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NBS SPECIAL PUBLICATION 400

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

Semiconductor Measurement Technology:

The Capabilities and

Limitations of Auger

Sputter Profiling for

Studies of Semiconductors
NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU or BTANBAJaCS

LHSBARY

Semiconductor Measurement Technology:

The Capabilities and Limitations

of Auger Sputter Profiling

for Studies of Semiconductors ^

S. A. Schwarz, C. R. Helms, W. E. Spicer

Stanford Electronics Laboratories

Electrical Engineering Department

Stanford University

Stanford, CA 94305

and

N. J. Taylor

Varian Associates

61 1 Hansen Way

Palo Alto, CA 94303

Sponsored by the

Defense Advanced Research Projects Agency

1400 Wilson Boulevard

Arlington. VA 22203

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued September 1981
Library of Congress Catalog Card Number: 81-600003

National Bureau of Standards Special Publication 400-67

Nat. Bur. Stand. (U.S.), Spec. Publ. 400-67, 53 pages (Sept. 1981) CODEN: XNBSAV

(

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON; 1981
TABLE OF CONTENTS

Page

Abstract. 1

1 . Introduction 2

2. Basic Equipment 2

2.1 Electron Spectrometer and Electron Gun 2 2.2 The Ion Gun 3 2.3 The Specimen Holder 4

3. Sensitivity and Spatial Resolution 4

4. Electron Escape Depth Broadening 6

4.1 Introduction 6 4.2 The Electron Mean Free Path 7 4.3 A Deconvolution Formula 8 4.4 Off-Normal Detection 10 4.5 Surface Roughness and Experimental Nonlinearities 14

5. Ion Bombardment Effects 15

5.1 Introduction 15 5.2 Atomic Interactions 16 5.2.1 Introduction 16 5.2.2 Nuclear Energy Loss 16 5.2.3 Electronic Energy Loss 20 5.2.4 Atomic Displacements 21 5.2.5 Summary 21 5.3 A Geometrical Model of Sputtering 21 5.3.1 Introduction 21 5.3.2 Development 22 5.3.3 Computation 25 5.3.4 Experimental Comparisons 25 5.3.5 Discussion 29 5.3.6 Summary 32 5.4 An Ion Knock-On Mixing Model 32 5.4.1 Introduction 32 5.4.2 Development 32 5.4.3 Experiment 33 5.4.4 Extension to Higher Energies 34 5.4.5 Summary 37

6. Experimental Methods in ASP Studies of the Si-SiO^ Interface 38

6.1 Introduction 38 6.2 Experimental Suppression of Profile Broadening 38 6.3 Electron Stimulated Desorption 39 6.4 Experimental Procedure 41 6.5 Crater-Edge Profiling 42

6.6 Experimental Results for the Width of the Si-Si02 Interface 43

References 44

iii
LIST OF ILLUSTRATIONS

Page

1. Typical beam diameter versus beam current with LaBg emitter—solid curve .... 6

2. Maximum sensitivity of AES as a function of electron beam diameter 7

3. Experimentally observed variations of the electron escape depth as a function

of the electron energy 8

4. Effect of escape depth broadening on a step function concentration profile ... 10

5. Electron escape depths for Si and Si02 as a function of electron energy 12

6. Auger depth profile of the oxygen concentration in an MNOS sample 12

7. Auger sputter profile of thermally grown Si-Si02 interface 13

8. An Auger sputter profile of the Si-Si02 interface is deconvolved through the

use of Eq. (10) in the text 13

9. Four situations yielding equivalent measured profiles 14

10. The 10% to 90% width Ay^ and 50% position shift Ay^ as a function of the

roughness parameter Ax 15

11. Schematic illustration of the sputtering and mixing processes resulting from

ion bombardment 16

12. (a) A particle of mass approaches and deflects an initially stationary

particle (b) These particles are modeled as billiard balls with adjustable radii 17

13. Reduced stopping power as a function of reduced energy for the Thomas-Fermi

potential, the inverse square potential, and for electronic energy loss 19

14. Reduced range versus reduced energy for the Thomas-Fermi potential and the

inverse square potential 19

15. Definition of ellipsoid parameters and cross-sectional areas 23

16. Illustration of the sputtering yield variation with ion energy 26

17. The relative sputtering yield is plotted as a function of the nuclear energy

loss E for several values of 3 26

18. Sputtering yields of Ag versus ion energy for Xe"*", Kr"*", Ar"*", and Ne"*" ions

at normal incidence 27

19. The surface factor B derived from Rosenberg and Wehner is plotted as a function of atomic number Z 28

20. The surface factor B is divided by the square root of the atomic mass

and plotted in relation to the periodic table for the transition metals 28

21. Sputtering yields of Au bombarded by 45-keV ions normalized to Ar"*" yield .... 29

22. Pictorial representation of the sputtering yields angular dependence 30

23. Sputtering yield ratios at normal and 50° incidence versus Ar"*" ion energy;

experimental and theoretical 30

iv
ILLUSTRATIONS (continued)

Page

24. Relative sputtering yield increases as a function of incident angle; experimental and theoretical 31

25. Schematic illustration of a random walk with N steps of length a-;^ and

a net distance traveled R 34

26. A step function concentration profile is broadened by ion knock-on mixing

into an erf profile with a 10% to 90% width of 3.6 W 34

27. Average and standard deviation of sputtering yields in thermal SiO^ as a function of ion energy for Ne"*", Ar"*", and Xe"*" bombardment ..t^ 34

28. Average and standard deviation of the measured 10% to 90% Si-Si02 interface

widths as a function of ion energy for Ne"*", Ar"*", and Xe"*" bombardment 35

29. The effect of ESD on the Oj^l ^^LW lii^ss from SiOg and SiOj^

shown as a function of irradiation time for an electron beam flux larger

than 2 x 10 ^'^ cm" 2 s~ 1 at 2 keV 39

30. The total desorption cross section of oxygen at 2 keV shown as a function

of primary flux for a silicon oxide 40

31. The upper part shows the dependence of the cross section on primary electron

energy; the lower part shows how the secondary electron density depends on primary electron energy 41

32. Schematic illustration of the crater formed by sputtering a thin layer of

Si02 on Si 42

33. Sequential Si^yy spectra obtained while sputtering through the Si-Si02

interface 43

LIST OF TABLES

Page

1. Maximum Estimated AES Sensitivities 5

2. Values of Surface Factor B 27

3. Comparison of Monte Carlo Calculations of the Broadening Induced by Ar"*" Bombardment of Si with the Predictions of the Present Model 36

4. Oxide Thickness Dependence of the Width of the Si-SiO^ Transition Region .... 43

V
PREFACE

This study was carried out at Stanford University and Varian Associates 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 efforts 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 work was supported by the Defense Advanced Research

Projects Agency, ARPA Order 2397, through the National Bureau of Standards' Semiconductor

Technology Program, Contract 5-35944. This contract was monitored by Dr. K. F. Galloway as the Contracting Officer's Technical Representative. Dr. W. M. Bullis provided technical

review of this report for the National Bureau of Standards.

Disclaimer

Certain commercially available equipment, instruments, or materials are identified in this

publication in order to adequately specify the experimental procedure. Such identification

does not imply recommendation or endorsement by the National Bureau of Standards, nor does

it imply that the materials or equipment identified are necessarily the best available for

the purpose.

vi
Semiaonduator Measurement Technology:

The Capabilities and Limitations of Auger Sputter

Profiling for Studies of Semiconductors

by

S. A. Schwarz, C. R. Helms, and W. E. Spicer

Stanford Electronics Laboratories

Electrical Engineering Department

Stanford University

Stanford, California 94305

and

N. J. Taylor

Varian Associates

Palo Alto, California 94303

Abstract

Materials characterization is a critical area in current silicon

integrated circuit technology. Those techniques that are commonly

used include Auger sputter profiling, x-ray photoelectron spectroscopy, secondary ion mass spectrometry, and Rutherford backscattering. All of these techniques have unique capabilities and limitations for studies of silicon device structures. In this paper, we describe the capabilities and limitations of Auger sputter profiling

especially with regard to sensitivity, spatial resolution, depth

resolution, and chemical state determination. Although much of the

discussion centers on Auger sputter profiling, the results are also

applicable to x-ray photoelectron spectroscopy and secondary ion mass spectrometry.

Key words: Auger electron spectroscopy (AES) ; metal-oxidesemiconductor (MOS) ; secondary ion mass spectrometry (SIMS); semiconductor devices; sputtering; x-ray photoelectron spectroscopy

(XPS, ESCA).

1
1. INTRODUCTION

The purpose of this report is to provide critical information concerning the use of

electron spectroscopy and ion milling for the analysis of materials used in silicon

integrated circuit technology. The emphasis of this report is placed on Auger electron

spectroscopy (AES) ; however, many of the results are also applicable to x-ray photoelectron

spectroscopy (XPS) and secondary ion mass spectrometry (SIMS) . We concentrate on the use

of these techniques to obtain elemental profiles perpendicular to the surface of a specimen

of interest in IC technology. In addition to elemental profiles, the use of AES to perform

chemical state (i.e., the difference between Si in bulk Si vs Si in Si02) determination is

also discussed. Most of the discussion centers on effects important in Si and Si02

,

although it is not limited to those materials alone.

