3S

ibli- tions A111D3 Qa7tD37

NATL INST OF STANDARDS & .jECH R-j C.

A1 11 03087637

a^7iiiV7"Mo°»^^^ SPECIAL PUBLICATION 400

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Semiconductor Measurement Technology'-

Angular Sensitivity

of Controlled

Implanted Doping Profiles
NATIONAL BUREAU OF STANDARDS

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DEC 5 1978

Semiconductor Measurement Technology: Y\d icc

Angular Sensitivity of Controlled igo

Implanted Doping Profiles

Robert G. Wilson, Howard L. Dunlap, and

Douglas M. Jamba

Hughes Research Laboratories

3011 Malibu Canyon Road

Malibu, CA 90265

and

David R. Myers

Electron Devices Division

Center for Electronics & Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

Jointly supported by;

The Defense Advanced Research Projects Agency

and

The National Bureau of Standards

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued November 1978
Library of Congress Cataloging in Publication Data Main entry under title: Angular sensitivity of controlled implanted doping profiles. (Semiconductor measurement technology) (NBS special publications ; 400-49)

Supt. of Doc. no.: C 13.10:400-49

1 . Semiconductor doping. 2. Ion implantation. 3. Integrated circuits.

I. Wilson, Robert G. II. Series. III. Series: United States. National Bureau of Standards. Special publication ; 400-49. QC100.U57 no. 400^9 [TK7871.85] 602Ms 78-10624

[62I.3815'2'028]

National Bureau of Standards Special Publication 400-49

Nat. Bur. Stand. (U.S.), Spec. Publ. 400-49,61 pages (Nov. 1978) CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1978

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-01 997-6 Price $2.50

(Add 25 percent additional for other than U.S. mailing).
CONTENTS

PAGE

1. Introduction and Summary 1

2. Experimental Techniques 3

2.1. Capacitance-Voltage Profiling 3

2.2. Silicon Crystal Alignment and Angular Control 4

2.3. Characterization of Depth Distribution Variation with

Alignment Angle 8

3. Experimental Results 11

4. Analysis 34

4.1. The Continuum Model 34

4.2. Classification of Ion Trajectories 37

4.3. The Critical Angle 39

4.4. Implications for Implantations into Single Crystalline

Substrates 41

4.4.1. Physical Interpretation of the Critical Angle . . 41

4.4.2. Crystal Orientation for Minimal Channeling .... 41

4.4.3. Effects of Channeling on Ion Distributions .... 42

4.4.4. Effect of Amorphous Surface Layers 43

5. Influence of Scanning 43

5.1. Mechanical Target Scanning 44

5.2. Electrostatic Beam Scanning 44

References 46

Appendix A 48

Appendix B 53

LIST OF FIGURES

1. Schematic of target geometry used for alignment of the

target crystal 5

iii
PAGE

2. Scattering yield as a function of (\) at constant 9 = 3.5

deg for 140-keV protons incident on the (111) face of

silicon 5

3. Polar coordinate plot of the data in figure 2 showing the

{110} planes 6

4. Target goniometer for alignment and angular control . . 7

5. Example of the determination of the area integrals chosen

for data reduction for the case of an imperfectly channeled

distribution = 9

6. Explanation of regions of implanted depth distributions 10

7. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV boron in (111) silicon 13

8. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV boron in (KDO) silicon 14

9. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV boron in (110) silicon 15

10. Depth distributions of carrier concentration as a function of

alignment angle for 75-keV boron in (111) silicon 16

11. Depth- distributions of carrier concentration as a function of

alignment angle for 75-keV boron in (110) silicon 17

12. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV arsenic in (110) silicon 18

13. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV arsenic in (111) silicon 19

14. Depth distributions of carrier concentration as a function of

alignment angle for 75-keV arsenic in (110) silicon 20

15. Depth distributions of carrier concentration as a function of

alignment angle for 150-keV indium in (110) silicon 21

16. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV boron in (111) silicon 22

17. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV boron in (110) silicon 23

18. Magnitudes of channeling and dechanneling versus alignment

angle for 75-keV boron in (111) silicon 24

iv
PAGE

19. Magnitudes of channeling and dechanneling versus alignment

angle for 20-keV boron in (111) silicon 25

20. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV arsenic in (110) silicon 26

21. Magnitudes of channeling and dechanneling versus alignment

angle for 20-keV arsenic in (111) silicon 27

22. Magnitudes of channeling and dechanneling versus alignment

angle for 150-keV indium in (110) silicon 28

23. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV indium in (110) silicon 29

24a. Random fraction (lioear) of in^lanted depth distributions

versus the ratio of the selected random equivalent angle of

incidence to the calculated critical channeling angle 31

24b. Random fraction (log) of implanted depth distributions

versus the ratio of the selected random equivalent angle of

incidence to the calculated critical ahanneling angle 32

25. SIMS atom-depth distributions for 150-keV boron as a function of alignment angle away from the [110] axis of silicon . . 33

26. Illustration of symbols used to describe channeling parameters for an atomic string 35

27. Hypothetical channeling trajectories in a simple cubic

crystal 38

B-1. Sensitivity of implanted depth distribution to implantation

angle for 450-keV phosphorus in <111>, <110>, and <100>

silicon 53

B-2. Implanted depth distributions for 150-keV boron in <111>

silicon from Seidel 54

V

PREFACE

This study was carried out at the Hughes Research Laboratories as a part

of the Semiconductor Technology Program in the Electron Devices Division

at the National Bureau of Standards. The Semiconductor Technology Program serves to focus NBS research to enhance the performance, interchangeability, and reliability of discrete semiconductor devices and integrated

circuits through improvements in measurement technology for use in specifying materials and devices in national and international commerce and

for use by industry in controlling device fabrication processes. The

Hughes portions of this work were supported by the Defense Advanced Research Projects Agency, ARPA Order 2397, Program Code 6D10, through the

National Bureau of Standards Semiconductor Technology Program, Contract

5-35891. The contract was monitored by Richard L. Raybold as the Contracting Officer's Technical Representative. Drs . W. M. Bullis and K. F.

Galloway provided technical review of this report for the National Bureau

of Standards.

The authors wish to thank Dr. C. L. Anderson for his thorough reading of

the manuscript and many constructive suggestions, acknowledge A. J. Mohr

and R. R. Hart for designing and building the precision target goniometer,

and wish to thank Dr. J. Comas and H. B. Dietrich of the Naval Research

Laboratories for providing the SIMS measurements and for useful discussions, respectively.

During the conduct of this work, D. R. Myers received support from an NBS-NRC postdoctoral fellowship.

vii

Angular Sensitivity of Controlled Implanted Doping Profiles

by

Robert G. Wilson, Howard L. Dunlap, Douglas M. Jamba,

and David R. Myers

Abstraat: Ion implantation can be used to produce accurately controlled doping profiles for silicon

devices and integrated circuits . The work reported

here determines the angle at which the ion beam must

strike the substrate in order to maintain control over

the channeled and random equivalent depth distributions

of carriers as measured by 1-MHz differential capacitancevoltage (C-V) profiling. A method to calculate the classical critical angle for channeling (ip^) is presented.

Data are presented that characterize the variation in

the depth distribution of carriers with substrate orientation, incident ion species, and incident ion energy,

for a range of critical angles. This study establishes

the degree of control of the angle between the ion beam

and the crystallographic orientation needed to produce

the limiting cases of either optimal channeling or maximum randomization of ion trajectory in the substrate. For the cases studied here, the angle between

the ion beam and the substrate orientation must be

controlled to within 0.5 ± 0.2 deg to obtain the optimally channeled depth distribution for implantation

directly into the low index crystallographic orientations. Alternatively, to minimize unintentional channeling, the substrate must be oriented so that the

nearest low index crystallographic direction is at

least twice the classical critical angle away from the

beam direction. The substrate tilt angles required to

satisfy these conditions can exceed the 7- to 10-deg

tilt commonly used in ion implantation. The implications of these results for uniform and reproducible ion

implantation within the semiconductor industry are discussed.

Key Words: C-V profiling; controlled doping profiles; critical channeling angle; ion beam scanning;

ion channeling; ion implantation; Rutherford backscattering alignment; silicon crystallographic orientation.

