2 h.





13






- - Electrically active arsenic, as-lased S- - - Electrically active arsenic, after 7500C Boron as-lased


Interstitial injection Boron after 7500C a Arsenic/
S/ Boron




Depth


Figure 1.5 Representative arsenic and boron profiles in Rousseau et al.'s experiment. Boron diffusivity is enhanced up to a factor of 460 when arsenic is deactivated.



Normally, these anneals will not cause any significant diffusion of boron. But, the diffusivity of the boron buried layer was enhanced by a factor of up to 460 for the 2h anneal. Arsenic deactivation occurred in parallel to the enhancements in boron diffusivity.

Extended X-ray Absorption Fine Structure (EXAFS) measurements [33] and theoretical calculations [34] suggest that arsenic deactivates in the form of arsenicvacancy complexes. Since the equilibrium concentration of vacancies is much smaller than the concentration of inactive arsenic, a huge amount of vacancies should be generated in the bulk. These vacancies have been postulated to come from arsenic deactivation assisted interstitial-vacancy pair generation. The generated





14


vacancies are incorporated in the inactive arsenic-vacancy complexes and the interstitials diffuse towards the surface and the bulk, and enhance boron diffusion.

Another study has shown the importance of this phenomenon in bipolar transistors [35]. After arsenic was implanted to form the emitter of the device, it was activated at 11000C for 10s. The wafer was then cut in two, with one half undergoing a deactivation anneal at 7500C for 2h. The two halves were then annealed at 10000C for 15s so that the final active arsenic concentration in both halves would be equal. There should not be any difference in the electrical characteristics of these two transistors since the inert diffusion of boron or arsenic is negligible at 7500C with respect to 10000C or 11000C. However, the electrical measurements show that the Gummel number is considerably reduced in the transistors that have received the 7500C anneal, because the interstitial injection during arsenic deactivation enhances the diffusion of both arsenic and boron. Therefore, the devices exhibit higher beta, lower output resistance and earlier punchthrough breakdown (Figure 1.6).

Shibayama et al. [36] were the first to observe the diffusivity enhancement underneath a high concentration arsenic layer. In their study, arsenic was diffused into silicon from an arsenosilicate glass at 10000C. The diffusivity of both arsenic and boron were enhanced upon a low temperature anneal between 500-8000C.





15




As & B without the deactivation anneal S- -- As & B with the deactivation anneal


Emitter \ Base


/ I


/ \

/ I


Depth


No deactivation anneal / /




IrB
- - Deactivation afineal / /

/ /











Collector emitter voltage Figure 1.6 Schematic representation of the emitter and base profiles, and electrical characteristics of an npn bipolar transistor with and without a deactivation anneal.





16


1.1.4 Dislocation Loops



A dislocation loop is an extra layer of silicon atoms having a disc shape. Dislocation loops form when there is a high supersaturation of silicon interstitials during thermal annealing. The major cause of excess interstitials and dislocation loops is ion-implantation. Ion-implantation induced dislocation loops have been extensively studied [37]. Dislocation loops act as sinks and sources for interstitials and vacancies, affecting point defect concentrations and dopant diffusion as a result [38]. They increase the p-n junction leakage current by gettering metallic impurities along their peripheries. The stress fields that they generate in silicon also affect dopant redistribution [38]. The analysis of dislocation loops is therefore crucial in understanding and interpreting the effect of processing conditions on device electrical characteristics.

Since arsenic deactivation injects a huge amount of excess interstitials, one may expect dislocation loop formation as a result. In fact, several Transmission Electron Microscopy (TEM) observations have revealed dislocation loops in laser and then thermally annealed high concentration arsenic samples [21,22,39-42]. These loops have been found to be composed of silicon atoms [42]. It was suggested in the same work that arsenic clustering injects the excess silicon interstitials needed to form the loops. Nearly all studies have concluded that the number of atoms bound by the loops or any other extended defects is much smaller than the inactive arsenic dose. When an electron beam was used for initial annealing instead of a laser, dislocation loops were still observed after thermal annealing. In Chapter





17


II, the dislocation loops formed after laser and subsequent thermal annealing will be discussed in more detail.

On the other hand, in implanted and thermally annealed high concentration arsenic samples, a band of arsenic-related precipitates and dislocation loops were detected [37,44,45]. These defects lie at the projected range of the implant where arsenic concentration is at its maximum. They form when arsenic concentration exceeds its equilibrium active concentration. The defects that form at the peak of the implanted profile have been classified as type-V defects [37]. It is interesting to note that type-V dislocation loops are observed only in arsenic-implanted samples [37].

Upon high temperature annealing (>9000C), end-of-range (type-II) dislocation loops dissolve much faster in the presence of gallium, phosphorus and arsenic if their concentrations exceed their solid solubility [46]. During enhanced elimination of type-II loops, the precipitates were also observed to be dissolving.



1.2 Organization



The focus of this thesis is analysis and modeling of the phenomena related to the arsenic activation/deactivation process. Chapter II presents the extended defects that form as a result of the interstitial supersaturation during arsenic deactivation. Understanding the mechanism of these defects is important for both defect engineering and an evaluation of their effect on arsenic deactivation induced interstitials and, therefore, dopant diffusion near high concentration arsenic layers. Chapter II reports the results of TEM observations on samples which were doped





18


with different arsenic doses above the equilibrium active concentration and received a laser anneal to activate all of the dopant, followed by thermal annealing. Various characteristics of the observed defects are evaluated and comparisons with published data are made.

Chapter III presents the results of boron enhanced diffusion due to high dose arsenic implantation in silicon. This study is made to investigate the possible effects of arsenic deactivation on implant damage enhanced diffusion. The behavior of both type-V and type-II loops is studied with TEM. Reduction in enhanced diffusion is observed with increasing arsenic dose at three different temperatures. The possible explanations for this reduction are also included in Chapter III.

Chapter IV contains an investigation of the vacancy population during arsenic activation. Since arsenic is believed to deactivate through the formation of arsenic-vacancy complexes, these complexes are expected to dissolve and generate free vacancies during arsenic activation. The vacancy population is monitored using antimony buried layers.

Chapter V presents a general kinetic model for extended defects. This model is applied to arsenic deactivation in silicon. The model calculates the evolution of the arsenic precipitate size density. It reproduces various trends and a good agreement is obtained between the simulations and the experiments.

In Chapter VI, various numerical methods are evaluated for the solution of the rate equations in extended defect simulation. The derivations of these methods are presented. The accuracies of these methods are evaluated using the arsenic deactivation model in Chapter V.





19


Chapter VII presents an arsenic deactivation model including dislocation loop formation and the interaction of the interstitials with the inactive arsenic structures. The model shows quantitative agreement with the arsenic deactivation and boron enhancement data. It is also in qualitative agreement with the properties of the loops in the deactivated layer. Finally, Chapter VIII presents the conclusions of this dissertation and recommendations for future experimental and modeling efforts.














CHAPTER II
TRANSMISSION ELECTRON MICROSCOPY ANALYSIS OF EXTENDED DEFECTS IN HEAVILY ARSENIC DOPED, LASER, AND THERMALLY ANNEALED LAYERS IN SILICON


2.1 Introduction



Arsenic is the most commonly used dopant for creating n' layers in silicon, such as the source/drain regions in a MOSFET and the emitter of a bipolar transistor. In order to get high conductivity, arsenic is often incorporated into these layers in excess of its equilibrium active concentration. Subsequent thermal annealing gives rise to inactive arsenic. As mentioned in Chapter I, deactivation of arsenic is accompanied by silicon interstitial injection and the enhancement of the boron layers underneath the arsenic layer [32]. This reaction can be written as:



mAs + nSi A sm Vn + nI 2-1



where As represents a substitutional arsenic atom, AsnV, the inactive arsenic complex, V a vacancy and I an interstitial.The reaction can be modified accordingly if the inactive arsenic complex also includes silicon.

Several transmission electron microscopy (TEM) observations have revealed precipitate-like defects, rod-shaped structures and/or dislocation loops in laser and



20





21


thermally annealed samples which have been doped with arsenic in excess of its equlibrium active level [21,22,39-42]. Lietoila et al. [22] have suggested that rodlike defects may be arsenic precipitates, whereas Armigliato et al. [40] have reported that all defects observed by TEM cannot explain the amount of electrically inactive arsenic in their experiments. No extended defects were detected by Lietoila et al. for a much smaller arsenic dose. Parisini et al. [41] measured the number of atoms bound by various types of interstitial-type defects at different annealing temperatures and confirmed the large discrepancy between the concentration of inactive arsenic and the concentration of atoms in observable defects. They proposed that the extended defects are formed as a result of agglomeration of silicon interstitials which are created during laser annealing. In a later work [42], based on double-crystal x-ray diffractometry (DCD) and extended x-ray absorption fine structure analysis (EXAFS) measurements, they suggested that deactivation of arsenic is the cause of excess interstitials. They also found that the dislocation loops are composed of silicon atoms. When an electron beam was used for annealing instead of a laser, similar defects were observed upon subsequent thermal treatment between 600-9000C [43].

On the other hand, a band of arsenic related precipitates and dislocation loops were detected after solid phase epitaxy of arsenic layers doped in excess of its equilibrium active level [37,44,45]. These defects were shown to lie at a depth corresponding to the projected range of the implant. In addition, half-loop dislocations that are located near the surface were observed to grow during arsenic precipitate dissolution even after 72h at 9000C [37]. Jones et al. found that the





22


elimination of end-of-range damage (category-II dislocation loops) is enhanced in the presence of a high concentration arsenic layer [46]. Both half-loop formation and enhanced elimination of category-II loops occur when arsenic peak concentration exceeds its solid solubility.

Understanding the mechanism of these defects is important for both defect engineering and an evaluation of the effects of arsenic deactivation on point defects and, therefore, dopant diffusion underneath high concentration arsenic layers. This chapter reports the results of TEM observations on samples which were doped with different arsenic doses above the equlibrium active concentration, received a laser anneal to activate all of the dopant and finally thermally annealed.



2.2 Experiment



Arsenic was implanted into <100>, 10 Q-cm p-type silicon substrates at doses ranging from 4xl015 to 3.2x1016 cm-2 with an energy of 35 keV. Completely active, box-shaped profiles were obtained by repeated laser pulse annealing (308 nm XeCl, 35 ns FWHM pulses, silicon melt duration 75 ns). The melt-region thickness of about 200 nm was considerably larger than the depth of the implant; thus any major implant damage in the as-implanted layer was effectively annealed out. The samples then received additional rapid thermal anneals at 700 or 7500C for durations that resulted in no appreciable diffusion. Further experimental details about the preparation of these samples can be found in Rousseau et al. [13] and Luning et al.[23].






23


The defects were studied by TEM using both bright field and weak beam conditions. Both plan-view and cross-section samples were analyzed with a JEOL 200 CX electron microscope operating at 200 keV. All micrographs were taken with a g220 condition.

The quantification of the defects on the TEM pictures were done by counting them and measuring the longest dimension of the defect. The density of the defects can be found from the following expression:



NM2
D NM2 2-2 "p



where D is the areal density of the defects, N is the number of defects in the area of interest, M is the magnification, and Ap is the analyzed area on the picture. The loops are assumed to lie on [111] planes where the picture shows the defects through <100> direction. The areal density of the atoms bound by the loops was found by measuring the largest dimension of the loops and using the following formula:




N Ld d 2-3 bound A p11




where r is the radius of a loop and is equal to half of the largest dimension, and dll1 is the areal density of silicon on the [111] plane. The F3 factor projects the





24


analyzed area onto the [111] plane. So, Equation 2-3 effectively calculates the areal density of the bound atoms on the [111] plane.



2.3 TEM Results



The as-lased samples were completely free of any visible defects. Subsequent thermal annealing revealed a very strong dose dependence of the defect structure in the arsenic doped layer. This phenomenon can be seen in Figure 2.1 to Figure 2.4 which show plan-view TEM micrographs of samples after a thermal treatment at 7500C for 2h. Density and size information about the defects are listed in Table 2.1 along with the inactive arsenic dose.

In contrast to the absence of any extended defects at the lowest dose (4x1015 cm-2), large dislocation loops and rod-like defects are observed upon increasing the dose by just a factor of two. For the next two doses, only dislocation loops are detected. Upon increasing the arsenic dose, the density of the loops increases dramatically. Especially, the 1.6x1016 cm-2 sample exhibits almost fifty times more loops than the 8x1015 cm-2 sample. The concentration of atoms bound by the loops was found to be around 30-50 times smaller than the inactive arsenic concentration and is insufficient to directly account for most of the inactive arsenic.

Figure 2.5 and Figure 2.6 show the plan-view micrographs of the samples which were doped with a dose of 1.6x1016 cm-2 and annealed at 7000C for 15s (short-time) and 100 min (long-time). Very dense fine particles appear after the short-time anneal whereas the long-time sample exhibits a high density of loops.





25

























Figure 2.1 Plan-view TEM micrograph of the sample implanted with 4x1015 cm-2 and annealed at 7500C (bright field).























Figure 2.2 Plan-view TEM micrograph of the sample implanted with 8x015 cm-2 and annealed at 7500C (weak beam dark field).





26

























Figure 2.3 Plan-view TEM micrograph of the sample implanted with 1.6x1016 cm-2 and annealed at 7500C (weak beam dark field).























Figure 2.4 Plan-view TEM micrograph of the sample implanted with 3.2x1016 cm-2 and annealed at 7500C (weak beam dark field).





27
























Figure 2.5 Plan-view TEM micrograph of the sample implanted with 1.6x1016 cm-2 and annealed at 7000C for 15s (weak beam dark field).























Figure 2.6 Plan-view TEM micrograph of the sample implanted with 1.6x 1016 cm-2 and annealed at 7000C for 100 min (weak beam dark field).






28




Table 2.1: Summary of TEM observations made on the samples annealed at 7500C for 120 minutes.

Density of Inactive Surface
Dose Defect Size Density Bound As
Conc.
(cm-2) Type (AO) (cm2) Atoms Dose
(cm3)
(cm-2) (cm2)

4x1015 2.3x1020 None 2.2x1015

Dislocation
200- 1200 3.3x109 1.2x1014 loops

8x1015 4.5x1020 4.9x1015

Rod-like
400- 2800 1.8x109 defects

Dislocation
1.6x1016 9.1x1020 50- 350 1.3x1011 3.5-4.5x1014 1.3x1016 loops

Dislocation
3.2x1016 1.9x1021 100 400 > 2.5x1011 > 6x1014 2.9x1016 loops




Further analysis showed that the defects in the short-time sample are dislocation

loops with a density of around 6x1011 cm-2 and average size of 90 A. Recently,

Rutherford back-scattering (RBS) measurements were made on the same samples

[47]. It was demonstrated that the backscattered angular-scan spectra for silicon

have the same minimum in both the as-lased and short-time samples whereas the

minimum yield of arsenic increases. Furthermore, silicon minimum yield was






29


shown to increase appreciably in the long-time sample, and both arsenic and silicon angular-scan spectra were characteristic of a large degree of dechanneling.

Figure 2.7 to Figure 2.10 show the cross-section views of the samples implanted with doses of 8x1015 and 1.6x1016 cm-2. For the higher dose, the defects lie uniformly in a region from the surface down to a depth of about 180 nm, which coincides well with the junction depth. The uniformity of the defects in the arsenic layer is in contradiction with an earlier TEM work where dislocation loops were observed to lie at the amorphous-crystalline interface for a similar surface concentration [41,42]. Except for the intrusion of rod-like defects to a depth of 230250 nm in the 8x1015 cm-2 sample, the confinement of the defects to the arsenic layer suggests that inactive arsenic complexes reduce the formation energy of the loops.

In a similar study [42], it has been found that the loops are composed of silicon atoms. It has been suggested in the same work that arsenic clustering injects the excess silicon interstitials needed to form the loops. As mentioned before, buried boron layers show enhanced diffusion as a result of arsenic deactivation, suggesting that arsenic deactivation is accompanied by interstitial injection [32]. TEM observations in this study involve exactly the same samples for the 7500C, 2h anneal. The enhancements for these samples are shown in Table 2.2. There is a large increase in boron diffusivity at an arsenic concentration of 4.5x1020 cm-3 and the enhancement keeps decreasing as the dose is increased. The TEM results show that the number of atoms bound by the loops increases with arsenic concentration. Therefore, the loops seem to be responsible for the reduction in boron diffusivity.





30
























Figure 2.7 Cross-section TEM micrograph of the sample implanted with 1.6x1016 cm-2 and annealed at 7000C for 15 s (weak beam dark field).






















Figure 2.8 Cross-section TEM micrograph of the sample implanted with 1.6x1016 cm-2 and annealed at 7000C for 100 min (weak beam dark field).





31

























Figure 2.9 Cross-section TEM micrograph of the sample implanted with 8x1015 cm-2 and annealed at 7500C for 2h (weak beam dark field).























Figure 2.10 Cross-section TEM micrograph of the sample implanted with 1.6x1016 cm-2 and annealed at 7500C for 2h (weak beam dark field).





32




Table 2.2: Enhancement of buried boron layer diffusivity for various arsenic doses [32].

Surface Concentration Inactive As Dose (cm-2) Enhancement
(cm-3) dose (cm-2) 4x1015 2.3x1020 30 2.2x1015 8x1015 4.5x1020 460 4.9x1015 1.6x 1016 9.1x1020 230 1.3x1016 3.2x1016 1.9x1021 110 2.9x1016



The dislocation loop density gets higher as the arsenic dose is increased, although the interstitial supersaturation decreases. From nucleation theory, the loop density is expected to decrease as the interstitial supersaturation gets smaller, which seems to contradict these experimental observations. But, since loop nucleation occurs at the very early stages of the deactivation anneal, the density of the loops is determined by the interstitial supersaturation at the beginning of the anneal. Instead of the time averaged interstitial supersaturation, it is enough that the initial interstitial supersaturation be higher at higher arsenic concentrations for the loops to be denser.

At the lowest arsenic concentration (2.3x1020 cm-3), the enhancement is 15 times smaller than the one at the next higher concentration (4.5x1020 cm-3), although the inactive arsenic doses are comparable. Also, no dislocation loops are observed at the lowest concentration. This suggests that another deactivation mechanism may be dominant in this sample, such as the simultaneous formation of arsenic-interstitial pairs.





33


2.4 Conclusions



The properties of the extended defects that are formed during arsenic deactivation were investigated. The density of the dislocation loops depends on the chemical arsenic concentration. As the arsenic concentration increases, more interstitials are injected during deactivation, and, therefore, a higher density of loops form. The number of atoms bound by the loops is much smaller than the inactive arsenic dose. The loops are confined in the arsenic layer, indicating that the inactive arsenic reduces the formation energy of the loops. Finally, the increase in the number of the atoms bound by the loops explains the reduction in the buried boron layer diffusivity at higher arsenic concentrations.














CHAPTER III
HIGH DOSE ARSENIC IMPLANTATION INDUCED TRANSIENT ENHANCED DIFFUSION


3.1 Introduction



Ion implantation of dopants into silicon introduces damage in the form of interstitials and vacancies. If the damage is above a certain level, an amorphous layer forms. Upon thermal annealing, the amorphous layer grows back into crystalline silicon. If arsenic has been implanted at high doses, end-of-range loops appear below the original amorphous/crystalline (a/c) interface, whereas type-V loops form at the projected range (Figure 3.1). When a dopant layer is present beyond the a/c interface, its diffusion is enhanced because of the ion-implant damage. It has been previously suggested that the damage beyond the a/c interface is the main cause of the enhanced diffusion of dopants after amorphizing implants [48,49].

As mentioned in Chapter II, arsenic deactivation is accompanied by interstitial injection. Buried boron layers have been observed to exhibit enhanced diffusion when arsenic is deactivated at the surface [32]. In Chapter II, the high level of interstitial injection is also confirmed by TEM studies of type-V dislocation loops formed during arsenic deactivation in initially defect-free laser annealed samples [39].



34





35



After ion implantation After annealing





End-of-range
implant O
damage










a/c interface type-V loops end-of-range loops

Figure 3.1 Schematic representation of damage and loop formation in high dose arsenic implanted silicon.



Although arsenic deactivation creates excess interstitials and causes dislocation loop formation. it is not yet clear how much effect it has on the enhanced diffusion caused by high dose arsenic implantation. While excess interstitials should contribute to the implant damage enhanced diffusion, type-V loops may decrease the amount of enhanced diffusion by absorbing the interstitials. In this work [50], arsenic was implanted into silicon at various doses with the same energy. Buried boron layers were used as markers of interstitial supersaturation. Most of the chosen doses give rise to peak arsenic concentrations above the equilibrium active concentration. The density of type-V loops is a very strong function of the arsenic concentration, and the interstitial supersaturation during arsenic deactivation





36


increases abruptly above a certain arsenic concentration. Hence, an abrupt change in the diffusivity of the buried boron layer can be expected if arsenic deactivation has an appreciable effect on damage enhanced diffusion.



3.2 Experiment



The boron buried layers were prepared in Texas Instruments. After depositing 200 A of oxide on <100> silicon to reduce ion channeling, boron was implanted at 10 keV with a dose of 3x1012 cm-2. The oxide was then etched with an HF solution and an approximately 0.6 gtm thick epi layer was grown. Arsenic was implanted at 50 keV at 70 tilt with doses ranging from 4x1014 to 4x1015 cm-2. The peak arsenic concentrations determined from SIMS are shown in Table 3.1 along with the implanted doses. The arsenic concentrations were normalized to the implanted dose.The samples were annealed at three different times temperatures: 7500C 2h, 9000C Imin, and 10500C 15s. It has been previously reported that the damage enhanced diffusion due to interstitial cluster dissolution is complete for boron implants within the anneal times selected for each temperature [7,51 ].

Arsenic and boron profiles were obtained by secondary ion mass spectrometry (SIMS) using an oxygen beam. Since the boron dose was low, the sample was tilted at an angle so that the boron yield was higher during sputtering. The defects were studied by transmission electron microscopy with a JEOL 200 CX electron microscope operating at 200 keV. Plan-view and cross-section samples were analyzed in g220 and gill conditions.





37



Table 3.1: Peak arsenic concentration vs. arsenic implant dose

Dose (cm-2) 4x1014 8x1014 1.6x1015 2.4xl015 4x1015 Peak Concentration (cm-3) 1.1x1020 2x1020 4x1020 6.4x1020 lx1021



3.3 Results and Discussion



The annealed profiles of the boron buried layer are shown in Figure 3.2 for different arsenic doses at 7500C. The doses of the original boron SIMS profiles were normalized to that of the unannealed sample. The damage enhanced diffusion of the boron buried layer is reduced as the arsenic dose is increased. This trend is also observed after the 9000C and 10500C anneals. The reduction in the diffusivity is also supported by the arsenic SIMS profiles. After the 7500C anneal, the highest dose arsenic profile moves 200 A less than the 8x1014 cm-2 profile. The enhancements in the boron diffusivity can be seen in Figure 3.3 to Figure 3.5. The enhancement was found by finding the diffusivity that best matches the experimental profile and dividing it by the reference inert diffusivity which is given by:




D = 0.757ex( 3.46) 3-1




At both 7500C and 9000C, the boron diffusivity drops nearly by a factor of 2 from the lowest to the highest arsenic dose. The cross-sectional TEM (XTEM)






38





1 0 18I ... .. I .. . . .
None
G---- 8x1014 cm-2 E 3-0 2.4x1015 cm-2
0 4x1015 cm-2 C 1017

(D
C)
C
o 1016 1015



10 15 . . . , ,
0.4 0.5 0.6 0.7 0.8 0.9 Depth (ptm)


Figure 3.2 Buried boron profiles for different arsenic doses after the 7500C, 2hr. anneal.


1 8 0 0 . . . . . . . . .. . . . . . . .



1600



1400

w
1200



1000



8 0 0 . . . . ..
Oe+00 le+15 2e+15 3e+15 4e+15
Arsenic Dose (cm-2) Figure 3.3 The enhancement of boron diffusivity as a function of arsenic dose at 7500C.





39


5 5 0 . . . . . . . . . . . . . .

500

C
0 450
E
C
cz 400
-c
w
350

= 300 250

2 0 0 . . . . .., ..
Oe+00 le+15 2e+15 3e+15 4e+15
Arsenic Dose (cm-2) Figure 3.4 The enhancement of boron diffusivity as a function of arsenic dose at 9000C.


3 5 . . . . . . . . . .. . . . .





30





8 25





2 0 .. . .. .
Oe+00 le+15 2e+15 3e+15 4e+15
Arsenic Dose (cm-2) Figure 3.5 The enhancement of boron diffusivity as a function of arsenic dose at 10500C.





40























(a)






















(b)


Figure 3.6 Weak beam-dark field cross-section TEM micro raphs of the sample implanted with an arsenic dose of (a) 1.6x 1015 cm-2, (b) 2.4x 1015 cm- and annealed at 7500C.





41


analysis of the samples reveals that a high density of type-V loops forms when the peak arsenic concentration is 6.4x1020 cm-3 at both 7500C and 9000C. On the other hand, only a very low density of type-V loops form at a peak concentration of 4x1020 cm-3 (Figure 3.6). These results are consistent with the dislocation loop results in Chapter II. The diffusivity data shows that the abrupt appearance of a high density of type-V loops does not have a drastic effect on damage enhanced diffusion. It has been previously suggested that the enhanced diffusion after amorphizing implants is mainly caused by the damage beyond the a/c interface [48,49]. Since type-V loops form at the projected range, they may not absorb an appreciable amount of the interstitials that are beyond the a/c interface and blocked by the end-of-range loops (Figure 3.1). Moreover, XTEM micrographs show that there is not any intrusion of the type-V loops into the end-of-range loop layer even at the highest dose, suggesting a lack of strong interaction between type-V loops and end-of-range damage. Still, type-V loops may be contributing to the decrease in the enhanced diffusivity, although the decrease in the enhanced diffusivity starts before their formation. It is interesting that the buried layer diffusivity does not increase at the arsenic peak concentration of 4x 1020 cm-3 although a great amount of interstitial supersaturation is expected [52] and nearly no type-V loops form at this concentration. The end-of-range loops should be acting as very efficient sinks for these excess interstitials and preventing them to contribute to the enhanced diffusion.