This paper is divided into six sections. After the Introduction, Section 2 contains a brief description of modern equipment used for Auger sputter profiling (ASP). Next, in

Section 3, the sensitivity and spatial resolution are discussed. In Section 4, the effect

of electron escape depth, in particular, the broadening it produces during profiling, is

discussed. The ion beam used for profiling also causes knock-on induced broadening; these

effects are discussed in Section 5. Finally, Section 6 covers the application of Auger

sputter profiling to studies of the Si-Si02 interface, including the use of AES to determine

the chemical state of elements and the effect of electron stimulated desorption.

2. BASIC EQUIPMENT

2 . 1 Electron Spectrometer and Electron Gun

Because of the commercial availability of cylindrical mirror analyzers (with integral

electron guns) and because most depth profiling has been carried out using them to date, we shall specifically consider this type of analyzer and gun. Other types of analyzers could

be used, however, bearing in mind the desirability of a large angle of acceptance (for

signal-to-noise considerations) and adequate separation between the specimen and analyzer

to accommodate the ion beam without danger of sputtering material from the analyzer or the

electron gun onto the specimen.

The electron beam should be capable of being focused onto the region of the specimen

of interest located at the focal point of the analyzer. In most general studies on patternless thin films, a minimum electron beam diameter of from 10 to 30 )Jm is adequate. This is

the kind of film we shall be considering here for the most part. The profiling of actual

circuits may require beams of diameter down to and below 1 ym, depending upon the region to

be profiled. In these cases, the effects of the geometrical constraints are obviously more

severe than those we are considering here. Nevertheless, the same principles apply. In high spatial resolution cases, it may even develop that the information cannot be found

because of an unfavorable signal-to-noise/specimen damage tradeoff imposed by the small

specimen, as discussed in the next section.

For an electron beam diameter in the range of 10 to 30 ym, beam currents in the range

of 1 to 100 yA are desirable. To avoid electron beam-induced dissociation and desorption

effects, particularly of oxides, reduced exposure is required during the acquisition of

data. This means that in order to obtain adequate signal-to-noise ratio, it may be necessary to increase the area from which the information is acquired. Uniform exposure over

the acceptance area of the analyzer is best accomplished by scanning the electron beam over

the focal region of the analyzer. This can be accomplished by using a TV raster of the

electron beam over the specimen surface. Provided this raster is kept less than about 200

ym on an edge, the Auger signal is not seriously affected by the rastering since the raster

falls inside the 90% signal contour of the typical analyzer.

Another requirement of the electron beam, in addition to its being rastered (both for

density reduction and image specimen capability) , is that it be capable of being deflected

2
on the specimen in a dc manner for centering at the focal point of the analyzer. The latter

is required for "crater-edge profiling" [1] . The beam current should also be capable of

being readily measured and adjusted and held reasonably constant over the time required for

a typical profile (5 min to 1 hr)

.

To date, most profiling has been done in "static" vacuum systems. Such a system is

first pumped down with sorption, sputter-ion, and titanium sublimation pumps (TSP)

(sometimes after bakeout for ~8 hr at 250°C) to a base pressure of about 10~10 Torr. Fresh

titanium is then sublimed onto the pumping chamber walls, the ion pump is turned off, and

an inert sputtering gas such as argon is introduced, typically to a pressure of 10~^ to 5

x

10~^ Torr. The fresh titanium keeps the active-gas partial pressure many orders of magnitude below that of the inert sputtering gas. The methane level may rise, however, after a period of 30 min or so to two orders of magnitude below that of the argon, and the pressure

of carbon monoxide will rise to a lesser degree. Their effect on the profiling, in which

usually at least ten atomic layers per minute are being removed, is almost always negligible. The introduction of argon has two main effects on the electron gun. Some of the argon

is ionized by the electron beam within the electron gun^ and while the loss of electrons

from the beam is negligible, the positive ions within the gun cause a perturbation in the

electric fields, requiring a readjustment of the lenses to approximate the original beam.

Some ions are also accelerated towards the filament, sputter cleaning it (and perhaps

changing the electron emission) and, of course, eroding it. If the filament current is

held constant, there will then be a higher temperature and thus higher evaporation at the

eroded region, thereby hastening failure. The filament should therefore be conservatively

operated as much as possible to maintain its lifetime. This means keeping the filament

temperature as low as possible, consistent with adequate beam current. Thus, during the

life of the filament, the filament current should be progressively reduced to attempt to maintain constant temperature at the eroded center. Obviously, it is difficult to prescribe any detailed steps. The user, knowing principles of the mechanism of filament failure, however, can in a gross sense, take broad steps to prolonging filament life. The

condition of the filament can be checked, for example, by measuring the anode current at a given beam energy and filament current with minimum Wehnelt (extractor) bias. The filament

current may then be reduced accordingly.

In dynamic systems, filament sputtering is greatly reduced. In such a system, the

sputtering gas is introduced into the ionizer of the ion gun, and the system is then held

at a pressure several orders of magnitude less than that in the ionizer by the use of a re- strictive aperture in the ion gun. Such guns differ from most of those that have been used

to date in that two lenses (instead of the single lens) in addition to the source lens are

used. The restrictive aperture is conveniently located at the beam crossover after the

first lens. In this case, the inert gas is continuously leaked into the ionizer to

compensate for that pumped by the system pump.

2.2 The Ion Gun

The purpose of the ion gun is, of course, to produce an ion beam usually of inert gas

ions (Ar, Xe, Ne, Kr) of suitable energy and density and of sufficient cross-sectional size

and uniformity to uniformly sputter-etch away (in ideal cases) thin surface films. Most

films studied lie in the range of from a few Angstroms to 1 ym thick. The ion gun should

be capable of producing ion-beam current densities of several hundred microamps per square

centimeter, and the energy range of the ions should be controllable from a few hundred to a few thousand electronvolts . At the higher energies and current densities, the sputtering

rate for most materials lies in the range of from 10 to 50 nm/min. Thus, the sputtering

time for a 1 ym thick film is 100 to 20 min. The factors determining the choice of energy

and rate are discussed in later sections.

Most of the ion guns used to date in conjunction with Auger spectrometers have had

purely electrostatic ionization regions in which the ionization has been created by electrons accelerated to about 200 eV frcrni a hot filament. A suitable extraction region, often

gridded, helps form a beam which is subsequently focused and deflected electrostatically.

In guns of this type, an optimum pressure in the ionization region lies between 10~5 and

10-4 Torr. As mentioned earlier, in "static" systems, the whole system is brought to this

pressure after turning off the ion pump. All of the experience reported here is in"

3
systems of this type. The operational difference between this and the differentially

pumped ion gun arrangement would be expected to be in the lower residual gas level in the

latter case and, as mentioned previously, the improvement in filament life. The deflection

plates are necessary to bring the center of the ion beam to the focal point of the analyzer, at which point the electron beam is directed. Poor positioning results in poor

depth resolution. Rastering should also be provided on the deflection plates. This serves two functions:

(1) It provides a flatter crater bottom by smearing out the small variations in

intensity created near the beam center by both nonuniform ionization and, in some cases, the inadvertent "imaging" of the transverse extraction grid (in

guns with such a grid) . The falloff diameter is also extended by the rastering, thereby providing flatness over a wider area. This is of particular

importance when it is necessary to also raster the electron beam because of

electron beam damage effects.

(2) It provides a convenient control over the ion beam current density. It is

useful to be able to reduce the beam current density to a predetermined level

by increasing the raster a chosen amount as an interface is approached. This

enables more data points or improved signal-to-noise to be obtained in the

vicinity of the interface.

2 . 3 The Specimen Holder

Carousel specimen holders have been extensively used in depth profiling. One station

of the carousel should contain a Faraday cup with which a number of important measurements

and setup procedures can be carried out. The specimens should be held firmly to the holder

or tray using suitable springs.

From observation of the aperture of the Faraday cup using the electron beam raster, it

is possible to first bring one side of the periphery of the aperture to the focal point of

the analyzer. This is done by reducing the raster to zero, setting the beam energy to 2 keV, and then observing the elastic peak at 2 keV and optimizing it through translation

along the axis such that its intensity is maximized. The raster is then restored and the

Faraday cup translated horizontally, perpendicular to the analyzer axis, until the aperture

is centered at the center of the raster —the focal point of the analyzer. This aperture

can now be used to position the ion beam by maximizing the ion beam current into the cup

using the deflection and focus controls of the ion gun.

From the aperture dimensions (including its thickness) and the angle between the aperture and the ion beam axis, the ion beam current density (in the axial direction) can be

measured. The sputtering rate for a particular specimen is proportional to this density

and a function of ion beam energy and angle. If the angle between the ion beam and the

specimen surface is increased, the actual current density at the surface is reduced as the

cosecant of the angle. To a certain degree, this reduction in ion beam density is compensated for by a corresponding increase in sputtering rate.

If the ion gun is rastered , the Faraday cup can also be used to measure the ion beam

current density distribution by translating the cup horizontally and vertically and recording the current into the cup as a function of position. For small amounts of movement,

e.g., ±3 mm, the effect of the change in angle subtended by the aperture at the exit of the

gun usually can be neglected.