1. INTRODUCTION AND SUMMZ^Y

This report presents the results of a study to determine how control of

carrier depth distributions resulting from ion implantation into single

1
crystal silicon depends on the angle of incidence between the ion beam

and the substrate crystallographic orientation. It is well known that

ion range distributions in single crystal targets can be affected by ion

channeling, the phenomenon in which ions are steered down the axial lattice channels by correlated collisions with the ordered arrangement of

the substrate atoms. This effect leads to increased penetration depths

for the ions that channel and also reduces the amount of radiation damage caused by the ion beam. With the present emphasis on shallower ac- tive regions in semiconductor devices, the extent of ion channeling

should be minimized to reduce the formation of deeply penetrating tails

in the dopant distribution, thereby leading to more predictable dopant

profiles. Alternatively, when ion channeling is intentionally employed

as a doping technique (for example, to create buried layers) , it is important to be able to estimate how well the beam must be collimated and

oriented to the crystal direction to obtain the optimally channeled distribution. Unlike most previous studies of ion channeling, the present

work considers a range of atomic number (Zj^) and energy (Ej) representative of most laboratory implantation today. This work presents experimental data that demonstrate the change in the distribution of carriers

with substrate orientation, incident ion species, and ion energy. The

data empirically establish the control needed to guarantee a particular

quality of channeled implanted carrier depth distribution and demonstrate that the implantation angle must be controlled to within 0.5 ± 0.2 deg to retain the optimally channeled distribution. A simple procedure is developed to calculate the classical critical angle for ion

channeling , which is then correlated with the experimental data.

Both the theory and the data clearly indicate that to minimize unintentional channeling during implantation, the wafer must be tilted so that

the nearest low index crystal direction is at an angle to the beam direction of at least twice the critical angle. The present work thus

demonstrates that the angle required to minimize unintentional channeling can under some conditions exceed the 7- to 10-deg tilt commonly used

in implantation to simulate or achieve the "random equivalent" condition.

The experimental technique used in this investigation was to implant

ions at various angles away from accurately channeled alignment and toward the direction of random equivalent (RE) orientation up to the random

equivalent angle of about 7 deg, and to record the changes in depth distribution of carriers measured by differential capacitance-voltage (C-V)

profiling. The implantation dose was usually 1.5 x 10^^ cm~^, and the

implants were annealed at 800°C for 20 or 30 min, which was found to fully activate all of these low fluence implants. The implantation angle was controlled to better than 0.1 deg for small angles (0.0 to 3.0 deg)

away from axial alignment by the combination of Rutherford backscattering

[1] and a' target goniometer capable of controlling the angle to oibout

0.02 deg. The less sensitive angles from 3 to 7 deg were varied by tilting a standard target mount with the angle measured goemetrically . The

ions studied were boron, arsenic, and indium at 300, 150, 75, 40, and 20

keV to fill in the range of critical angles from 2 to 7 deg. In order to

provide a comparison between these C-V electrical profiles and corresponding atomic depth distributions, a set of profiles was measured for 150-
keV boron as a function of alignment away from the [110] axis of silicon

using secondary ion mass spectroscopy (SIMS)

.

There are three previously reported investigations related to this study

.

One is a limited set of partial profiles reported by Seidel [2] for 150-

keV boron in (111) silicon. Another is a set of profiles for phosphorus

in (111) silicon, reported by Moline [3] and by Moline and Reutlinger [4] » A detailed set of profiles was reported by Reddi and Sansbury [5] for 450-

keV phosphorus in the major lattice directions of silicon. These last

data were analyzed and are included in the data compilation used in this

report.

2. EXPERIMENTAL TECHNIQTJES

2.1. Capacitance-Voltage Profiling

The depth distributions of acceptor or donor electrical activity were measured by the differential capacitance-voltage technique. This technique has been discussed by Moline [3] ^ Seidel [2], and Reddi and Sansbury [5] ; however, the present work uses reverse-biased Schottky barriers

on implanted layers in '^10- or 100-Q»cm silicon substrates, rather thaxi

the p-n junction or epilayer techniques. Acceptor impurities were implanted into p-type substrates, while donor impurities were implanted into n-type substrates. The C-V profiler used was an improved version of

that described by Gordon, Stover, and Harp [5]. Contact was made to the

back surface of the wafer by an annealed IQ-*-^ cm~^ implant of boron (for

p-type substrates) or arsenic (for n-type substrates) . The implanted samples were annealed in nitrogen gas drawn from liquid nitrogen. Schottky

barrier diodes of '^'0.13-itim diameter were formed by evaporation of '^1000

K of aluminum (on p-type silicon) or gold (on n-type silicon) . The background level corresponding to the substrate doping was subtracted from

the C-V profiles. The corrections to C-V profiles proposed by Kennedy,

et at. [7] and by Moline [3] , and calculated and illustrated by Reddi and

Sansbury [5] and by Moline [3] , had only a small effect on the profiles

reported in this work. This correction has its greatest effect on the

tail regions of the profiles. Although the correction affects only 0.1

to 1 percent of the implanted ions, this is sufficient to cause an apparent change of 1 to 10 percent in the magnitude of a channeling tail when

10 percent of the ions channel.

The effect of experimental factors on the C-V profiling equations for

n{x) and x has been examined in terms of the sensitivity of the measurement system to the quality factor [= (wCsRg) "'^

] of the diodes studied,

where co is the angular measurement frequency, and Cg and Rs are, respectively, the capacitance and series resistance of the Schottky barrier diode (corrected to include spreading resistance) . The results show that

for the 0.13-mm diameter Schottky barriers with zero-bias capacitances of

1 to 15 pF and the 10- and 100-J^*cm siabstrate resistances corrected for

spreading resistances, the C-V profiles are accurate to 1 or 2 percent

for n(x) <_ 10^^ cm~^. For Co > 20 pF, errors greater than 2 percent may

begin to occur near 10^ cm~^; however, the distributions for these con3
ditions are closer to the surface than 1000 A and such data are not used

or reported.

2.2. Silicon Crystal Alignment and Angular Control

Two techniques were used in this work to vary the implantation angle , one

for angles from 0 to 3 deg with an accuracy of 'vO.02 deg and one for angles from 3 to 7 deg with an accuracy of 'vO.7 deg. Reduced accuracy was tolerable for the larger angles because of the lower sensitivity of implantation profile to angle in this range (near the random equivalent

orientation)

.

Rutherford backscattering of light ions was used in combination with a precision target goniometer to align the silicon crystals for the low

angle implantation.

The silicon crystals were accurately aligned at small angles by a technique similar to that originally described by Andersen, et at. [1] , but

with adjustments in crystal position so that the channeling axis was made collinear with the axis of rotation. This technique is based on

the measurement of the decrease in backscattered proton (or alpha) yield

as the major crystal planes are rotated through a highly collimated proton beam. The backscattered protons are detected by a surface barrier

detector of 8- to 15-keV FWHM resolution located about 8 cm from the

goniometer face, as illustrated in figure 1. Referring to figure 1, the

backscattered proton yield as a function of azimuthal angle (j) at a con- stant tilt angle of 6 = 3.5 deg is shown in figure 2 for 140-keV protons

incident on the (111) face of a silicon crystal. An energy discriminator is adjusted to permit only protons scattered near the surface to be

counted. Distinct dips or decreases are observed whenever a major crystal plane is rotated through the beam. Figure 3 is a polar coordinate

plot showing the {110} planes, the intersection of which locates the [111]

axis with respect to the center of rotation, which is aligned with the

beam axis.

The center of the circle in figure 3 represents the axis of rotation and

and the radius corresponds to the tilt angle 6 . Azimuthal angles corresponding to the various planar dips in figure 2 are marked off on the

circumference and connected by straight lines representing that plane in

the stenogram. (Straight lines are appropriate in this case since the

small conical section involved in these diagrams renders the spherical

angle essentially flat.)

In the particular case shown in figure 3, coordinates of the [111] axis

are (j) = 270 deg, 6 = 0.9 deg. At these settings the beam is aligned

with the [111] axis to about 0.05 deg. However, in order to tilt the sam- ple through the [111] axis at various values of (|>, the front face is adjusted in situ to bring the [111] axis into coincidence with the center

of rotation. The long dashed lines in figure 3 represent the adjusted

positions of the {110} planes, showing that the adjusted [111] axis is at

the center of rotation and thus is aligned with the ion beam at 0 = 0 deg

for any value of ^.

4
GONIOMETER

TARGET

CRYSTAL

COOLED

SOLID STATE

DETECTOR

ALIGNMENT

ON BEAM

SURFACE

NORMAL

Figure 1. Schematic of target geometry used for

alignment of the target crystal.

RANDOM LEVEL

240 180 120

AZIMUTRAL ANGLE . DEGREES

Figure 2. Scattering yield as a function of ^ at constant 6 = 3.5 deg

for 140-keV protons incident on the (111) face of silicon. (See fig. 1

for <f and 6 .

)

This technique assures alignment of the silicon crystal with the incident

implantation ion beam to within less than 0.1 deg. The same ion beam system is used to deliver the proton beam for alignment, an alpha beam for

alignment verification, and the implantation ion beam, simply by changing

the species in the ion source.