The density and the number of atoms bound by both the type-V and the endof-range loops are plotted in Figure 3.7 for 7500C and 10500C. Both the density and





42


the number of bound atoms show an increase as the arsenic dose is increased, suggesting that the loops are responsible for the reduction in boron diffusivity. A low density of rod-like defects (6x108 cm-2) was observed at the dose of 8x1014 cm 2 along with the loops. For the 10500C anneal, no type-V loops were observed in the XTEM micrographs for all the doses. So, the abrupt increase in the loop density at this temperature is only due to end-of-range loops.

Two mechanisms may exist if the reduction in the enhanced diffusivity is caused only by the dose dependence of the implant damage below the a/c interface. The depth of the amorphous layer has been observed to increase with dose [53]. More of the implant damage beyond the a/c interface may be incorporated into the amorphous layer at higher doses. This mechanism may reduce the enhanced diffusion. However, a possible decrease in the implant damage below the a/c interface is inconsistent with our experimental loop data where both the loop density and the number of bound atoms increase even when only end-of-range loops exist. So, the damage and therefore the excess interstitials beyond the a/c interface are actually increasing with higher arsenic doses. This may not necessarily mean a larger interstitial supersaturation during the whole enhanced diffusion. A higher interstitial supersaturation at the beginning of the anneal can cause a higher density of end-of-range dislocation loops, which in turn can capture more interstitials during the anneal, decreasing the enhanced diffusion. This statement is supported by the results of other experiments, such as the decrease in enhanced diffusion at higher arsenic concentrations during arsenic deactivation in laser annealed samples [52] and the reduction in boron diffusion with increasing boron dose [8]. Arsenic





43


4 e + 14 I......... ...... 5 e + 10 ....... ......... ......... ........


-E -- 7500C 7500C
3 10500C 4e+10 [3-. 10500C 3e+14

> E
0 3e+10
E
2e+14 a. 2e+10
o o &Z le+14
S le+10


Oe+00 S.....F Oe+00
Oe+00 le+15 e+15 3e+15 4e+15 Oe+00 le+15 2e+15 3e+15 4e+15
Arsenic Dose (cm-2) Arsenic Dose (cm2)

(a) (b) Figure 3.7 Arsenic dose dependence of (a) the density of the bound atoms by loops, and
(b) the density of the loops.



deactivation induced interstitials may also contribute to the supersaturation and increase the density of end-of-range loops, besides nucleating the type-V loops.



3.4 Conclusions



Buried boron layers were used to quantify the transient enhanced diffusion after high-dose arsenic implantation. The enhancement in boron diffusivity decreases with increasing arsenic dose at 750, 900 and 10500C. At the same time, the number of atoms bound by the loops increase, suggesting that the dislocation





44


loops are responsible for the reduction in boron diffusivity. Finally, arsenic deactivation induced interstitials do not increase the enhanced diffusion.














CHAPTER IV
INVESTIGATION OF VACANCY POPULATION DURING ARSENIC ACTIVATION IN SILICON


Recent experimental investigations have shown that electrical deactivation of arsenic in silicon creates excess silicon interstitials [52]. This has been attributed to the formation of arsenic-vacancy clusters and generation of silicon interstitials during this process. As pointed out in Chapter II, this high level of interstitial injection is also confirmed by TEM studies of type-V dislocation loops formed during arsenic deactivation in the same initially defect-free laser annealed samples [39].

The formation of a large number of arsenic-vacancy clusters has been confirmed with positron annihilation measurements [54]. Furthermore, extended xray absorption fine-structure (EXAFS) results combined with Rutherford BackScattering (RBS) measurements also indicate that the deactivation of arsenic proceeds through the formation of arsenic vacancy complexes below 7500C [55]. Upon electrical activation of arsenic, these complexes are expected to dissolve and generate free vacancies. In this work [56], antimony doping superlattice (DSL) structures were used to detect any possible vacancy injection into the bulk during the activation of arsenic. Since antimony diffuses predominantly through a vacancy mechanism, its diffusion is enhanced when there is a supersaturation of vacancies [24].



45





46


4.1 Experimental Details



The DSL structures used in the experiment contained six narrow antimony buried marker layers with 10 nm widths, peaks spaced 100 nm apart and doped to a concentration of 1.5x1019 cm-3. They were grown by low temperature molecular beam epitaxy on Si(100) floatzone substrates [57]. The samples were split into three during ion-implantation: no implant, arsenic implant, and germanium implant. Since germanium is similar to arsenic in mass and size, it allows us to monitor any possible effects of similar ion-implantation damage on antimony diffusion if the damage is not completely wiped out during the damage anneal. Arsenic was implanted at 50 keV at 70 tilt with doses of 3x1015 cm-2 and 8x1015 cm-2, while germanium was implanted at only 8x1015 cm-2. All the samples were capped with an approximately 2000 A layer of oxide and then a nitride layer to prevent the evaporation of arsenic. They were annealed at 11500C for 5s in order to eliminate the implantation damage. After the samples were subjected to a deactivation anneal at 7500C for 2h, some of them were further annealed either at 8500C for 4 h or 9500C for 30 min to electrically activate some of arsenic. The unimplanted, arsenic and germanium doped samples were annealed very close to each other during each thermal cycle so that there would not be any thermal variations between these splits. Figure 4.1 shows a flowchart of the experimental steps.

Chemical arsenic and antimony concentrations were measured by SIMS. Plan-view samples were studied by TEM with a JEOL electron microscope





47




Starting material: Silicon
with DSLs




As implant Ge implant No implant 50 keV 50 keV 3x1015 & 8x1015 cm2 8x1015


Prevent arsenic evaporation: Oxide and nitride deposition



Eliminate implant damage: Anneal at 1150'C for 5s


S Deactivation anneal: 750oC for 2 hr.



Activation anneals: 8500C & 9500C



As & Sb SIMS As Electrical Measurements
As TEM


Figure 4.1 A flowchart of the experiment.





48


operating at 200 keV. Spreading and sheet resistance measurements were made on arsenic doped samples.

In order to find the antimony diffusivity during the activation anneals, the following procedure was employed: For each spike, the SIMS profile after the deactivation anneal was supplied as an initial profile to the process simulation program FLOOPS. The antimony diffusivity was assumed to have the form DSb = aD}rf, where a is an enhancement factor and the reference diffusivity DW is the default inert antimony diffusivity in FLOOPS, and is given by:




DSg = 0.21exp- ) +(n/ni)15exp 4-1




The diffusion of the initial profile was simulated with FLOOPS for different values of a until the error between the simulated and the experimental profiles was minimized. The enhancement or the retardation in antimony diffusivity in the arsenic or germanium doped samples was found by dividing the diffusivity in these samples to the diffusivity extracted from the unimplanted samples which were annealed under the same conditions.



4.2 Results and Discussion



Figure 4.2 shows the antimony SIMS profiles in the as-deposited DSL sample, and in the high dose (8x 1015 cm-2) arsenic sample which has been subjected to the 9500C,





49


1020

As-deposited E 8x1015 cm2 As, 9500C 30 min

o 1019

C 0


E C


10.17.. L .........
0.00 0.10 0.20 0.30 0.40 0.50 0.60 Depth (m)
Figure 4.2 Antimony SIMS profiles in the as-deposited DSL sample and the sample implanted with 8x 1015 cm-2 arsenic and annealed at 9500C for 30 min after the damage and deactivation anneals.


0 8x1015 cm-2, 7500C 13---- 8X1015 cm-2, 7500C + 9500C 30 min 1021 0 3x1015 cm-2, 7500CO &--A 3x1015 cm-2, 7500C + 9500C 30 mi


1020





10



0.00 0.10 0.20 0.30 Depth (gm)
Figure 4.3 Arsenic SIMS profiles. The temperatures in the legends represent the anneals after the damage anneal at 11500C.






50


2.5
(0--- 8x1015 cm-2, 8500C 4h
3--- 8x1015 cm2, 9500C 30min
2.0 3x1015 cm2, 8500C 4h
SA-- 3x1015 cm-2, 9500C 30min E 1.5
-4


S1.0


c 0.5


0.0 I I I
0.2 0.3 0.4 0.5 Depth ( m )
Figure 4.4 Enhancement in the antimony diffusivity as a function of depth in the arsenic doped samples. The thermal cycles shown in the legends represent only the activation anneals.


30 min activation anneal. Antimony inside the arsenic layer exhibits considerable amount of more diffusion than antimony outside the arsenic layer. This can be attributed to an increase in the equilibrium concentration of free vacancies inside the arsenic layer. Figure 4.3 presents the arsenic profiles in the both the high (8x1015 cm-2) and low (3x1015 cm-2) dose samples after the deactivation and the 9500C, 30 min activation anneal. A significant amount of arsenic diffusion takes place during the activation anneal.

Figure 4.4 shows the enhancement in the antimony diffusivity during the activation anneals in the arsenic doped samples. This enhancement was calculated by dividing the antimony diffusivity in the arsenic doped samples to the inert antimony diffusivity extracted from the unimplanted samples. The inert antimony diffusivity was found to be around 40% less than the default diffusivity in FLOOPS





51


(Equation 4-1) at 8500C and 5% less at 9500C. The enhancements in antimony diffusivity are very close to unity, indicating that there is no observable vacancy supersaturation during arsenic activation in these samples. The activation of arsenic was confirmed by both sheet resistance (Table 4.1) and spreading resistance measurements (Figure 4.5). The spreading resistance data shows that diffusion of arsenic into the bulk as well as the higher activation level of arsenic at 9500C contribute to the amount of more electrically active arsenic.

The positron annihilation experiments show that the average number of vacancies per inactive arsenic atom is between 1/2 and 1/4 in an arsenic doped silicon sample which has been laser annealed and then thermally annealed at 7500C (concentration of arsenic = 8x1020 cm-3) [54]. RBS and EXAFS measurements have led Brizard et al. to propose the existence of arsenic-vacancy clusters which have a vacancy/arsenic ratio of around 1/3 [55]. Thus, it is unexpected that there is not any significant enhancement in the arsenic doped samples since a very large amount of free vacancies is expected to be released upon the dissolution of these clusters during the activation anneals.

To investigate the possibility that the generated vacancies may be absorbed by the extrinsic extended defects either left over from the damage anneal or created by the subsequent deactivation anneal, a plan-view TEM study of the arsenic doped samples was undertaken (Table 4.1). Dislocation loops were observed in the samples after the deactivation anneal, and they completely dissolve during the activation anneals with the exception of the 8500C high dose sample where only a very small amount of loops has survived the activation anneal.





52



Table 4.1: Summary of the electrical and TEM measurements on the arsenic doped samples.

Density of The total Anneal sequence
Arsenic after the Sheet atoms bound by amount of after the
dose damage anneal Resistance dislocation electrically
(1015 cm-2 ) (f /sq ) loops active arsenic
2 OC ) -2
(O) ( cm-2) ( cm-2 ) 8 750 71.8 1.1x1014 1.1x1015
8 750 + 850 4h 48.7 Very few loops
8 750 + 950 30min 30.0 No loops 3x1015 3 750 76.4 2.3x1013 1.1x1015 3 750 + 850 4h 63.4 No loops 1.5x1015 3 750 + 950 30min 50 No loops 2x1015




1021
0 7500C
---E 7500C + 9500C 30 min
E
c 1020
0

a)




10
C.)

C 1019
0
U



1018
0.00 0.10 0.20 Depth (gm)
Figure 4.5 Spreading resistance measurements of the arsenic doped layer for the high (8x1015 cm-2) arsenic dose. The temperatures in the legends represent the anneals after the damage anneal at 11500C.





53


Table 4.1 also shows the total amount of electrically active arsenic obtained by integrating the electron concentration from the spreading resistance measurements with depth. In the high dose sample, the ratio of the density of atoms bound by the loops to the activated amount of arsenic during the 9500C activation anneal is roughly 1/17, whereas in the low dose sample this ratio is 1/40. These ratios are much smaller than the vacancy/arsenic ratio in the clusters calculated from either the positron annihilation or EXAFS measurements. Therefore, even if the loops are annihilated by only absorbing the vacancies generated by the activation process, this mechanism alone is not enough to explain the lack of vacancy injection into the bulk assuming that vacancies are generated with a ratio indicated by the positron annihilation and EXAFS measurements.

The unaccounted vacancies may be either recombining at the surface or with the interstitials created during the deactivation anneal and possibly trapped by an impurity such as arsenic or carbon. In fact, carbon has been observed to be an efficient sink for excess interstitials. At high enough doses, carbon can mostly eliminate the transient enhanced diffusion [58] which is believed to be caused by excess interstitials. The carbon profiles have also been measured along with arsenic and antimony. Figure 4.6 shows the carbon profiles after the deactivation anneal for the unimplanted and high dose arsenic samples. In the unimplanted sample, a rapidly decreasing carbon concentration can be observed at the surface. This is believed to be caused by carbon-related particles residing on top of the surface. On the other hand, in the high dose arsenic sample, carbon profile exhibits a peak around 80 nm and a deeper penetration at the surface, suggesting that the observed





54



1021

SG-: Unimplanted
E
o2 _-E0 8x1015cm-2 As
1020


~ 1019
C


.4


O
C

C 1018


1017
0.00 0.10 0.20 0.30 0.40 0.50 Depth (gpm)
Figure 4.6 Carbon SIMS profiles in the unimplanted and high dose arsenic samples after the deactivation anneal.



carbon in this sample is actually inside silicon, rather than at the top of the surface. This high concentration of carbon may be capturing the excess interstitials injected during the deactivation cycle and creating a sink for excess vacancies.

Another explanation for the unaccounted vacancies is a possible increase in the ratio of the concentration of clusters that have a higher vacancy/arsenic ratio, such as As2V, to the concentration of higher order clusters which have a smaller vacancy/arsenic ratio, such as As4V. This can especially happen in the regions where chemical arsenic concentration is not very high (i.e. diffused regions) and the formation of arsenic rich clusters is kinetically limited. Therefore, instead of being injected into the bulk, the excess vacancies may be recaptured by the relatively more vacancy rich arsenic-vacancy complexes.





55


7.0 I ,

> 6.0 G- Ge, 8500C 4h
a 6.0
-E Ge, 9500C 30min
5.0

E 4.0

._ 3.0 E 2.0



0.0
0.2 0.3 0.4 0.5 Depth ( pm )

Figure 4.7 Enhancement in the antimony diffusivity as a function of depth in the germanium doped samples. The thermal cycles shown in the legends represent only the activation anneal.


Figure 4.7 shows the enhancement in the antimony diffusivity in germanium doped samples during the activation anneals. Unlike arsenic, antimony diffusion is enhanced by a factor of 2 to 4 in these samples.



4.3 Vacancy Population in the Partial Absence of Dislocation Loops



A second set of samples was prepared in order to find out whether the enhancement in antimony diffusivity increases after the dislocation loops dissolve completely. These samples were prepared like the previous ones (Figure 4.1) except that the activation anneals were done without any oxide or nitride on the surface. The activation anneal conditions were 16 hours at 8500C, and 1 and 2 hours at





56


9500C. These anneal times were longer than the time when all or most of the dislocation loops had completely dissolved (Table 4.1). Therefore, the vacancy population in the partial absence of the loops can be determined from these samples. The anneals involved either unimplanted or high dose (8x1015 cm-2) arsenic samples.

Figure 4.8 and Figure 4.9 compare the antimony profiles of the unimplanted and high dose arsenic samples at the fourth peak after the deactivation anneal and the activation anneals of 8500C, 16h and 9500C, lh. Although these profiles are quite similar after the deactivation anneal, the high dose arsenic sample exhibits more antimony diffusion than the unimplanted sample during the activation anneals. This indicates that antimony diffusion is enhanced in the high dose arsenic samples. Figure 4.10 shows the enhancements in the antimony diffusivity which are between

1.5 and 2 at both temperatures.

As discussed before, these enhancements may have been caused by the vacancies injected during the arsenic activation. Non-equilibrium diffusion of arsenic may also have created this enhancement. Since dopant atoms are believed to diffuse by pairing with point defects, rapid dopant diffusion can carry a large number of dopant-defect pairs to the bulk. These dopant-defect pairs can create excess point defects upon dissolution if the recombination of the vacancies and interstitials is not as fast as their generation through dopant diffusion. This effect becomes more significant as the dopant concentration and diffusivity increase. It has been proposed as the mechanism responsible for the enhanced diffusion observed in the tail of the high concentration phosphorus profiles [59-62]. Although the inert





57



1020 _-O Unimplan'ed, 7500C
0 8x1015 cm-2 As, 7500C 0--1 Unimplanted, 7500C + 8500C 16h
E -- 8x1015 cm-2 As, 7500C + 8500C 16h
c 1019
o0


101
o


E 1017



1016
0.30 0.35 0.40 Depth (gm)
Figure 4.8 Comparison of the antimony profiles of the unimplanted and high dose arsenic samples after the deactivation and activation (8500C, 16h) anneals. During the activation anneal, antimony diffusion is enhanced in the arsenic sample.

1020 _--) Unimp laned, 7500C
0 8x10 5 cm-2 As, 7500C T a -- El Unimplanted, 7500C + 9500C 1h
E H--- 8x10 5 cm-2 As, 7500C + 9500C 1h
a 1019
o


Q 101
0
o


E 1017



1016 e Al
0.30 0.35 0.40 Depth (gm)
Figure 4.9 Comparison of the antimony profiles of the unimplanted and high dose arsenic samples after the deactivation and activation (9500C, lh) anneals. During the activation anneal, antimony diffusion is enhanced in the arsenic sample.





58


2.5


2.0

0
E 1.5

0~- 8500C 16h
S1.0
a [3--1 9500C lh
E
S0.5 9500C 2h
a 0.5
-C
C
0.0 I I
0.2 0.3 0.4 0.5 Depth ( Lm )

Figure 4.10 Enhancement in the antimony diffusivity as a function of depth in the high dose (8x1015 cm-2) arsenic doped samples. The thermal cycles shown in the legends represent only the activation anneals.


arsenic diffusivity is smaller than that of phosphorus, non-equilibrium diffusion of arsenic may still be responsible for the small enhancements in these samples.



4.4 Conclusions



The effect of arsenic activation on vacancy population has been studied using antimony buried layers. The antimony diffusivity has been found to be very close to its inert diffusivity during arsenic activation in the presence of dislocation loops, indicating that there is no observable vacancy injection under these conditions. The density of the atoms bound by the loops are not sufficient to absorb all the vacancies which are expected to be generated in an amount indicated by the positron






59

annihilation and EXAFS measurements. Other possible mechanisms that can explain the lack of vacancy injection in the presence of the loops include surface recombination, recombination with trapped interstitials generated during the deactivation anneal and absorption of vacancies by relatively more vacancy rich arsenic defects, such as As2V clusters. On the other hand, antimony diffusion is enhanced for the same anneals when germanium is present at the surface.

In the partial absence of the loops, antimony diffusion is enhanced by a factor of 1.5-2 during arsenic activation. Vacancy injection during arsenic activation as well as non-equilibrium diffusion may explain this enhancement.














CHAPTER V
A KINETIC MODEL FOR ARSENIC DEACTIVATION


5.1 The Physical Structure of Inactive Arsenic



In the arsenic-silicon phase diagram, monoclinic SiAs phase is the closest one to a dilute arsenic-silicon (solute-solvent) mixture [63]. In this phase, arsenic has three nearest neighbors, whereas silicon has four [64]. The monoclinic phase has also been observed in arsenic implanted silicon at very high arsenic concentrations (-lx1022 cm-3) [65,66]. Nobili et al. have determined the solid solubility of arsenic associated with the monoclinic phase [67]. The solid solubility is defined as the equilibrium concentration of the solute (arsenic) when the solid mixture is in contact with an infinitely large film of the second phase. Figure 5.1 shows the solid solubility value along with the equilibrium active concentration of arsenic. The solid solubility of arsenic is about an order of magnitude larger than its equilibrium active level.

At equilibrium, monoclinic SiAs precipitates start to form above solid solubility, whereas arsenic is substitutionally dissolved in silicon below the equilibrium active concentration. The inactive arsenic structure between these two limits has been the subject of much recent research. RBS [55] and X-ray standing wave measurements [68] show that this inactive arsenic structure is coherent with




60





61



1022
G-e Equilibrium active concentration
I0-E3 Solid solubility


E



0 4




1 o


7.0 7.5 8.0 8.5 9.0 9.5 10.0 104/Tr ( K1)
Figure 5.1 The temperature dependences of the solid solubility associated with the monoclinic SiAs phase and the equlibrium active concentration.



the silicon lattice. This result suggests that the inactive arsenic does not have the crystal structure of the monoclinic SiAs phase, since the monoclinic phase, having a crystal structure different from silicon, would create incoherence in silicon [40,52]. EXAFS measurements on high concentration arsenic samples demonstrate that the number of the nearest neighbors of an arsenic atom decreases from four silicon atoms in laser annealed samples to an average of 2.5 to 3.5 in deactivated samples. This result can be explained by the formation of arsenic-vacancy complexes (AsmVn) in which arsenic has less than four neighbors. Recent positron annihilation experiments have also found evidence of a high density of vacancies related to inactive arsenic [54]. Moreover, theoretical calculations indicate that the formation of arsenic-vacancy complexes is an energetically favorable process [34,69]. The





62


interstitial injection observed during arsenic deactivation also indirectly supports the existence of arsenic- vacancy complexes [32].

Very small (-15 A) precipitates have been identified by TEM in deactivated arsenic samples [40]. These precipitates have been proposed to have a zinc-blende structure. In this structure, every alternating silicon atom is replaced by an arsenic atom and both silicon and arsenic have four nearest neighbors of the other species. The aforementioned EXAFS measurements show that the number of silicon first neighbors of arsenic tends back to four atoms at high temperatures (>7500C) [33]. This observation has been connected to the co-existence of arsenic-vacancy complexes and zinc-blende type AsSi precipitates.

In summary, the inactive arsenic structure that is formed between the limits of solid solubility and equilibrium active concentration is believed to be arsenicvacancy complexes. At high temperatures, the vacancy content seems to be decreasing with vacancies being replaced by silicon atoms.



5.2 Previous Models for Inactive Arsenic



Clustering and precipitation have been proposed to explain the formation of electrically inactive arsenic in silicon. In clustering models, multiple arsenic atoms are assumed to come together and form a new defect which is electrically inactive at room temperature. These clusters may also contain point defects. For example, an As2V cluster can be formed by the following reaction:





63


2 As + V As2V 5-1



On the other hand, precipitation models consider the formation of much larger structures that may contain thousands of dopant atoms. The precipitates may form at any size whereas clusters are assumed to have on the order of a few atoms. The size distribution of precipitates depend on the initial supersaturation of dopant atoms, the time and the temperature of the anneal and other kinetic factors such as diffusivity and reaction rates.

Many TEM observations have concluded that extended defects in high concentration arsenic doped samples are not sufficient enough to account for most of the inactive arsenic [39-41]. This evidence favors the clustering explanation such that most of the inactive arsenic may be in the form of clusters which are too small to be observed by TEM. However, it is also possible that very small coherent silicon-arsenic precipitates can be responsible for the unobserved inactive arsenic.

As mentioned earlier, Armigliato et al. [40] have identified very small precipitates in heavily arsenic doped samples. It is well known that the electrically active arsenic concentration at equilibrium (i.e. for long anneal times) is very insensitive to the chemical arsenic concentration [12]. This has been put forward as suggestive evidence for precipitation [12] since cluster models predict that the active arsenic concentration depend on the chemical concentration at equilibrium. However, the equilibrium electron concentration can be made independent of the chemical concentration if one assumes that the clusters are charged at the annealing temperature [70]. As mentioned in Chapter I, reverse annealing [12,13] has been





64


shown to occur in arsenic implanted samples, suggesting the existence of precipitates having a distribution of sizes of different free energy. But, reverse annealing can also be explained by the existence of multiple clusters [13]. It certainly rules out the single cluster model. All of the experimental data suggests that the most reasonable assumption for inactive arsenic is the coexistence of clusters and precipitates [24,42,55]. The clusters can form at the beginning of the deactivation cycle and act as embryos for larger precipitates.

Most of the previous quantitative models for inactive arsenic has been single cluster models. Sheet resistances and electron concentrations in arsenic doped layers have been fit with various equilibrium cluster models [71-73]. Dynamic clustering models have been used to fit the initial stages of deactivation [42] and the effect of ramp-down on the sheet resistance [19]. Luning et al. [23] have pointed out that single clustering models can not at the same time account for the rapid arsenic deactivation at the beginning and the slow one at long times that they observe in their experiments.

Some of the quantitative precipitation models that have been proposed in the literature solve for the whole size distribution of precipitates. This kind of model has been demonstrated for antimony precipitation [74], arsenic and phosphorus precipitation [18], and oxygen precipitation [75]. The dopant precipitation model by S. Dunham [18] has been shown to exhibit reverse annealing. However, it has not been applied extensively to arsenic and does not account for interstitial injection and dislocation loop formation. The oxygen precipitation model includes the interstitial injection and bulk stacking fault growth observed during oxygen





65


precipitation. A recently proposed precipitation model solves for the first three moments of the precipitate size distribution, making it computationally less intensive [76].