3. SENSITIVITY AND SPATIAL RESOLUTION

Questions of sensitivity and spatial resolution in AES must be dealt with together

since, for a constant brightness source, an increase in spatial resolution can only be

achieved through a reduction in beam current and therefore a loss in sensitivity for a

4
given data collection time. By spatial resolution, we mean the dimensions parallel to the

surface of the sample; the resolution perpendicular to the specimen's surface is determined

by the escape depth which is discussed in the following section. In order to ensure that

the analysis of this section has the most general applicability, figures for source brightness and signal-to-noise ratio will be taken from currently available commercial equipment.

In addition to the interdependence of these two factors, electron beam-induced damage will

also affect sensitivity and spatial resolution limits. One such effect is electron stimulated desorption of oxygen from SiO^ » which is discussed in more detail in Section 6.3.

In order to discuss sensitivity, we will consider a baseline case with the following

parameters: lock-in amplifier detection system providing an output of d(E- N(E))/dE,

where E is energy and N(E) is the distribution of electrons, 100 yA beam current, 2.4%

analyzer resolution, 30 min data collection time, 10 V peak-to-peak modulation voltage, 50

V scan, and signal averaging using a multichannel analyzer or minicomputer.

In general, the signal-to-noise ratio is given by

^ = A/I¥ l^f' V (1) N \E / ptp

where A is a constant, I is the beam current, (AE/E) is the resolution of the analyzer, t is time, and ^ptp modulation voltage. This assumes that the value of

Ae/E chosen, as well as ^ptp' do not contribute any broadening to the line shape which

limits both ^ptp ^"^^ t° ^ most transitions. Also, the /t dependence can only be realized for random noise and can be significantly affected by any coherent noise

present. Within these assumptions, we will define the maximum AES sensitivity as the con- centration of the element with the strongest Auger transition for which S/N = 1.

Remarkable as it may seem, no measurements of this maximum sensitivity are available.

From extrapolating data taken at much less ideal conditions, a value for the maximum sensitivity of AES of -IQI^ cm~3 can be estimated. This value of maximum sensitivity, however,

does not correspond to all elements, but to the maximum strength AES transitions such as the

Ag MNN transition or the CI LMM transition. Maximum sensitivities for other elements of

interest are listed in Table 1, within ± half order of magnitude. These values are based

on the assumption that there are no interference effects from neighboring transitions.

Table 1

MAXIMUM ESTIMATED AES SENSITIVITIES

Element Sensitivity Comments

B inl8 -3 10 cm Ar interference

C 3 ,^17 -3

X 10 cm background contamination

N 3 ,^17 -3

X 10 cm

0 3 .^17 -3

X 10 cm background contamination

F 3 .^17 -3

X 10 cm

Na ,^18 -3 10 cm beam-induced drift

Al 3 ,^17 -3

X 10 cm Si interference

Si 3 ,^17 -3

X 10 cm

P 3 ,^17 -3

X 10 cm Si interference

CI

,^17 -3 10 cm Ar interference

As 3 .^18 -3

X 10 cm

Sb -,^17 -3 10 cm

5
To obtain these sensitivities within a 30-inin data collection time, a 100 yA beam

current would be required. Presently, typical guns with LaBg emitters can provide this beam

current with a minimum spot size of less than 10 pm in diameter. This corresponds to a current density of 100 A/cm^ , a power density of 5 x 10^ W/cm^ , and a total power dissipation of ~l/2 W. These levels are sufficient to cause local melting of silicon under typical

conditions. To bring beam effects to acceptable levels under these conditions, rastering

the electron beam over a 100 x 100 to 200 x 200 ym area is required. Typical values for

beam diameter versus beam current are shown in Fig. 1 as the solid curve; the dashed curve

is the maximum current versus beam size to ensure that no significant damage is occurring in

Si. In Fig. 2, the variation of maximum sensitivity of AES as a function of beam diameter

is presented. The solid curve is for Si; the two dashed curves represent the limit in Si02

for beam energies of 4.5 keV with the indicated amounts of elemental silicon present in the

spectrum due to electron stimulated desorption. It should be stressed at this point that

much instrumentation exists in the field today that does not possess the capabilities mentioned above. For example, instruments with beam currents of 10 yA, 0.3% analyzer resolutions, and without minicomputer facilities, are common. In this case, a factor of 10

degradation in sensitivity is probable.

Fig. 1. Typical beam diameter versus beam current with LaBg

emitter--solid curve. Dashed segment corresponds to the approximate increase in beam size necessary to keep the local sample

temperature down to reasonable levels in silicon.

4. ELECTRON ESCAPE DEPTH BROADENING

4 . 1 Introduction

Auger electrons lose energy via several scattering mechanisms before escaping into vacuum at the specimen surface. If this energy loss is significant, the Auger electron no

longer has an energy characteristic of the element from which it came. The electron escape

depth L is defined as the mean free path between "lossy" scattering events. The majority

of Auger electrons generated within a distance L from the surface escape without significant energy loss. In an Auger sputter profiling (ASP) experiment, the measured elemental

signal strength represents an average concentration in the surface region of thickness ~L. Thus, the depth resolution of ASP is limited by the escape depth.

6
BEAM SIZE (/im)

Fig. 2. Maximum sensitivity of AES (to chlorine or silver transitions) as a function of electron beam

diameter. Solid curve derived from Fig. 1. Dashed

curves correspond to the degradation in sensitivity

in Si02 due to electron stimulated desorption esd.

The 10% and 1% Si curves correspond to beam size and

sensitivity such that the spectra will contain 10%

or 1% contribution from elemental silicon due to esd.

Electron escape depth broadening is examined in the following sections. In Section

4.2, the energy and substrate dependence of L is briefly discussed. In Section 4.3, we derive a simple formula which allows for the deconvolution of electron escape depth broadening from the measured profile. An appropriate deconvolution formula for a cylindrical

mirror analyzer (CMA) detector is derived in Section 4.4, and some experimental results are presented as examples. The effects of surface roughness and experimental nonlinearities

are examined in Section 4.5.

4 . 2 The Electron Mean Free Path

Extensive theoretical and experimental investigations of the electron mean free path

have been performed; these have been reviewed by Powell [2] . Theoretical calculations [3] relate the electron escape depth L to the inelastic scattering mean free path, as men- tioned in the Introduction. Experimentally [2] , L is often determined by depositing a thin layer of material onto a substrate and monitoring the decreased Auger signal strength

from the substrate atoms. The signal strength varies exponentially as e-x/L with the

thickness x of the layer, provided that the detector only accepts electrons which are emitted normal to the specimen surface. This exponential dependence is examined in the

next section.

A compilation [4] of experimentally measured electron escape depths for several materials is shown in Fig. 3. Most of the data in this figure lies close to a universal electron escape depth curve which exhibits a minimum at an energy of ~100 eV. Optimum depth

resolution is obtained in an ASP experiment for electron kinetic energies at the escape

depth minimum.

Several elastic and inelastic scattering mechanisms affect the Auger electron. Iso- tropic elastic scattering is usually ignored since as many electrons are scattered into a given direction as are scattered away from it [2] . In a crystalline solid where scattering

is not isotropic, angular variations in the electron escape depth may become apparent [5].

7
10 100 1000 10000

ELECTRON ENERGY ABOVE THE FERMI LEVEL (eV)

Fig. 3. Experimentally observed variations of the electron escape depth as a function of the electron energy. Compiled by Lindau and Spicer [4].

Electron-phonon scattering events are characterized by small energy losses [4] , typically

in the range of 10 to 50 meV , and are therefore negligible. The mean free path is thus

independent of temperature. Electron-electron scattering mechanisms are of prime importance in determining the mean free path. Collective interactions such as bulk and surface

plasmons and exchange and correlation effects need also be considered [6,7].

As the electron energy decreases below 100 eV, the escape depth increases. This is

due, in part, to the fact that electrons lying well below the Fermi level in energy can no

longer be excited into an unoccupied state. Beyond 100 eV, the escape depth increases as the collision cross section of the electron decreases.

4 . 3 A Deconvolution Formula

The concentration of an element in an interfacial region may vary dramatically over distances of a few monolayers (~1 nm) . An ASP depth profile of this interface will, of course, be broadened by the electron escape depth effect. In this section, we derive a simple deconvolution formula [8,9] which corrects for this broadening effect.

8
We mentioned in the last section that the Auger intensity varies exponentially with

the depth of Auger emission. The exponential variation is based on the premise that a layer

of thickness Ax has a probability (Ax/L) of scattering the Auger electron. The probability of an Auger electron traveling a distance, x through x/Ax layers is then

(2)

-x/L

If Ax << L, Eq. (2) reduces to e .In most cases of practical interest, the exponential is a good approximation. However, in some cases of experimental interest, Ax may be

the thickness of a monolayer and could then be a sizable fraction of L. In such a case, an approach similar to that leading to Eq. (2) is necessary. Gallon [10] describes such an approach.