The ion beam is collimated to 0.1 deg by two 5-mm diameter apertures

spaced 3 m apart. The ion beam is generally focused to a 3-mm diameter

spot at the target, which is located 3.5 m from the mass separator. The

physical separation between beam spots differing by 1 amu is 20 mm at mass 30 and 5 mm at mass 120 when the beam collimators are removed. This

indicates, for example, that with the apertures in place a ^ beam would

be free of ^^B; but a ^^^Te beam would be contaminated by ^^^Te. A

contamination-free (i.e., hydrocarbons) target environment is provided by

ion pumps located in both the collimator drift tube and the target chamber and by a combination of an oil-free mechanical pump and cryogenic

5
4>

180*'

Figure 3 . Polar coordinate plot of the data in figure 2 showing the

{110} planes (solid lines) . The intersection of the planes determines

the coordinates of the [111] direction (<p = 270 deg, 9 = 0.9 deg, in

this case) . The long dotted lines represent adjusted positions of the

{110} planes showing that the [111] axis coincides with the axis of rotation after adjustment of the goniometer face.

sorption roughing, and by a cryowall at the entrance to the target chamber. The pressure in the goniometer target chamber is typically 10"^

torr

.

The target goniometer is shown in figure 4. The orientation of the silicon crystal is adjusted by a stepping motor driven system controlled

from outside the vacuum system. Three independent angular variations are possible. A tilt angle 9 about a vertical axis through the target face

is introduced through the large horizontal gear which can be seen in the

photograph. Rotation in azimuth about a horizontal axis is introduced

through the vertical disk to which the crystal is attached. The disk is

adjusted in situ by means of the three peripheral screws to permit the

6
Figure 4. Target goniometer for alignment and angular control.

introduction of the third independent angular displacement. Counters,

driven by slave motors, display the angular position of the stepping motor drives to within 0.02 deg. Stepping rates of up to a maximum of 80

per second are controllable by the operator in eight speed ranges and

two directions . At the maximum stepping rate an entire rotation can be

traversed in about 4.5 min. The speed is controlled electrically by

means of an oscillator which drives a flip-flop, which in turn drives a pulsing circuit. The angle between the incoming ions and the desired

silicon crystal direction is thus controlled to <0.1 deg and the sampletilt angle can be varied and controlled to about 0.02 deg. The angular

7
control accuracy for implanted depth distributions obtained for samples

aligned by this technique is therefore <0.1 deg.

For the larger angles, the silicon samples were simply tilted to the desirable angle by rotating the target mount in a routine implantation system with the silicon sample oriented so that the tilt occurs in the direction toward the random equivalent (e.g., 7-deg tilt about the vertical

axis, with a (110) plane rotated 18 deg from the vertical for a (111) wafer.)

In the case of the technique used for the larger angle, the accuracy of

alignment depends on several factors in combination. The silicon sam- ples are cut and polished to be within eibout 0.5 to 1 deg of the designated crystal face. The target holder can be positioned to within about

0.5 deg of the desired angle between 0 and 7 deg. Ion beam scanning produces an angular deviation over a standard test sample area (6 mm square

around the center) of 0.2 deg. Thus, the first of these is the greatest

and the combination of all errors should cause a deviation between the

direction of the incident ions and the desired crystal direction of 'v-l deg, absolute.

2.3 Characterization of Depth Distribution Variation

with Alignment Angle

It was necessary to devise a method to characterize the change in depth

distribution of carrier concentration with alignment angle as the profiles were varied from maximum (optimal) channeling conditions to minimum

channeling conditions. The technique selected was to measure the differential integrals of the areas between the various depth distributions as illustrated in figures 5 and 6. Figure 5 represents the determination

of the extent of channeling and dechanneling for the case of an implant

with angular alignment which yields intermediate amounts of channeling.

The optimally channeled profile cam only be determined empirically; however, the minimum channeling distribution Ccin be estimated by using the

Gaussian approximation to the LSS reuidom distribution [8]. Thus, the

magnitude of the channeling tail is the fraction of the implanted dose

that penetrates beyond the Gaussian approximation to the LSS random distribution (i.e., the area integral®); while the extent of dechanneling

is the fraction of the implanted dose that is lost from the optimally

channeled distribution (i.e., the area integral®). The choice of the

Gaussian approximation to represent the random distribution neglects

the contribution of higher order moments in the solution of the LSS

range equations. These higher order moments are responsible for the

skewed nature of implants in amorphous silicon or in high dose (amorphizing) implants into initially crystalline silicon. Although neglect of

these higher order moments can lead to variations of 10 to 15 percent between the Gaussian approximation and actual random impurity distributions

in noncrystalline silicon for which the possibility of ion channeling is

eliminated, only small skewness is observed in this study for these low

fluence implants into crystalline silicon. The uncertainty due to the

neglect of higher order moments is small compared with the great variations encountered in random yield as the substrate is rotated away from

8
DISTRIBUTION A GAUSSIAN * DISTRIBUTION

IMPERFECTLY CHANNELED

DISTRIBUTION

OPTIMALLY CHANNELED

DISTRIBUTION

ANTED

THE V-V

FRACTION OF IMPLANTEC

IONS DEEPER THAN " GAUSSIAN DISTRIBUTION, OR THE MAGNITUDE OF THE CHANNELING TAIL

IMPERFECTLY CHANNELED

IBUTION

OPTIMALLY CHANNELED

DISTRIBUTION

FRACTION OF IMPLANTED

IONS LOST FROM THE OPTIMALLY CHANNELED

DISTRIBUTION ®

DEPTH, (jm DEPTH, Jim

(b)

Figure 5. Example of the determination of the area integrals chosen for

data reduction for the case of an imperfectly channeled distribution,

(a) The area integral used to estimate channeling is the fraction of the

total number of implanted ions that penetrate beyond the Gaussian approx- imation to the random distribution. (b) The area integral used to estimate dechanneling is the fraction of the total number of implanted ions

that no longer fall within the optimally channeled distribution.

low index crystallographic orientations toward the beam direction. The

number of ions lost from the optimally channeled distribution is developed by the area integral @. The use of the term "optimally channeled"

is justified because the accuracy of angular control in this work is

0.05 deg and the depth distributions are shown in this work not to change

until the alignment angle exceeds about 0.3 to 0.5 deg from axial alignment. This angle of 0.3 to 0.5 deg is defined as ii^, the critical dechanneling angle (see fig. 6) . A representative plot of the fractions

® and @ as a function of alignment angle is shown in figure 6 for 300-

keV boron in (110) silicon. Curve (I) which plots the relative magni9

tude of area (T) shows that a maximxjm number of ions is channeled as long

as the alignment angle is less than iJjq. As the alignment angle is increased beyond i^q, more and more ions are dechanneled, thereby building

up the random distribution and reducing the number of ions in the channeled distribution. At sufficiently large angles, all of the ions are scattered, mostly into a random distribution, although a small number

may be deflected to follow channeled paths. Curve®, which plots the

relative magnitude of the area @, shows that no ions are lost from the

optimally channeled distribution in the region from perfect alignment

= 0) to the critical dechanneling angle ^q. Then, as the alignment angle is increased, ions are lost into the lattice by nuclear scattering.

Finally, the only ions that penetrate beyond the random distribution are those that are deflected into channels.

3. EXPERIMENTAL RESULTS

The data obtained in this study are summarized in table 1 for the ionenergy orientation combinations examined. Examples of the 'depth distribution of electrical activity versus alignment angle (the angle between

the ion beam and the nearest low index silicon crystallographic direction)

for alignment angles from 0 to 7 deg are shown in figures 7 through 15,

for nine of the ion-energy-orientation combinations listed in table 1.

From these profiles several trends in the data become obvious. Channeled

implantations lead to increased penetration depths, with the peak of the

perfectly channeled distribution occurring at depths that vary from 1.5

times deeper than the random peak (for 300-keV boron into (111) silicon)

to as much as 30 times deeper than the random peak (for 75-keV arsenic

into (110) silicon) . Along with the variation in penetration depths from

channeled to random implants, there is also a significant change in the

shape of the resulting ion distributions as the angle of incidence for

the beam is altered. Finally, the depth of the near-surface peak in electrical activity changes as the angle of incidence is varied. As is discussed in 4.4.3, the near-surface peak is not due solely to ions that follow a random trajectory, and thus does not always occur at the depth predicted by range theory for amorphous targets

.