The next section will present a general extended defect model which can be applied to arsenic deactivation as a precipitation model [77]. The model calculates the evolution of the precipitate size distribution and is able to account for various phenomena related to arsenic activation and deactivation. The interaction of arsenicvacancy complexes with interstitials and dislocation loops will be included into the model in Chapter VII.



5.3 A Kinetic Model for Extended Defects



In the literature, the evolution of extended defects has usually been described by two phases: a nucleation and a growth phase. The nucleation theories study the formation of stable nuclei in a supersaturated solution while the growth theories try to determine the growth rate of these particles after they are formed. This is a somewhat artificial distinction since the nucleation and the growth of an extended defect is a continuous event. However, it makes the modeling problem more tractable and less computation intensive.

The classical nucleation theory was first formulated by Volmer and Weber 70 years ago [78]. It was later developed by several authors [79-82]. In this approach, the defects are assumed to grow or shrink by gaining or losing one atom at a time.





66



Ei.1 Ei









Ei Eijl









Figure 5.2 Schematic representation of the reactions taking place during extended defect formation. The defects are assumed to grow or shrink by gaining or losing one atom at a time.


This process, as shown in Figure 5.2, can be written as a set of reactions in the following form:



Ei- + El Ei Ei + E, Ei+1 5-2



where Ei represents a defect containing i solute atoms and El is a single solute atom. El may be an arsenic atom or a silicon interstitial, where Ei is then an arsenic precipitate (or cluster) or a dislocation loop. In this formulation, the collision and fusion of defects are ignored, as well as the fission of defects into two or more other defects. The formulation may not be valid in non-dilute solutions where the concentration of the solute is comparable to the concentration of solvent.





67


According to reactions 5-2, the change in the density of the i-sized defect is given by the following equation:




fi
t = (Pi- fi- 1 aifi) (Pifi Oi+ fi + 1), i 2 2 5-3




where i- is the forward and a t is the reverse reaction rates of the first reaction in 5-2. Equation 5-3 can be put in a more convenient form:




i i- i -J i>, i2 5-4




where Ji is the rate at which defects of size i become defects of size i+l and is defined by:




i = ifi i + fi + 1 5-5




Equation 5-3 does not apply to the case of i=l, i.e. the single solute atoms. The concentration of the single solute atoms can be found from the mass conversation equation:





68



fl + ifi = Ct 5-6 i=2



where Ct is the total solute concentration and is a given.

The forward reaction rate can be found by a treatment similar to the one given by Turnbull and Fisher [83]. The free energy diagram of the right hand side of reaction 5-2 is shown in Figure 5.3. Here Gi represents the non-mixing component of the free energy of defect Ei when El is taken as the reference phase. Agf is the reaction barrier between EI+Ei and the activated complex which turns into Ei+1. The forward reaction rate can be written as:




i= Aidnt dexp(Agf 5-7




where Ai is the surface area of the size-i defect, Xd is the lattice spacing around the defect, Cn" is the concentration of El atoms at the interface of the defect, vd is the vibration frequency and Agf is the energy barrier. Ai dCint is the number of El atoms that are around each Ei defect and are ready to react with Ei. vdexp(- kT is the number of times that this reaction takes place per unit time.

The diffusivity of the El atom in the solvent can roughly be written as:




D = v exp -_AgD 5-8 k T





69


Free
Energy i gb



ggf
Energy---------------------Gi+ - - ---/- ---
Activated
Gi ---Complex I
EI+E, I Eil
I I I Configuration

Figure 5.3 Schematic representation of free energies related to the following reaction between the extended defects and a single atom: Ei + El Ei+1.



where k is the lattice spacing, v is the vibration frequency and AgD is the migration energy. If the lattice spacing and the vibration frequency do not change near a defect and, most importantly, the migration energy, AgD, is equal to the reaction barrier, Agf, then




=i = AiCi"nt 5-9




The interface solute concentration around a defect, C"nt, is not necessarily equal to the far-field solute concentration, fi, because the transport of the solute atoms to the defect may not be fast enough to resupply all the solute atoms that have reacted with the defect. So, the solute may be depleted around the defect. For





70


convenience the diffusion of the solute atoms is assumed to be fast enough so that Cjnt = fl. So the forward reaction rate becomes:




Pi = AiD f 5-10




The reverse reaction rate can be found from the forward reaction rate and the thermal equilibrium condition, as suggested by Katz [81]. At thermal equilibrium, the detailed balance condition requires all fluxes to be equal to zero. So, from Equation 5-5:



fieq
a li+ = iq 5-11




where fieq is the density of size-i defects at equilibrium.

Upon minimizing the Gibbs free energy of a system consisting of defects of all sizes, the solute and solvent atoms, one can obtain the following expression for the density of the defects at thermal equilibrium:




1 = f exp Wi-Wi+l) 5-12 fieq C kT





71


where Wi is the interfacial free energy of a single i-sized defect, C,,sol is the solubility, k is Boltzmann's constant and T is the absolute temperature. Previously, it has been incorrectly assumed that the solute concentration is equal to its solubility at thermal equilibrium for this system [82,84] although Equation 5-12 is the only result of applying thermodynamics to this system. If the mixture was in touch with an infinitely big film of the second phase of the solute-solvent system, then the solute concentration would reach to its solubility at thermal equilibrium.

The interfacial free energy of a size-i defect, Wi, depends on the size of the defect. In the classical nucleation model, it is proportional to the surface area of the defect if the defect is large:



Wi = cAi 5-13



where Y is the interfacial surface energy per area and is defined by this equation. If the defect is spherical:




(367c 1/3.2/3
Ai = C2 5-14




where Cp is the density of the solute atoms in the defect. For small defects, the interfacial free energy is expected to deviate from the size dependence expressed in Equation 5-13. Terms that are proportional to the linear dimension of the defect plus





72


other terms may become more important. An empirical relation relating the interfacial free energy to defect size can be used [18]:





Wi = Clia' + c2ia2 + ... 5-15





where a1, a2,... shapes the size dependence of the interfacial free energy and c1, c2... are constants. Since the interfacial free energy is proportional to the surface area for large defects, a, can be set to 2/3 for spherical defects, to 1/2 for planar ones, etc. If the defect creates stress in the lattice, the strain energy term should also be included in Wi.



5.4 Simulation Results



Equations 5-3, 5-6, 5-10, 5-11, 5-12, 5-14, and 5-15 were implemented into FLOOPS. The interaction between the precipitates and point defects was not included in the model. The simulated experimental data was taken from Luning et al. [23]. In that work, arsenic was implanted into silicon at various doses, followed by laser annealing. Then, the samples were subjected to thermal annealing at various temperatures. The laser annealing activated all of the dopant, thus giving a clear initial condition for the simulations, i.e. the active concentration fl, is equal to the total dopant concentration, Cr at the beginning. The profiles were box-shaped and no appreciable diffusion of arsenic was observed; therefore a single chemical dopant concentration could





73


be used instead of the whole arsenic profile for each simulation. The discrete rate equations were solved without any rediscretization. The initial density of all precipitates was assumed to be very small. As the boundary condition, the density of an arbitrarily large precipitate was taken to be zero.

The arsenic diffusivity used in the simulations has the following form [18]:




DAs Do + D (n)[1 + (fl] 5-16




where Do and D. are the neutral and negative components of inert arsenic diffusivity, n is the electron concentration and ni is the intrinsic carrier concentration. The term, [ + ( takes into account the experimentally observed power law dependence of the arsenic diffusivity on the active concentration [31]. Do, D_ and CO have Arrhenius dependences on temperature.

The simulation parameters are given in Table I. The solubility, Csol,is taken to be equal to the equilibrium active concentration of arsenic. The only parameters that were fitted during the simulations are the interfacial energy coefficients c1 and c2, and the reference concentration Co.

Figure 5.4 to Figure 5.7 show a comparison of simulations with the arsenic deactivation data obtained between 500 and 8000C for chemical arsenic concentrations of lx1021 cm-3 and 4.4x1020 cm-3. The simulations successfully reproduce the experimental data. All of the simulations exhibit a very fast deactivation of arsenic at the beginning of the thermal anneal just like the





74


Table 5.1: Parameter values used for simulations of arsenic deactivation Activation
Parameter Pre-exponential Activation Energy (eV)

Do 0.0666 cm2/s 3.44 D 12.8 cm2/s 4.05 CO 3x1023 cm-3 0.631

m 3.5 a, 2/3

C1 0.13 eV

a2 1/3

C2 0.115 eV X 2.7x10-8 cm CP 2.5x 1022 cm-3

Csol 2.2x 1022 cm-3 0.47



experiments. This is due to the rapid formation of small clusters which have relatively small formation energies. The slow deactivation after around a few minutes is also replicated by the simulations. This slow deactivation could not be reproduced by single size cluster models [23]. Figure 5.8 shows the simulated size distributions of the 1x1021 cm-3 sample after 5 and 124 minutes at 7000C. The distribution becomes broader for the longer anneal, suggesting that the slow deactivation is due to further precipitation at larger sizes.





75



5e+20


E 0 Experiment
a 4e+20
c Simulation

2 3e+20


o 2e+20 0 0 0 0Sle+20


Oe+00
0 20 40 60 80 100 120 140 160 180 200 Time (min)
(a)

5e+20


E 0 Experiment
0 4e+20
S- Simulation



0 o oooo
o 2e+20




Oe+00

0 20 40 60 80 100 120 140 160 180 200
Time (min)

(b)

Figure 5.4 Comparison of experiments and simulation at 500C at a chemical arsenic concentration of (a) lx1021 cm-, (b) 4.4x1020 cm-





76


5e+20


E O Experiment
o 4e+20
a c- Simulation


a)
3e+20

0
o 2e+20
000000000

Sle+20


0e+00
0 20 40 60 80 100 120 140 160 180 200 Time (min)

(a)

5e+20 I


E 0 Experiment
o 4e+20
c ,- Simulation
0

c 3e+20


0
C 0
o 2e+20


a le+20


Oe+00 I I I I I
0 20 40 60 80 100 120 140 160 180 200 Time (min)

(b)

Figure 5.5 Comparison of experiments and simulation at 6000C at a chemical arsenic concentration of(a) lx1021 cm-3, (b) 4.4x 1020 cm-3.





77



5e+20 I


E O Experiment
o 4e+20
r Simulation
0

3e+20
o
O
o 2e+20
(

1 e+20


Oe+00 I I I I I I
0 20 40 60 80 100 120 140 Time (min)
(a)

5e+20 I I I


E O Experiment
o 4e+20
c e Simulation
0

C 3e+20

o
o 2e+20


1 e+20


Oe+00
0 20 40 60 80 100 120 140 Time (min)

(b)

Figure 5.6 Comparison of experiments and simulation at 7000C at a chemical arsenic concentration of (a) lx1021 cm-3, (b) 4.4x 1020 cm-3.





78


5e+20 I C,?
E O Experiment
a 4e+20
C Simulation

E 3e+20

CD




le+20
1 e+20



Oe+00 I
0 5 10 15
Time (min)

(a)

5e+20


E O Experiment
S4e+20
c- Simulation
0

3e+20
Q

o 2e+20 0O


) le+20


Oe+00 ' I , I
0 5 10 15
Time (min)

(b)

Figure 5.7 Comparison of experiments and simulation at 8000C at a chemical arsenic concentration of (a) lx1021 cm-3, (b) 4.4x1020 cm-3.





79





1020
~- 5 min S-El 124 min
E

0 1019


0

C 1018




1o17
0 5 10 15 20 Size

Figure 5.8 Simulated defect size distributions for the 1x1021 cm-3 sample after 5 min and 124 min at 7000C.



5.5 Conclusions



An arsenic deactivation model that takes into account the size distribution of inactive arsenic structures was presented. The rate equations that describe the evolution of the size distribution were derived from the kinetic theory and thermodynamics. The model is in good quantitative agreement with the experimental arsenic deactivation data, and successfully reproduces the rapid deactivation at the beginning and the slow deactivation after a few minutes.














CHAPTER VI
A COMPARISON OF VARIOUS NUMERICAL METHODS FOR THE SOLUTION OF THE RATE EQUATIONS IN EXTENDED DEFECT SIMULATION


6.1 Introduction



Extended defects in silicon play an important role in the final electrical characteristics of silicon devices. Precipitation/clustering of dopant atoms determine the carrier concentration in heavily doped regions. Dislocation loops affect the population of point defects and therefore dopant diffusion. { 311 } defects have recently been identified as an interstitial source during transient enhanced diffusion [85,86]. In general, extended defects form during phase transitions and as a result of aggregation of impurities such as dopants and point defects. The extended defects have been widely studied in the literature. Nucleation of clusters in gases, nucleation of vacancy voids [87,88], crystal nucleation in glasses [89] and crystal nucleation in amorphous silicon [90] are just a few examples.

In Chapter V, arsenic deactivation was simulated by solving the size distribution of electrically inactive arsenic precipitates. The rate equations describing the size distribution were directly solved without the necessity of a numerical method to reduce the number of equations. A small number (-50) of rate equations was enough to get a good fit to the experimental data. In addition, the




80





81


experimental arsenic profile was homogenous, so the rate equations which were solved at only one point on the arsenic profile were representative of all the other points.

Other extended defects such as dislocation loops and oxygen precipitates may contain millions of atoms. It is impossible to solve those many rate equations in a reasonable time with today's computer technology. Moreover, the impurity profiles are almost always inhomogenous, creating the necessity of solving different rate equations at each point in space. For these two reasons, the number of equations should be reduced to a reasonable level with an appropriate numerical technique [91].

The size evolution of the extended defects are described by the rate equations (also known as the discrete birth and death equations) which are introduced in Chapter V:




afi
= Ji- 1 Ji, i 2 2 6-1



i = ifi i + 1 fi + 1 6-2




where fi is the density of i-sized defect, Pi is the forward and ai+ 1 is the reverse reaction rates. As detailed in Chapter V, the reverse reaction rate can be found from the forward reaction rate and the thermal equilibrium condition:





82


feq
ei+ I qifq 6-3 I+1




where fieq is the density of i-sized defects at equilibrium. Upon substituting Equation 6-3 into Equation 6-2, an alternate form for Ji can be obtained:




J eqr fi fi+ 1 6-4 Ji = Pifi 64ffq





Several researchers [82,84,87,92] have worked on the solution of either the rate equations or its continuous form which is referred as the Fokker-Planck equation:




8 a a 2
-f(s, t) = -[A(s)f(s, t)] + [B(s)f(s, t)] 6-5 at T-7




where s is the continuous size variable, A and B are the drift and diffusion coefficients respectively. In spite of all this work, there still exists the need for a simple numerical method which can reproduce the solution of the rate equations with a sufficient degree of accuracy for large defect sizes (>1000). In this chapter, various numerical methods will be derived and they will be evaluated using the arsenic deactivation model of Chapter V. Two general techniques will be investigated: rediscretization and interpolation.





83


6.2 Rediscretization



In this approach, the rate equations are first put into a continuous form and then rediscretized. After finding a suitable continuous form, the equations are discretized using two different methods: linear and logarithmic discretization.



6.2.1 Continuous Form for the Rate Equations



The first continuous form for the rate equations has been given by Zeldovich [93] and Frenkel [80]:




f(s, t) J(s, t) 6-6 t Ts





J(s, t) = -P(s)feq() 6-7




These equations can be obtained by expanding Equations 6-1 and 6-4 into a Taylor series about i and keeping only the first two terms (the constant and the first derivative). This approach was later criticized by Goodrich [82]. He approximated the rate equations at the mid-points, rather than at the end-points. However, he used Equation 6-2 instead of Equation 6-4 in his derivation. Therefore, his analysis led to an equilibrium condition that is different from that of the discrete rate equations





84


(Equation 6-3). In contrast, the Frenkel-Zeldovich equation automatically contains the exact equilibrium conditions, because the starting point is Equation 6-4 which already includes the discrete equilibrium conditions. Shizgal and Barrett [84] suggested another methodology to approximate the rate equations with a continous form and compared all three methods to the exact solution. They found that their and Goodrich's approaches are more accurate than Frenkel's.

In order to approximate the rate equations with a continous form, the mathematical procedure suggested by Goodrich will be followed. First, the right
1
hand side of Equation 6-1 is expanded into a Taylor series around i- I up to the
2
second term. The resulting equation is:




a a 6-8
-f(s) J(s)





where s is the continous size variable. The implicit dependences off and J on t are not shown in order to make the derivation more clear. The same mid-point expansion is then applied to Equation 6-4, rather than Equation 6-2. As discussed in the previous paragraph, Equation 6-4 already contains the exact equilibrium conditions, therefore its continous form will also preserve them. Rewriting Equation
1
6-4 by substituting i- 2 in place of i, the following expression is obtained:





85



f I 7 1 6-9 J I~ - feql 2 6-9 -- 1+f
2 I




Expanding 3, feq, and separately into Taylor series around i, and keeping the feq
first two terms for p and f, and the first three terms for feq, the following feq
equation is obtained:




J(s) -[P(s) p(sa eq s)- feq eq s) + 6-10 2as J[s2as 8 a2s
2


s \q e




Substituting this equation into Equation 6-8, the following differential equations can be written for the discrete rate equations:




a-f(s) =-J(s) 6-11









feq was expanded up to the second derivative for the following reason: As mentioned in Chapter V, feq can be written as:





86


feq(s+ 1) fl (W(s) -W(s + 1)
-=- exp 6-13 feq() Csol kT



for s = i. fl represents the solute concentration, Csoi is the solubility and W is the interfacial free energy. From this iteration, feq can be found to be an exponential function of size s. If only the first two terms in the Taylor expansion are kept for eq feq_ I afeq
fe, namely fe e, this term will become negative if:
2as



feq < feq 6-14 2s



After finding an expression for feq from Equation 6-13 and inserting it into this inequality, the condition above can be rewritten as:




In i I T W(s) > 2 6-15 (Cs0l kTas



This condition can be met at large supersaturations or slowly changing interfacial free energy values. Then, the flux J(s) will be positive, which is completely nonphysical. The sign of the flux should only be decided by the ") term, as in the discrete rate equations. A similar analysis shows that the inclusion of the second derivative term in the expansion of feq guarantees that the approximate Taylor series for feq will always be positive as long as feq is expressed as similar to Equation 6-13 and W similar to 5-15.





87


Now that a continous form has been derived for the rate equations, the next step will be to discretize it for an arbitrary size spacing. Figure 6.1 shows an arbitrary segment of the size space for which Equations 6-11 and 6-12 will be discretized. For size 1, the right hand side of Equation 6-11 can be approximated as:




at Jk' 6-16




where 1' and k' are the mid-points in the respective interval and A is the size difference between the mid-points. The task is now reduced to finding an appropriate discrete expression for J at 1' and k'. Two discretization schemes will be investigated for this purpose: linear and logarithmic.



6.2.2 Linear Discretization



In this method, the function to be discretized, y(s), is assumed to be linear in size at each interval [k,l]:



y(s) = as + b 6-17



The value of this function and its derivative at the mid-point, k', can be approximated with the values of the function at the end-points, k and 1:





88






k k' I l' m
I I I Size





Akl AIm


Figure 6.1 An arbitrary interval in the size space for which the continuous rate equations are discretized.



Yk + 6-18 Yk' = 6-18 Yl-Yk 6-19 s k' Ak




If p, feq, and are assumed to be linear functions of size, one can obtain a
feq

discrete equation for Jk' by substituting these relations into Equation 6-12. Repeating the same procedure in the interval [1,m], a similar expression can be derived for J1r.



6.2.3 Logarithmic Discretization



In this scheme, the function to be discretized is assumed to be an exponential function of size:





89


y(s) = aebs 6-20



Similar to linear discretization, the value of the function and its derivative at the mid-point can be evaluated in terms of the values of the function at the end-points:




Yk' = 6-21


ak- kYIn -; 6-22 s k1 Yk


2 In
= [ kIj1 6-23





If p, feq, and f are assumed to be exponential in size, a discrete equation can be
feq
obtained for Jk' by substituting these relations into Equation 6-12.

There is one important problem with the logarithmic discretization method. The derivative of with respect to size is approximated as:
feq




(I= 1 f n (ff 6-24 Seq klf fekq Aklf kf7q




As one of the densities, such as ft, decreases, the derivative also decreases, eventually approaching zero for very small values of f1. This causes the flux, Jk', to





90


get smaller, which in turn decreases the rate of change of ft (Equation 6-16). This result is both counter-intuitive and incompatible with the original discrete rate equations. In the rate equations, the rate of change of fI increases as fI gets smaller (Equations 6-1 and 6-4).

This difficulty can be overcome by exploiting a technique that has been widely used in diffusion simulations and FLOOPS. This method works by mixing a small part of fk into fl and vice versa:




fk -'ofk +(1 a)f 6-25 flt afl + (1 )f k 6-26



where a is close to unity. If these substitutions are put into Equation 6-24, it can be found that Equation 6-24 is now compatible with the rate equations in the limit of small fl. In this work, the natural logarithm term in the derivative has not been changed in order to preserve the equilibrium conditions.



6.3 Interpolation



Figure 6.2 shows a segment of the size space where a solution for the discrete rate equations is desired. The rate equation for size I can be rewritten as:




af t f ft g feq 1+ 6-27
-t =eq Jeq q eq
_1 l I f1+ 1





91






k 1 m
I I I Size 1-1 1+1


Figure 6.2 An arbitrary interval in the size space. In the interpolation method, the density fl- is interpolated with fk andft and the density f ,+ with, andfm.



These equations include the densities for sizes 1- 1 and 1+ 1, i.e. fl-1 and fl+l" If only the solutions for fk, fI and f,, are desired, f-l_ and f1+l can be interpolated using these densities. Then, the rate equations will have only the densities whose solutions are desired.

In the linear interpolation case, the densities are assumed to be linear in size at each interval such as [k,l]. ft- I can be interpolated as:




S(1- k 1)ft+fk 6-28
1 -k



A similar expression can be obtained for fi+1. If these interpolations are substituted in Equation 6-27, the rate equations will only have fk, fl and fm as unknowns.

The exponential interpolation is similar to the linear one, except the densities are assumed to be exponential in size at each size interval. The exponential interpolation expression for fl 1 is given by:






92



(-k
fl-1 = (f(lkftk) 6-29




6.4 Comparison of Numerical Methods



The numerical techniques described in the previous sections were implemented in FLOOPS. Their accuracies in the solution of the rate equations were evaluated using the arsenic deactivation model in Chapter V. The chemical arsenic concentration was taken to be lx1021 cm-3. Table 6.1 shows the simulation parameters that are different than the ones used in Chapter V.

Figure 6.3 (a) shows the exact solution of the original discrete rate equations with these parameters. The equations have been solved up to size 2000. The exact solution will be a reference point in comparing the different numerical techniques. Figure 6.3 (b) shows the integrated dopant concentration in the precipitates. This concentration has been calculated by taking the sum of the dopant concentration up to the size shown in the x-axis. Most of the dopant atoms are located between the


Table 6.1: Simulation parameters that are different from the ones in Chapter V.

Activation
Parameter Pre-exponential Energy (eV) Energy (eV)

Co 4.8x1021 cm-3 0.4

c/ 0.3 eV c2 0.0 eV





93



1020 . .... . I

1019

1018

E
E 1017

4
r 1016

1015

1014 1013
1 10 100 1000 Size

(a) 1e+21

E
c 8e+20
0
o

C
S6e+20

O
C 4
CL
4e+20
0
o





Oe+00 I

Size

(b)

Figure 6.3 (a) Exact solution of the rate equations for the simulation described in the text. (b) The integrated dopant concentration for the exact solution.




Full Text
129
40.A. Armigliato, D. Nobili, S. Solmi, A. Bourret, and P. Werner, J. Electrochem. Soc.
133, 2560(1986).
41. A. Parisini, A. Bourret, and A. Armigliato in Microscopy of Semiconducting Materials
1987, Inst. Phys. Conf. Ser. No. 87 (Institute of Physics, Oxford, 1987), p. 491.
42. A. Parisini, A. Bourret, A. Armigliato, M. Servidori, S. Solmi, and R. Fabbri, J. Appl.
Phys. 67, 2320(1990).
43. Y. Yamamoto, T. Inada, T. Sugiyama, and S. Tamura, J. Appl. Phys. 53, 276 (1982).
44. N. R. Wu, D. K. Sadana, and J. Washburn, Appl. Phys. Lett. 44, 782 (1984).
45. S. J. Pennycook, R. J. Culbertson, and J. Narayan, J. Mater. Res. 1, 476 (1986).
46. K. S. Jones, S. Prussin, and E. R. Weber, J. Appl. Phys. 62, 4114 (1987).
47. S. Luning, Ph.D. Dissertation, Stanford University, 1996.
48. T. O. Sedgwick, A. E. Michel, V. R. Deline, S. A. Cohen, and J. B. Lasky, J. Appl.
Phys. 63, 1452 (1988).
49.S. Solmi, F. Cembali, R. Fabbri, M. Servidori, and R. Canteri, Appl. Phys. A 48, 255
(1989).
50.O. Dokumaci, M. E. Law, V. Krishnamoorthy, and K. S. Jones, in Ion-Solid
Interactions for Materials Modification and Processing, edited by D. B. Poker, D. Ila,
Y. Cheng, L. R. Harriott, and T. W. Sigmon (Mater. Res. Soc. Proc. 396, Pittsburgh,
PA, 1996), p. 167.
51.R. B. Fair, IEEE Trans. Electron Devices 35, 285 (1988).
52.P. Rousseau. Ph.D. Dissertation, Stanford University, 1996.