We now define x to be a variable representing the position of the surface after some amount of sputtering in an ASP experiment, f (x) , the actual profile which we hope to determine, and A(x), the measured Auger depth profile. We assume, for the moment, that the

surface region is uniformly excited by the electron beam, i.e., the probability of creating

an Auger electron does not vary with depth. This is generally a valid assumption since the

high energy electrons used to stimulate Auger emission have larger mean free paths than the

escape depth L of interest. Nonuniformity could be introduced by the backscattering effect, but we will defer consideration of this until Section 4.4. We also assume .that the

detected Auger electrons are emitted normal to the surface. We may express A(x) as a weighted sum of the actual concentration f{x) with the exponential probability of escape:

f (X + x" ) e~^ '^'^ dx" . (3) 0

Note that, if f(x) is a flat profile, A(x) = f (x) ^ f^.

If Eq. (3) is integrated by parts, the desired deconvolution formula is immediately

obtained

:

f (x) = A(x) - L ^^r^ . (4) dx

Thus, the actual concentration profile can be determined simply by differentiating the measured profile, multiplying by L, and subtracting the product from the measured profile.

It is most instructive to examine the derivation of Eq. (4) from first principles.

Suppose then that a layer of material Ax is sputtered away. The change in signal flux

AA(x) has two components. The first component is the number of Auger electrons scattered

by the layer Ax, which is proportional to the flux A(x) and the probability of scattering

(Ax/L) . The second component is the number of Auger electrons produced in the layer of

thickness Ax, which is proportional to f (x) Ax. We may write

AA(x) = ^mI^y) ~ ("^onst) f(x) Ax . (5)

For a flat profile, A(x) = f (x) = fg and Aa(x) = 0; thus, the constant must be 1/L. We rewrite Eq. (4) as follows:

AA(x) ^ A(x) - f (x) Ax L

If we let Ax ^ 0, Eq. (6) reduces to Eq. (4).

Example

Consider [11] a step function concentration profile (an abrupt interface) where

9
Applying Eq. (3) , we obtain

f (x) = 0 X < 0

(7) f (x) = 1 X > 0 .

x/L

A(x) = e X < 0

(8) A{x) =1 X > 0 .

f(x) and A(x) are illustrated in Fig. 4. The measured profile is an exponential

which has a width of 2.2 L between the 10% and 90% points.

BROADENING OF A STEP INTERFACE DUE TO

ELECTRON ESCAPE DEPTH

-z. o

bJO

-z. o

o

2.2L

^^0.7L-

-2L -L

DEPTH

Fig. 4. Effect of escape depth broadening on a step function

concentration profile. From Helms et al.[ll].

4.4 Off-Normal Detection

The previous derivation was restricted to normal detection of Auger electrons. If,

instead, these electrons were emitted at an angle 0 to the surface normal, they would

have to travel a distance x ' /cos 9 to emerge from depth x'. Equations (3) and (4) are corrected for this effect by replacing L with L cos 0

:

/oo

f(x + X') e-^'/^ ^ dx- (9)

dA (x

)

f (x) = A(x) - L cos 0 ,

• (10) dx

As mentioned in Section 4.2, L may be a function [5] of 6.

The actual Auger apparatus may accept electrons which are emitted at a variety of

angles 0. In this case, we write

10
g(0) Jq f (X + X-) e"^'/^ %x- d9

A(x) = — . (11)

/ ,a\ -x'/L cos 0 ^ , ^„ Jq g(9) e dx' d0

Here, g (0 ) is the solid angle of acceptance for the detector. If we define

G(x') =/ f(0) e"^"/^ ^ d0 (12)

we may rewrite Eq. (11) as follows;

/n, f + x') G(x') dxA(x) = . (13)

i^ G (x ' ) dx '

Deconvolution may be performed numerically and is facilitated by approximating G(x') as follows

:

(x-) = X =1

i

-x ' /L cos 9

.

G(x') = / G. e

^ (14)

A useful approximation in some cases is to select an appropriate average value of 0 for use in Eq.. (10) .

One common electron detector used in Auger experiments is the cylindrical mirror analyzer (CMA) . The CMA accepts electrons which are emitted at an angle of 42.3 ± 6 deg about

the CMA axis. If the specimen surface is normal to the CMA axis, an appropriate 9^^g in

Eq. (10) is 42.3 deg ( cos 9^yg — 0.74) . The experiments described below were performed in a Varian 2730 Auger spectrometer in which the specimen normal is 30 deg off the CMA axis.

We have numerically evaluated the response of this system to a step function concentration

profile. The resulting profile has a 10% to 90% width of 1.65 L rather than 2.2 L. We choose 0 such that 2.2 (L cos 0 ) = 1.65 L or cos 0 =0.75.

ave ave ave

Some examples relating to the measurement of the interface between silicon and silicon

dioxide will clarify the deconvolution technique. First, however, we need to find appropriate values for the escape depth L in Si and Si02 . Experimental measurements from two

groups [4,12] are shown in Fig. 5 [13].

Examples

We consider first an MNOS structure in which a layer of Si02 is sandwiched between

Si3N4 and Si. An ASP experiment [14] is performed in which the Ojq^l peak at 502 eV is monitored. The results are shown in Fig. 6. The dashed curve [8] is a niimerical deconvolution accounting for the CMA geometry with L (502 eV) = 1.0 nm from Fig. 5. The points in

the figure represent an application of Eq. (10) with cos 0ave ~ 0.75. In both cases, the

peak concentration of oxygen is increased by ~30%.

Next, we consider the Si-Si02 interface formed by thermal oxidation. The Oj^ll ^^0^ eV) and free Sijj^ (92 eV) peaks are monitored while sputtering through the interfacial

region. (When Si is bonded to O, the LW peak shifts from 92 to 78 eV.) A typical concentration profile [11] is shown in Fig. 7. This same profile is rescaled and drawn in Fig. 8. The dashed curves are the deconvolved profiles and were obtained through the use of Eq. (10)

with cos 0ave ~ 0.75 as before. The oxygen profile is shifted to the right by ~0.8 nm

and its 10% to 90% width changes from 3.8 to 3.3 nm. The silicon profile is shifted -0.4

nm, and its 10% to 90% width is reduced from 2.2 to 2.1 nm. The distance between the 50%

points of the oxygen and silicon profiles is reduced from 1.2 to 0.7 nm. This 0.7 nm difference is accounted for by the presence of an SiOj^ phase in the interfacial region [15]

.

11
Fig. 5. Electron escape depths for Si and Si02 as a function of

electron energy. Data of Lindau and Spicer [4] (A) and Flitsch

and Raider [12] (A) are shown.

Fig. 6. Auger depth profile of the oxygen concentration in an MNOS sample (solid line) . Numerical

escape depth deconvolution (dashed line) and application of Eq. (10) (points) are shown. From Schwarz

et al. [8]

.

12
8

00

o

ft

Si

85.0 90.0 95.0 lOOO 105.0 DEPTH (nm)

Fig. 7. Auger sputter profile of thermally grown

Si-SiO interface. From Helms et al. [11]

.

DEPTH (nm)

Fig. 8. An Auger sputter profile of the SiSi02 interface (solid lines) is deconvolved

through the use of Eq. (10) in the text (dashed

lines)

.

13
It is interesting to note that, if the value for L (502 eV) used in Eq. (10) is too

large, the deconvolved oxygen profile will initially rise above the bulk level before dropping to zero. Thus, the deconvolution technique provides an estimate of the upper limit of

the value of L.

4 . 5 Surface Roughness and Experimental Nonlinearities

Surface roughness has an obvious broadening effect on the Auger depth profile. In some

cases, surface roughness may be induced by the ion beam [16]. In this section, we examine

the electron escape depth broadening of a "linear" interface. The solution to this problem

will indicate how surface or interface roughness and sputtering nonuniformities affect the

measured profile. We will also investigate the effect of electron backscattering on the

deconvolution technique.

Consider a specimen in which the concentration of an element is constant for some distance and then decreases linearly to zero over a distance Ax. This situation is illustrated in Fig. 9a. The measured profile is characterized by its width Ay^^ and its position Ay2. Here, we define Ay-j^ as the 10% to 90% width and

Ay2 as the distance of the measured 50% point from the actual

50% concentration position in the specimen. A straightforward

calculation using Eq. (3) leads to the results shown in Fig.

10. When Ax < L, Ayj^ ~ 2.2 L, as noted previously. The

Ay2 curve illustrates that the measured profile is shifted

toward the specimen surface by a distance of ~L in all cases. This effect was observed in the previous example.

a. A linear interface

These results apply to all of the situations illustrated

in Fig. 9. For example, suppose the electron beam is not positioned in the center of the sputtered crater, but is insteai

located on a sloping portion of the crater edge. The Auger

electrons will exit through a surface which is not parallel

to the interface. Assume the interface is abrupt as in Fig.

9b. Over the width of the electron beam, the distance of the

surface from the interface varies by an amount Ax. The results of Fig. 10 apply. Surface and interface roughness of

order Ax are shown in Figs. 9c and 9d. Note that this

roughness is symmetrical.

Examples

In the crater-edge profiling technique [1], a 5.0 nm depth profile is typically obtained by sweeping the electron

beam over a lateral distance of 2 mm. The diameter of the

electron beam may be 100 ym. Thus, we have

5 nm _ Ax

2 mm ~ 100 ym '

Ax = 0.25 nm, Ax/L ~ 0.5, and from Fig. 10 we see that very

little broadening is induced.