The data provided by these experiments for all the poinbinations of table

1 were analyzed as described in 2.3. and the results plotted versus the

angle of incidence. (The critical angle, as calculated in Appendix A, is

also indicated.) Representative results are shown in figures 16 through

23. In the curves shown in figures 18 through 22, the solid data points

represent accurate alignment and were obtained using Rutherford backscattering; the open data points for the less sensitive larger angles were obtained by tilting the target holder. Data given in [5] f'or 450-keV

phosphorus were also analyzed and plotted in a similar manner; the results are shown in Appendix B. When the data are plotted in this manner,

several additional trends become apparent. The angle at which the random

yield increases to a value halfway between the value for 0-deg incidence

and the saturation random yield is referred to as ^1/2- This angle is seen to vary from approximately 0.8 i)^. to \p(.. In addition, the random

fraction is seen to saturate when the alignment angle is between 1.6 \1)q

11
Table 1. Implantation Angular Control Data

c deg

Energy

keV

Ion

Silicon

Orientation

Random

Fraction

7 deg

%

at

'^o deg

Fraction Not

in Distribution at 1 deg

Off Axis

Same at

2 deg

Off Axis

%

1.97 300 B 100 97 . 3 0. 3 40 54

2 . 16 300 B nil.

100

93.9 0.4 39 56

2.33 450 P 93.0 0.2 60 67

2 . 44 300 B 92 . 4 0.6 38 62

2.3/ 450 P 95 .

0

0.2 48

' 67

2 . 94 450 P 110 > 90 0.2 58 72

2.95 300 As 100 86 .

9

0.2 12 25

3.12 75 B 100 87 .

8

0.45 38 59

3 . 29 300 As 111 87.4 0. 35 12 2 3 3 . 40 300 In 111 _ 14 29

3.45 75 B 111 86 . 7 0.7 16 34

3 . 84 300 As 110 84 .

1

0.6 11 31

3.92 150 In 111 111 6 J . 0

_ _ J / 3 . 9o 1 b B 110 on n 0.4 19

3 . 98 300 In 110 lb . 0 0 . 3 15 3 / 4 . 00 150 Al 110 92.7 0.35 22 4b

4.41 /5 As 111 46 . b 0.6 7 18

A f 1 4 . 61 IbO In 110 % 0.4 6 2 i 4 . /9 20 B

Til 111 / 3 . 0 5

o 5.19 75 As 110 61. 6 0.3 8 21

5.22 40 In 111 57.0 12 22

5.32 75 In 110 56.5 15 28

5.61 20 B 110 71.4 12 15

5.87 20 As 111 24.0 3 5 6. 10 40 In 110 31. 3 11 17

6. 86 20 As 110 23.9 4 7

^tpQ is defined here as the angle at which deviation from the optimally

channeled distribution begins. and is called the critical dechanneling

angle

.

From Reddi and Sansbury [5]

.

i

12
10 17

10 16

10 15

1014

BORON

300 keV

1.5x lO^^cm'

i[111] Si

Figure 7. Depth distributions of carrier concentration as a function

alignment angle for 300-keV boron in (111) silicon.

13
1017

<

I-z

UJO

z

o

o

QC

LU

CC

QC

<

10 16

10 15

10 14

DEPTH, Mm

Figure 8. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV boron in (100) silicon.

14
0 1 2 3

DEPTH, jum

Figure 9. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV boron in (110) silicon.

15
10 17

CO

I EoZ

g

<

z

UJo

z

o

o

OC

UJ

OC

OC<

o

10 16

10 15

1014

Figure 10. Depth distributions of carrier concentration as a function of

alignment angle for 75-keV boron in (111) silicon.

16
DEPTH, Mm

Figure 11. Depth distributions of carrier concentration as a function of

alignment angle for 75-keV boron in (110) silicon.

17
18
DEPTH, Mm

Figure 13. Depth distributions of carrier concentration as a function of

alignment angle for 300-keV arsenic in (111) silicon.

19
0 12 3

DEPTH, Mm

Figure 14. Depth distributions of carrier concentration as a function of

alignment angle for 75-keV arsenic in (110) silicon.

20

BORON

300 keV

0 2 4 6 8

ALIGNMENT ANGLE, degree

Figure 16. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV boron in (111) silicon. (Error bars are not indicated

on the figure; experimental uncertainties are described in the text.)

22
100

2

<

X

H

DC

Q- 4

UJ ^ Q _

C/5 O I- — Z) Q DO

LU GC

I-

- <

LL CO O ^

S < O o

H

<

80

9 60

40

20

T

0

BORON

300 keV

1.5 X lO^^cm"

[110] Si

2 4 6

ALIGNMENT ANGLE, degree

U- _

CO D

O 00 2 CO 25

2 LU < 2

-J Z

^ <

— o

o>

Z -I o <

< Q_ cc O

Figure 17. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV boron in (110) silicon. (Error bars are not indicated

on the figure; experimental uncertainties are described in the text.)

23
100 T BORON

75 keV

ALIGNMENT ANGLE, degree

Figure 18. Magnitudes of channeling and dechanneling versus alignment,

angle for 75-keV boron in (111) silicon. (Error bars are not indicated

on the figure; experimental uncertainties are described in the text.)

24
100

BORON

20 keV

0 2 4 6 8

ALIGNMENT ANGLE, degree

Figure 19. Magnitudes of channeling and dechanneling versus alignment

angle for 20-keV boron in (111) silicon. (Error bars are not indicated

on the figure; experimental uncertainties are described in the text.)

25
100

ARSENIC

300 keV

0 2 4 6 8

ALIGNMENT ANGLE, degree

Figure 20. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV arsenic in (110) silicon. (Error bars are not indicated on the figure; experimental uncertainties are described in the

text.)

26
0 2 4 6 8

ALIGNMENT ANGLE, degree

Figure 21. Magnitudes of channeling and dechanneling versus alignment

angle for 20-keV arsenic in (111) silicon. (Error bars are not indicated

on the figure; experimental uncertainties are described in the text.)

27
0 2 4 6 8 10

ALIGNMENT ANGLE, degree

Figure 22. Magnitudes of channeling and dechanneling versus alignment

angle for 150-keV indium in (110) silicon. (Error bars are not indicated

on the figure; experimental uncertainties are described in the text.)

28

J
100

INDIUM

0 2 4 6 8

ALIGNMENT ANGLE, degree

Figure 23. Magnitudes of channeling and dechanneling versus alignment

angle for 300-keV indium in (110) silicon. (Error bars are not indicated

on the figure; experimental uncertainties are described in the text.)

29
to 2 ip^. (Recall that the substrate angles are uncertain by 0,7 deg for

alignment angles greater than 3 deg.) The fraction of the random equivalent distribution deeper than the Gaussian approximation to the amorphous

distribution is given in column 5 of table 1. (Recall that these values

may be in error by a few percent in estimating the true random fraction

due to the neglect of higher-order moments in the solution to the LSS

equations.) These data are plotted versus the ratio of alignment angle

to the critical angle in figure 24. These data also show a saturation of

random yield for ^ = 2 ip^

.

The sensitivity of the channeled distributions to angular alignment is

demonstrated in columns 7 and 8 of table 1. Column 7 presents the fraction of the implanted ions lost from the optimally channeled distribution for an alignment angle of 1 deg, while column 8 presents the fraction of the implanted ions lost from the optimally channeled distribution for an alignment angle of 2 deg. These data show that within the error due to neglect of higher order moments the implants characterized

by a smaller critical angle are more sensitive to angular alignment,

as expected. Column 6 is ip^, the approximate angle at which the channeling distribution begins to deviate from the optimally channeled distribution; and the angle is called the critical dechanneling angle. This

angle is most likely the angle at which the ion trajectory begins to deflect out of a single axial chemnel and wanders among several axial channels (as is described in 4.1.). Moline and Reutlinger [4] have also

noted that this angle is just less than 0.5 deg for the isolated case of

100- and 300-keV phosphorus. From the data presented in this table, the

ion beam must be controlled to be within 0.5 ± 0.2 deg to guarantee that

the optimally channeled depth distribution for implantations directly

into low index crystallographic orientations is obtained.

One set of SIMS atomic profiles was measured for comparison with the C-V

carrier profiles. SIMS profiling was accomplished by rastering a 5-keV

2.5- to 5-nA beam over a region of the sample surface with secondary

ions accepted only over the crater center. The depth scale was determined by averaging a series of measurements of the crater depth using a surface profilometer and sampling the crater from several different directions, while the concentration scale was determined by setting the

integrated secondary ion yield equal to the known ion fluence. A background subtraction was performed to eliminate the effects of residual

interferences. The case selected was 150-keV boron in (110) silicon.

The material, alignment technique, implantation conditions, and annealing conditions were identical except that the ion fluence for the SIMS

measurement was 1 x 10^^ cm~^, while that for the C-V measurements was

1.5 X 10^^ cm~^. This difference in ion fluence was dictated by the

relative sensitivities of the two measurement techniques and could account for some difference in shape of depth distribution because of the

randomizing effects of the greater damage in the higher fluence implant

for SIMS. Both fluences are low relative to the amorphization fluence

and the annealing condition of 800°C for 20 min is not likely to cause significant redistribution. The data from the SIMS measurement are shown

in figure 25. Data for four alignments are shown in order to give repre30
in'

Figure 24a. Random fraction (linear) of implanted depth

distributions versus the ratio of the selected random equivalent angle of incidence {^2.^1 ^ <3ie<3) to the calculated critical channeling angle.