10
where A+ represents the substitutional donor atom, Xc represents a point defect
with charge c. Since the point defects are charged, their concentration will depend
on free carrier concentrations. For example, the concentration of negatively charged
point defects with respect to their intrinsic values is given by [24]:
Cx~c
(cx.cy W
1-2
where C c denotes the concentration of X L defects, (C c) their concentration in
A A
intrinsic silicon, n the electron and ni the intrinsic electron concentration. This
equation has been written under the assumptions that the environment is inert and
the reactions between point defects and electrons are so fast that they may be
considered in chemical equilibrium.
The diffusivity of a dopant is proportional to the concentration of the mobile
dopant-defect pairs. Since the number of dopant-defect pairs is proportional to the
number of point defects and the number of point defects depend on the free carrier
concentration, the diffusivity depends on the free carrier concentration under
extrinsic conditions. Actually, if the dopant-defect reactions and the defects are in
equilibrium, the diffusivity for a donor atom can be written as:
D = D 0 + D
1-3


127
13.P. M. Rousseau, P. B. Griffin, P. G. Carey, and J. D. Plummer, in Process Physics and
Modeling in Semiconductor Technology, Electrochemical Society Proceedings, No.
93, edited by G. R. Srinivasan, K. Taniguchi, and C. S. Murthy (The Electrochemical
Society, Pennington, NJ, 1993), p. 130.
14.D. Nobili, A. Armigliato, M. Finetti, and S. Solmi, J. Appl. Phys. 53, 1484 (1982).
15.L. J. Borucki, Proceedings of the IEDM, p.753, 1990.
16.J. L. Altrip, A. G. R. Evans, J. R. Logan, and C. Jeynes, Solid State Electronics 33, 659
(1990).
17.N. D. Young, J. B. Clegg, and E. A. Maydell-Ondrusz, J. Appl. Phys. 61, 2189 (1987).
18. S. T. Dunham, J. Electrochem. Soc. 142, 2823 (1995).
19. M. Orlowski, R. Subrahmanyan, and G. Huffman, J. Appl. Phys. 71, 164 (1992).
20. A. H. Perera, W. J. Taylor, and M. Orlowski, Proceedings of the IEDM, p.835, 1993.
21. N. Natsuaki, M. Tamura, and T. Tokuyama, J. Appl. Phys. 51, 3373 (1980).
22. A. Lietoila, J. F. Gibbons, T. J. Magee, J. Peng, and J. D. Hong, Appl. Phys. Lett. 35,
532 (1979).
23. S. Luning, P. M. Rousseau, P. B. Griffin, P. G. Carey, and J. D. Plummer, Proceedings
of the IEDM, p.457, 1992.
24. P. M. Fahey, P. B. Griffin, and J. D. Plummer, Rev. Mod. Phys. 61, 289 (1989).
25. B. J. Masters, and J. M. Fairfield, J. Appl. Phys. 40, 2390 (1969).
26. J. S. Makris, and B. J. Masters, J. Electrochem. Soc. 120, 1253 (1973).


65
precipitation. A recently proposed precipitation model solves for the first three
moments of the precipitate size distribution, making it computationally less
intensive [76].
The next section will present a general extended defect model which can be
applied to arsenic deactivation as a precipitation model [77]. The model calculates
the evolution of the precipitate size distribution and is able to account for various
phenomena related to arsenic activation and deactivation. The interaction of arsenic-
vacancy complexes with interstitials and dislocation loops will be included into the
model in Chapter VII.
5.3 A Kinetic Model for Extended Defects
In the literature, the evolution of extended defects has usually been described
by two phases: a nucleation and a growth phase. The nucleation theories study the
formation of stable nuclei in a supersaturated solution while the growth theories try
to determine the growth rate of these particles after they are formed. This is a
somewhat artificial distinction since the nucleation and the growth of an extended
defect is a continuous event. However, it makes the modeling problem more
tractable and less computation intensive.
The classical nucleation theory was first formulated by Volmer and Weber 70
years ago [78], It was later developed by several authors [79-82]. In this approach,
the defects are assumed to grow or shrink by gaining or losing one atom at a time.


I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
'Kevin S. Jones
Associate Professor of Materials Science
and Engineering
This dissertation was submitted to the Graduate Faculty of the College of
Engineering and to the Graduate School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
May 1997
Winfred M. Phillips
Dean, College of Engineering
Karen A. Holbrook
Dean, Graduate School


30
i z: o
Figure 2.7 Cross-section TEM micrograph of the sample implanted with 1.6x10 cm
and annealed at 700C for 15 s (weak beam dark field).
Figure 2.8 Cross-section TEM micrograph of the sample implanted with 1.6x10 cm
and annealed at 700C for 100 min (weak beam dark field).


28
Table 2.1: Summary of TEM observations made on the samples annealed at 750C for
120 minutes.
Dose
(cm'2)
Surface
Cone.
(cm'3)
Defect
Type
Size
(A0)
Density
(cm'2)
Density of
Bound
Atoms
(cm'2)
Inactive
As
Dose
(cm'2)
4xl015
2.3x1020
None
-
-
-
2.2xl015
Dislocation
loops
200- 1200
3.3xl09
1.2xl014
8xl015
4.5xl020
Rod-like
defects
400 2800
1.8xl09
-
4.9xl015
1.6xl016
9.1xl020
Dislocation
loops
50 350
1.3x10
3.5-4.5xl014
1.3xl016
3.2xl016
1.9xl021
Dislocation
loops
100 400
>2.5x10
> 6xl014
2.9xl016
Further analysis showed that the defects in the short-time sample are dislocation
loops with a density of around 6x10 cm and average size of 90 A. Recently,
Rutherford back-scattering (RBS) measurements were made on the same samples
[47]. It was demonstrated that the backscattered angular-scan spectra for silicon
have the same minimum in both the as-lased and short-time samples whereas the
minimum yield of arsenic increases. Furthermore, silicon minimum yield was


36
increases abruptly above a certain arsenic concentration. Hence, an abrupt change in
the diffusivity of the buried boron layer can be expected if arsenic deactivation has
an appreciable effect on damage enhanced diffusion.
3.2 Experiment
The boron buried layers were prepared in Texas Instruments. After
o
depositing 200 A of oxide on <100> silicon to reduce ion channeling, boron was
implanted at 10 keV with a dose of 3xl012 cm 2. The oxide was then etched with an
HF solution and an approximately 0.6 pm thick epi layer was grown. Arsenic was
implanted at 50 keV at 7 tilt with doses ranging from 4xl014 to 4xl015 cm'2. The
peak arsenic concentrations determined from SIMS are shown in Table 3.1 along
with the implanted doses. The arsenic concentrations were normalized to the
implanted dose.The samples were annealed at three different times temperatures:
750C 2h, 900C lmin, and 1050C 15s. It has been previously reported that the
damage enhanced diffusion due to interstitial cluster dissolution is complete for
boron implants within the anneal times selected for each temperature [7,51].
Arsenic and boron profiles were obtained by secondary ion mass
spectrometry (SIMS) using an oxygen beam. Since the boron dose was low, the
sample was tilted at an angle so that the boron yield was higher during sputtering.
The defects were studied by transmission electron microscopy with a JEOL 200 CX
electron microscope operating at 200 keV. Plan-view and cross-section samples
were analyzed in g22o and gill conditions.


26
Figure 2.3 Plan-view TEM micrograph of the sample implanted with 1.6xl016 cm'2 and
annealed at 750C (weak beam dark field).
i j
Figure 2.4 Plan-view TEM micrograph of the sample implanted with 3.2x10 cm_i and
annealed at 750C (weak beam dark field).


22
elimination of end-of-range damage (category-II dislocation loops) is enhanced in
the presence of a high concentration arsenic layer [46]. Both half-loop formation
and enhanced elimination of category-II loops occur when arsenic peak
concentration exceeds its solid solubility.
Understanding the mechanism of these defects is important for both defect
engineering and an evaluation of the effects of arsenic deactivation on point defects
and, therefore, dopant diffusion underneath high concentration arsenic layers. This
chapter reports the results of TEM observations on samples which were doped with
different arsenic doses above the equlibrium active concentration, received a laser
anneal to activate all of the dopant and finally thermally annealed.
2.2 Experiment
Arsenic was implanted into <100>, 10 £2-cm p-type silicon substrates at
doses ranging from 4xl015 to 3.2xl016 cm'2 with an energy of 35 keV. Completely
active, box-shaped profiles were obtained by repeated laser pulse annealing (308 nm
XeCl, 35 ns FWHM pulses, silicon melt duration 75 ns). The melt-region thickness
of about 200 nm was considerably larger than the depth of the implant; thus any
major implant damage in the as-implanted layer was effectively annealed out. The
samples then received additional rapid thermal anneals at 700 or 750C for
durations that resulted in no appreciable diffusion. Further experimental details
about the preparation of these samples can be found in Rousseau et al. [13] and
Luning et al.[23],


99
equations. For example, it produces a more accurate solution for Neq=40. In spite of
being more accurate in some cases, it will be shown in the next section that the
exponential interpolation method is unstable and produces oscillations in the active
concentration for a small number of equations.
6.4.2 Comparison of Active Concentrations
As mentioned in Chapter V, the active concentration is obtained from the
following relationship:
/l =£,-£'/, MO
i = 2
where Ct is the chemical dopant concentration, and f¡ is the density of the i-sized
precipitates. From a process modeling point of view, the solution of the active
concentration is more important than the size distribution of the precipitates. The
final judgment on a numerical method should be based on how accurate it can
reproduce the active concentration, although there may be inaccuracies in the
solution of the size distribution.
Figure 6.7 and Figure 6.8 compare the evolution of the active concentration
obtained with different numerical methods for A=20 and Neq=195. The linear
rediscretization technique completely fails to reproduce the exact solution. A denser
grid should be used if this method is to be utilized in the solution of the rate


88
k
k'
l
m
-1 Size
A
Figure 6.1 An arbitrary interval in the size space for which the continuous rate equations
are discretized.
y* =
yt+ Vi
2
6-18
By = yi-yk
ds k Akl
6-19
If B, feq, and are assumed to be linear functions of size, one can obtain a
r
discrete equation for Jk> by substituting these relations into Equation 6-12.
Repeating the same procedure in the interval [l,m\, a similar expression can be
derived for J¡,.
6.2.3 Logarithmic Discretization
In this scheme, the function to be discretized is assumed to be an exponential
function of size:


51
(Equation 4-1) at 850C and 5% less at 950C. The enhancements in antimony
diffusivity are very close to unity, indicating that there is no observable vacancy
supersaturation during arsenic activation in these samples. The activation of arsenic
was confirmed by both sheet resistance (Table 4.1) and spreading resistance
measurements (Figure 4.5). The spreading resistance data shows that diffusion of
arsenic into the bulk as well as the higher activation level of arsenic at 950C
contribute to the amount of more electrically active arsenic.
The positron annihilation experiments show that the average number of
vacancies per inactive arsenic atom is between 1/2 and 1/4 in an arsenic doped
silicon sample which has been laser annealed and then thermally annealed at 750C
(concentration of arsenic = 8xl020 cm'3) [54]. RBS and EXAFS measurements have
led Brizard et al. to propose the existence of arsenic-vacancy clusters which have a
vacancy/arsenic ratio of around 1/3 [55]. Thus, it is unexpected that there is not any
significant enhancement in the arsenic doped samples since a very large amount of
free vacancies is expected to be released upon the dissolution of these clusters
during the activation anneals.
To investigate the possibility that the generated vacancies may be absorbed
by the extrinsic extended defects either left over from the damage anneal or created
by the subsequent deactivation anneal, a plan-view TEM study of the arsenic doped
samples was undertaken (Table 4.1). Dislocation loops were observed in the
samples after the deactivation anneal, and they completely dissolve during the
activation anneals with the exception of the 850C high dose sample where only a
very small amount of loops has survived the activation anneal.


75
Figure 5.4 Comparison of experiments and simulation at 500C at a chemical arsenic
concentration of (a) lxlO21 cm'3, (b) 4.4xl020 cm'3.


102
equations. The linear interpolation method can reproduce the shape of the evolution
curve, but it is much less accurate than either the exponential interpolation or the
logarithmic discretization technique. As the number of equations is reduced, the
linear interpolation method gets consistently more inaccurate.
Figure 6.9 shows a comparison of the logarithmic rediscretization and the
exponential interpolation techniques for Neq=60. The exponential interpolation
method causes oscillations in the active concentration at small times. It is also less
oo
accurate than the logarithmic rediscretization method. So, the summation ^ i/(
i = 2
seems to be conserved better in the logarithmic rediscretization technique for small
grids, making it more accurate in representing the active concentration.
Figure 6.10 shows the percentage error in the active concentration obtained
with the logarithmic rediscretization method relative to the exact solution. For the
smallest grid used in the simulations (Neq=20), the relative error does not exceed
20%. Therefore, the logarithmic rediscretization method performs satisfactorily for
the solution of the active concentration even for a reduction of 100 in the number of
rate equations.
6.5 Conclusions
Various numerical methods were evaluated for the solution of the rate
equations that describe the size evolution of extended defects. These methods
include linear and logarithmic rediscretization, and linear and exponential
interpolation. A new continous form was derived for the rate equations. The


73
be used instead of the whole arsenic profile for each simulation. The discrete rate
equations were solved without any rediscretization. The initial density of all precipitates
was assumed to be very small. As the boundary condition, the density of an arbitrarily
large precipitate was taken to be zero.
The arsenic diffusivity used in the simulations has the following form [18]:
5-16
where Da and D_ are the neutral and negative components of inert arsenic
diffusivity, n is the electron concentration and , is the intrinsic carrier
, takes into account the experimentally
concentration. The term,
observed power law dependence of the arsenic diffusivity on the active
concentration [31]. Da, D_ and Ca have Arrhenius dependences on temperature.
The simulation parameters are given in Table I. The solubility, Cso¡,is taken
to be equal to the equilibrium active concentration of arsenic. The only parameters
that were fitted during the simulations are the interfacial energy coefficients c¡ and
c2, and the reference concentration C0.
Figure 5.4 to Figure 5.7 show a comparison of simulations with the arsenic
deactivation data obtained between 500 and 800C for chemical arsenic
concentrations of 1 x 1021 cm'3 and 4.4xl020 cm'3. The simulations successfully
reproduce the experimental data. All of the simulations exhibit a very fast
deactivation of arsenic at the beginning of the thermal anneal just like the


38
Depth (pm)
Figure 3.2 Buried boron profiles for different arsenic doses after the 750C, 2hr. anneal.
Arsenic Dose (cm'2)
Figure 3.3 The enhancement of boron diffusivity as a function of arsenic dose at 750C.


35
After ion implantation After annealing
End-of-range
implant
damage
a/c interface
Figure 3.1 Schematic representation of damage and loop formation in high dose arsenic
implanted silicon.
Although arsenic deactivation creates excess interstitials and causes
dislocation loop formation, it is not yet clear how much effect it has on the enhanced
diffusion caused by high dose arsenic implantation. While excess interstitials should
contribute to the implant damage enhanced diffusion, type-V loops may decrease
the amount of enhanced diffusion by absorbing the interstitials. In this work [50],
arsenic was implanted into silicon at various doses with the same energy. Buried
boron layers were used as markers of interstitial supersaturation. Most of the chosen
doses give rise to peak arsenic concentrations above the equilibrium active
concentration. The density of type-V loops is a very strong function of the arsenic
concentration, and the interstitial supersaturation during arsenic deactivation
I I
type-V loops end-of-range
loops


74
Table 5.1: Parameter values used for simulations of arsenic deactivation
Parameter
Pre-exponential
Activation
Energy (eV)
D0
0.0666 cm2/s
3.44
D.
12.8 cirr/s
4.05
C0
3xl023 cm'3
0.631
m
3.5
al
2/3
C1
0.13 eV
a2
1/3
c2
0.115 eV
X
2.7xl0'8 cm
CP
2.5xl022 cm'3
n
^ sol
2.2x1022 cm'3
0.47
experiments. This is due to the rapid formation of small clusters which have
relatively small formation energies. The slow deactivation after around a few
minutes is also replicated by the simulations. This slow deactivation could not be
reproduced by single size cluster models [23], Figure 5.8 shows the simulated size
distributions of the lxl021 cm'3 sample after 5 and 124 minutes at 700C. The
distribution becomes broader for the longer anneal, suggesting that the slow
deactivation is due to further precipitation at larger sizes.


I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Mark E. Law, Chairman
Associate Professor of Electrical and
Computer Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
QVIaS-
Professor of Electrical and Computer
Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Associate Professor of Electrical and
Computer Engineering


TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS ii
ABSTRACT vi
CHAPTERS
I INTRODUCTION 1
1.1 Dopant Activation/Deactivation 3
1.1.1 Electrically Active Dopant Concentration 5
1.1.2 Dopant Diffusion 9
1.1.3 Point Defect Injection 12
1.1.4 Dislocation Loops 16
1.2 Organization 17
II TRANSMISSION ELECTRON MICROSCOPY ANALYSIS OF
EXTENDED DEFECTS IN HEAVILY ARSENIC DOPED, LASER,
AND THERMALLY ANNEALED LAYERS IN SILICON 20
2.1 Introduction 20
2.2 Experiment 22
2.3 TEM Results 24
2.4 Conclusions 33
III HIGH DOSE ARSENIC IMPLANTATION INDUCED TRANSIENT
ENHANCED DIFFUSION 34
3.1 Introduction 34
3.2 Experiment 36
3.3 Results and Discussion 37
3.4 Conclusions 43
IV INVESTIGATION OF VACANCY POPULATION DURING ARSENIC
ACTIVATION IN SILICON 45
4.1 Experimental Details 46
4.2 Results and Discussion 48
4.3 Vacancy Population in the Partial Absence of Dislocation Loops 55
4.4 Conclusions 58
IV


18
with different arsenic doses above the equilibrium active concentration and received
a laser anneal to activate all of the dopant, followed by thermal annealing. Various
characteristics of the observed defects are evaluated and comparisons with
published data are made.
Chapter III presents the results of boron enhanced diffusion due to high dose
arsenic implantation in silicon. This study is made to investigate the possible effects
of arsenic deactivation on implant damage enhanced diffusion. The behavior of both
type-V and type-II loops is studied with TEM. Reduction in enhanced diffusion is
observed with increasing arsenic dose at three different temperatures. The possible
explanations for this reduction are also included in Chapter III.
Chapter IV contains an investigation of the vacancy population during
arsenic activation. Since arsenic is believed to deactivate through the formation of
arsenic-vacancy complexes, these complexes are expected to dissolve and generate
free vacancies during arsenic activation. The vacancy population is monitored using
antimony buried layers.
Chapter V presents a general kinetic model for extended defects. This model
is applied to arsenic deactivation in silicon. The model calculates the evolution of
the arsenic precipitate size density. It reproduces various trends and a good
agreement is obtained between the simulations and the experiments.
In Chapter VI, various numerical methods are evaluated for the solution of
the rate equations in extended defect simulation. The derivations of these methods
are presented. The accuracies of these methods are evaluated using the arsenic
deactivation model in Chapter V.


81
experimental arsenic profile was homogenous, so the rate equations which were
solved at only one point on the arsenic profile were representative of all the other
points.
Other extended defects such as dislocation loops and oxygen precipitates
may contain millions of atoms. It is impossible to solve those many rate equations in
a reasonable time with todays computer technology. Moreover, the impurity
profiles are almost always inhomogenous, creating the necessity of solving different
rate equations at each point in space. For these two reasons, the number of equations
should be reduced to a reasonable level with an appropriate numerical technique
[91].
The size evolution of the extended defects are described by the rate equations
(also known as the discrete birth and death equations) which are introduced in
Chapter V:
V,-
dt
6-1
Ji = Pi/r/+i/i+i
6-2
where f¡ is the density of i-sized defect, P(- is the forward and ai + 1 is the reverse
reaction rates. As detailed in Chapter V, the reverse reaction rate can be found from
the forward reaction rate and the thermal equilibrium condition:


121
positron annihilation and EXAFS measurements. The role of the surface on the
recombination and generation of point defects should also be determined.


ACKNOWLEDGEMENTS
I would like to thank my advisor, Dr. Mark E. Law, for his support, guidance, and
patience throughout my studies in the University of Florida. His great sense of humor,
wide knowledge of processing physics, and excellent teaching abilities make him an ideal
professor to work with. I would like to thank Drs. Gijs Bosman, Jerry G. Fossum, and
Robert M. Fox for their guidance as members of my doctoral committee. I am grateful to
Dr. Kevin S. Jones for coming up with several valuable ideas during the course of this
work.
I am very grateful to Viswanath Krishnamoorthy, Sushil Bharatan, Jinning Liu, and
Brian Beaudet for their help in the TEM work. I would like to thank James Chamblee and
Steve Schein for helping me in my experiments, and Mary Turner for her extensive
administrative help.
I was very fortunate to share my time at the university with several nice people:
Srinath Krishnan, Chih-Chuan Lin, Jonathan Brodsky, Samir Chaudhry, Stephen Cea,
Ming-Yeh Chuang, Susan Earles, David Zweidinger, Doug Weiser, and Glenn Workmann.
I was lucky to have two very friendly office-mates: Ahmed Ejaz Nadeem and Heman
Rueda.
This dissertation would have been impossible without the unconditional and
unending support of my parents, Osman Dokumaci and Esin Dokumaci, and my sister,
Merva Dokumaci. I am very grateful to have been blessed with such a good family.
li


86
fKs+ 1) Jj_exp(W(s)-W(s+\)
f\s)
C
sol
kT
6-13
for 5 = j. /, represents the solute concentration, Csol is the solubility and W is the
interfacial free energy. From this iteration, feq can be found to be an exponential
function of size s. If only the first two terms in the Taylor expansion are kept for
\ 3 f'
feq, namely feq---^- this term will become negative if:
eq
fec?
1 2 ds
1 dfq
6-14
After finding an expression for feq from Equation 6-13 and inserting it into this
inequality, the condition above can be rewritten as:
CsolJ kTds
6-15
This condition can be met at large supersaturations or slowly changing interfacial
free energy values. Then, the flux J(s) will be positive, which is completely non
physical. The sign of the flux should only be decided by the term, as in
the discrete rate equations. A similar analysis shows that the inclusion of the second
derivative term in the expansion of feq guarantees that the approximate Taylor
series for feq will always be positive as long as fq is expressed as similar to
Equation 6-13 and W similar to 5-15.


CHAPTER VII
AN ARSENIC DEACTIVATION MODEL INCLUDING THE
INTERACTION OF ARSENIC DEACTIVATION WITH
INTERSTITIALS AND DISLOCATION LOOPS
7.1 Introduction
As mentioned in Chapter V, arsenic deactivates with vacancies. During the
formation of arsenic-vacancy complexes, interstitials are injected into the bulk, and
boron diffusion is enhanced underneath the arsenic layers (Figure 7.1). The reaction
for the formation of arsenic-vacancy complexes can be written as:
mAs + nSi <=> As,V + nl 7-1
The enhanced diffusion due these excess interstitials have been shown to
affect the device characteristics significantly [35,52], In Chapter II, several
properties of the dislocation loops that are formed during arsenic deactivation were
investigated. The density of atoms bound by the loops increases at higher arsenic
concentrations. This explains the reduction in the boron diffusivity at higher arsenic
concentrations. Dislocation loops can also indirectly influence the arsenic
deactivation process by absorbing interstitials and thereby affecting reaction 7-1. In
order to accurately predict the arsenic deactivation process and its effects on the
104


95
Table 6.2: The grids used in the simulations. A size step of 1 is used up to size SZ1 and a
size step of A is used up to size 2000.
Grid #
SZ1
Size Step (A)
Number of
equations (Neq)
1
100
2
1050
2
100
3
734
3
100
4
575
4
100
5
480
5
100
10
290
6
100
20
195
7
100
50
138
8
100
100
119
9
50
50
89
10
50
100
70
11
20
50
60
12
20
100
40
13
10
200
20
number of equations is decreased, the linear interpolation method becomes much
less accurate (A=50, Neq=60). The logarithmic rediscretization technique produces a
much better solution for the same grid.
Figure 6.6 shows the size distribution obtained with the exponential
interpolation and logarithmic rediscretization methods. For Neq=70, logarithmic
rediscretization is more accurate. However, it has been found that the accuracy of
the exponential interpolation technique is not proportional to the number of


72
other terms may become more important. An empirical relation relating the
interfacial free energy to defect size can be used [18]:
W¡ = cxia' + c2ia>+ ...
5-15
where a¡, a2,... shapes the size dependence of the interfacial free energy and c¡,
c2,... are constants. Since the interfacial free energy is proportional to the surface
area for large defects, a¡ can be set to 2/3 for spherical defects, to 1/2 for planar
ones, etc. If the defect creates stress in the lattice, the strain energy term should also
be included in W¡.
5.4 Simulation Results
Equations 5-3, 5-6, 5-10, 5-11, 5-12, 5-14, and 5-15 were implemented into
FLOOPS. The interaction between the precipitates and point defects was not
included in the model. The simulated experimental data was taken from Luning et
al. [23], In that work, arsenic was implanted into silicon at various doses, followed by
laser annealing. Then, the samples were subjected to thermal annealing at various
temperatures. The laser annealing activated all of the dopant, thus giving a clear initial
condition for the simulations, i.e. the active concentration/;, is equal to the total dopant
concentration, C, at the beginning. The profiles were box-shaped and no appreciable
diffusion of arsenic was observed; therefore a single chemical dopant concentration could


19
Chapter VII presents an arsenic deactivation model including dislocation
loop formation and the interaction of the interstitials with the inactive arsenic
structures. The model shows quantitative agreement with the arsenic deactivation
and boron enhancement data. It is also in qualitative agreement with the properties
of the loops in the deactivated layer. Finally, Chapter VIII presents the conclusions
of this dissertation and recommendations for future experimental and modeling
efforts.