Next, we again consider the Si-Si02 interface profile

of Fig. 8. We saw there that the measured oxygen profile

had a 10% to 90% width of 3.8 nm. After deconvolution, this width was reduced to 3.3 nm and

the curve was shifted 0.8 nm. As an approximation, we may use Fig. 10 with L = (0.75) 1.0 nm = 0.75 nm. Ay^^/L = 3.8/0.75 = 5.1. This corresponds to Ax/L ^6.0 or Ax = 4.5 nm. The original 10% to 90% width is (0.8) 4.5 nm = 3.6 nm. The shift corresponding to this Ax

is Ay2/L - 0.8 or Ay2 = 0.6 nm.

Finally, we consider the effect of backscattering on the deconvolution technique. A certain fraction of the electron beam is backscattered by nuclei in the specimen and

14

d

AX

b. A sloping surface

c. Surface roughness

WWW.'ax

d. Interface roughness

Fig. 9. Four situations

yielding equivalent measured profiles.
6

Ax/L

Fig. 10. The 10% to 90% width Ay^^ and 50% position

shift Ay^ as a function of the roughness parameter Ax.

redirected toward the surface where further Auger excitation can occur. In a homogeneous

medium, backscattering does not affect the assumption of uniform excitation in the surface

region. Backscattering coefficients differ from material to material. Smith and Gallon

[17] show that the fraction of backscattered electrons increases with the electron energy

and the mass of the nuclei. Thus, as one approaches an interface between two dissimilar

materials, the backscattered component of the Auger signal will change, thereby affecting

the measured profile. One can account for this by inserting an excitation function B(E,x)

into Eq. (3)

:

oo If -x'/L COS 6 A(x) =71 f{x + x') B(E,x) e ^ dx ' . (15)

It is also possible to account for electron beam attenuation or ion stimulated Auger in the

excitation function. In this case, B is also a function of x'. Numerical deconvolution

is again called for.

5. ION BOMBARDMENT EFFECTS

5 . 1 Introduction

In the previous chapter, we discussed a broadening mechanism inherent in the Auger

detection process —the electron escape depth. We now turn our attention to a broadening

mechanism inherent in the sputtering process—ion knock-on mixing.

Ions incident on a specimen surface create an atomic collision cascade in the bulk of

the material. Some atoms in this cascade reach the surface and escape. The other atoms

are displaced from their original position, resulting in a broadening of the measured depth

profile. This process is illustrated in Fig. 11.

15
SPUTTERING

MIXING

Fig. 11. Schematic illustration of the sputtering and mixing

processes resulting from ion bombardment.

In this chapter, we will present elementary models of the sputtering [18] and mixing

[19] processes. These models lead to simple formulas, allowing us to estimate the extent of

sputtering and broadening as a function of the ion type, energy, and angle for a particular

target material. We begin by developing a standard billiard-ball picture of atomic interactions in Section 5.2. The approach here is intuitive rather than rigorous so as to lend

understanding to the models. In Section 5.3, the sputtering model is presented and compared

to previous experimental and theoretical work. In Section 5.4, the ion knock-on mixing

model is developed and compared to recent experimental data from ASP experiments and to other experiments and theory in the literature.

5 . 2 Atomic Interactions

5.2.1 Introduction

A bombarding ion imparts most of its energy to nuclei and electrons in the

specimen. Subsequently, this energy is transferred to phonons , raising the specimen temperature, and to other forms of radiation: x-rays, Auger electrons, etc. In Section 5.2.2, we examine the nuclear energy loss which is of prime importance in determining the movements of

atoms and the resulting lattice damage. We present a standard billiard-ball model [20,21]

of nuclear collisions which is commonly used to predict the range of the incident ion, i.e.,

the total path length travelled by the ion. In Section 5.2.3, we briefly examine the Firsov

model [21,22] of electronic energy loss. We then conclude with a discussion of the KinchinPease formula [23,24] which predicts the number of atomic displacements caused by the ion.

5.2.2 Nuclear Energy Loss

The nuclear energy loss process has been extensively studied in the last 50

years. Many models of varying sophistication have been developed; they have been reviewed

by Carter and Colligon [20] . In the last decade, these models have been put to very practical use in the development of ion implantation [21]

.

Figure 12a is a schematic illustration of a nuclear collision in which a particle of mass M-j^ approaches and deflects an initially stationary particle These particles exert a mutual coulombic force on each other at all times. This force is, of course, greatest when the particles are closest together. At distances greater than 0.1 nm, the nu- clei are effectively screened by their surrounding electrons, and the mutual force drops off

quite rapidly with distance. The effective time of interaction then is actually quite

short. Hence, nuclear collisions may be effectively modeled by instantaneous two-body

collisions governed by conservation of momentum and energy. This classical billiard-ball

model breaks down at very low energies [20] (<~10 eV) , where many-body collisions occur and

at high energies [20,25] (>~1 MeV) , where quantum mechanical diffraction effects arise.

16
(a) (b)

Fig. 12. (a) A particle of mass approaches and deflects an initially stationary particle (b) These particles are modeled as billiard balls with adjustable radii. From Carter and

Colligon [20]

.

The energy transfer and angular deflection in the collision illustrated in Fig.

12a are functions of the energy of particle 1. At low energies, the particle moves slowly,

the interaction time is relatively long, and the transferred impulse (force-time product) is

large. Thus, large angle scattering is expected. At high energies, the transferred impulse

is smaller and the scattering angle decreases. This energy dependence is accounted for by

allowing the radii of the hard sphere analogs in Fig. 12b to vary with energy. Specifically,

the diameter of the sphere is defined as the distance of closest approach in a head-on collision between the two particles. The diameter is, therefore, dependent on energy and on the strength of the interatomic potential.

The distance of closest approach in a head-on collision is calculated as follows. Suppose particle 1 with mass fi-^ and energy Eq approaches a stationary particle of mass M2 . In the center-of-mass system (CM), the particles approach each other so that the

net momentum is zero and the net energy [20] is

CM ^1 + ^

(16)

At the distance of closest approach, rQ , the kinetic energy in the CM system is

completely converted to potential energy, i.e., the velocity of both particles drops to zero. Thus, we may write

V(r^) = E^^ (17)

where V(r) is the interatomic potential.

V(r) may be expressed as a screened coulomb potential [20,21] as follows:

Z Z e^

V(r) = f(-) (18)

^ \a/ 4TTe^r

where Zi and Z2 are the atomic numbers of the two nuclei, e is the unit change, f (r/a)

is a screening function, and a is a screening length. For a single atom, the Thomas-Fermi

screening length [26] is 0.885 ag/zV^ where ao is the Bohr radius (0.0529 niii) • For

two interacting atoms, the Thomas-Fermi screening parameter is an rms sum [20,2ll:
a a = 0.885 ^

. (19)

Many screening functions f (r/a) are found in the literature [20]. One of

these, f(r/a) = a/r, is commonly used as it leads to a simple formula for the ion range.

If this is substituted into Eq. (18) , an inverse square potential is obtained:

^1

V(r) <^ — = -Y (20)

2 I 2/3 2/3 r

' >1 " ^2 From Eqs. (17) and (20) , we obtain

^1 ^ - (21)

2 M + 0 ^0 1

2

A most important quantity, both in this development and in the ion knock-on mixing model, is the mean free path between collisions i. According to the kinetic theory of

gases [27], i is equal to the reciprocal of the product of the density of particles n and

their interaction cross section "^^q- From Eq. (21) , we have

112M

2 " mfH7 mTTmT ^0 • ^^^^

n-rTr^ 112

The probability of a collision after a particle has traveled a distance Ax is Ax/£ (as

in the electron escape depth case of Chapter 4)

.

The maximum kinetic energy which can be transferred from a particle of mass

and energy E^ to a stationary particle of mass is YEq/ where

2

• (M^ + M^)

(23)

For random scattering (isotropic scattering in the CM system) , the average energy transfer

in a collision [20] is (1/2) YE^.

In order to determine the ion range, we need to examine one further quantity,

the stopping power (dE/dx) j^^^-,]^ , i.e., the energy loss per unit distance. This is usually

calculated [20,21] by integrating a probable energy transfer over the scattering cross sec- tion O as follows

(il)

" " /T(a) da . (24)

nucl

We will make a quick estimate for (dE/dx) i^m-.l > however, which leads to the proper result

for the inverse square potential. We estimate the probable energy loss Ae in a length Ax

by the average energy loss per collision (1/2) yEg multiplied by the probability of colliding Ax/Ji. This yields, with the use of Eq. (22),

(^) - IB _ .,3^ \dx/ , 21 2M^ ^

' nucl 2

Equation (24) yields the same result. Note that, since £ <^ Eq , (dE/dx) j^^^,]^ is independent of energy. This allows us to determine the ion range R as follows:

18
R = 2M^E

2 0

where

k =

(i)

niTC^Y (M^ + ) nucl

= 2kE,

,„2/3 2/3 , 0.0018 J^l ^ ^2 /^ ^ ^2

^1^2

(26)

nm eV

-1

(27)

As expected, the range decreases when the atomic sizes Z or density

parameter k plays an important role in the following sections.

increases

.

The

Finally, it is necessary to consider the limitations of our choice of screening

function f (r/a) = a/r. When r < a at high energies, f (r/a) > 1 which is, of course, impossible. For r < a, then it is useful to let f (r/a) = 1 and assume coulombic scattering. The foirm f (r/a) = a/r is also inaccurate for large r, i.e., at low energies.