31
Figure 24b. Random fraction (log) of implanted depth distributions versus the ratio of the selected random equivalent

angle of incidence i^j-n ~ ^ ^^9) to the calculated critical

channeling angle.

32
DEPTH, /im

Figure 25. SIMS atom-depth distributions for 150-keV boron as a func

tion of alignment angle away from the [110] axis of silicon. Solid

curves are drawn through the individual data points from the SIMS mea

surement. Typical data points are represented by the circles and tri

angles

.

33
sentative steps between optimuin alignment and (110) random equivalent

alignment. The SIMS data of figure 25 should be compared with the C-V

data of figures 9 and 10, which are for ion energies a factor of two

greater than and less than that used to obtain the SIMS energy. The

shapes of the curves and the qualitative nature of the transition between alignment conditions are seen to be in good agreement. The quantitative differences cam be explained by the fact that the sets of alignment angles for the SIMS profile and for the C-V measurements were made

in different directions away from 0-deg alignment, that is, the angle 6 was varied at different values of (see figs. 1 and 2) .

The depths of the peaks in the carrier concentration profiles of figures

7 through 13 are seen to shift as the alignment angle is varied. In most

of the cases examined in this study, the peak moves uniformly from the

random peak toward the optimally channeled peak as the ion beam approaches a low index crystallographic direction. This behavior is clearly exhibited by the boron profiles of figures 7, 9, and 25. However, the

arsenic profiles of figures 12 and 13 do not follow this trend. In those

profiles, the near-surface peak first moves deeper as the alignment angle

decreases from the random equivalent angle, then shifts rapidly back toward the surface to even shallower depths than the depth of the random

equivalent peak. Eltekov et at. [9] have performed calculations which

illustrate shifts in the peak of the dopant distribution, as described

above. The physical reasons for this shift in the peak location are discussed in 4.4.3.

4, ANALYSIS

While satisfactory theories are available to predict ion ranges in amor- phous targets, there are at present no such theories to predict ion distributions in single crystals. Thus, this section provides a physical

picture of the channeling process based on the analytic model of Lindhard

[10] . This model is of sufficient generality to provide a means to characterize a wide variety of implantation parameters and to explain trends

in the data. Lindhard 's model begins with the concept of a string of

atoms, which leads to the classification of an ion's trajectory in a single crystal according to its "transverse energy", i.e., the component of

the ion's energy in the plane perpendicular to the atomic string. Classification of the ion's trajectory according to transverse energy in turn

leads to the concept of a critical angle. It is then shown that while

the critical angle describes only the limit of applicability of the con- tinuum model, this concept provides a useful means of characterizing the

implantation conditions. Finally, the implications obtained from this

model for implantation into single crystal substrates are explored.

4.1. The Continuum Model

The stopping of energetic ions in crystals is typically addressed as a problem in classical mechanics [11] in which the scattering of an ion

from an atom initially at rest is described as the motion of the ion in

the central field of the ion-atom potential. Typically, the ion-atom

34
combination is modeled by the Thomas-Fermi potential [11] , because of

its simplicity and generality. The use of this potential, combined with

a velocity-dependent electronic stopping power, leads to LSS-type range

equations for implantations into amorphous substrates. Solutions of

these equations yield predictions of ion range distributions accurate

to approximately 10 percent for ion range and approximately 30 percent in

the standard deviation in the projected range of the implanted ions

[8,12] . Solutions to the range equations have been coirpiled by a variety

of authors (e.g., [8,12,13]), and are used to predict ion ranges for industrial implants. However, these models are based on the assun^tion

that the svibstrate atoms are randomly distributed, and therefore by their

nature cannot predict the effects of the ordered nature of the crystalline lattice that are responsible for channeling.

To model the channeling effect, Lindhard approximated the substrate lattice by a series of strings of atoms parallel to the low index crystalline directions. If V(r) is the potential energy between an isolated

atom and the incident ion, then the potential of an ion due to an infinite string of atoms at an average spacing d along the z axis (fig. 26)

is given by:

00 oo CO V = y V(r ) = y V(/p^ + z^) = y V(/p^ + n d ) . (1)

T ^ n ^ n n ^ n

n=-co n=-°° n=-°o

Lindhard then argued that since the ions are moving with high velocity,

and since the collision angles are small for channeled trajectories,

the channeled ion would interact with many atoms at once. For these

ions, details of the atomic nature of the lattice would become blurred,

so that the atomic distribution would appear uniform. Mathematically,

this would imply the limit of a continuous string

T

oo |- If / 2 2\l/2

dz = U(p) (2)
Using Lindhard's approximation to the Thomas-Fermi potential [9]:

2 V(r) =

47Te r o

1 -

2 2 2 1/2

(r + K a )^

the integral (2) becomes

1 r \( 2 2\l/2

U(p) = - J dz V [z + p

j

h^2'

47T£ d

o

? (p/a) ,

(3)

(4)

where

5 (p/a) = In { (Ka/P) + l} , (5)

and

2/3 2/3-1/2

a = 0.8853 a i^, + Z ' ) (6)

In these expressions d is the average atomic spacing along the chosen

crystallographic direction, r is the separation between the ion and

the substrate atom, is the atomic number of the ion, Z2 is the atomic

number of the substrate atom, Zq is the permittivity of vacuum (8.854 x 10"^2 F/m) , e the electronic charge (1.602 x 10"^^ C) , K is an adjustable constant, p is the perpendicular distance from the ion to the string,'

and a is the Thomas-Fermi screening radius with ag being the Bohr radius

(0.528 A) . Over a wide range of ion energies, the best fit to the potential U(p) is obtained by setting K = /J [10].

Since the potential energy now depends only on p (the distance from the

string) , the only effective forces on the ion are normal to the row. This treatment neglects the contribution of electronic stopping which,

since it is purely frictional, provides no directional effects. The

model has thus reduced the classification of the ion's trajectory in

a three-dimensional crystal to the problem of the motion of the ion in

a plane perpendicular to the atomic string. Neglecting electronic stopping, the total energy of the ion in this transverse plane (Ej^) is a constant, equal to the sum of the potential energy U(p) plus the transverse kinetic energy E^i. For an ion incident to the string at an angle

|

\p with initial kinetic energy E given by

1 2 E = - V

where is the mass of the ion and v is the incident velocity of the

ion, the transverse kinetic energy is given by

(7)

Ki ^ -(vsin^)

1 2 2 2 - M^' y ^ = Eijj (8)

36
(The approximation sin \l) \p is valid if ^ is small.) The total transverse energy is given by

E , = U(p) + = U(p) + Elp^ . (9)

1 J^-

1

4.2. Classification of Ion Trajectories

The continuum model leads to the understanding of channeled trajectories

as characterized by the motion of an ion in a plane perpendicular to a single atomic string. The results obtained from this model are applied

to trajectories in a real crystal by treating the crystal as a periodic

arrangement of parallel strings. Thus, the potential energy for an ion

entering the crystal is a sum of the potentials from each of the atomic

strings. Because the crystal is periodic, only the potential in a single

axial channel need be considered to understand the potential throughout

the entire crystal. The ion-atom potential as given by eq (3) is a re- pulsive potential. Thus, the potential energy rises from a minimum value

in the center of an axial channel to an infinite value as the ion approaches the center of any atomic string. It is important to note that

in the region between the strings that form the boundary of the axial

channel, the potential assumes an intermediate value — a higher potential

energy than it has at the center of the channel, but lower than the potential energy very near the atomic strings.

The continuum model predicts three types of stable trajectories and a fourth (unstable) trajectory [14] . The three stable trajectories are illustrated in figure 27, looking down the atomic strings at the projection of the ion's motion in the plane perpendicular to the atomic strings

The first type of ion motion is the perfectly channeled (or hyperchanneled) trajectory (fig. 27a) . This trajectory occurs for ions that enter the crystal in a region of low potential energy with a very low trans

verse kinetic energy. Because of their low transverse energy, the motion

of these ions is confined to a single axial channel. These are the ions

that penetrate the deepest into the crystal and produce the "optimally

channeled" distribution referred to in section 3. of this report.

Ions with somewhat higher values of transverse energy (fig. 27b) wander

among the strings of atoms. While these ions have enough transverse energy to overcome the potential barrier that confines the perfectly channeled ions to a single axial channel, they do not have enough transverse

energy to approach the string of atoms closely enough to see the atoms as

: individual scattering centers. The continuum model still describes the

motion of this class of ions, which follow what is referred to as a

I "channeled" trajectory.