59
annihilation and EXAFS measurements. Other possible mechanisms that can
explain the lack of vacancy injection in the presence of the loops include surface
recombination, recombination with trapped interstitials generated during the
deactivation anneal and absorption of vacancies by relatively more vacancy rich
arsenic defects, such as As2V clusters. On the other hand, antimony diffusion is
enhanced for the same anneals when germanium is present at the surface.
In the partial absence of the loops, antimony diffusion is enhanced by a
factor of 1.5-2 during arsenic activation. Vacancy injection during arsenic activation
as well as non-equilibrium diffusion may explain this enhancement.


6
Depth
Figure 1.3 Representative boron profiles after ion-implantation and diffusion. The profile
is not completely electrically active although the peak concentration is much below the
equilibrium active concentration.
of boron at the peak has been attributed to the large supersaturation of interstitials
just after ion-implantation [9-11]. If boron atoms are assumed to form clusters
through a reaction with silicon interstitials, a high supersaturation of interstitials
will increase the rate of formation of boron clusters, thus decreasing the electrically
active boron concentration. Precipitation has been another explanation for boron
deactivation in implanted samples [7].
Arsenic and phosphorus have been shown to exhibit a phenomenon called
reverse annealing [12-14] (Figure 1.4). After being annealed at 650C, high
concentration arsenic samples have been subsequently annealed at 750C [12].


55
Figure 4.7 Enhancement in the antimony diffusivity as a function of depth in the
germanium doped samples. The thermal cycles shown in the legends represent only the
activation anneal.
Figure 4.7 shows the enhancement in the antimony diffusivity in germanium
doped samples during the activation anneals. Unlike arsenic, antimony diffusion is
enhanced by a factor of 2 to 4 in these samples.
4.3 Vacancy Population in the Partial Absence of Dislocation Loops
A second set of samples was prepared in order to find out whether the
enhancement in antimony diffusivity increases after the dislocation loops dissolve
completely. These samples were prepared like the previous ones (Figure 4.1) except
that the activation anneals were done without any oxide or nitride on the surface.
The activation anneal conditions were 16 hours at 850C, and 1 and 2 hours at


54
0.00 0.10 0.20 0.30 0.40 0.50
Depth (pm)
Figure 4.6 Carbon SIMS profiles in the unimplanted and high dose arsenic samples after
the deactivation anneal.
carbon in this sample is actually inside silicon, rather than at the top of the surface.
This high concentration of carbon may be capturing the excess interstitials injected
during the deactivation cycle and creating a sink for excess vacancies.
Another explanation for the unaccounted vacancies is a possible increase in
the ratio of the concentration of clusters that have a higher vacancy/arsenic ratio,
such as As2V, to the concentration of higher order clusters which have a smaller
vacancy/arsenic ratio, such as As4V. This can especially happen in the regions
where chemical arsenic concentration is not very high (i.e. diffused regions) and the
formation of arsenic rich clusters is kinetically limited. Therefore, instead of being
injected into the bulk, the excess vacancies may be recaptured by the relatively more
vacancy rich arsenic-vacancy complexes.


114
q* = (c,*)
int
*: (?) *r (-
k; + k;
1-22
The ratio KJ/ KJ is kept as a fitting parameter, while ( q*)"U is taken from
Zimmermann et al. [97]. Finally, all the parameter values are listed in Table 7.1. The
fitted parameters are shown in the first four columns. The common parameters with
the model of Chapter V can be found in Table 5.1.
Table 7.1: Parameter values for simulations of arsenic deactivation
Parameter
Pre-exponential
Activation
Energy (eV)
cl
0.3
c2
0.86
Kf/ K¡
1.6x1 O'4
ks
0.1 cm/s
(q*r
1.94xl027 cm'3
3.835
D,
2.58x1 O'2 cm2/s
0.965
f,
0.5
b
3.14 A
F
7.55xl0n dynes/cm2
V
0.3
0.028 eV
(cv*r
2.3xl021 cm'3
1.08
k-B
8.16x 10"4 cmJ/s
3.19


27
Figure 2.5 Plan-view TEM micrograph of the sample implanted with 1.6xl016 cm'2 and
annealed at 700C for 15s (weak beam dark field).
1 ?
Figure 2.6 Plan-view TEM micrograph of the sample implanted with 1.6x10 cm' and
annealed at 700C for 100 min (weak beam dark field).


106
precipitation of oxygen. This model solves for the whole size distribution of both
the oxygen precipitates and stacking faults, and is able to account for a wide range
of experiments.
In this chapter, an arsenic deactivation model including the generation of
interstitials and formation of dislocation loops will be presented. The model will be
shown to predict several qualitative features related to the arsenic deactivation
process.
7.2 Model for the Inactive Arsenic-Vacancv Complexes
The following reaction will be considered between the arsenic-vacancy
complexes, substitutional arsenic, and the point defects:
P,: + As <=> Pi + j + al 7-2
where P- is an arsenic-vacancy complex including i As atoms, and I is the silicon
interstitial. It is assumed that the growth of arsenic-vacancy structures proceeds
through the release of interstitials. This model is intended to be used for the laser
and then thermally annealed samples. The initial conditions are taken to be the
conditions just after the laser anneal. Since positron annihilation measurements
suggest that there is not a significant amount of free vacancies left behind after the
laser anneal [54], the free vacancies have not been considered in reaction 7-2. The
surface may be a source of free vacancies during thermal annealing, but the very fast


71
where W¡ is the interfacial free energy of a single i-sized defect, Cso¡ is the
solubility, k is Boltzmanns constant and T is the absolute temperature. Previously, it
has been incorrectly assumed that the solute concentration is equal to its solubility
at thermal equilibrium for this system [82,84] although Equation 5-12 is the only
result of applying thermodynamics to this system. If the mixture was in touch with
an infinitely big film of the second phase of the solute-solvent system, then the
solute concentration would reach to its solubility at thermal equilibrium.
The interfacial free energy of a size-i defect, W¡, depends on the size of the
defect. In the classical nucleation model, it is proportional to the surface area of the
defect if the defect is large:
5-13
W; = O A;
where a is the interfacial surface energy per area and is defined by this equation. If
the defect is spherical:
5-14
where Cp is the density of the solute atoms in the defect. For small defects, the
interfacial free energy is expected to deviate from the size dependence expressed in
Equation 5-13. Terms that are proportional to the linear dimension of the defect plus


49
Figure 4.2 Antimony SIMS profiles in the as-deposited DSL sample and the sample
implanted with 8x1015 cm'2 arsenic and annealed at 950C for 30 min after the damage
and deactivation anneals.
Figure 4.3 Arsenic SIMS profiles. The temperatures in the legends represent the anneals
after the damage anneal at 1150C.


108
7-5
Ap(i) is the surface area of P, DAs is the diffusivity of arsenic, X is the lattice
spacing, and f p{ 1) is the substitutional arsenic concentration.
Since there is a large supersaturation of interstitials during arsenic
deactivation, DAs should depend on this supersaturation. If the vacancy component
of the arsenic diffusivity can be neglected when there is a large supersaturation of
interstitials, DAs can be expressed as:
7-6
where C¡ is the interstitial concentration, C* is the equilibrium interstitial
concentration, and f¡ represents the interstitial component of arsenic diffusivity.
The equilibrium ratio of the defects includes the interaction with interstitials:
Wp(i)-WP(i+\)
kT
7-7
Csol is taken to be the equilibrium active concentration, and Wp is the interfacial
free energy. For simplicity, Wp is taken to be proportional to the surface area of the
defect:


32
Table 2.2: Enhancement of buried boron layer diffusivity for various arsenic doses [32],
Surface Concentration
Inactive As
Dose (cm'2)
(cm"3)
Enhancement
dose (cm"2)
4xl015
2.3xl020
30
2.2xl015
8xl015
4.5xl020
460
4.9xl015
1.6xl016
9. lxlO20
230
1.3xl016
3.2xl016
1.9xl021
110
2.9xl016
The dislocation loop density gets higher as the arsenic dose is increased, although
the interstitial supersaturation decreases. From nucleation theory, the loop density is
expected to decrease as the interstitial supersaturation gets smaller, which seems to
contradict these experimental observations. But, since loop nucleation occurs at the
very early stages of the deactivation anneal, the density of the loops is determined
by the interstitial supersaturation at the beginning of the anneal. Instead of the time
averaged interstitial supersaturation, it is enough that the initial interstitial
supersaturation be higher at higher arsenic concentrations for the loops to be denser.
At the lowest arsenic concentration (2.3xl020 cm"3), the enhancement is 15
times smaller than the one at the next higher concentration (4.5xl020 cm"3),
although the inactive arsenic doses are comparable. Also, no dislocation loops are
observed at the lowest concentration. This suggests that another deactivation
mechanism may be dominant in this sample, such as the simultaneous formation of
arsenic-interstitial pairs.


107
initial deactivation of arsenic at low temperatures (500-800C) in laser annealed
samples suggests that the deactivation proceeds through bulk processes, i.e. through
the generation of interstitial-vacancy pairs in the bulk [32] if the vacancy diffusivity
is relatively low.
The positron annihilation experiments also show that the average number of
vacancies per inactive arsenic atom is between 1/2 and 1/4. Based on EXAFS and
RBS measurements, Brizard et al. have proposed the existence of arsenic-vacancy
clusters which have a vacancy/arsenic ratio of around 1/3 [55]. In the model, this
number will be assumed to be 1/4. Since all the vacancies in the arsenic-vacancy
complexes are assumed to be generated through the formation of interstitial-vacancy
pairs, the number of injected interstitials will be equal to the number of generated
vacancies. Thus, a is taken to be 1/4.
The size evolution of the arsenic-vacancy complexes is modeled using the
rate equations derived in Chapter V. The rate of change in the density of Pi is given
by:
7-3
Jpd) = M0/?(0
fp(i) f p(i + 1)
7-4
fP\i) /?(/+!).
where is the forward reaction rate, and fp is the equilibrium concentration of i-
sized arsenic-vacancy complexes. The forward reaction rate can be written as:


130
53. H. Cerva, and G. Hobler, J. Electrochem. Soc. 139, 3631 (1992).
54. D. W. Lawther, U. Myler, P. J. Simpson, P. M. Rousseau, P. B. Griffin, and J. D.
Plummer, Appl. Phys. Lett. 67, 3575 (1995).
55. C. Brizard, J. R. Regnard, J. L. Allain, A. Bourret, M. Dubus, A. Armigliato, and A.
Parisini, J. Appl. Phys. 75, 126 (1994).
56. O. Dokumaci, H. -J. Gossmann, K. S. Jones, and M. E. Law, to be published in Defects
in Electronic Materials II, edited by J. Michel, T. A. Kennedy, K. Wada, and K.
Thonke (Mater. Res. Soc. Proc., 1997).
57. H. -J. Gossmann, F. C. Unterwald, and H. S. Luftman, J. Appl. Phys. 73, 8237 (1993).
58. S. Nishikawa, A. Tanaka, and T. Yamaji, Appl. Phys. Lett. 60, 2270 (1992).
59. S. M. Hu, P. Fahey, and R. W. Dutton, J. Appl. Phys. 54, 6912 (1983).
60. F. F. Morehead, and R. F. Lever, Appl. Phys. Lett. 48, 151 (1986).
61. B. J. Mulvaney, and W. B. Richardson, Appl. Phys. Lett. 51, 1439 (1987).
62. S. T. Dunham, J. Electrochem. Soc. 139, 2628 (1992).
63. R. W. Olesinky, and G. J. Abaschian, Bull. Alloy Phase Diagrams 6, 254 (1985).
64. T. Wadsten, Acta Chem. Scand. 19, 1232 (1965).
65. A. Parisini, D. Nobili, A. Armigliato, M. Derdour, L. Moro, and S. Solmi, Appl. Phys.
A 54, 221 (1992).
66.A. Armigliato, and A. Parisini, J. Mat. Res. 6, 1701 (1991).


94
sizes 50-700. Therefore, the accuracy of a numerical method will mostly depend on
how well it can reproduce the size distribution in this range.
Table 6.2 shows the grids used in the simulations. Thirteen different grids
have been tried. The grids are defined such that a size step of 1 is used up to size
SZ1 and a size step of A up to size 2000. A size step of 1 represents the size step in
the discrete rate equations. The number of equations (Neq) that has resulted from
each grid is also shown in Table II.
6.4.1 Comparison of Size Distributions
Figure 6.4 shows a comparison of the size distributions obtained by the linear
and logarithmic rediscretization methods. For a size spacing of 4 (A=4), the linear
rediscretization technique reproduces the exact solution accurately except at the tail
of the profile. But, when A is increased to 20, it becomes completely unstable and
gives a completely different size distribution. On the other hand, the logarithmic
rediscretization method fits the exact solution very accurately for the same size
spacing.
Figure 6.5 shows a comparison of the linear interpolation with the
logarithmic rediscretization method. Since logarithmic rediscretization has been
found to be the most accurate and stable method in the simulations, all the other
techniques are compared to this method. The linear interpolation method reproduces
the exact solution fairly accurately for A=20. This is the same size spacing for
which the linear discretization technique has failed. As A is increased and the


123
dislocation loops are responsible for the reduction in boron diffusivity. Arsenic
deactivation induced interstitials did not increase the transient enhanced diffusion.
In order to further understand the effects of arsenic deactivation on transient
enhanced diffusion, a comparison study with germanium or silicon can be done.
This study may separate the effects of type-V loops from those of end-of-range
loops. A better study would be to implant germanium or silicon into laser annealed
arsenic samples and measure the enhanced diffusion. This way, one can change the
amount of arsenic-induced interstitials and the amount of end-of-range implant
damage independently of each other.
In Chapter IV, the effect of arsenic activation on vacancy population was
studied using antimony marker layers. The antimony diffusivity was found to be
very close to its inert value during arsenic activation in the presence of dislocation
loops, indicating that there is no observable vacancy injection under these
conditions. The density of atoms bound by the loops is not sufficient to absorb all
the vacancies which are expected to be generated in an amount as indicated by the
positron annihilation and EXAFS measurements. Other possible mechanisms that
can explain the lack of vacancy injection in the presence of the loops include
surface recombination, recombination with trapped interstitials generated during the
deactivation anneal and absorption of vacancies by relatively more vacancy rich
arsenic defects, such as AstV clusters. On the other hand, antimony diffusion is
enhanced for the same anneals when germanium is present at the surface. In the
partial absence of the loops, antimony diffusion is enhanced by a factor of 1.5-2
during arsenic activation. Vacancy injection during arsenic activation as well as


69
Free
Energy
G:
Configuration
Figure 5.3 Schematic representation of free energies related to the following reaction
between the extended defects and a single atom: E¡ + E] <=> Ei+1.
where X is the lattice spacing, v is the vibration frequency and AgD is the
migration energy. If the lattice spacing and the vibration frequency do not change
near a defect and, most importantly, the migration energy, AgD, is equal to the
reaction barrier, Agy, then
5-9
The interface solute concentration around a defect, C\nt, is not necessarily
equal to the far-field solute concentration, f¡, because the transport of the solute
atoms to the defect may not be fast enough to resupply all the solute atoms that have
reacted with the defect. So, the solute may be depleted around the defect. For


Density (cm3) Density (cm
98
(a)
(b)
Figure 6.6 A comparison of the size distributions obtained by (a) the exponential
interpolation, and (b) the logarithmic rediscretization methods.


2
NMOS PMOS Bipolar
Figure 1.1 A cross-section of the active layers in a typical BiCMOS process.
dopant concentration is increased, because it is limited by the precipitation and
clustering processes. These processes determine the electrical activation/
deactivation behavior of dopants. They need to be understood in order to obtain
lower sheet and contact resistances and to assess their effects on other electrical
properties of the devices.
Arsenic is the most commonly used dopant in the fabrication of n-type layers
because of its high electrical activation and low diffusivity, making it a suitable
candidate for shallow junction technology. In this chapter, a review of literature on
dopant activation/deactivation in silicon will be provided with an emphasis on
arsenic. Some of the phenomena related to activation/deactivation and their effects
on silicon devices will be discussed. The reasons of why a further understanding


CHAPTER II
TRANSMISSION ELECTRON MICROSCOPY ANALYSIS OF
EXTENDED DEFECTS IN HEAVILY ARSENIC DOPED, LASER,
AND THERMALLY ANNEALED LAYERS IN SILICON
2.1 Introduction
Arsenic is the most commonly used dopant for creating n+ layers in silicon,
such as the source/drain regions in a MOSFET and the emitter of a bipolar
transistor. In order to get high conductivity, arsenic is often incorporated into these
layers in excess of its equilibrium active concentration. Subsequent thermal
annealing gives rise to inactive arsenic. As mentioned in Chapter I, deactivation of
arsenic is accompanied by silicon interstitial injection and the enhancement of the
boron layers underneath the arsenic layer [32]. This reaction can be written as:
mAs + nSi <=> AsmVn + nl 2-1
m n
where As represents a substitutional arsenic atom, AsmVn the inactive arsenic
complex, V a vacancy and 7 an interstitial.The reaction can be modified accordingly
if the inactive arsenic complex also includes silicon.
Several transmission electron microscopy (TEM) observations have revealed
precipitate-like defects, rod-shaped structures and/or dislocation loops in laser and
20


133
94.I. Clejan,and S. T. Dunham, Process Physics and Modeling in Semiconductor
Technology, Electrochemical Society Proceedings, Vol. 96-4, edited by G. R.
Srinivasan, C. S. Murthy, and S. T. Dunham (The Electrochemical Society,
Pennington, NJ, 1996), p. 398.
95.R. Y. S. Huang, and R. W. Dutton, J. Appl. Phys. 74, 5821 (1993).
96.C. D. Meekison, Phil. Mag. A 69, 379 (1994).
97.H. Zimmermann, and H. Ryssel, J. Electrochem. Soc. 139, 256 (1992).
98.C. Boit, F. Lau, and R. Sittig, Appl. Phys. A 50, 197 (1990).
99.G. B. Bronner, and J. D. Plummer, J. Appl. Phys. 61, 5286 (1987).
100.M. D. Giles, IEEE Trans. Computer Aided Design 8, 460 (1989).
101.J. P. John, and M. E. Law, J. Electrochem. Soc. 140, 1489 (1993).
102.D. J. Roth, and J. D. Plummer, J. Electrochem. Soc. 141, 1074 (1994).
103.M. E. Law, IEEE Trans. Computer Aided Design 10, 1125 (1991).
104.H. Park, and M. E. Law, J. Appl. Phys. 72, 3431 (1992).
105.C. C. Lin, M. E. Law, and R. E. Lowther, IEEE Trans. Computer Aided Design 12,
1209(1993).


CHAPTER VIII
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
This dissertation focused on the issues related to the analysis and modeling
of arsenic deactivation in silicon. Chapter II shows the properties of the extended
defects that are formed during arsenic deactivation in laser and then thermally
annealed samples at 700 and 750C. The density of the dislocation loops shows a
strong dependence on the chemical arsenic concentration. As the arsenic
concentration increases, more interstitials are injected during arsenic deactivation,
and, therefore, a higher density of loops form. The density of atoms bound by the
loops is much smaller than the inactive arsenic dose. The loops are confined in the
arsenic layer, indicating that the inactive arsenic reduces the formation energy of the
loops. The increase in the density of atoms bound by the loops explains the
reduction in the buried boron layer diffusivity at higher arsenic concentrations.
More TEM work on similar samples is necessary to further confirm these
conclusions. Additional TEM studies can also be correlated to extended
investigations on enhanced diffusion of boron [52],
In Chapter III, buried boron layers were used to quantify the transient
enhanced diffusion after high-dose arsenic implantation. The enhancement in boron
diffusivity decreases with increasing arsenic dose at 750, 900 and 1050C. At the
same time, the density of atoms bound by the loops increase, suggesting that the
122


25
15 2
Figure 2.1 Plan-view TEM micrograph of the sample implanted with 4x10 cm and
annealed at 750C (bright field).
15 2
Figure 2.2 Plan-view TEM micrograph of the sample implanted with 8xl013 cm' and
annealed at 750C (weak beam dark field).


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53
Table 4.1 also shows the total amount of electrically active arsenic obtained
by integrating the electron concentration from the spreading resistance
measurements with depth. In the high dose sample, the ratio of the density of atoms
bound by the loops to the activated amount of arsenic during the 950C activation
anneal is roughly 1/17, whereas in the low dose sample this ratio is 1/40. These ratios are
much smaller than the vacancy/arsenic ratio in the clusters calculated from either the
positron annihilation or EXAFS measurements. Therefore, even if the loops are
annihilated by only absorbing the vacancies generated by the activation process, this
mechanism alone is not enough to explain the lack of vacancy injection into the bulk
assuming that vacancies are generated with a ratio indicated by the positron annihilation
and EXAFS measurements.
The unaccounted vacancies may be either recombining at the surface or with
the interstitials created during the deactivation anneal and possibly trapped by an
impurity such as arsenic or carbon. In fact, carbon has been observed to be an
efficient sink for excess interstitials. At high enough doses, carbon can mostly
eliminate the transient enhanced diffusion [58] which is believed to be caused by
excess interstitials. The carbon profiles have also been measured along with arsenic
and antimony. Figure 4.6 shows the carbon profiles after the deactivation anneal for
the unimplanted and high dose arsenic samples. In the unimplanted sample, a
rapidly decreasing carbon concentration can be observed at the surface. This is
believed to be caused by carbon-related particles residing on top of the surface. On
the other hand, in the high dose arsenic sample, carbon profile exhibits a peak
around 80 nm and a deeper penetration at the surface, suggesting that the observed


24
analyzed area onto the [111] plane. So, Equation 2-3 effectively calculates the areal
density of the bound atoms on the [111] plane.
2.3 TEM Results
The as-lased samples were completely free of any visible defects.
Subsequent thermal annealing revealed a very strong dose dependence of the defect
structure in the arsenic doped layer. This phenomenon can be seen in Figure 2.1 to
Figure 2.4 which show plan-view TEM micrographs of samples after a thermal
treatment at 750C for 2h. Density and size information about the defects are listed
in Table 2.1 along with the inactive arsenic dose.
In contrast to the absence of any extended defects at the lowest dose (4xl015
cm'), large dislocation loops and rod-like defects are observed upon increasing the
dose by just a factor of two. For the next two doses, only dislocation loops are
detected. Upon increasing the arsenic dose, the density of the loops increases
dramatically. Especially, the 1.6xl016 cm'2 sample exhibits almost fifty times more
loops than the 8xl015 cm'2 sample. The concentration of atoms bound by the loops
was found to be around 30-50 times smaller than the inactive arsenic concentration
and is insufficient to directly account for most of the inactive arsenic.
Figure 2.5 and Figure 2.6 show the plan-view micrographs of the samples
which were doped with a dose of 1.6xl016 cm'2 and annealed at 700C for 15s
(short-time) and 100 min (long-time). Very dense fine particles appear after the
short-time anneal whereas the long-time sample exhibits a high density of loops.


85
(7. i
1 ~ 2
feq i
V 2
/
1
+ 2
, + 2;
6-9
/
Expanding P, / and separately into Taylor series around i, and keeping the
fq
f
first two terms for P and , and the first three terms for / the following
fq
equation is obtained:
2 ds
6-10
JL(X')
3.i l/'V
Substituting this equation into Equation 6-8, the following differential equations can
be written for the discrete rate equations:
- -TsJ(s)
6-11
m= -[pw-^pw
(I)+/e?(s)
a_
ds
£
e?
/
6-12
was expanded up to the second derivative for the following reason: As
mentioned in Chapter V, feq can be written as:


48
operating at 200 keV. Spreading and sheet resistance measurements were made on
arsenic doped samples.
In order to find the antimony diffusivity during the activation anneals, the
following procedure was employed: For each spike, the SIMS profile after the
deactivation anneal was supplied as an initial profile to the process simulation
program FLOOPS. The antimony diffusivity was assumed to have the form
Dsb = cxD£|f, where a is an enhancement factor and the reference diffusivity DrseJ
is the default inert antimony diffusivity in FLOOPS, and is given by:
4-1
The diffusion of the initial profile was simulated with FLOOPS for different
values of a until the error between the simulated and the experimental profiles was
minimized. The enhancement or the retardation in antimony diffusivity in the
arsenic or germanium doped samples was found by dividing the diffusivity in these
samples to the diffusivity extracted from the unimplanted samples which were
annealed under the same conditions.
4.2 Results and Discussion
Figure 4.2 shows the antimony SIMS profiles in the as-deposited DSL sample,
and in the high dose (8x1015 cm'2) arsenic sample which has been subjected to the 950C,


101
Figure 6.9 Comparison of the active concentrations for A=50 and Neq=60, obtained with
the logarithmic rediscretization, and the exponential interpolation methods.
Figure 6.10 Percentage error in the active concentration obtained with the logarithmic
rediscretization method relative to the exact solution


CHAPTER V
A KINETIC MODEL FOR ARSENIC DEACTIVATION
5.1 The Physical Structure of Inactive Arsenic
In the arsenic-silicon phase diagram, monoclinic SiAs phase is the closest
one to a dilute arsenic-silicon (solute-solvent) mixture [63], In this phase, arsenic
has three nearest neighbors, whereas silicon has four [64]. The monoclinic phase
has also been observed in arsenic implanted silicon at very high arsenic
concentrations (~lxl022 cm'3) [65,66]. Nobili et al. have determined the solid
solubility of arsenic associated with the monoclinic phase [67]. The solid solubility
is defined as the equilibrium concentration of the solute (arsenic) when the solid
mixture is in contact with an infinitely large film of the second phase. Figure 5.1
shows the solid solubility value along with the equilibrium active concentration of
arsenic. The solid solubility of arsenic is about an order of magnitude larger than its
equilibrium active level.
At equilibrium, monoclinic SiAs precipitates start to form above solid
solubility, whereas arsenic is substitutionally dissolved in silicon below the
equilibrium active concentration. The inactive arsenic structure between these two
limits has been the subject of much recent research. RBS [55] and X-ray standing
wave measurements [68] show that this inactive arsenic structure is coherent with
60


4
Figure 1.2 The temperature dependence of the equilibrium active concentration of arsenic
[1].
The electrically active dopant concentration in high concentration layers is
determined by the activation/deactivation processes during thermal anneal.
Generally speaking, it is a function of the anneal temperature and time, the dopant,
the chemical dopant concentration, and the state of the surface layer just after the
ion-implantation (amorphous or non-amorphous). Under equilibrium conditions, the
active concentration of dopant atoms in silicon, such as arsenic and boron, has been
found to exhibit an Arrhenius dependence on temperature. For example, Figure 1.2
shows the equilibrium active concentration of arsenic as a function of temperature
[1], Todays integrated circuit processing conditions usually keep the silicon-dopant
system away from equilibrium. Therefore, it is not simply possible to accurately
model the active dopant concentration just as a function of temperature.