This is because, for E < 100 eV, the mean free path % predicted by Eq. (22) is less than

the nearest neighbor distance d in the material. Below this energy, then, it is reasonable to let £ remain constant and equal to d.

3.0

In Fig. 13, (dE/dx) j^^^j^ is plotted in terms of normalized parameters as a function of energy [20,28]. The constant (dE/dx)nucl of Eq. (25) is shown as a horizontal

dashed line labeled S^O) . The dash-dot line labeled represents the electronic stopping power (dE/dx)ex which will be discussed in the next subsection. The solid curve is

calculated numerically using a Thomas-Fermi

screening function. The behavior of this

curve can .be illustrated by making estimates

of (dE/dx)nucl low and high energies as we did in Eq. (25), i.e., (dE/dx) ^j^^-j^ ~

YEq/2J,. At low energies, we let £ = d and

thus (dE/dx)nucl °^ Eq. At high energies,

V(ro) = C2/ro = Eq[^ leads, from Eq. (22) , to 2- Eq and then, from Eq. (25) , (dE/dx) j^m;]^ ^ 1/E. The E+1 dependence at low energies and E"-^ dependence at high

energies indeed describes the behavior observed in Fig. 13. We emphasize, though,

that these estimates do not yield identical

results to Eq. (24) .

IDO

I

2.0

cco

UJo 1.0

Z)Q

ILI

//

y y ^

r 1 1 1 1 1 1 1 1

1 0 0.2 0.4 0,6 0.8

REDUCED ENERGY (e)

1.0

0 12 3 4

REDUCED ENERGY^'2(e"2)

Fig. 13. Reduced stopping power as a function of reduced energy for the

Thomas-Fermi potential (solid line)

,

the inverse square potential (dashed

line) , and for electronic energy loss

(dash-dot line) . Parameters are defined

in the text. (yiz. Refs. 20 and 28).

UJO

z

<Q

UJO

Q

UJ

300

200

100

50

20

105

// / / / / / / / / / / / / / / / //

//

//

//

/A 1 III ill 1 0.5 1 2 5 10 20 50 200

REDUCED ENERGY (€)

1000

Fig. 14. Reduced range versus reduced energy for the Thomas-Fermi

potential (solid line) and the in- verse square potential (dashed line)

Parameters are defined in the text.

(Viz. Refs. 20, 28, and 29.)

19
In Fig. 14, the simple range equation, Eq. (26), is compared to the Thomas-Fermi

range calculation [20,28,29]. We see that Eq. (26) is a good first approximation to the

Thomas-Fermi theory. At low energies, Eq. (26) overestimates the range somewhat while, at high energies, it significantly underestimates the range.

The reduced parameters in Figs. 13 and 14 are defined as follows:

aM

^ = ^0 • 2 (28)

Z^Z^e (M^ + M^)

2 p = R • irnYa • (29)

When £ > 5 in Fig. 14, the inverse square approximation becomes inaccurate. For Si incident on Si, this occurs at an energy of ~50 keV. For Au incident on Au, this energy is ~1

MeV.

5.2.3 Electronic Energy Loss

The theory of electronic energy loss is complex and need not be discussed here

in detail. Lindhard and Winther [30] have shown that, over the energy range of interest

here, (dE/dx) , is proportional to the velocity of the ion:

el

(i) = k'E^^^ . (30)

el

In the Firsov model [21,22] of electronic stopping, the constant k' is given by [21]

-1/2 -1 1/2

k' = 3.28(Z^ + Z^) n nm eV • (31)

The electronic energy loss is illustrated in Fig. 13 by the dash-dot line. At

high energies, this is seen to be the dominant energy loss mechanism and therefore must be

taken into account in a range calculation. This is done as follows:

0 dE

nucl el (i)

(32)

From Eqs. (25) and (27), (dE/dx) , = l/2k so that

nucl

2e1/2

(33)

2k

2 3 Using the approximation In (1 + x) = x - x /2 + x /3 . . .

, we get

R = 2]^E^(l - J

kk'E^/^) . (34)

Since (dE/dx) nucl is independent of energy, we know that the total energy lost in nuclear

collisions E is given by R = 2kE . Thus, we may rewrite Eq. (34) as follows:

N N

If Ej^/Eq < 1/2, it is best to use Eq. (33). These approximations will prove most useful

in the sputtering model.

20
5.2.4 Atomic Displacements

The number of atomic displacements N induced by the incident ion is predicted

by the Kinchin-Pease formula [23,24] as follows:

N = — (36)

where is the nuclear energy loss of the ion and is the energy required to displace

an atom from its lattice position. The assumption here is that, after N displacements

have occurred, there are E^/2E^ atoms traveling through the lattice with average energy

2E(j. No further displacements can then occur, since one of the collision partners would

have an energy less than E^.

The choice of an appropriate is somewhat controversial [20] . We have chosen

an approach similar to Seitz [31] where we set

E, = 4Ah . (37) d a

Here, AH^ is the heat of atomization per atom. For example, E^ is 15.2 eV for Si. This

value is commonly used [24,32]. The factor of 4 comes from two considerations. First, AH^

accounts for the energies of half of each broken bond since these bonds are shared by neighboring atoms; hence, a factor of 2. Secondly, the lattice does not have time to relax. The

relaxation energy is assumed to account for a further factor of 2. The uncertainty in the

factor of 4 is accounted for in the models discussed in the next section.

5.2.5 Summary

We have shown that, in a useful first approximation, the range R and the mean

free path £ are proportional to the ion energy. The constant of proportionality contains

a charge term derived from a screened coulomb potential and a mass term derived from momentum conservation. At very low energies, £ is approximated by the nearest neigbor distance

d. We have also seen that the electronic energy loss becomes significant at higher

energies. A corrected range value and the nuclear energy loss E^ can then be easily

determined.

Finally, we have seen that the number of atomic displacements caused by the

incident ion is proportional to the nuclear energy loss Ej^ and inversely proportional to

the bonding energy 4t\Hg^. All of these observations will prove useful in the following

sections

.

5 . 3 A Geometrical Model of Sputtering

5.3.1 Introduction

The field of sputtering has been thoroughly reviewed by several authors [20,33].

Many models of the sputtering process have been proposed and can, in general, be classed

into two categories. First are the simple or empirical models which usually are valid over

a limited range of ion energy and contain adjustable parameters. Second are the more so- phisticated models, requiring computer calculations which may involve Monte Carlo techniques

or sets of integro-differential equations.

We have developed an elementary model of sputtering based on geometrical considerations which leads to a simple sputtering yield equation. The equation is valid over a broad range of ion energies (roughly 0.1 to 100 keV) and also accounts for the yield variation with the incident angle of the ion. For applicable materials, the accuracy of the

equation is on a par with any of the other existing models.

21
In this section, we present a complete discussion of the sputtering model. The

model is developed in Section 5.3.2, and necessary computations are performed in Section

5.3.3. Experimental comparisons are presented in Section 5.3.4. In Section 5.3.5, we discuss the assumptions and limitations of the model.

5.3.2 Development

In the sputtering process [20,33], an energetic ion incident on the target sur- face creates an atomic collision cascade in the bulk of the material. Some atoms in this

cascade will reach the surface and escape. The sputtering yield S is defined as the number of atoms ejected per incident ion.

In order to model the sputtering process, it is useful to examine the region in

which the collisions occur. We define a statistical region in which the atomic displacements are probable. At low ion energies, where the ion gives up most of its energy near the

point of impact, the shape of this region is spherical. This does not suggest that the ac- tual damage cluster has a spherical shape; rather, it implies that the probability of displacing an atom depends only on the distance of that atom from the point of impact.

The intersection of the statistical region with the target surface defines an affected surface area. The major assumption of our model is that the sputtering yield is

proportional to this area. This assumption is supported by the experimental observation

[20,33] that, irrespective of the ion energy, most sputtered atoms have enerqies of -10 eV

and are emitted from a depth of a nanometer or so. Monte Carlo calculations [32] bear this

out also.

We now define two parameters, A and B, which will be discussed in detail

later on. A is the fraction of atoms in the statistical region which are displaced. B is

the fraction of displaced atoms at the surface that actually escape. Thus, we find the volume of the statistical region as follows:

E/2E^

VOL = nA

where n is the density of the material and E/2E^, from the Kinchin-Pease fonnula Eq.

(36) , is the number of displacements caused by the ion. (Henceforth, E refers specifically to the nuclear energy loss ^j^*'

The sputtering yield S is given by

2/3

S = B(An) • AREA . (39)

2 /3

Here, (An) is the number of displaced atoms per unit surface area, and the AREA is, of course, defined by the intersection of the statistical region with the surface.

We might expect the affected area to be related to the volume as follows:

2/3

AREA = f (E) • (VOL) . (40)

We would then have, from Eqs. (38) and (39),

,2/3

f(E) . (41)

d^'

In fact, we will obtain an equation of this form.