Ions with transverse energy greater than some critical value (Eq) aproach the string of atoms closely enough to see the substrate atoms as individual scattering centers (fig. 27c) . Transverse energy is no

jlonger conserved, and the continuum model of the atomic string no longer

jholds. Since the orderly arrangement of lattice atoms plays no part in
0 O O
influencing the trajectory of this last class of ions, the substrate

atoms are randomly arranged in regard to the ion's motion. The distribution of the last type of ions should therefore be described by the

range theories for amorphous targets.

Finally, there is a fourth type of unstable ion trajectory. This trajectory is followed by ions with transveiJ'se energies just above the critical

energy. The motion of these "quasi-channeled" ions initially resembles a channeled trajectory; however, these ions have enough transverse energy

to ultimately penetrate to the core of the atomic strings and thereby become deflected into a random trajectory. The number of deflections inside the channel an ion undergoes in this state before suffering a large

angle scattering event is controlled entirely by chance [15] ; however,

while the ion is in this state, it spends much of its time in regions of

the channel near the atomic strings. Thus, these ions see a greater elastic stopping power (typically 50 percent greater [15]) than for random

trajectories, until such time as the ion becomes deflected into a random

trajectory.

4.3. The Critical Angle

The continuum model does not describe the motion of ions with transverse

energy above the critical value E^. By eq (9) the transverse energy is a sum of a potential energy term and a kinetic energy term. Two concepts

are related to that of a critical transverse energy, i.e., the critical

approach distance and the critical angle. The critical approach distance

(p^) is the distance from an atomic string within which an ion can approach the string with zero transverse kinetic energy = 0) and can

still exceed the critical energy. The critical angle (ij^^,) is the angle

at which an ion can enter the crystal in a region of zero potential energy (U = 0) and have transverse kinetic energy equal to the critical

energy. Thus,

ECO= EI|J^ = U(p ) . (10)

c

The ability to predict channeling behavior from the continuum model thus

reduces to the problem of finding the critical approach distance (Pq) as

a function of incident ion energy E. Fortunately, a solution to this

problem has been given by Morgan and van Vliet [14] , on the basis of com- puter modeling. They found that the minimum distance of approach to the

string (Pmin) is given by

2a/a ,^ -/a a , Pmin = ^ ^1 - 19 + W (11) .

for 0.02 < a < 350, where a is defined in eq (6) and a is given by

a = f^ (12)

39
where

2Z Z e d E'=^^. (13)

4tt£ a

o

So far, channeling behavior has been estimated as if the lattice atoms

were frozen in place; however, the real lattice is characterized by

thermal vibrations. These vibrations are modeled in the Debye approximation [16] where the rms displacement (uj-jjig) of the lattice atoms from

their equilibrium potential is given by

u = 12.1 { [(j)(e/T)/(0/T) + l/4]/M^e} A (14)

rras ^

where M2 is the atomic mass of the substrate (28.086 for silicon) , 6 is

the Debye temperature (543 K for silicon), T is the absolute temperature,

and ({)(9/T) is the Debye function (tabulated in Abramowitz and Stegun

[17]). The value of u^ms silicon at 293 K is 0.075 A.

In the presence of thermal vibrations, the critical approach distance is

given by [15]

:

= p^. + . (15) c mm rms

It can be seen from the form of eq (11) that at high ion energies the

critical approach distance is limited by the thermal vibrations of the

lattice, while at low ion energies, the critical approach distance is

limited by the nature of the ion-atom potential. Finally, the critical

angle can be calculated from eq (10) by substituting from eq (15)

into the expression for string potential (eq (4) )

:

il) = /U(p )/E . (16) c c

The above approach is valid over a range of incident energies characterized by a range of a from 0.02 to 350. In the case of very high implanta

tion energies (a < 0.02) the computer fit to Pmin/^' "° longer appropri

ate, so that Lindhard [10] calculates the critical angle from

= = 1 I (17)

In the low energy limit (a > 350) , the computer fit again is no longer

appropriate, and Lindhard calculates the critical angle from

40
ij;^ = ijj^ = (/372 a/d tjj^) (18)

Lindhard obtained eqs (17) and (18) by analyzing the asymptotic behavior

of U(p) in the high energy and the low energy limits, respectively [10].

The procedure for calculating the critical angle is summarized in Appendix A.

4.4. Implications for Implantations into Single Crystalline Substrates

4.4.1. Physical Interpretation of the Critical Angle

The critical angle as calculated above describes only the limit of applicability of the model used and not the angular extent of channeling

behavior. Experience obtained from channeling experiments on a variety

of ion-target combinations indicates that the critical angle corresponds

very closely to the angle at which the random fraction is halfway between the value for 0-deg beam incidence and the saturation random value.

This latter angle is referred to as ^i/2t and the experience obtained to

date [14] indicates that

\/2 = ^^c (1^)

with

k = 0. - 1.0 (20)

Both experimental studies and computer simulations indicate that channeling characteristics persist until the angle of incidence for the beam is

at least twice the classical critical angle away from the nearest low index crystalline direction [15] , as also is seen in the work reported here

for ions and energies characteristic of industrial implantation condition

4.4.2. Crystal Orientation for Minimal Channeling

From the data presented and from the previous discussion, it is seen that

the substrate must be tilted so that the nearest low index crystalline

direction is twice the calculated critical angle away from the beam direc

tion to minimize the extent of ion channeling. This angle can exceed the

7- or 8-deg tilt commonly used for randomization in implantation today,

especially for implants made at low energy or high atomic number. Examination of table 1 indicates that for the ions studied here, the critical

angle varies from 1.97 deg to 6.86 deg, requiring tilt angles of from at

least 4 deg to almost 14 deg for maximum random yield. When 2 ex- ceeds the commonly employed random equivalent tilt angle for (111)-

oriented silicon of 7- to 10-deg, care should be given to whether the use

of the larger angle may cause another planar or axial channeling condition to be approached within 2 ij^^ (see fig. 2 for an illustration) .

41
In addition to predicting the angle needed to maximize the random yield

(i.e., twice , the continuiam model describes additional useful trends

in the data. As was discussed in 4.3., a circle of radius Pc around each

atomic string describes the area in which an ion entering even at 0-deg

incidence will follow a random trajectory. For ions unifoirmly distributed about the entire crystal surface, an estimate of the random fraction for 0-deg incidence can be obtained by multiplying the area within

Pc of the string (ttp^) by the number of strings per unit area [15] . Thus, the random fraction for 0-deg incidence R.F. (0) is given by

2 R.F. (0) = up Nd , (21)

c

where Nd is the number of strings per unit surface area: N is the atomic

density of the target (4.866 x 10^^ cm~^ for silicon) and d is the average atomic spacing along the string. Since the critical approach distance increases as the critical angle increases (eq (11) )

, the continuum

model explains an apparent paradox: that as the angular requirements

for channeling to occur become less restrictive (i.e., as increases),

the fraction of ions that never become channeled increases (due to the

increase in Pc) • Thus, performing a given implantation at a lower energy may or may not increase the channeled fraction, depending on the ion

and substrate orientation chosen.

4.4.3. Effects of Channeling on Ion Distributions

In 4.2. of this report, four different types of ion trajectories, each

with its own directional effects and stopping power, were described. At

present, the final depth distribution of implanted ions in general can be predicted for only one of the four components of the ion beam, namely,

for those ions that follow a random trajectory on entering the crystal.

As a result, one must exercise great caution in applying the range theory developed for amorphous targets to predict the results of implantations into single-crystal targets. It is impossible at present to predict the ion range distribution in single-crystal targets without extensive computer modeling for each set of implantation conditions, as was

done for the case of 200-keV boron implanted into (111) -oriented silicon

in [9] . Physically, as the angle of beam incidence is changed, the transverse kinetic energy of the incident ions also is changed. This alters

the relative fraction of ions that follow each type of trajectory (since

the type of trajectory an ion follows is determined by its transverse

energy) ; however, the details of each trajectory and the relative magnitudes of each of the beam components depend in an intricate manner on

the details of the ion-substrate potential. Thus, many features of the

final range distribution cannot be predicted on the basis of intuition.

An example of this can be found in the present experimental results by

considering the location of the near-surface peak in the distribution of

electrical activity as a function of alignment angle (figs. 7 through

13) . Only when the angle of incidence is approximately twice the critical angle does the location of the near-surface peak coincide with that

predicted by the range theory for amorphous targets . Peaks that occur

42
deeper than the random peak indicate that the channeled component of the

beam, with its reduced stopping power, is dominating the formation of the

ultimate depth distribution of the implanted ions. Peaks that occur closer to the surface than the random peak (such as is seen in the arsenic profiles of figs. 12 and 13) indicate the importance of the quasichanneled component with its greatly increased stopping power. Until

adequate theoretical models can be developed, empirical profiles are the

only guide toward understanding the physical phenomena.