113
the dislocation loops, c, and c, respectively, and the equilibrium interstitial
concentration, C*. The dislocation loop properties, such as the peak loop radius
and the density of the atoms in the loops are very sensitive to c2 and C*. The
enhancement in the buried boron layer diffusivity also depends on these parameters.
However, there is orders of magnitude difference in the reported values of
Cj* under intrinsic conditions [97-99]. In addition, C¡* depends on the carrier
concentration under extrinsic conditions. Since our simulations involve high
concentration arsenic layers, C* has to be modified to take into account this
dependence, which can be expressed as:
C
where ( C,*)mt is the intrinsic equilibrium interstitial concentration, K¡ represent
the equilibrium constants, and c is the charge state of the interstitials. Values for
K¡ have been extracted from the simulations of oxidation enhanced and transient
enhanced diffusion of dopants under extrinsic conditions [100-102]. But, there is
not a good agreement between these values. For simplicity, the interstitials are
assumed to be either positively or double negatively charged. Then, Equation 7-21
can be rewritten as:


131
67.D. Nobili, S. Solmi, A. Parisini, M. Derdour, A. Armigliato, and L. Moro, Phys. Rev. B
49,2477 (1994).
68.A. Herrera-Gmez, P. M. Rousseau, G. Materlik, T. Kendelewicz, J. C. Woicik, P. B.
Griffin, J. Plummer, and W. E. Spicer, Appl. Phys. Lett. 68, 3090 (1996).
69.M. Ramamoorthy, and S. T. Pantelides, Phys. Rev. Lett. 76, 4753 (1996).
70.E. Guerrero, H. Potzl, R. Tielert, M. Grasserbauer, and G. Stingeder, J. Electrochem.
Soc. 129, 1826(1982).
71.R. O. Schwenker, E. S. Pan, and R. F. Lever, J. Appl. Phys. 42, 3195 (1971).
72.R. B. Fair, and G. R. Weber, J. Appl. Phys. 44, 273 (1973).
73.M. Y. Tsai, F. F. Morehead, J. E. E. Baglin, and A. E. Michel, J. Appl. Phys. 51, 3230
(1980).
74.T. Brabec, M. Schrems, M. Budil, H. W. Poetzl, W. Kuhnert, P. Pongratz, G. Stingeder,
and M. Grasserbauer, J. Electrochem. Soc. 136, 1542 (1989).
75.S. Senkader, J. Esfandyari, and G. Hobler, J. Appl. Phys. 78, 6469 (1995).
76.1. Clejan, and S. T. Dunham, J. Appl. Phys. 78, 7327 (1995).
77.O. Dokumaci,and M. E. Law, Process Physics and Modeling in Semiconductor
Technology, Electrochemical Society Proceedings, Vol. 96-4, edited by G. R.
Srinivasan, C. S. Murthy, and S. T. Dunham (The Electrochemical Society,
Pennington, NJ, 1996), p. 37.
78.M. Volmer, and A. Weber, Z. Phys. Chem. 119, 227 (1926).
79.R. Becker, and W. Doring, Ann. Phys. 24, 719 (1935).


17
II, the dislocation loops formed after laser and subsequent thermal annealing will be
discussed in more detail.
On the other hand, in implanted and thermally annealed high concentration
arsenic samples, a band of arsenic-related precipitates and dislocation loops were
detected [37,44,45]. These defects lie at the projected range of the implant where
arsenic concentration is at its maximum. They form when arsenic concentration
exceeds its equilibrium active concentration. The defects that form at the peak of the
implanted profile have been classified as type-V defects [37], It is interesting to note
that type-V dislocation loops are observed only in arsenic-implanted samples [37].
Upon high temperature annealing (>900C), end-of-range (type-II)
dislocation loops dissolve much faster in the presence of gallium, phosphorus and
arsenic if their concentrations exceed their solid solubility [46]. During enhanced
elimination of type-II loops, the precipitates were also observed to be dissolving.
1.2 Organization
The focus of this thesis is analysis and modeling of the phenomena related to
the arsenic activation/deactivation process. Chapter II presents the extended defects
that form as a result of the interstitial supersaturation during arsenic deactivation.
Understanding the mechanism of these defects is important for both defect
engineering and an evaluation of their effect on arsenic deactivation induced
interstitials and, therefore, dopant diffusion near high concentration arsenic layers.
Chapter II reports the results of TEM observations on samples which were doped


77
Figure 5.6 Comparison of experiments and simulation at 700C at a chemical arsenic
concentration of (a) lxlO21 cm'3, (b) 4.4x1020 cm'3.


9
Because of this macroscopically clean state of silicon just after laser
annealing, laser annealing and subsequent thermal annealing have been used
numerous times to investigate the deactivation kinetics of dopants [3,5,6,12,13,21-
23]. Subsequent thermal annealing deactivates dopants at temperatures as low as
300C [12]. Since laser annealing activates all of the dopants, there is no
uncertainty concerning the initial activation conditions. In one of the studies, box
shaped profiles have been created by repeated laser pulse annealing [23], This
allows one to interpret the electrical measurements as characteristic of a single
doping concentration. This is not possible with simple thermal annealing since the
dopant concentration is a function of depth in that case.
1.1.2 Dopant Diffusion
Substitutional dopants in silicon, such as arsenic, phosphorus and boron, are
believed to diffuse via interactions with point defects: interstitials and vacancies
[24], These point defects can exist in various charge states. A chemical reaction
between the substitutional dopant and point defects can be envisioned that converts
the immobile substitutional dopant to a mobile dopant-defect pair. For a donor
atom, this reaction can be written as:
A+ +XC A+Xc
1-1


23
The defects were studied by TEM using both bright field and weak beam
conditions. Both plan-view and cross-section samples were analyzed with a JEOL
200 CX electron microscope operating at 200 keV. All micrographs were taken with
a g22o condition.
The quantification of the defects on the TEM pictures were done by counting
them and measuring the longest dimension of the defect. The density of the defects
can be found from the following expression:
D =
NM2

P
2-2
where D is the areal density of the defects, N is the number of defects in the area of
interest, M is the magnification, and Ap is the analyzed area on the picture. The
loops are assumed to lie on [111] planes where the picture shows the defects
through <100> direction. The areal density of the atoms bound by the loops was
found by measuring the largest dimension of the loops and using the following
formula:
N
bound
2-3
where r is the radius of a loop and is equal to half of the largest dimension, and d¡¡¡
is the areal density of silicon on the [111] plane. The ¡3 factor projects the


70
convenience the diffusion of the solute atoms is assumed to be fast enough so that
Cjnt = /j So the forward reaction rate becomes:
P, = a|/, 5-10
The reverse reaction rate can be found from the forward reaction rate and the
thermal equilibrium condition, as suggested by Katz [81]. At thermal equilibrium,
the detailed balance condition requires all fluxes to be equal to zero. So, from
Equation 5-5:
a
j+ i
fiq
flh
5-11
where f is the density of size-i defects at equilibrium.
Upon minimizing the Gibbs free energy of a system consisting of defects of
all sizes, the solute and solvent atoms, one can obtain the following expression for
the density of the defects at thermal equilibrium:
ffU
fiq
f 1
c
exp
iWi W¡ + i
sol
kT
5-12


Active Arsenic Concentration ( cm'J ) Active Arsenic Concentration ( cm
78
Time (min)
(b)
Figure 5.7 Comparison of experiments and simulation at 800C at a chemical arsenic
concentration of (a) lxlO21 cm-3, (b) 4.4x1020 cm'3.


12
All the results mentioned above indicate that dopant diffusivities get
increasingly sensitive to the amount of electrically active dopant concentration as
the concentration is increased. Therefore, high concentration dopant diffusion is
tightly coupled to the dopant activation/deactivation phenomena which determine
the electrically active dopant concentration. From a modeling point of view, even
small errors in the prediction of the electrically active dopant concentrations can
result in a big error in dopant diffusivities and make the diffusion simulations
unreliable. This point may become more and more important in the future as the IC
technology requires higher carrier concentrations and therefore higher temperatures
in the sub-micron regime.
1.1.3 Point Defect Injection
A recent study by Rousseau et al. [32] confirmed the interaction between
point defects and dopant activation/deactivation (Figure 1.5). Boron buried layers
were used as markers of interstitial supersaturation in the bulk. These layers were
obtained by first growing a boron doped silicon epi-layer on silicon and then
growing an undoped silicon layer on top of it. Arsenic was implanted and the wafers
were laser annealed. The laser annealing achieved full electrical activation of
arsenic and a flat arsenic concentration, and destroyed the implant damage by
melting the surface layer. For control purposes, another wafer was doped with
germanium in exactly the same way. Germanium is similar to arsenic in size and
mass. Next, the wafers were annealed at 750C in an inert ambient for 15s and 2 h.


33
2.4 Conclusions
The properties of the extended defects that are formed during arsenic
deactivation were investigated. The density of the dislocation loops depends on the
chemical arsenic concentration. As the arsenic concentration increases, more
interstitials are injected during deactivation, and, therefore, a higher density of
loops form. The number of atoms bound by the loops is much smaller than the
inactive arsenic dose. The loops are confined in the arsenic layer, indicating that the
inactive arsenic reduces the formation energy of the loops. Finally, the increase in
the number of the atoms bound by the loops explains the reduction in the buried
boron layer diffusivity at higher arsenic concentrations.


56
950C. These anneal times were longer than the time when all or most of the
dislocation loops had completely dissolved (Table 4.1). Therefore, the vacancy
population in the partial absence of the loops can be determined from these samples.
The anneals involved either unimplanted or high dose (8xl015 cm'2) arsenic
samples.
Figure 4.8 and Figure 4.9 compare the antimony profiles of the unimplanted
and high dose arsenic samples at the fourth peak after the deactivation anneal and
the activation anneals of 850C, 16h and 950C, lh. Although these profiles are
quite similar after the deactivation anneal, the high dose arsenic sample exhibits
more antimony diffusion than the unimplanted sample during the activation anneals.
This indicates that antimony diffusion is enhanced in the high dose arsenic samples.
Figure 4.10 shows the enhancements in the antimony diffusivity which are between
1.5 and 2 at both temperatures.
As discussed before, these enhancements may have been caused by the
vacancies injected during the arsenic activation. Non-equilibrium diffusion of
arsenic may also have created this enhancement. Since dopant atoms are believed to
diffuse by pairing with point defects, rapid dopant diffusion can carry a large
number of dopant-defect pairs to the bulk. These dopant-defect pairs can create
excess point defects upon dissolution if the recombination of the vacancies and
interstitials is not as fast as their generation through dopant diffusion. This effect
becomes more significant as the dopant concentration and diffusivity increase. It has
been proposed as the mechanism responsible for the enhanced diffusion observed in
the tail of the high concentration phosphorus profiles [59-62]. Although the inert


5
The following sections will describe various phenomena which are related to
dopant activation/deactivation in silicon.
1.1.1 Electrically Active Dopant Concentration
When the ion-implantation damage exceeds a certain level, an amorphous
layer is formed. Dopants in amorphous layers can be electrically activated up to a
concentration many times higher than their equilibrium activation levels. During
thermal annealing, arsenic has been observed to activate up to 5xl020cm'3 at 560C
[2] even though the equilibrium active concentration of arsenic at 700C is around
lxlO20 cm'3 (Figure 1.2). The carrier concentration increases until the amorphous
layer crystallizes completely. Further annealing causes arsenic to deactivate rapidly
[2,3]. Non-equilibrium activation is also observed for boron [4,5] and antimony [6]
in amorphized layers. In the case of boron, a preamorphization step is done since
impractical high doses of boron are necessary to get an amorphous layer during
boron implantation.
The higher activation effect is totally reversed when the sample is not
amorphized by the implant. There are several reports indicating that active boron
concentration remains much below its equilibrium activation level after ion-
implantation and a low temperature anneal [7-9], As shown in Figure 1.3, the tail of
the boron profile undergoes an enhanced diffusion due to ion-implant damage. The
peak is immobile, because boron at the peak region is either in the form of clusters
or precipitates which can not diffuse through the lattice. The suppressed activation


120
defects should be experimentally determined. Actually, a buried high concentration
arsenic layer can be used to separate the surface from the bulk processes occurring
during arsenic deactivation. Two buried phosphorus layers, one between the arsenic
layer and the surface, the other deeper than the arsenic layer can be utilized to
quantify the interstitial diffusion flux to the surface and to the bulk. Similarly, the
vacancy fluxes can be measured with antimony buried layers. If the density of
interstitials bound by the loops in the arsenic layer increases significantly, this will
mean that surface has an important role during arsenic deactivation in the simulated
samples.
1.1 Conclusions
An arsenic deactivation model that includes the interaction of arsenic-
vacancy complexes with interstitials and dislocation loops was presented. The
model shows good quantitative agreement with the experimental results of active
arsenic concentration and buried boron layer diffusivity for a thermal anneal at
750C for 2h. It is also in good qualitative agreement with the peak loop radius and
the density of atoms bound by the loops. There is a big discrepancy between the
simulations and the experiments for the density of atoms bound by the loops. In
order to model the arsenic deactivation better, one should first understand the
discrepancy between the number of atoms bound by the loops and the number of
interstitials that are expected to be generated in an amount as indicated by the


CHAPTER I
INTRODUCTION
Heavily doped layers are one of the basic components of semiconductor
device technology. As semiconductor devices are scaled down to sub-micron
dimensions, the design and the development of these regions become increasingly
complex. Figure 1.1 illustrates various heavily doped layers in a typical BiCMOS
process. The source/drain regions of the MOS transistors are doped with a high
concentration of dopants in order to obtain a low sheet resistance. The buried layers
below the MOS devices are used to minimize latch-up. For the bipolar transistor,
heavy doping is utilized in the emitter to increase the current gain. The heavily
doped extrinsic base and buried collector regions reduce the parasitic resistances
associated with the bipolar transistor.
As device dimensions shrink, the absolute value of the threshold voltage of
short-channel MOS transistors decreases. One way to reduce this effect is to
fabricate shallower source/drain junctions. The resulting increase in the source/
drain sheet resistance should be countered by increasing the electrically active
dopant concentration. As the device dimension is reduced, the metal/silicon contact
resistance also increases due to the reduction in the area of the contact. The contact
resistance can be decreased by utilizing higher active dopant concentrations.
However, the active dopant concentration does not increase indefinitely as the


90
get smaller, which in turn decreases the rate of change of f¡ (Equation 6-16). This
result is both counter-intuitive and incompatible with the original discrete rate
equations. In the rate equations, the rate of change of f¡ increases as gets smaller
(Equations 6-1 and 6-4).
This difficulty can be overcome by exploiting a technique that has been
widely used in diffusion simulations and FLOOPS. This method works by mixing a
small part of fk into f¡ and vice versa:
fk afk+ (1
-a)//
6-25
/, -> a/, + (1
-a )/*
6-26
where a is close to unity. If these substitutions are put into Equation 6-24, it can be
found that Equation 6-24 is now compatible with the rate equations in the limit of
small f¡. In this work, the natural logarithm term in the derivative has not been
changed in order to preserve the equilibrium conditions.
6.3 Interpolation
Figure 6.2 shows a segment of the size space where a solution for the discrete
rate equations is desired. The rate equation for size / can be rewritten as:
a/z
dt
Pi-i /,
eq
(7,-i
ft)
-p,/r
(fl
//+7
U-9,
i
i
a
-o i
v
U
feq
J/+ \'
6-27


14
vacancies are incorporated in the inactive arsenic-vacancy complexes and the
interstitials diffuse towards the surface and the bulk, and enhance boron diffusion.
Another study has shown the importance of this phenomenon in bipolar
transistors [35]. After arsenic was implanted to form the emitter of the device, it was
activated at 1100C for 10s. The wafer was then cut in two, with one half
undergoing a deactivation anneal at 750C for 2h. The two halves were then
annealed at 1000C for 15s so that the final active arsenic concentration in both
halves would be equal. There should not be any difference in the electrical
characteristics of these two transistors since the inert diffusion of boron or arsenic is
negligible at 750C with respect to 1000C or 1100C. However, the electrical
measurements show that the Gummel number is considerably reduced in the
transistors that have received the 750C anneal, because the interstitial injection
during arsenic deactivation enhances the diffusion of both arsenic and boron.
Therefore, the devices exhibit higher beta, lower output resistance and earlier
punchthrough breakdown (Figure 1.6).
Shibayama et al. [36] were the first to observe the diffusivity enhancement
underneath a high concentration arsenic layer. In their study, arsenic was diffused
into silicon from an arsenosilicate glass at 1000C. The diffusivity of both arsenic
and boron were enhanced upon a low temperature anneal between 500-800C.


79
Figure 5.8 Simulated defect size distributions for the lxlO21 cm'3 sample after 5 min and
124 min at 700C.
5.5 Conclusions
An arsenic deactivation model that takes into account the size distribution of
inactive arsenic structures was presented. The rate equations that describe the
evolution of the size distribution were derived from the kinetic theory and
thermodynamics. The model is in good quantitative agreement with the
experimental arsenic deactivation data, and successfully reproduces the rapid
deactivation at the beginning and the slow deactivation after a few minutes.


83
6.2 Rediscretization
In this approach, the rate equations are first put into a continuous form and
then rediscretized. After finding a suitable continuous form, the equations are
discretized using two different methods: linear and logarithmic discretization.
6.2.1 Continuous Form for the Rate Equations
The first continuous form for the rate equations has been given by Zeldovich
[93] and Frenkel [80]:
6-6
6-7
These equations can be obtained by expanding Equations 6-1 and 6-4 into a Taylor
series about i and keeping only the first two terms (the constant and the first
derivative). This approach was later criticized by Goodrich [82], He approximated
the rate equations at the mid-points, rather than at the end-points. However, he used
Equation 6-2 instead of Equation 6-4 in his derivation. Therefore, his analysis led to
an equilibrium condition that is different from that of the discrete rate equations


21
thermally annealed samples which have been doped with arsenic in excess of its
equlibrium active level [21,22,39-42], Lietoila et al. [22] have suggested that rod
like defects may be arsenic precipitates, whereas Armigliato et al. [40] have
reported that all defects observed by TEM cannot explain the amount of electrically
inactive arsenic in their experiments. No extended defects were detected by Lietoila
et al. for a much smaller arsenic dose. Parisini et al. [41] measured the number of
atoms bound by various types of interstitial-type defects at different annealing
temperatures and confirmed the large discrepancy between the concentration of
inactive arsenic and the concentration of atoms in observable defects. They
proposed that the extended defects are formed as a result of agglomeration of silicon
interstitials which are created during laser annealing. In a later work [42], based on
double-crystal x-ray diffractometry (DCD) and extended x-ray absorption fine
structure analysis (EXAFS) measurements, they suggested that deactivation of
arsenic is the cause of excess interstitials. They also found that the dislocation loops
are composed of silicon atoms. When an electron beam was used for annealing
instead of a laser, similar defects were observed upon subsequent thermal treatment
between 600-900C [43].
On the other hand, a band of arsenic related precipitates and dislocation
loops were detected after solid phase epitaxy of arsenic layers doped in excess of its
equilibrium active level [37,44,45]. These defects were shown to lie at a depth
corresponding to the projected range of the implant. In addition, half-loop
dislocations that are located near the surface were observed to grow during arsenic
precipitate dissolution even after 72h at 900C [37], Jones et al. found that the


8
level. The deactivation is observed both at the tail and the peak of the profiles. It
was suggested that inactive arsenic is in the form of arsenic-point defect pairs [15].
Another explanation has recently been given: Although the electrically active
arsenic concentration is below its equilibrium value and no deactivation is expected,
significant deactivation will still take place if the free energy of formation of very
small inactive arsenic clusters is small enough [18]. The electrically active arsenic
concentration is also dependent on the rate of ramp-down at the end of a thermal
anneal. A slower ramp-down rate has been observed to increase the arsenic sheet
resistance by 30% [19], In a BiCMOS process, it was demonstrated that the sheet
resistance of arsenic doped polysilicon increases upon doubling the ramp-down time
[20]. It was also shown in the same study that a subsequent 15 second RTA step
significantly reduces n+ silicon and polysilicon sheet resistances and the poly/mono
silicon contact resistance by dissolving the precipitates formed during ramp-down.
Laser annealing is another way of activating dopants in semiconductors.
Although it is not widely used by industry, it has proved to be a very useful research
tool. During laser annealing, a laser beam is directed to the silicon surface, melting
the surface layer to a depth which is dependent on the incident laser power. The melt
layer regrows very rapidly, incorporating nearly all of the dopant atoms onto
substitutional sites. Therefore, up to a certain concentration, dopants can be totally
activated with laser annealing. For example, phosphorus has been shown to activate
up to a concentration of 5xl021 cm'3 and arsenic up to 3xl021 cm'3 [21], Laser
annealing also wipes out implantation damage and prevents the formation of
extended defects like dislocation loops and stacking faults.


112
the arsenic-vacancy complexes, and the density of the atoms bound by the loops,
respectively. They are defined by:
Np=^ifp(i) 7-18
i = 2
i = 2
7-19
The interstitials satisfy the following boundary condition at the surface:
J, = 4 (c, C,*)
7-20
where J ¡ is the interstitial flux, and k's is the surface recombination velocity. A
similar equation can be written for vacancies.
7.5 Simulation Parameters
The equations presented in the previous sections were implemented in
FLOOPS. The simulated structure is shown in Figure 7.1. The simulations involved
a thermal anneal at 750C for 2h for three different arsenic concentrations:
4.5xl020, 9.1xl020, and 1,9x 1021 cm'3. The dislocation loop rate equations were
solved using the linear interpolation method. The most important parameters were
found to be the interface energy coefficients of the arsenic-vacancy complexes, and


64
shown to occur in arsenic implanted samples, suggesting the existence of
precipitates having a distribution of sizes of different free energy. But, reverse
annealing can also be explained by the existence of multiple clusters [13]. It
certainly rules out the single cluster model. All of the experimental data suggests
that the most reasonable assumption for inactive arsenic is the coexistence of
clusters and precipitates [24,42,55]. The clusters can form at the beginning of the
deactivation cycle and act as embryos for larger precipitates.
Most of the previous quantitative models for inactive arsenic has been single
cluster models. Sheet resistances and electron concentrations in arsenic doped
layers have been fit with various equilibrium cluster models [71-73]. Dynamic
clustering models have been used to fit the initial stages of deactivation [42] and the
effect of ramp-down on the sheet resistance [19]. Luning et al. [23] have pointed out
that single clustering models can not at the same time account for the rapid arsenic
deactivation at the beginning and the slow one at long times that they observe in
their experiments.
Some of the quantitative precipitation models that have been proposed in the
literature solve for the whole size distribution of precipitates. This kind of model
has been demonstrated for antimony precipitation [74], arsenic and phosphorus
precipitation [18], and oxygen precipitation [75], The dopant precipitation model by
S. Dunham [18] has been shown to exhibit reverse annealing. However, it has not
been applied extensively to arsenic and does not account for interstitial injection
and dislocation loop formation. The oxygen precipitation model includes the
interstitial injection and bulk stacking fault growth observed during oxygen


109
wP(i) = c,r/3
7-8
where c, is kept as a fitting parameter.
7.3 Model for Dislocation Loops
The evolution of dislocation loops can be described by the following
reaction:
Lf + / => L
+1
7-9
where L¡ represents a loop containing i silicon atoms. Similar to arsenic-vacancy
complexes, the size evolution of the loops is calculated using the rate equation
formalism in Chapter V. Namely:
§¡/l(0 = JL0-l)-JLW
7-10
JL(i) = VL(i)fL\i)
/(0
/?(i+ D-
7-11
In this case, the forward reaction rate is given by:


124
non-equilibrium diffusion may explain this enhancement. In order to eliminate the
effect of any trapped interstitials, this study can be repeated in samples which are
not contaminated with carbon. Also, positron annihilation measurements can
provide information on the vacancy/inactive arsenic ratio after partial arsenic
activation.
In Chapter V, an arsenic deactivation model that takes into account the size
distribution of inactive arsenic structures was presented. The rate equations that
describe the evolution of the size distribution were derived from the kinetic theory
and thermodynamics. The model is in good quantitative agreement with the
experimental arsenic deactivation data, and successfully reproduces the rapid
deactivation at the beginning and the slow deactivation after a few minutes.
Although this model is quite sufficient for thermal annealing of laser annealed
samples, its range of validity should be checked by comparing the model predictions
with the active arsenic concentration in ion-implanted samples.
In Chapter VI, various numerical methods were evaluated for the solution of
the rate equations that describe the size evolution of extended defects. These
methods include linear and logarithmic rediscretization, and linear and exponential
interpolation. A new continous form for the rate equations was derived. The
accuracy of the numerical methods was evaluated using the arsenic deactivation
model in Chapter V. The logarithmic rediscretization method was found to be the
most accurate and stable numerical technique for the representation of both the size
distribution of defects and the active concentration. Higher order discretization
methods can increase the accuracy of the simulation [105].