As a first example, suppose that the disturbed region is spherical with a radius

r and centered at a depth X below the surface (A. < r) . The area defined by the intersection of the sphere with the surface is easily shown to be

22
From Eq. (38) , we know that

2 / . AREA = TTr (1 - —) . (42)

4 3 ^/2E

If we assume X << r, we readily find from Eq. (39) that

2/3 Thus, at very low energies, we might expect the yield to vary as E and inversely as the

bonding energy E^/^.

d

Note that, for X = 0, the shape of the statistical region is hemispherical.

Equation (43) for the full sphere is still used, however. Half the incident ion energy is

assumed to be carried off by the sputtered atoms. We will elaborate on this argument later.

It is also important to note that the surface atoms are acted upon from one side only, i.e.,

from the interior of the specimen. Thus, we might expect the value of B to be 0.5 if all

displaced surface atoms escape and B ~ 1 if contributions from deeper layers are included.

In fact, we will show that B ~ 0.2 in most materials. Finally, we observe that the parameter A does not appear in Eq. (44).

We know that the incident ion does not release its energy immediately upon

impact; rather, the ion travels some distance into the target, releasing its energy gradually. Again, we will make use of a statistical quantity k representing the energy loss

rate averaged over many incident ions. Recall that the total ion range is R = 2kE.

We expect the statistical region to be a perturbation of the sphere. The perturbed or elongated sphere is treated most naturally as an ellipsoid with major axis a and

minor axis b as in Fig. 15. The volume of the ellipsoid is (4/3)7rab^ and from Eq. (38) we have

The area defined by the intersection of the ellipsoid centered at depth X with the surface

is (for normal ion incidence)

2/ X^' AREA = TTb (1 J

I . (46)

Fig. 15. Definition of ellipsoid parameters and cross-sectional areas.

23
The ellipsoid is centered about the path of the ion, which suggests that we let X equal

half the ion range:

X = kE . (47)

We now define the length of the ellipsoid as a perturbation of the sphere, so that

a = r + X • (48)

where r is defined in Eq. (44) and X is half the range. We also assume that the damage

volume is the same so that

ab^ = r^ . (49)

At low energies, when X << r, a ~ r and the statistical region is a hemisphere as before.

At high energies, a~X, and the length of the ellipsoid is nearly equal to the ion range.*

It is again important to recognize that the ellipsoid is a statistical construct

which allows us to predict the degree to which the surface is excited. The actual path of

the ion is not a straight line into the solid, and the damage cluster formed by the ion will

not resemble an ellipsoid. The true path of the ion is irrelevant to the sputtering process, however, so long as it does not return to the surface. (This is unlikely at near nomal incidence.) Thus, for computational purposes, we treat the ion as though it travels

a straight line path.

Substituting Eqs . (48) and (49) into Eq. (46), we obtain

In this form, refinements to X or r (i.e., to the range estimate or the Kinchin-Pease

formula) can be incorporated.

Substituting for r and X from Eqs. (44) , (47) , and (45) , we obtain

S = B|^^^ —11-1 - ... I I (51)

where

1/3

B = k(| TTE^An) . (52)

Note that this is in the form of Eq. (41)

.

If the ion is incident at an angle 0 to the surface normal, as in Fig. 15, the

AREA of Eq. (46) becomes

\ a cos 6 + b sin 0/ \ /

This leads to an equation similar to Eq. (51) , which we present in the next subsection.

Another way to define the length of the ellipsoid is to set the distance between foci equal

to the ion range. In this case,

a - b = X This assumption considerably complicates the resulting equations, but it could be used in

a computer calculation.

24
5.3.3 Computation

We note in Eq. (51) that the parameter A appears only in the expression for

B, and there it is raised to the 1/3 power. Thus, the equation is relatively insensitive

to variations of A. We have found that, in all of our comparisons to this experiment, good

results are obtained with A = 0.0012 (a1/3 ^ 0.1). We will discuss this parameter further

in the next subsection. If we let A = 0.0012, we have

B = 0.343 k(nAH )'^^^ eV~^^^ . (54)

The definitions of k , k ' , Ah , and E (the nuclear energy loss) are found in Section 5.2.

a If we define

Eq. (51) can be rewritten as

X = TTT , (55)

1 + Be^

S = 0.302 ^ X(l - X^) . (56)

B(AH

a

In the case where 9 5^ 0, we let

2 (be^/^) (i.BE^/^)

X = . (57)

2 . / „ 2/3\ 2 „ ;in 0 + II + Be I cos

Then,

S = 0.302

^ X(l - X^ cos^ 6) . (58)

B(AH

a

When 9=0, Eqs. (57) and (58) reduce to Eqs. (55) and (56)

The maximum sput

From Eq. (58) , this leads to The maximum sputtering yield S occurs at an energy E for which dS/dX=0.

max

X = . (59) max ^ cos o

In particular, when 9=0, Eq. (59) leads to

-3/2

E = 1.60B eV . (60) max

The variation of the sputtering yield at normal incidence as a function of

energy is illustrated pictorially in Fig. 16. The normalized yield S [B (37T-'-/2/8e^) ] ~1 is

plotted in Fig. 17 as a function of the nuclear energy loss for several values of B.

5.3.4 Experimental Comparisons

We used Sigmund's [33] compilation of experimental data to test the sputtering

model. Figure 18 illustrates the application of Eq. (56) to silver with B = 0.30. The

figure shows experimental data points and the low and high energy theoretical curves of

Sigmund [33] (dashed lines) . The heavy solid lines are calculated from our model and agree

well with the experiment. Comparisons were also made for Si, Ge, Cd, Zn, Pd, Cu, and Au from Sigmund's paper. In each case, good results were obtained with A = 0.0012. Values of. the surface factor B which best fit the data are listed in Table 2. 25
Fig. 16. Illustration of the sputtering yield variation

with ion energy.

NUCLEAR ENERGY LOSS (keV)

Fig. 17. The relative sputtering yield is plotted as a func

tion of the nuclear energy loss E for several values of 3

26
T TTT 1 1 r-T?

a WEHNER et al O ALMEN 9t al. • GUSEVA

o ALMEN et al.

Xe-^-»- Ag

E (keV)

(a) 30

I p-i-n 1 r-r a WEHNER et al 25 - O ALMEN et al. • GUSEVA

20 - A KEYWELL

PEROVIC et al 15-0 PERT et al.

o ALMEN et al. 10 - /

n

.—t-i->—

r

Ar' —»• Ag

30

—I

T—1 1 1 r—1—n 1 r 1

1 1 . 1

D WEHNER et al. 25 O ALMEN et al. • GUSEVA

20 A KEYWELL £^ N

\

15 - \

10 Kr*—^Ag

5

OC J—LJ 1 1 1 LJ 1 1 III 1 1 1 t t 10' 10'11 E (keV)

(b) 30

25

20

15

10

5

0

10

I I I I 1

1—r-n- D WEHNER et al. - O ALMEN et al. A KEYWELL

~I I m I

I I I I

Ne* Ag

rgA^ o 8 Rqo ^ ^ ^

I I I I I LJJ I II'

10' E (keV)

(d)

10

Fig. 18. Sputtering yields of Ag versus ion energy for (a) Xe , (b) Kr , (c) Ar , and (d) Ne+ ions at normal incidence. Data compilation from Sigmund [l9]. Solid curves result from the present model. Sigmund 's theoretical curves (dashed) are also shown.

Table 2

VALUES OF SURFACE

FACTOR B

Element B

Si 0 . 10 Ge 0 . 14 Cu 0 . 18 Zp 0 .27 Pd 0 .23 Ag 0 .30

Cd 0 . 36 Au 0 .45

Surface factors

derived from Sigmund 's data compilation [33].

The surface factor B can be determined from the

work of Rosenberg and Wehner [34], who measured the sputtering

yields of many elements under 400 eV Xe"*" bombardment. Note that

3 for Xe+ is typically very small due to the short range, i.e. , small value of k. Reference to Fig. 17 indicates that, at 400

eV, the relative sputtering yield is nearly independent of the

substrate. For 400 eV Xe"*", Eq. (59) reduces to

B

(Ah ) a 2/3

(61)

Thus, B

(AH,) 2/3.

is determined by multiplying the measured yield by

It is interesting to note that previous low energy

sputtering theories [33] contain a l/Ej-, dependence where Ej^ is a surface binding energy bearing a strong relation to AH^.

The values of B/ determined from Rosenberg and Wehner, are plotted in Fig. 19. These values are normalized to B = 0.30

for silver. They agree fairly well with the values obtained in

Table 2. Discrepancies may be due to various second-order effects, such as Xe saturation. Figure 19 illustrates two trends:

a periodic dependence and a mass dependence. Note that Zn and

Cd in Table 2 continue the upward trend observed in the transition metals. In Fig. 20, we have divided B by /vi for the

transition metals and plotted the results in relation to the

periodic table. (In addition to the values derived from Wehner, Zn and Cd from Table 2 are included in the figure.) We will discuss these results further in the next subsection.

27
0.5

0.4

CDP

03

u 0.2 D

in 01

•Au

•Ag

• •

•

•Cu • — •

•

•*

« • •

• •

••

• U*

;

; Ge

•

•.

S'

1 20 AO 60 80

ATOMIC NUMBER -Z

100

Fig. 19. The surface factor B derived from

Rosenberg and Wehner [34] is plotted as a function of atomic number Z.