4.4.4. Effect of Amorphous Surface Layers

It must be noted that the theory that has been explained in this report

applies to the case of implantation directly into the surface of a single crystal. This development specifically neglects consideration of

the effect of amorphous surface layers (such as Si02, SisNii, or unan- nealed previous high-fluence implantations) on the extent of ion channeling. The reduction of ion channeling for a crystalline substrate

perfectly oriented to the ion beam direction but covered by an amorphous

surface layer can be estimated by analytic procedures [18] . These ex- pressions do not consider the effect of substrate tilt on the extent of

ion channeling for the composite structure. Furthermore, these expressions have been experimentally examined only for high energy hydrogen

or helium backscattering and have not been tested for heavy ion implantation.

5. INFLUENCE OF SCANNING

If it is desired to achieve uniform device characteristics everywhere

over a 5- to 10-cm diameter silicon wafer using either intended random

equivalent or well channeled implants, the data reported in the preceding sections of this report show that the angle of incidence of the

ions must be controlled everywhere over the wafer to guarantee con- trolled depth profiles. In this section, industrial production implantation target chamber/beam scanning techniques are considered, and the application of the results presented in this report to industry practice

is discussed.

Uniform implantation of large wafers requires some method for scanning

the ion beam across the wafers or of scanning the wafers in a stationary

beam. Some of the techniques presently in use can result in angular

variations across the surface of a wafer or from wafer to wafer that can create significant variations in depth distribution and therefore can cause loss of control of junction depth or device characteristics, resulting in poor yield. Other scanning techniques maintain a constant angle

of incidence, but that angle may not be the angle required. In such

cases, channeling may occur and may cause junctions or distributions to

be deeper than were designed using LSS range statistics.

There are two general techniques for scanning, namely, electrostatic beam

scanning and mechanical target scanning. Ion beam scanning techniques

are discussed by Wittkower [19] , Wilson and Brewer [20] , and Dearnaley,

Freeman, Nelson, and Stephen [21]. Sometimes the two are combined, one

43
in each dimension. Two types of each scanning technique will be considered to establish criteria that can be applied to other techniques.

As ion beam currents are increased in advanced implantation systems , mechanically scanned target systems are favored, because 1) electrostatic

scanning removes the space-charge neutralizing electrons from the ion

beam which results in expansion of the beam, and 2) of the need to distribute the input power over a number of wafers to reduce heating effects

Crystalline wafers of 75-mm diameter oriented to within about 1 deg of a low index plane after polishing are assumed in the following discussion.

5.1. Mechanical Target Scanning (Ion Beam Fixed)

Case A

SCAN: Wafers are mounted on a disk that rotates about an axis parallel

to the ion beam and translates linearly from side to side in a plane nor- mal to the ion beam. In another version, the target mount is translated

linearly in two directions in a plane normal to the ion beam.

ANGULAR CONDITION: The angle is constant for all wafer surfaces, so an- gular uniformity is good everywhere; but the angle between the ion beam

and the wafer orientation is near 0 deg so channeling can be significant.

DISCUSSION: For nominal channeling, this condition is ideal. If ran- dom equivalent depth distributions are desired, the axis of rotation

should be tilted at twice the critical angle from the direction of the

ion beam.

Case B

SCAN: The wafers are mounted on the surface of a cylinder which is ro- tated about an axis normal to the ion beam and is translated along the

axis of rotation (or the ion beam is scanned in one dimension)

.

ANGULAR CONDITION: The angle of incidence between the ions and the wafei

crystallographic axes varies over each wafer surface from 0 deg to "^1 to

9 deg, depending on the diameter of the cylinder, so the perfect channeling condition may occur in one location on the wafer and the random

equivalent in another. There is no angular control.

DISCUSSION: Angular control is not possible if the cylinder surface is

normal to the ion beam direction. If the cylinder facets are wedged j or machined at twice ii^, then implants for minimal channeling can be

achieved.

5.2. Electrostatic Beam Scanning (Wafers Fixed)

Case A

SCAN: The ion beam is scanned in two dimensions to -cover one wafer

mounted on a surface normal to the beam or tilted 7 deg from the normal,

i

and the wafers are sequenced into the beam scan area.

44
ANGULAR CONDITION: The angle of incidence typically varies to 2 deg over a wafer surface, and therefore channeling cannot be controlled.

This condition is probably adequate to achieve uniform random equivalent

implants if the wafer surface is tilted 2 i^i^ from the normal.

DISCUSSION: Nominal channeling cannot be achieved. No modifications

are required for random equivalent implants

.

Case B

SCAN: Double deflection scanning is used, which is the same as for

Case A except that the beam is deflected a second time to make it parallel to the beam axis.

ANGULAR CONDITION: The angle is everywhere properly controlled for the

random equivalent condition if the wafer plane is tilted at twice i)^.

If the wafer plane is normal to the beam, then the angle is everywhere

proper for nominal channeling.

DISCUSSION: If the proper angular alignment is achieved, no modifications are required for nominal channeling or random equivalent.

If is small enough to require accurate alignment to achieve channeling, then a goniometer and a simple Rutherford backscattering alignment

system is required to produce well channeled implants for the parallel

beam scanning or double deflection approach. The samples must be implanted individually in this case and implantation times will increase

significantly. Accurate channeling alignment cannot be achieved when a number of wafers are mounted on one surface and implanted together as in

the mechanical scanning techniques unless each wafer is polished to within '^O.l deg of the same orientation.

45
REFERENCES

1. Andersen, J. U. , Davies, J. A.^ Nielsen, K. 0.,, and Andersen, S. L.,

An Experimental Study of the Orientation of (p,Y) Yields in Monocrystalline Aluminum, Nual, Instrum, Methods 3£, 210-215 (1965)

.

2„ Seidel, T. E., Distribution of Boron Implanted Silicon, Proa. Second International Conference on Ion Implantation in Semiconductors,

Garmisch-Partenkirchen, May 24-28, 1971, pp. 47-57 (Springer-Verlag

,

Berlin, 1971)

„

3. Moline, R. A., Ion Implanted Phosphorus in Silicon: Profiles Using

C-V Analysis, J. Appl. Phys , 42, 3553-3558 (1971).

4. Moline, R. A., and Reutlinger, G. W. , Phosphorus Channeled in Silicon: Profiles and Electrical Activity, Proc. Second International

Conference on Ion Implantation in Semiconductors, GarmischPartenkirchen, May 24-28, 1971, pp. 58-69 (Springer-Verlag, Berlin,

1971)

.

5. Reddi, V. G. K., and Sansbury, J. D., Channeling and Dechanneling

of Ion-Implanted Phosphorus in Silicon, J. Appl. Phys, £4, 2951-

2963 (1973)

.

6. Gordon, B. J., Stover, H. L., and Harp, R. S., A New Impurity Profile Plotter for Epitaxy and Devices, Silicon Device Processing

,

C. P. Marsden, Ed, NBS Special Publication 337, pp. 2 73-284 (November 1970)

.

7. Kennedy, D. P., Murley, P. C, and Kleinfelder, W. , On the Measurement of Impurity Atom Distributions in Silicon by the Differential

Capacitance Technique, IBM J. Res. Development, September 1968, pp.

399-408; and Kennedy, D. P., and O'Brien, R. R. , On the Measurement

of Impurity Atom Distributions in Silicon by the Differential Capacitance Technique, IBM J. Res. Development , March 1969, pp. 212-

214.

8. Brice, D. K. , Spatial Distribution of Ions Incident on a Solid

Target as a Function of Instantaneous Energy, Sandia Labs Report

SC-PR-71-0599, Albuquerque, New Mexico (1971), and Appl. Phys

.

Lett. 16_, 103-106 (1970) .

9. Eltekov, V. A., Karpuzov, D. S., Martynenko, Y. V., Rubakha , E. A.,

Simonov, V. A., and Yurasova, V. E., Computer Studies of Boron Ion

Channeling in Silicon Single Crystals, Proc. International Conference on Atomic Collisions, in Solids (IV) , 1971, S. Andersen, K.

Bjorkqvist, B. Domeij, and N. G. E. Johansson, Eds., (Gordon and

Breach, London, 1972) , pp. 113-118.

10. Lindhard, J., Influence of Crystal Lattice on Motion of Energetic

Charged Particles, Kgl . Danske Videnskab. Selskab^ Mat.-Fys. Medd.

34 (14) (1965)

.

46
11. Sigmund, P., Collision Theory of Displacement Damage, Rev. Roum.