46
4.1 Experimental Details
The DSL structures used in the experiment contained six narrow antimony
buried marker layers with 10 nm widths, peaks spaced 100 nm apart and doped to a
concentration of 1.5xl019 cm'3. They were grown by low temperature molecular
beam epitaxy on Si(100) floatzone substrates [57]. The samples were split into three
during ion-implantation: no implant, arsenic implant, and germanium implant. Since
germanium is similar to arsenic in mass and size, it allows us to monitor any
possible effects of similar ion-implantation damage on antimony diffusion if the
damage is not completely wiped out during the damage anneal. Arsenic was
implanted at 50 keV at 7 tilt with doses of 3xl015 cm'2 and 8xl015 cm'2, while
germanium was implanted at only 8xl015 cm'2. All the samples were capped with an
approximately 2000 A layer of oxide and then a nitride layer to prevent the
evaporation of arsenic. They were annealed at 1150C for 5s in order to eliminate
the implantation damage. After the samples were subjected to a deactivation anneal
at 750C for 2h, some of them were further annealed either at 850C for 4 h or
950C for 30 min to electrically activate some of arsenic. The unimplanted, arsenic
and germanium doped samples were annealed very close to each other during each
thermal cycle so that there would not be any thermal variations between these splits.
Figure 4.1 shows a flowchart of the experimental steps.
Chemical arsenic and antimony concentrations were measured by SIMS.
Plan-view samples were studied by TEM with a JEOL electron microscope


ANALYSIS AND MODELING OF ARSENIC ACTIVATION
AND DEACTIVATION IN SILICON
By
HACI OMER DOKUMACI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1997


Collector Current Dopant Concentration
15
Depth
Figure 1.6 Schematic representation of the emitter and base profiles, and electrical
characteristics of an npn bipolar transistor with and without a deactivation anneal.


CHAPTER VI
A COMPARISON OF VARIOUS NUMERICAL METHODS FOR THE
SOLUTION OF THE RATE EQUATIONS IN EXTENDED DEFECT
SIMULATION
6.1 Introduction
Extended defects in silicon play an important role in the final electrical
characteristics of silicon devices. Precipitation/clustering of dopant atoms
determine the carrier concentration in heavily doped regions. Dislocation loops
affect the population of point defects and therefore dopant diffusion. {311} defects
have recently been identified as an interstitial source during transient enhanced
diffusion [85,86]. In general, extended defects form during phase transitions and as
a result of aggregation of impurities such as dopants and point defects. The
extended defects have been widely studied in the literature. Nucleation of clusters in
gases, nucleation of vacancy voids [87,88], crystal nucleation in glasses [89] and
crystal nucleation in amorphous silicon [90] are just a few examples.
In Chapter V, arsenic deactivation was simulated by solving the size
distribution of electrically inactive arsenic precipitates. The rate equations
describing the size distribution were directly solved without the necessity of a
numerical method to reduce the number of equations. A small number (-50) of rate
equations was enough to get a good fit to the experimental data. In addition, the
80


Active Arsenic Concentration (cm
117
Figure 7.3 Comparison of simulations with experiments for the active arsenic
concentration after the 750C, 2h anneal.
Figure 7.4 Comparison of simulations with experiments for the boron diffusivity
enhancement after the 750C, 2h anneal.


100
Figure 6.7 Comparison of the active concentrations for A=20 and Neq=195, obtained
with the (a) linear rediscretization, and (b) logarithmic rediscretization methods.
Figure 6.8 Comparison of the active concentrations for A=20 and Neq=195, obtained
with the (a) linear interpolation, and (b) exponential interpolation methods.


118
Chemical Arsenic Concentration ( cm'3 )
Figure 7.5 Comparison of simulations with experiments for the peak loop radius after the
750C, 2h anneal.
Chemical Arsenic Concentration ( cm'3 )
Figure 7.6 Comparison of simulations with experiments for the density of atoms bound by
the loops after the 750C, 2h anneal.


REFERENCES
1. M. Derdour, D. Nobili, and S. Solmi, J. Electrochem. Soc. 138, 857 (1991).
2. A. Lietoila, R. B. Gold, J. F. Gibbons, T. W. Sigmon, P. D. Scovell, and J. M. Young, J.
Appl. Phys. 52, 230 (1981)
3. A. Kamgar, F. A. Baiocchi, and T. T. Sheng, Appl. Phys. Lett. 48, 1090 (1986).
4. E. Landi, S. Guimaraes, and S. Solmi, Appl. Phys. A 44, 135 (1987).
5. S. Solmi, E. Landi, and F. Baruffaldi, J. Appl. Phys. 68, 3250 (1990).
6. S. Solmi, F. Baruffaldi, and M. Derdour, J. Appl. Phys. 71, 697 (1992).
7. S. Solmi, F. Baruffaldi, and R. Canteri, J. Appl. Phys. 69, 2135 (1991).
8. N. E. B. Cowem, K. T. F. Janssen, and H. F. F. Jos, J. Appl. Phys. 68, 6191 (1990).
9. P. A. Stolk, H. -J. Gossmann, D. J. Eaglesham, D. C. Jacobson, J. M. Poate, and H. S.
Luftman, Appl. Phys. Lett. 66, 568 (1995).
10. H. U. Jger, J. Appl. Phys. 78, 176 (1995).
11. N. E. B. Cowem, H. F. F. Jos, and K. T. F. Janssen, Mater. Sci. Eng. 5 4, 101 (1989).
12. D. Nobili, A. Carabelas, G. Celotti, and S. Solmi, J. Electrochem. Soc. 130, 922
(1983).
126


93
(a)
(b)
Figure 6.3 (a) Exact solution of the rate equations for the simulation described in the
text, (b) The integrated dopant concentration for the exact solution.


47
Starting material: Silicon
with DSLs
No implant
As implant
50 keV
3xl015 & 8xl015 cm'2
Ge implant
50 keV
8xl015 cm2
I
Prevent arsenic evaporation:
Oxide and nitride deposition
Eliminate implant damage:
Anneal at 1150C for 5s
;
Deactivation anneal:
750C for 2 hr.
t
Activation anneals:
850C & 950C
1
l
As & Sb SIMS
As Electrical Measurements
As TEM
Figure 4.1 A flowchart of the experiment.


41
analysis of the samples reveals that a high density of type-V loops forms when the
peak arsenic concentration is 6.4xl020 cm"3 at both 750C and 900C. On the other
hand, only a very low density of type-V loops form at a peak concentration of
4xl020 cm'3 (Figure 3.6). These results are consistent with the dislocation loop
results in Chapter II. The diffusivity data shows that the abrupt appearance of a high
density of type-V loops does not have a drastic effect on damage enhanced
diffusion. It has been previously suggested that the enhanced diffusion after
amorphizing implants is mainly caused by the damage beyond the a/c interface
[48,49], Since type-V loops form at the projected range, they may not absorb an
appreciable amount of the interstitials that are beyond the a/c interface and blocked
by the end-of-range loops (Figure 3.1). Moreover, XTEM micrographs show that
there is not any intrusion of the type-V loops into the end-of-range loop layer even
at the highest dose, suggesting a lack of strong interaction between type-V loops
and end-of-range damage. Still, type-V loops may be contributing to the decrease in
the enhanced diffusivity, although the decrease in the enhanced diffusivity starts
before their formation. It is interesting that the buried layer diffusivity does not
increase at the arsenic peak concentration of 4xl020 cm"3 although a great amount
of interstitial supersaturation is expected [52] and nearly no type-V loops form at
this concentration. The end-of-range loops should be acting as very efficient sinks
for these excess interstitials and preventing them to contribute to the enhanced
diffusion.
The density and the number of atoms bound by both the type-V and the end-
of-range loops are plotted in Figure 3.7 for 750C and 1050C. Both the density and


115
7.6 Comparison with Experiments
The boron enhancement and arsenic deactivation data was taken from
Rousseau et al. [32], and the dislocation loop data was obtained from Chapter II.
Since arsenic is totally active after the laser anneal, the initial active concentration
is equal to the chemical concentration. The formation of arsenic-vacancy complexes
is simulated for a single arsenic chemical concentration since arsenic is
homogeneously distributed. Similarly, for the interstitial concentration in the loop
equations, the value in the middle of the arsenic profile is used. Although the
interstitial concentration changes with depth because of surface recombination, it is
fairly homogenous except very close to the surface. In addition, the cross-section
TEM results of Chapter II show that dislocation loops are homogeneously
distributed throughout the arsenic layer, justifying our procedure.
Figure 7.2 shows the size distribution of dislocation loops for two different
arsenic concentrations. As the arsenic concentration increases, the density of the
loops increases and the peak loop radius decreases. This is in good qualitative
agreement with the experimental loop data. The simulations show that the initial
interstitial supersaturation increases as the arsenic concentration is increased since
deactivation of arsenic produces more interstitials (reaction 7-2). As a result, a
higher density of loops form (reaction 7-9).
Figure 7.3 and Figure 7.4 show comparisons of the simulations with the
experimental active arsenic concentration and the boron diffusivity enhancement
data. The simulations predict the active arsenic concentration within 20% of the


66
Figure 5.2 Schematic representation of the reactions taking place during extended defect
formation. The defects are assumed to grow or shrink by gaining or losing one atom at a
time.
This process, as shown in Figure 5.2, can be written as a set of reactions in the
following form:
Ej-i + E] <=> E¡ E¡ + E, Ei+, 5-2
where E¡ represents a defect containing i solute atoms and Ej is a single solute atom.
Ej may be an arsenic atom or a silicon interstitial, where Ej is then an arsenic
precipitate (or cluster) or a dislocation loop. In this formulation, the collision and
fusion of defects are ignored, as well as the fission of defects into two or more other
defects. The formulation may not be valid in non-dilute solutions where the
concentration of the solute is comparable to the concentration of solvent.


where fis the density of i-sized defects at equilibrium. Upon substituting
Equation 6-3 into Equation 6-2, an alternate form for J¡ can be obtained:
R
i J i + l J
6-4
Several researchers [82,84,87,92] have worked on the solution of either the
rate equations or its continuous form which is referred as the Fokker-Planck
equation:
6-5
[£(*)/(*, 0]
where s is the continuous size variable, A and B are the drift and diffusion
coefficients respectively. In spite of all this work, there still exists the need for a
simple numerical method which can reproduce the solution of the rate equations
with a sufficient degree of accuracy for large defect sizes (>1000). In this chapter,
various numerical methods will be derived and they will be evaluated using the
arsenic deactivation model of Chapter V. Two general techniques will be
investigated: rediscretization and interpolation.


Finally, I would like to thank all my friends in Gainesville for making this period of
my life an enjoyable and meaningful one.


50
Figure 4.4 Enhancement in the antimony diffusivity as a function of depth in the arsenic
doped samples. The thermal cycles shown in the legends represent only the activation
anneals.
30 min activation anneal. Antimony inside the arsenic layer exhibits considerable amount
of more diffusion than antimony outside the arsenic layer. This can be attributed to an
increase in the equilibrium concentration of free vacancies inside the arsenic layer. Figure
4.3 presents the arsenic profiles in the both the high (8xl015 cm'2) and low (3xl015 cm'2)
dose samples after the deactivation and the 950C, 30 min activation anneal. A significant
amount of arsenic diffusion takes place during the activation anneal.
Figure 4.4 shows the enhancement in the antimony diffusivity during the
activation anneals in the arsenic doped samples. This enhancement was calculated
by dividing the antimony diffusivity in the arsenic doped samples to the inert
antimony diffusivity extracted from the unimplanted samples. The inert antimony
diffusivity was found to be around 40% less than the default diffusivity in FLOOPS


diffusion after high dose arsenic implantation was quantified using buried boron layers.
Dislocation loops were also studied in these samples. The enhancement in boron
diffusivity decreases at higher arsenic doses. The effect of arsenic activation on vacancy
population was investigated with antimony marker layers. There is not any observable
vacancy injection during arsenic activation in the presence of dislocation loops. Small
enhancements in antimony diffusion were observed after the loops had dissolved.
An arsenic deactivation model that takes into account the size distribution of
inactive arsenic structures was developed in FLOOPS. The model successfully reproduces
the initial rapid deactivation of arsenic and the slow deactivation after the first few
minutes. Various numerical methods were evaluated for the numerical solution of the rate
equations that describe the size evolution of extended defects. The logarithmic
rediscretization method was found to be the most accurate and stable technique for
reducing the number of rate equations. The inclusion of the interactions between the
arsenic-vacancy complexes, interstitials and dislocation loops led to a more general and
physical arsenic deactivation model which can account for several experimental trends.
Vll


39
Arsenic Dose (cm'2)
Figure 3.4 The enhancement of boron diffusivity as a function of arsenic dose at 900C.
Figure 3.5 The enhancement of boron diffusivity as a function of arsenic dose at 1050C.


61
104/T ( K'1 )
Figure 5.1 The temperature dependences of the solid solubility associated with the
monoclinic SiAs phase and the equlibrium active concentration.
the silicon lattice. This result suggests that the inactive arsenic does not have the
crystal structure of the monoclinic SiAs phase, since the monoclinic phase, having a
crystal structure different from silicon, would create incoherence in silicon [40,52],
EXAFS measurements on high concentration arsenic samples demonstrate that the
number of the nearest neighbors of an arsenic atom decreases from four silicon
atoms in laser annealed samples to an average of 2.5 to 3.5 in deactivated samples.
This result can be explained by the formation of arsenic-vacancy complexes
(AsmVn) in which arsenic has less than four neighbors. Recent positron annihilation
experiments have also found evidence of a high density of vacancies related to
inactive arsenic [54], Moreover, theoretical calculations indicate that the formation
of arsenic-vacancy complexes is an energetically favorable process [34,69]. The


40
(a)
(b)
Figure 3.6 Weak beam-dark field cross-section TEM micrographs of the sample implanted
with an arsenic dose of (a) 1.6xl015 cm'2, (b) 2.4xl015 cm'2 and annealed at 750C.


105
Depth
Figure 7.1 An illustration of the phenomena observed during arsenic deactivation. The
samples have been laser annealed and then thermally annealed. This is the simulated
structure in this chapter.
surrounding doped layers, interstitial injection and dislocation loop formation
should also be included in an arsenic deactivation model.
A recent dopant precipitation model takes into account the interaction of
point defects with precipitates [94], It keeps track of the first three moments of the
precipitate size distribution instead of the whole distribution. It has not been applied
to a wide range of experimental arsenic deactivation data and does not include
dislocation loop formation. A recently proposed oxygen precipitation model [75]
takes into account the influence of point defects and bulk stacking faults on the


Density (cm~d) Density (cm
96
(a)
(b)
Figure 6.4 A comparison of the size distributions obtained by (a) the linear
rediscretization, and (b) the logarithmic rediscretization methods.


16
1.1.4 Dislocation Loops
A dislocation loop is an extra layer of silicon atoms having a disc shape.
Dislocation loops form when there is a high supersaturation of silicon interstitials
during thermal annealing. The major cause of excess interstitials and dislocation
loops is ion-implantation. Ion-implantation induced dislocation loops have been
extensively studied [37]. Dislocation loops act as sinks and sources for interstitials
and vacancies, affecting point defect concentrations and dopant diffusion as a result
[38]. They increase the p-n junction leakage current by gettering metallic impurities
along their peripheries. The stress fields that they generate in silicon also affect
dopant redistribution [38], The analysis of dislocation loops is therefore crucial in
understanding and interpreting the effect of processing conditions on device
electrical characteristics.
Since arsenic deactivation injects a huge amount of excess interstitials, one
may expect dislocation loop formation as a result. In fact, several Transmission
Electron Microscopy (TEM) observations have revealed dislocation loops in laser
and then thermally annealed high concentration arsenic samples [21,22,39-42].
These loops have been found to be composed of silicon atoms [42], It was suggested
in the same work that arsenic clustering injects the excess silicon interstitials
needed to form the loops. Nearly all studies have concluded that the number of
atoms bound by the loops or any other extended defects is much smaller than the
inactive arsenic dose. When an electron beam was used for initial annealing instead
of a laser, dislocation loops were still observed after thermal annealing. In Chapter


57
Figure 4.8 Comparison of the antimony profiles of the unimplanted and high dose arsenic
samples after the deactivation and activation (850C, 16h) anneals. During the activation
anneal, antimony diffusion is enhanced in the arsenic sample.
1020
*T
i
E
o
c 1019
o
To
c
Q)
£ 1018
o
O
>
c
o
! io'7
c
<
1016
0.30 0.35 0.40
Depth (pm)
Figure 4.9 Comparison of the antimony profiles of the unimplanted and high dose arsenic
samples after the deactivation and activation (950C, lh) anneals. During the activation
anneal, antimony diffusion is enhanced in the arsenic sample.


91
k
1
/
t i
/-1 l+l
m
J Size
Figure 6.2 An arbitrary interval in the size space. In the interpolation method, the
density//.; is interpolated with/, and/ and the density f¡+¡ with// and fm.
These equations include the densities for sizes /- 1 and / + 1 i.e. fand //+,.
If only the solutions for fk, f¡ and fm are desired, //_, and fl+] can be
interpolated using these densities. Then, the rate equations will have only the
densities whose solutions are desired.
In the linear interpolation case, the densities are assumed to be linear in size
at each interval such as [A:,/]. //_ | can be interpolated as:
fi-x
(l-k- 1)// + /*
l-k
6-28
A similar expression can be obtained for //+1. If these interpolations are
substituted in Equation 6-27, the rate equations will only have fk, f¡ and fm as
unknowns.
The exponential interpolation is similar to the linear one, except the densities
are assumed to be exponential in size at each size interval. The exponential
interpolation expression for //_, is given by:


132
80. J. Frenkel, Kinetic Theory of Liquids (Oxford, Oxford, 1946).
81. J. L. Katz, and M. D. Donohue, Adv. Chem. Phys. 40. 137 (1979).
82. F. C. Goodrich, Proc. R. Soc. London, Ser. A 277, 167 (1964).
83. D. Turnbull, and J. C. Fisher, J. Chem. Phys. 17, 71 (1949).
84. B. Shizgal, and J. C. Barrett, J. Chem. Phys. 91, 6505 (1989).
85. D. J. Eaglesham, P. A. Stolk, H. J. Gossmann, and J. M. Poate, Appl. Phys. Lett. 65,
2305 (1994).
86. N. E. B. Cowem, G. F. A. van de Walle, P. C. Zalm, and D. W. E. Vandenhoudt, Appl.
Phys. Lett. 65, 2981 (1994).
87. M. F. Wehner, and W. G. Wolfer, Phil. Mag. A 52, 189 (1985).
88. J. B. Adams, and W. G. Wolfer, Acta Metall. Mater. 41, 2625 (1993).
89. A. L. Greer, P. V. Evans, R. G. Hamerton, D. K. Shangguan, and K. F. Kelton, J.
Crystal Growth 99, 38 (1990).
90. H. Kumomi, and T. Yonehara, J. Appl. Phys. 75, 2884 (1994).
91. O. Dokumaci, and M. E. Law, in SISPAD96 (Japan Society of Applied Physics,
Tokyo, Japan, 1996), p.37.
92. K. F. Kelton, A. L. Greer, and C. V. Thompson, J. Chem. Phys. 79, 6261 (1983).
93.J. B. Zeldovich, Acta Physicochim. (USSR) 18, 1 (1943).


103
accuracy of the numerical methods was evaluated using the arsenic deactivation
model in Chapter V. The logarithmic rediscretization method was found to be the
most accurate and stable numerical technique for the representation of both the size
distribution of defects and the active concentration.


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ANALYSIS AND MODELING OF ARSENIC ACTIVATION
AND DEACTIVATION IN SILICON
By
HACI OMER DOKUMACI
May 1997
Chairman: Dr. Mark E. Law
Major Department: Electrical and Computer Engineering
Heavily doped layers are one of the basic components of semiconductor device
technology. As device dimensions shrink, higher electrically active dopant concentrations
are required to fabricate devices with desirable properties. However, clustering and
precipitation limit the obtainable active dopant concentration. Because of its high
solubility and low diffusivity, arsenic is the most commonly used dopant for the
fabrication of n+ layers in silicon. The electrical activation and deactivation process of
arsenic needs to be understood to assess its effects on the electrical properties of devices.
The focus of this thesis is analysis and modeling of phenomena related to electrical
activation and deactivation of arsenic. The properties of the dislocation loops formed
during arsenic deactivation were investigated with transmission electron microscopy. The
loops are confined inside the arsenic layer, suggesting a strong link between loop
formation and inactive arsenic. The reduction in buried boron layer diffusivity can be
explained by the increase in the number of atoms bound by the loops. Transient enhanced
vi


43
(a) (b)
Figure 3.7 Arsenic dose dependence of (a) the density of the bound atoms by loops, and
(b) the density of the loops.
deactivation induced interstitials may also contribute to the supersaturation and
increase the density of end-of-range loops, besides nucleating the type-V loops.
3.4 Conclusions
Buried boron layers were used to quantify the transient enhanced diffusion
after high-dose arsenic implantation. The enhancement in boron diffusivity
decreases with increasing arsenic dose at 750, 900 and 1050C. At the same time,
the number of atoms bound by the loops increase, suggesting that the dislocation


V A KINETIC MODEL FOR ARSENIC DEACTIVATION 60
5.1 The Physical Structure of Inactive Arsenic 60
5.2 Previous Models for Inactive Arsenic 62
5.3 A Kinetic Model for Extended Defects 65
5.4 Simulation Results 72
5.5 Conclusions 79
VI A COMPARISON OF VARIOUS NUMERICAL METHODS FOR
THE SOLUTION OF THE RATE EQUATIONS IN EXTENDED
DEFECT SIMULATION 80
6.1 Introduction 80
6.2 Rediscretization 83
6.2.1 Continuous Form for the Rate Equations 83
6.2.2 Linear Discretization 87
6.2.3 Logarithmic Discretization 88
6.3 Interpolation 90
6.4 Comparison of Numerical Methods 92
6.4.1 Comparison of Size Distributions 94
6.4.2 Comparison of Active Concentrations 99
6.5 Conclusions 102
VII AN ARSENIC DEACTIVATION MODEL INCLUDING THE
INTERACTION OF ARSENIC DEACTIVATION WITH
INTERSTITIALS AND DISLOCATION LOOPS 104
7.1 Introduction 104
7.2 Model for the Inactive Arsenic-Vacancy Complexes 106
7.3 Model for Dislocation Loops 109
7.4 Point Defect Continuity Equations 111
7.5 Simulation Parameters 112
7.6 Comparison with Experiments 115
7.7 Conclusions 120
VIII CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK 122
REFERENCES 126
BIOGRAPHICAL SKETCH 134
v


68
/,+ S if, = Cf 5-6
i = 2
where C, is the total solute concentration and is a given.
The forward reaction rate can be found by a treatment similar to the one
given by Turnbull and Fisher [83], The free energy diagram of the right hand side of
reaction 5-2 is shown in Figure 5.3. Here G¡ represents the non-mixing component
of the free energy of defect E¡ when Ej is taken as the reference phase. Ais the
reaction barrier between Ej+Ej and the activated complex which turns into Ei+1. The
forward reaction rate can be written as:
Pi = Ai\dC¡ntVdexp[~
&8f
kT
5-7
where A¡ is the surface area of the size-i defect, Xd is the lattice spacing around the
defect, C"u is the concentration of Ej atoms at the interface of the defect, \d is the
vibration frequency and Agj- is the energy barrier. A¡XdC¡nI is the number of Ej
atoms that are around each E¡ defect and are ready to react with Ej. v the number of times that this reaction takes place per unit time.
The diffusivity of the Ej atom in the solvent can roughly be written as:
D = X vexp|-
5-8


62
interstitial injection observed during arsenic deactivation also indirectly supports
the existence of arsenic- vacancy complexes [32],
o
Very small (-15 A) precipitates have been identified by TEM in deactivated
arsenic samples [40]. These precipitates have been proposed to have a zinc-blende
structure. In this structure, every alternating silicon atom is replaced by an arsenic
atom and both silicon and arsenic have four nearest neighbors of the other species.
The aforementioned EXAFS measurements show that the number of silicon first
neighbors of arsenic tends back to four atoms at high temperatures (>750C) [33].
This observation has been connected to the co-existence of arsenic-vacancy
complexes and zinc-blende type AsSi precipitates.
In summary, the inactive arsenic structure that is formed between the limits
of solid solubility and equilibrium active concentration is believed to be arsenic-
vacancy complexes. At high temperatures, the vacancy content seems to be
decreasing with vacancies being replaced by silicon atoms.
5.2 Previous Models for Inactive Arsenic
Clustering and precipitation have been proposed to explain the formation of
electrically inactive arsenic in silicon. In clustering models, multiple arsenic atoms
are assumed to come together and form a new defect which is electrically inactive at
room temperature. These clusters may also contain point defects. For example, an
As2V cluster can be formed by the following reaction:


89
y(s) ae
bs
6-20
Similar to linear discretization, the value of the function and its derivative at the
mid-point can be evaluated in terms of the values of the function at the end-points:
-V = JyiJi
ds k Akl W
1
6-21
6-22
6-23
If p, feq, and are assumed to be exponential in size, a discrete equation can be
obtained for Jk. by substituting these relations into Equation 6-12.
There is one important problem with the logarithmic discretization method.
f
The derivative of with respect to size is approximated as:
d_
ds
fxl
= |AAln
(fifi)
Vr)
r M/?VT
6-24
As one of the densities, such as f¡, decreases, the derivative also decreases,
eventually approaching zero for very small values of f¡. This causes the flux, J ^, to


Density (cm'3) Density (cm
97
(a)
(b)
Figure 6.5 A comparison of the size distributions obtained by (a) the linear interpolation,
and (b) the logarithmic rediscretization methods.