Phys. 17, 323-870, 969-1000, and 1070-1106 (1972)

.

12. Gibbons, J. F., Johnson, W. S,, and Mylorie , S. W. , Frojeated

Range Statistics - Semiaondua tors and Related Materials, 2nd ed.,

(Stroudsburg, Dowden, Hutchinson and Ross, 1975).

13. Winterbon, K. 3., Ion Implantation Range and Energy Deposition Distributions 2_ (Plenxam, New York, 1975) .

14. Morgan, D. V., and Van Vliet, D., Critical Approach Distances and

Critical Angles for Channeling; Radiat. Eff. 8_, 51-61 (1971) .

15. Van Vliet, D., The Continuum Model of Directional Effects, Channelingj Theory Observation and Applications , D. V. Morgan, Ed (Wiley,

New York, 1973)

.

15. See, for example, Gemmell, D. S., Channeling and Related Effects in

the Motion of Charged Particles Through Crystals, Rev. Mod. Phys.

46 , 129-227 (1974)

.

17. Stegun, I. A., Miscellaneous Functions: Debye Function, in Handbook of Mathematical Functions for Formulas, Graphs, and Mathematical Tables, M. Abramowitz and I. A. Stegun, Eds, Nat. Bur. Stand.

j

Appl. Math. Ser. 55_ (June 1964), p. 998.

13. Lugujjo, E. , and Mayer, J. VJ. , Energy Dependence of He''" and H"*" Channeling in Si Overlaid with Au Films, Phys. Rev. B. 7_, 1782-

1791 (1973).

.19. Wittkower, A., Wafer Handling for Ion Implantation, Electronic Packaging and Production, 95-104 (May 1973).

20. Wilson, R. G., and Brewer, G. R. , Ion Beams, p. 457 (WileyInterscience Publishers, New York, 1973)

.

21. Dearnaley, G., Freeman, J. H., Nelson, R. S., and Stephen, J., Ion

Implantation (North Holland Publishing Company, Amsterdam, 1973)

.

47
APPENDIX A. CALCULATION OF THE CRITICAL ANGLE

In this report, it has been demonstrated that the crystals must be

oriented at twice the classical critical angle to minimize unintentional

channeling. This appendix provides an outline of the procedure used to

calculate the critical angle for implantations into silicon. The procedure is outlined as a series of steps.

STEP 1: Calculate a:

a = 0.8853 a„ (Z,^/^ + 2,^/^"^/=

B 1 2 or

a = 0.4685 {Z^^^^ + 14^^^)'-^^^ A , (Al)

STEP 2: Using the proper value of atomic spacing from table Al,

calculate E-'-

:

2 2Z Z e d

e' =

2

4Tr£: a

o or

Z d

e' = 403.2 —^eV-A (A2) a

STEP 3: Calculate a for the implantation energy E chosen (the implantation energy E is the product of the accelerating voltage times the

charge state of the ion, e.g., E = 400 keV for B"*"^ at 200 kV) :

e' a = ^

(A3) 2E

STEP 4: If 0.02 < a < 350

2a r- ,^ t/a a , , ^, p . = — /a (1 - — + —- (A4) mm 3 19 700

If a < 0.02 Go to step 9.

If a > 350 Go to step 10.

STEP 5: Calculate u for the implantation temperature using , 9 from

, -, , 2 table Al:

u = 12.1 {[$(x)/x + l/4]/M^e} (A5) rms 2

48
Table Al. Physical Constants for Silicon

Quantity Value for Silicon

^2 14

"M^ 28.086 amu

^100 ^'''^ ^

^10 , 3-^4° ^

d^^^ 4.703 A

u at 293°K 0.075 A

rms

N 4.995 X 10~^ (A)""^

e 543 K

Table A2 . Atomic Numbers (2.^^) For Commonly Implanted Impurities

B 5

Al 13

P 15

Ga 31

As 33

In 49

Sb 51

49
where

X = —

T

For room temperature implants into silicon:

u at 293 K = 0.075 A

rms STEP 6: Calculate p c

STEP 7: Calculate U(p ) c

p = v/p^. + u^ (A6) c mm rms

u(p ) = m {(^)^ + 1}

c 4TTe d p o c

Z 2 U(p ) - 201.6 In {3 (—) + 1} (A7)

c d p c

STEP 8: Calculate lb c

/U(p )

When a is not between 0.02 and 350, steps 9 and 10 replace steps 5

through 8.

STEP 9: If a < 0.02

*c = *i = I (fY'

''''

STEP 10: If a > 350, calculate from step 9. Then

Sample Calculation

+ 100 keV As implanted into <100> oriented silicon at room temperature

STEP 1: From equation (Al)

:

50
a = 0.4685 {33^^^ 4- 14^/3^-1/2 ^

a = 0.1165 A

STEP 2: From equation (A2):

(0.1165 A)^

e' = 5.324 X 10 eV

STEP 3: From equation (A3)

:

(1) (1 X 10^ eV) = 10^ eV

5.324 X 10^ eV ^„ a = = 26.62

2 (10^ eV)

STEP 4: From equation (A4)

2 0.1165 A /TT-—:r /, /26.62 26.62

P • = —^ /26.62 1 —— + •^mm 3 \ 19 700

p . = 0.307 A mm

STEP 5: At room temperature u = 0.075 A. rms STEP 6: From equation (A6)

:

p = \/(0. 3071 A)^ + (0.075 A)

^

p = 0.3162 A

c

STEP 7: From equation (A7)

:

U(p ) = 418.5 eV

c

51
STEP 8: From equation (A8)

/418 5 eV ^

^ V 10^ eV

il) =3.71 degrees.

c

52
APPENDIX B. DATA FROM THE LITERATURE

Two figures were constructed from data given in the literature for use

in this work. They are shown below as figures B-1 and B-2. The source

and explanations are given in the figure captions.

0 2 4 6

ALIGNMENT ANGLE, degree

Figure B-1. Sensitivity of implanted depth distribution to implantation

angle for 450-keV phosphorus in <111>, <110>, and <100> silicon. Data

obtained from an analysis of curves published by Reddi and Sansbury [5]

.

53
10 17

CO

I Eo

O

Q

10 15

BORON

150 keV

<ll1>Si

FROM SEIDEL (1971)

<111>

<111>+ 1° <111>+ 2°

<111>+ 7.4°

RANDOM

EQUIVALENT

0.2 0.4 0.6 0.8

DEPTH, Mm

1.0 1.2

Figure B-2. Implanted depth distributions for 150-keV

boron in <111> silicon from Seidel [2]

.

54
NBS-1 14A (REV. 1 1-77)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. SP 400-49

2, Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Semiaonduator Measurement Technology : Angular Sensitivity

of Controlled Implanted Doping Profiles

5. Publication Date November IV /o

6. Performing Organization <" (j,it

7. AUTHOR(S) Robert G. Wilson,

Howard L. Dunlap, Douglas M. Jamba, and David R. Myers

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

Hughes Research Laboratories NATIONAL BUREAU OF STANDARDS

3011 Halibu Canyon Road DEPARTMENT OF COMMERCE

Malibu, CA 90265 WASHINGTON, D.C. 20234

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ARPA - 1400 Wilson Boulevard, Arlington, VA 22209

The National Bureau of Standards

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15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 78-10624

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Ion implantation can be used to produce accurately controlled doping profiles for

silicon devices and integrated circuits. The work reported here determines the angle

at which the ion beam must strike the substrate in order to maintain control over the

channeled and random equivalent depth distributions of carriers as measured by 1-MHz

differential capacitance-voltage (C-V) profiling. A method to calculate the classical critical angle for channeling Hi^) is presented. Data are presented that characterize the variation in the depth distribution of carriers with substrate orientation, incident ion species, and incident ion energy, for a range of critical angles.

This study establishes the degree of control of the angle between the ion beam and the

crystallographic orientation needed to produce the limiting cases of either optimal

channeling or maximum randomization of ion trajectory in the substrate. For the cases studied here, the angle between the ion beam and the substrate orientation must be con- trolled to within 0.5 ± 0.2 deg to obtain the optimally channeled depth distribution

for implantation directly into the low index crystallographic orientations. Alternatively, to minimize unintentional channeling, the substrate must be oriented so that

the nearest low index crystallographic direction is at least twice the classical critical angle away from the beam direction. The substrate tilt angles required to satisfy

these conditions can exceed the 7- to 10-deg tilt commonly used in ion implantation.

The implications of these results for \iniform and reproducible ion implantation within

the semiconductor industry are discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

C-V profiling; controlled doping profiles; critical channeling angle; ion beam scanning; ion channeling; ion implantation; Rutherford backscattering alignment; silicon

crystallographic orientation.

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