63
2 As + V <=> As2V 5-1
On the other hand, precipitation models consider the formation of much larger
structures that may contain thousands of dopant atoms. The precipitates may form at
any size whereas clusters are assumed to have on the order of a few atoms. The size
distribution of precipitates depend on the initial supersaturation of dopant atoms,
the time and the temperature of the anneal and other kinetic factors such as
diffusivity and reaction rates.
Many TEM observations have concluded that extended defects in high
concentration arsenic doped samples are not sufficient enough to account for most
of the inactive arsenic [39-41]. This evidence favors the clustering explanation such
that most of the inactive arsenic may be in the form of clusters which are too small
to be observed by TEM. However, it is also possible that very small coherent
silicon-arsenic precipitates can be responsible for the unobserved inactive arsenic.
As mentioned earlier, Armigliato et al. [40] have identified very small
precipitates in heavily arsenic doped samples. It is well known that the electrically
active arsenic concentration at equilibrium (i.e. for long anneal times) is very
insensitive to the chemical arsenic concentration [12]. This has been put forward as
suggestive evidence for precipitation [12] since cluster models predict that the
active arsenic concentration depend on the chemical concentration at equilibrium.
However, the equilibrium electron concentration can be made independent of the
chemical concentration if one assumes that the clusters are charged at the annealing
temperature [70], As mentioned in Chapter I, reverse annealing [12,13] has been


87
Now that a continous form has been derived for the rate equations, the next
step will be to discretize it for an arbitrary size spacing. Figure 6.1 shows an
arbitrary segment of the size space for which Equations 6-11 and 6-12 will be
discretized. For size /, the right hand side of Equation 6-11 can be approximated as:
6-16
where /' and k' are the mid-points in the respective interval and A is the size
difference between the mid-points. The task is now reduced to finding an
appropriate discrete expression for J at /' and k'. Two discretization schemes will
be investigated for this purpose: linear and logarithmic.
6.2.2 Linear Discretization
In this method, the function to be discretized, y(s), is assumed to be linear in
size at each interval [k,l]:
6-17
y(s) = as + b
The value of this function and its derivative at the mid-point, k', can be
approximated with the values of the function at the end-points, k and /:


CHAPTER III
HIGH DOSE ARSENIC IMPLANTATION INDUCED TRANSIENT
ENHANCED DIFFUSION
3.1 Introduction
Ion implantation of dopants into silicon introduces damage in the form of
interstitials and vacancies. If the damage is above a certain level, an amorphous
layer forms. Upon thermal annealing, the amorphous layer grows back into
crystalline silicon. If arsenic has been implanted at high doses, end-of-range loops
appear below the original amorphous/crystalline (a/c) interface, whereas type-V
loops form at the projected range (Figure 3.1). When a dopant layer is present
beyond the a/c interface, its diffusion is enhanced because of the ion-implant
damage. It has been previously suggested that the damage beyond the a/c interface
is the main cause of the enhanced diffusion of dopants after amorphizing implants
[48,49],
As mentioned in Chapter II, arsenic deactivation is accompanied by
interstitial injection. Buried boron layers have been observed to exhibit enhanced
diffusion when arsenic is deactivated at the surface [32], In Chapter II, the high
level of interstitial injection is also confirmed by TEM studies of type-V dislocation
loops formed during arsenic deactivation in initially defect-free laser annealed
samples [39],
34


37
Table 3.1: Peak arsenic concentration vs. arsenic implant dose
Dose (cm'2)
4xl014
8xl014
1.6xl015
2.4xl0l
4xl015
Peak Concentration (cm'2)
l.lxl O20
2x 1020
4xl020
6.4x1020
lxlO21
3.3 Results and Discussion
The annealed profiles of the boron buried layer are shown in Figure 3.2 for
different arsenic doses at 750C. The doses of the original boron SIMS profiles were
normalized to that of the unannealed sample. The damage enhanced diffusion of the
boron buried layer is reduced as the arsenic dose is increased. This trend is also
observed after the 900C and 1050C anneals. The reduction in the diffusivity is
also supported by the arsenic SIMS profiles. After the 750C anneal, the highest
dose arsenic profile moves 200 A less than the 8xl014 cm'2 profile. The
enhancements in the boron diffusivity can be seen in Figure 3.3 to Figure 3.5. The
enhancement was found by finding the diffusivity that best matches the
experimental profile and dividing it by the reference inert diffusivity which is given
by:
D = 0.757exp(-^)
3-1
At both 750C and 900C, the boron diffusivity drops nearly by a factor of 2
from the lowest to the highest arsenic dose. The cross-sectional TEM (XTEM)


and modeling of arsenic activation/deactivation processes is needed will be
explained. Finally, the organization of this dissertation will be given.
1.1 Dopant Activation/Deactivation
Semiconductor technology relies on the ability to fabricate two types of
electrically different layers: n-type and p-type. These layers are obtained by doping
the semiconductor with electrically active donor or acceptor atoms. An electrically
active dopant atom provides a free carrier to the conduction or valence band. When
a dopant atom occupies a substitutional site, it creates an energy level that is very
close to one of the bands, making it electrically active.
There are several ways of introducing dopant atoms into the semiconductor
lattice. Ion-implantation is the most widely used technology for this purpose
because of its excellent controllability and reproducibility which are required by
todays integrated circuit technology.
During ion-implantation into silicon, the dopant atoms are accelerated to a
certain energy and targeted to the silicon substrate. They penetrate through the
surface, colliding with many host atoms before losing all their energy and coming to
rest. These collisions disturb the crystalline nature of silicon and create disorder in
the lattice in the form of point defects and amorphous zones. Most of the implanted
dopant atoms do not occupy substitutional sites in such a disordered state. In order
to transfer the dopants to substitutional sites and activate them, the substrate is
subjected to a temperature treatment at several hundreds degrees Celsius.


110
P(0 = al()j; C, 7-12
where D¡ is the diffusivity of interstitials. Since dislocation loops grow along their
edges, the sink area for the interstitials is taken to be the cross-sectional area of the
surrounding edge of a loop. Assuming circular disc-shaped loops, this sink area can
be written as:
AL(i) = 2k rL(i)b
7-13
where rL is the radius of the loop, and b is the magnitude of the Burgers vector
representing the thickness of the loop.
The equilibrium ratio of the loops is given by:
feLq(i+ O
feLqU)
c, fWL(i)-WL(i+ 1)
^expl kf
7-14
W L includes both strain and stacking fault energy terms [95,96]:
WL{i)
[lb~ rL{i)
2(1 -v)
8 rL(i)
b
-2 +
3-2V
4(1-v).
+ iE
Y
7-15


44
loops are responsible for the reduction in boron diffusivity. Finally, arsenic
deactivation induced interstitials do not increase the enhanced diffusion.


67
According to reactions 5-2, the change in the density of the i-sized defect is
given by the following equation:
5J' = (fc- //,) (P¡/¡ alt, f, ,,),/> 2 5-3
where (3-_ j is the forward and a, is the reverse reaction rates of the first reaction in
5-2. Equation 5-3 can be put in a more convenient form:
a/,
dt
-/,,/> 2
5-4
where J¡ is the rate at which defects of size i become defects of size i+1 and is
defined by:
Ji = (V-a,-+i/i +
5-5
Equation 5-3 does not apply to the case of i=l, i.e. the single solute atoms.
The concentration of the single solute atoms can be found from the mass
conversation equation:


58
Figure 4.10 Enhancement in the antimony diffusivity as a function of depth in the high
dose (8xl015 cm"2) arsenic doped samples. The thermal cycles shown in the legends
represent only the activation anneals.
arsenic diffusivity is smaller than that of phosphorus, non-equilibrium diffusion of
arsenic may still be responsible for the small enhancements in these samples.
4.4 Conclusions
The effect of arsenic activation on vacancy population has been studied using
antimony buried layers. The antimony diffusivity has been found to be very close to
its inert diffusivity during arsenic activation in the presence of dislocation loops,
indicating that there is no observable vacancy injection under these conditions. The
density of the atoms bound by the loops are not sufficient to absorb all the vacancies
which are expected to be generated in an amount indicated by the positron


13
Depth
Figure 1.5 Representative arsenic and boron profiles in Rousseau et al.'s experiment.
Boron diffusivity is enhanced up to a factor of 460 when arsenic is deactivated.
Normally, these anneals will not cause any significant diffusion of boron. But, the
diffusivity of the boron buried layer was enhanced by a factor of up to 460 for the 2h
anneal. Arsenic deactivation occurred in parallel to the enhancements in boron
diffusivity.
Extended X-ray Absorption Fine Structure (EXAFS) measurements [33] and
theoretical calculations [34] suggest that arsenic deactivates in the form of arsenic-
vacancy complexes. Since the equilibrium concentration of vacancies is much
smaller than the concentration of inactive arsenic, a huge amount of vacancies
should be generated in the bulk. These vacancies have been postulated to come from
arsenic deactivation assisted interstitial-vacancy pair generation. The generated


125
Chapter VII presented an arsenic deactivation model that includes the
interaction of arsenic-vacancy complexes with interstitials and dislocation loops.
The model shows good quantitative agreement with the experimental results of
active arsenic concentration and buried boron layer diffusivity as a function of
chemical arsenic concentration for a thermal anneal at 750C for 2h. It is also in
good qualitative agreement with the peak loop radius and the density of atoms
bound by the loops. However, there is a big discrepancy between the simulations
and the experiments for the density of atoms bound by the loops. In order to model
the arsenic deactivation better, one should first understand the discrepancy between
the density of atoms bound by the loops and the number of interstitials that are
expected to be generated in an amount as indicated by the positron annihilation and
EXAFS measurements. The role of the surface on the recombination and generation
of point defects should also be experimentally determined. A buried high
concentration arsenic layer can be used to separate the surface from the bulk
processes occurring during arsenic deactivation. Two buried phosphorus layers, one
between the arsenic layer and the surface, the other deeper than the arsenic layer can
be utilized to quantify the interstitial diffusion flux to the surface and to the bulk.
The number of interstitials bound by the loops can then give information on how
important the surface is in generating or annihilating point defects.


52
Table 4.1: Summary of the electrical and TEM measurements on the arsenic doped
samples.
Arsenic
dose
( 1015 cm'2)
Anneal sequence
after the
damage anneal
(C)
Sheet
Resistance
(£2/sq )
Density of
atoms bound by
dislocation
loops
( cm'2)
The total
amount of
electrically
active arsenic
(cm'2)
8
750
71.8
l.lxlO14
l.lxlO15
8
750 + 850 4h
48.7
Very few loops
-
8
750 + 950 30min
30.0
No loops
3xl015
3
750
76.4
2.3xl013
l.lxlO15
3
750 + 850 4h
63.4
No loops
1.5xl015
3
750 + 950 30min
50
No loops
2xl015
Figure 4.5 Spreading resistance measurements of the arsenic doped layer for the high
(8x10*5 cm"2) arsenic dose. The temperatures in the legends represent the anneals after the
damage anneal at 1150C.


84
(Equation 6-3). In contrast, the Frenkel-Zeldovich equation automatically contains
the exact equilibrium conditions, because the starting point is Equation 6-4 which
already includes the discrete equilibrium conditions. Shizgal and Barrett [84]
suggested another methodology to approximate the rate equations with a continous
form and compared all three methods to the exact solution. They found that their
and Goodrichs approaches are more accurate than Frenkels.
In order to approximate the rate equations with a continous form, the
mathematical procedure suggested by Goodrich will be followed. First, the right
hand side of Equation 6-1 is expanded into a Taylor series around i ^ up to the
second term. The resulting equation is:
6-8
where 5 is the continous size variable. The implicit dependences of / and J on t are
not shown in order to make the derivation more clear. The same mid-point
expansion is then applied to Equation 6-4, rather than Equation 6-2. As discussed in
the previous paragraph, Equation 6-4 already contains the exact equilibrium
conditions, therefore its continous form will also preserve them. Rewriting Equation
6-4 by substituting i ^ in place of i, the following expression is obtained:


42
the number of bound atoms show an increase as the arsenic dose is increased,
suggesting that the loops are responsible for the reduction in boron diffusivity. A
low density of rod-like defects (6xl08 cm'2) was observed at the dose of 8xl014 cm'
2 along with the loops. For the 1050C anneal, no type-V loops were observed in the
XTEM micrographs for all the doses. So, the abrupt increase in the loop density at
this temperature is only due to end-of-range loops.
Two mechanisms may exist if the reduction in the enhanced diffusivity is
caused only by the dose dependence of the implant damage below the a/c interface.
The depth of the amorphous layer has been observed to increase with dose [53],
More of the implant damage beyond the a/c interface may be incorporated into the
amorphous layer at higher doses. This mechanism may reduce the enhanced
diffusion. However, a possible decrease in the implant damage below the a/c
interface is inconsistent with our experimental loop data where both the loop
density and the number of bound atoms increase even when only end-of-range loops
exist. So, the damage and therefore the excess interstitials beyond the a/c interface
are actually increasing with higher arsenic doses. This may not necessarily mean a
larger interstitial supersaturation during the whole enhanced diffusion. A higher
interstitial supersaturation at the beginning of the anneal can cause a higher density
of end-of-range dislocation loops, which in turn can capture more interstitials
during the anneal, decreasing the enhanced diffusion. This statement is supported by
the results of other experiments, such as the decrease in enhanced diffusion at
higher arsenic concentrations during arsenic deactivation in laser annealed samples
[52] and the reduction in boron diffusion with increasing boron dose [8]. Arsenic


92
//_ i
l
6-29
6.4 Comparison of Numerical Methods
The numerical techniques described in the previous sections were
implemented in FLOOPS. Their accuracies in the solution of the rate equations were
evaluated using the arsenic deactivation model in Chapter V. The chemical arsenic
concentration was taken to be lxlO21 cm'3. Table 6.1 shows the simulation
parameters that are different than the ones used in Chapter V.
Figure 6.3 (a) shows the exact solution of the original discrete rate equations
with these parameters. The equations have been solved up to size 2000. The exact
solution will be a reference point in comparing the different numerical techniques.
Figure 6.3 (b) shows the integrated dopant concentration in the precipitates. This
concentration has been calculated by taking the sum of the dopant concentration up
to the size shown in the x-axis. Most of the dopant atoms are located between the
Table 6.1: Simulation parameters that are different from the ones in Chapter V.
Parameter
Pre-exponential
Activation
Energy (eV)
Co
4.8xl021 cm'3
0.4
ci
0.3 eV
c2
0.0 eV


7
Figure 1.4 Illustration showing the reverse annealing phenomenon in arsenic and
phosphorus doped samples.
Although the carrier concentration at the end of the 650C anneal is above the
equilibrium active concentration of arsenic at 750C, it still increases at the
beginning of the 750C anneal to a maximum. Normally, one would expect a faster
rate of deactivation upon increasing the temperature, since the electrically active
concentration is above the equilibrium value at that temperature. This phenomenon
has been claimed to be a solid proof that the electrically inactive dopant is in the
form of precipitates rather than a cluster.
In terms of activation/deactivation, arsenic has been the most studied dopant
in silicon because of its peculiar properties. Various studies [15-17] have reported
incomplete arsenic deactivation for concentrations below the equilibrium activation


76
Figure 5.5 Comparison of experiments and simulation at 600C at a chemical arsenic
concentration of (a) lxlO21 cm'3, (b) 4.4x1020 cm'3.


11
where Da is the diffusivity due to uncharged point defects, D_ due to negatively
charged defects, etc. At high concentrations and under the condition of charge
neutrality, for a single dopant:
n =
1-4
where CA+ is the active dopant concentration. So, ultimately the diffusivity
depends on the active dopant concentration under extrinsic conditions.
In so-called isoconcentration studies, the dopant under study is diffused in a
region which is homogeneously doped with either another dopant or an isotope of
the same dopant at a much higher concentration. This way, the carrier concentration
is controlled independently of the diffusing species. The isoconcentration
experiments have shown that arsenic [25], phosphorus [26], and antimony [27,28]
diffusion are enhanced with increasing electron concentration. Also, boron [29,30]
diffusivity is observed to increase with hole concentration.
Recent isoconcentration study by Larsen et al. [31] has revealed an even
stronger dependence of arsenic and antimony diffusion on donor concentration than
that expressed by Equations 1-3 and 1-4. The diffusivities of arsenic and antimony
have been found to be proportional to the third to fifth power of the background
90
phosphorus donor concentration for phosphorus concentrations greater than 2x10
cm'3. At the highest donor concentrations, the diffusion coefficients are identical for
arsenic, antimony and tin, although these dopants have different diffusivities at
lower electron concentrations.


CHAPTER IV
INVESTIGATION OF VACANCY POPULATION DURING ARSENIC
ACTIVATION IN SILICON
Recent experimental investigations have shown that electrical deactivation of
arsenic in silicon creates excess silicon interstitials [52], This has been attributed to
the formation of arsenic-vacancy clusters and generation of silicon interstitials
during this process. As pointed out in Chapter II. this high level of interstitial
injection is also confirmed by TEM studies of type-V dislocation loops formed
during arsenic deactivation in the same initially defect-free laser annealed samples
[39].
The formation of a large number of arsenic-vacancy clusters has been
confirmed with positron annihilation measurements [54], Furthermore, extended x-
ray absorption fine-structure (EXAFS) results combined with Rutherford
BackScattering (RBS) measurements also indicate that the deactivation of arsenic
proceeds through the formation of arsenic vacancy complexes below 750C [55],
Upon electrical activation of arsenic, these complexes are expected to dissolve and
generate free vacancies. In this work [56], antimony doping superlattice (DSL)
structures were used to detect any possible vacancy injection into the bulk during
the activation of arsenic. Since antimony diffuses predominantly through a vacancy
mechanism, its diffusion is enhanced when there is a supersaturation of vacancies
[24].
45


128
27.R. B. Fair, M. L. Manda, and J. J. Wortman, J. Mater. Res. 1, 705 (1986).
28. K. Nishi, K. Sakamoto, and J. Ueda, J. Appl. Phys. 59, 4177 (1986).
29. M. Miyake, J. Appl. Phys. 57, 1861 (1985).
30. A. F. W. Willoughby, A. G. R. Evans, P. Champ, K. J. Yallup, D. J. Godfrey, and M. G.
Dowsett, J. Appl. Phys. 59, 2392 (1986).
31. A. N. Larsen, K. K. Larsen, P. E. Andersen, and B. G. Svensson, J. Appl. Phys. 73,
691 (1993).
32.P. M. Rousseau, P. B. Griffin, and J. D. Plummer, Appl. Phys. Lett. 65, 578 (1994).
33.J. L. Allain, J. R. Regnard, A. Bourret, A. Parisini, A. Armigliato, G. Tourillon, and S.
Pizzini, Phys. Rev. B 46, 9434 (1992).
34.K. C. Pandey, A. Erbil, G. S. Cargill III, R. F. Boehme, and D. Vanderbilt, Phys. Rev.
Lett. 61, 1282 (1988).
35.P. M. Rousseau, P. B. Griffin, S. C. Kuehne, and J. D. Plummer, IEEE Trans. Electron
Devices 43, 547 (1996).
36.H. Shibayama, H. Masaki, H. Ishikawa, and H. Hashimoto, J. Electrochem. Soc. 123
742(1976).
37.K. S. Jones, S. Prussin, and E. R. Weber, Appl. Phys. A 45, 1 (1988).
38.H. Park, Ph.D. Dissertation, University of Florida, 1993.
39.O. Dokumaci, P. Rousseau, S. Luning, V. Krishnamoorthy, K. S. Jones, and M. E. Law,
J. Appl. Phys. 78, 828 (1995).



PAGE 1

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BIOGRAPHICAL SKETCH
Haci Omer Dokumaci was bom in Kahramanmaras, Turkey, in 1970. He received
his B.S. degree both in electrical engineering and physics from Bogazici University,
Turkey, in 1991 and his M.S. degree in electrical engineering from the University of
Florida, Gainesville, Florida in 1993. Since then, he has been pursuing a Ph.D. degree in
electrical engineering at the University of Florida. His research interests are
semiconductor process modeling, simulation, and integration, with emphasis on physical
models for dopant diffusion and activation.
134


Ill
where p is the shear modulus, v is the Poissons ratio, and Ey is the internal energy
associated with the stacking fault. Chapter II shows that dislocation loops are
formed only in the arsenic layer during deactivation, suggesting a reduction in the
formation energy of the loops due to the presence of arsenic. This reduction is
accounted by simply multiplying WL(i) by a constant factor c2, which is less than
unity. c2 is kept as a fitting parameter.
7.4 Point Defect Continuity Equations
The continuity equations for interstitials and vacancies can be written as:
dC,
Tt
d_
dx
(
n c *
D' C/ dx
\\
c *
c/ ))
dNp dN,
-k^qcy c,* cv*)*ajtr-7¡l
7-16
dCy
Tt
d_
dx
t 7t(
n c *
DyLy dx
\
c *
JJ
kB(C, Cy C* Cy' )
7-17
The first terms on the right hand side of Equations 7-16 and 7-17 represent the
diffusion of the defects, while the second terms take into account the bulk
recombination of interstitials with vacancies. The third and the fourth terms on the
right hand side of the interstitial continuity equation represent the generation of
interstitials by the arsenic-vacancy complexes, and the absorption of interstitials by
the dislocation loops, respectively. Np and NL are the concentration of arsenic in


119
absorbed by the loops or can diffuse into the bulk. The simulations show that the
diffusion flux to the bulk, which is limited by the enhancement in boron diffusivity,
is negligible. The bulk recombination is also insignificant, since the vacancies are
depleted very quickly at the beginning of the anneal due to a high concentration of
interstitials. This leaves only the surface recombination and loop absorption terms.
There is not a general agreement on the value of the recombination velocity in the
literature [62,103,104], Although a value that is much greater than the one obtained
from oxidation enhanced diffusion simulations is used, the surface recombination is
still negligible at the two higher arsenic concentrations. Thus, in the simulations,
the loops capture most of the interstitials for these arsenic concentrations. The
generated interstitial/deactivated arsenic ratio was taken to be 1/4 based on EXAFS
and positron annihilation experiments. But, the experiments show that the density of
atoms bound by the loops is 30-50 times smaller than the inactive arsenic
concentration. This explains the discrepancy between the experiments and our
simulations for the density of atoms in the loops. From a modeling point of view,
this discrepancy may be minimized if a different surface recombination or the fully
coupled diffusion model is used.
In order to model the arsenic deactivation better, one should understand the
discrepancy between the number of atoms bound by the loops and the number of
generated interstitials as suggested by the EXAFS and positron annihilation
measurements. Either the recombination of interstitials or the generation of
vacancies at the surface may be playing an important role during arsenic
deactivation. The role of the surface on the recombination and generation of point


31
IS 9
Figure 2.9 Cross-section TEM micrograph of the sample implanted with 8x10 cm' and
annealed at 750C for 2h (weak beam dark field).
16 ~2
Figure 2.10 Cross-section TEM micrograph of the sample implanted with 1.6x10 cm "
and annealed at 750C for 2h (weak beam dark field).


29
shown to increase appreciably in the long-time sample, and both arsenic and silicon
angular-scan spectra were characteristic of a large degree of dechanneling.
Figure 2.7 to Figure 2.10 show the cross-section views of the samples
implanted with doses of 8xl015 and 1.6x 1016 cm'2. For the higher dose, the defects
lie uniformly in a region from the surface down to a depth of about 180 nm, which
coincides well with the junction depth. The uniformity of the defects in the arsenic
layer is in contradiction with an earlier TEM work where dislocation loops were
observed to lie at the amorphous-crystalline interface for a similar surface
concentration [41,42], Except for the intrusion of rod-like defects to a depth of 230-
250 nm in the 8xl015 cm'2 sample, the confinement of the defects to the arsenic
layer suggests that inactive arsenic complexes reduce the formation energy of the
loops.
In a similar study [42], it has been found that the loops are composed of
silicon atoms. It has been suggested in the same work that arsenic clustering injects
the excess silicon interstitials needed to form the loops. As mentioned before,
buried boron layers show enhanced diffusion as a result of arsenic deactivation,
suggesting that arsenic deactivation is accompanied by interstitial injection [32],
TEM observations in this study involve exactly the same samples for the 750C, 2h
anneal. The enhancements for these samples are shown in Table 2.2. There is a large
increase in boron diffusivity at an arsenic concentration of 4.5x1020 cm'3 and the
enhancement keeps decreasing as the dose is increased. The TEM results show that
the number of atoms bound by the loops increases with arsenic concentration.
Therefore, the loops seem to be responsible for the reduction in boron diffusivity.


116
Figure 7.2 Comparison of loop size distributions for two different arsenic concentrations.
measurements. In addition, the model shows good agreement with the enhancement
in boron diffusivity, which decreases with increasing arsenic concentration. Since a
higher density of loops forms at the beginning of the anneal for a higher arsenic
concentration, the loops capture more interstitials during the rest of the deactivation
process. This results in a lower enhancement in the boron buried layer diffusivity.
Figure 7.5 and Figure 7.6 show the comparisons for the loop properties. The
model completely overestimates the density of the atoms bound by the loops. This
can be understood by interpreting the interstitial continuity equation (Equation 7-
16) and the surface recombination term in Equation 7-20. The interstitials generated
by the deactivation process can be annihilated in the bulk or at the surface, can be