Sc Ti V Cr Mn Fe Co Ni Cu Zn o o o o o o O o O

Y Zr Nb Mo Te Ru Rh Pd Ag Cd

X X X X X X X X

La Hf Ta W Re Os Ir Ft Au Hg

Fig. 20. The surface factor B is divided by the

square root of the atomic mass and plotted in relation to the periodic table for the transition metals.

28
Support for the Z, or mass dependence, of the sputtering model comes from the

experimental data of EerNisse [35] , who measured the sputtering yield of Au for low fluence

45-keV ion bombardment. Figure 21 shows a comparison of his experimental data with the

prediction of the present model. Reference to Eq. (28) indicates that the model still has

validity for light ion (He"*") bombardment of Au.

Fig. 21. Sputtering yields of Au bombarded by

45-keV ions normalized to Ar"^ yield. Solid curve results from the present model. Points are from

experimental data of EerNisse [35]

.

Next, we consider the angular dependence of the model. Figure 22 demonstrates

pictorially that the angular dependence of the sputtering yield is a function of energy.

Rol et al. [36] observed this effect in polycrystalline Cu. Their experimental results are compared with the sputtering model in Fig. 23. Molchanov et al. [37] observed the yield

variation of polycrystalline Cu with the incident angle for 27-]ceV Ar"*" ions. Their experimental data agrees well with the model, as shown in Fig. 24. At large angles, the ion may

escape from the sample before depositing all of its energy. This probably accounts for the

discrepancy between the model and experiment for 6 > 70°. At 27-keV, the angular dependence is described very well by a 1/cos 9 variation. (The 1/cos 9 dependence is a com- mon approximation [36].) Actually, this is a coincidence. At higher energies, the angular

dependence curve will lie above the 27-keV curve. At low energies, the angular dependence

curve will lie considerably below the 27-keV curve. As an example, for 2-keV Ar"*" bombardment, according to the model, the sputtering yield of Cu never increases by more than 40%.

5.3.5 Discussion

We have seen that the sputtering model just described agrees well with much

experimental data in the literature. It is important now to discuss the assumptions we have made and determine the limits of applicability of the model. At the outset, we note

that the model does not account for any of the following effects:
(1) channeling or focusing,

(2) multicomponent systems,

(3) ion beam flux dependence,

(4) reactive sputtering, and

(5) saturation with the sputtering species.

The model is strictly applicable to an amorphous material. Reasonable results may be

obtained in crystalline materials if the ions are not incident along a channeling direction

Multicomponent systems can sometimes be treated in an approximate way. In the next section

SiO_ is modeled as a lattice of Ne atoms with reasonable success.

Fig. 22. Pictorial representation of the sputtering

yields angular dependence. The normal-to-glancing

incidence ratio of sputtering yields decreases with

energy due to the increasing asymmetry of the disturbed

volume

.

S(0°) 5(50°)

1.0

0-9

0 8

0.7

0,6

0.5

0,4

0, 3

0,2

0, 1

0

COPPER (POLYCRYSTALLINE)

0 o EXPERIMENTAL (ROL et al.) PRESENT MODEL

0 10 20 30 40

Ar"" ION ENERGY (keV) 50

Fig. 23. Sputtering yield ratios at normal and 50°

incidence versus Ar+ ion energy; experimental [36]

and theoretical.

30
The parameter A, defined

earlier as the fraction of atoms in the

statistical region which are displaced, is

assumed constant in all materials. Since

the sputterdng equations depend only on a1/3, small variations in A will have

little effect. The value of A = 0.0012

may seem small, but two things must be

remembered. First, the statistical region

is probably larger than the actual damage

cluster. Secondly, in Eq. (52) the product

AE^ appears. is defined as 4AHa, but

the assignment of the factor of 4 is debatable, as discussed in Section 5.2. The un- certainty in this factor is incorporated

into the value of A. A should not vary

strongly with ion energy since the energy

lost per unit distance by the ion is a con-

"^0 30 60 90 stant independent of energy in our approxi-

^''^^^^ mation. At high energies where Srj(E) begins to decrease, this may no longer be true.

Fig. 24. Relative sputtering yield

increases as a function of incident angle; We have, to this point, modeled

experimental [37] and theoretical. sputtering as a bulk process and predicted

the extent to which the surface is excited.

The absolute yield is obtained using a scale

factor B which we defined as the fraction of excited surface atoms that actually escape.

B is strictly a property of the sample surface and does not depend on the mass or energy of

the impinging ion. The straight-line fit of Fig. 20 suggests the following empirical relation for this scale factor:

B = (geometric factor) (number valence electrons) /m . (62)

The geometric factor is related to the number of exposed atoms and may account, in part, for

the sputtering yield variation observed on different crystalline faces. For the close-packed

transition metals of Fig. 20, this factor is relatively constant. Since we have already

accounted for the lattice binding energy in the bulk calculation, the observed variation of

B must be related to an additional surface energy barrier. In this section, we suggest one possible model for the scale factor B which is consistent with the empirical relation.

To begin, we must first examine the energy and charge state of sputtered atoms.

Many workers have observed that the distribution of sputtered atoms peaks at an energy of

only a few electron volts and falls off rapidly with increasing energy [20]. The Monte Carlo

calculations of Harrison et al. [38] for Cu show this peak to occur at ~2 eV with a 1/E

falloff thereafter, consistent with experimental results. The great majority of sputtered

atoms are neutral (>99% in most cases) [39]. Prival [39] recently proposed a model of

sputtered ion emission in which a sputtered atom is initially displaced as an ion core and

then neutralized. He considers an atom with an average emission energy and determines its

probability of neutralization using a free electron density of states in the metal. The

results are consistent with observed neutral-to-ion yield ratios.

An ion must surmount an additional surface energy barrier due to the coulomb

image force. The additional energy is on the order of the electron work function (less due

to correlation and exchange) and should have a magnitude of a few electron volts . This en- ergy is quite significant since the distribution of excited surface atoms is heavily

weighted at low energies. A large majority of the atoms which are excited at the surface

have an imparted energy of 10 eV or less. Those which are quickly neutralized have a much

greater chance of escaping than those which remain ionized. As a first approximation, we suggest that B, the fraction of escaping atoms, varies monotonically with the neutralization probability of an emitted ion. The neutralization probability may be roughly proportional to the number of valence electrons which can interact with the ion, as desired.

Alternatively, the neutralization probability could be related to the periodic behavior of

the ionization potential [40] . The /m dependence may arise as follows. The energy

31
distribution of emitted atoms is roughly the same in most materials due to an equipartitioning of the incident ion energy. Since the velocity v equals /2E/M, sputtered atoms from

light materials have significantly greater velocities. The probability of neutralization is

expected to be proportional to the time spent within some mean distance of the surface and

hence to /m. Further comparisons to elemental sputtering data should prove useful in testing the validity of this model.

The first-order range approximation X = kE allows us to develop a fairly simple sputtering equation. At low energies where A << r, the accuracy of this approximation

is unimportant. At higher energies, the constant stopping power approximation allowed us to

continue using an ellipsoidal statistical region (rather than a pear-shaped distribution in

which more displacements occur on one end than the other). At high energies, the approximations break down in several respects. The range is underestimated, and therefore the yield

will probably be overestimated. The electronic energy loss and the nuclear energy loss vary

as the ion travels deep into the solid. The values near the surface are important, however.

If one uses a value of k such that l/2k = {dE/dx)nucl at Eg, better answers will be

obtained at high energies.

5.3.6 Summary

In this section, we have developed a sputtering model which is easily implemented and predicts the yield dependence on ion mass and incident angle over a broad range

of energies. The relative sputtering yield can be predicted without any adjustable parameters. A scale factor B is derived from experiment and yields information about the sample

surface. An empirical relationship for B is suggested in the text and appears to work

well

.

Experimental comparisons indicate that the model is reasonably accurate. We emphasize that the model is not rigorous, but rather is based on a number of reasonable as- sumptions. Thus, the use of sophisticated calculations for the range or the number of displacements does not appear justified at this time. The sputtering model should prove to be

of practical use to experimentalists and designers.

5 . 4 An Ion Knock-On Mixing Model

5.4.1 Introduction

Depth profiles obtained from ASP or SIMS experiments are broadened by ion beaminduced atomic mixina [32,16,42]. This effect was illustrated in Fig. 11. In Section 5.4.2, we develop a model for ion knock-on mixing [19] based on an analogy to thermal diffusion

theory. The model leads to a simple relationship which predicts the broadening observed in

a sputter profiling experiment. We show that the broadening of the Si-Si02 interface for low

energy Ne"*", Ar+, and Xe"*" bombardment is consistent with the mixing model in Section 5.4.3.

We then extend the model to higher energies and compare it to Monte Carlo calculations [32]

and experimental data in Section 5.4.4.

5.4.2 Development

The ion knock-on mixing model [19,41] developed here is based on an analogy to

thermal diffusion theory. A similar approach has been taken by Haff and Switkowski [42]

.

In their paper, an effective diffusion coefficient D is derived in terms of various parameters, including a cascade radius and the stopping power of the ion. A diffusion time t must be inferred in order to determine the broadening observed in a sputter profiling experiment. In our model, an effective broadening parameter W^ = Dt is derived and expressed

in terms of the sputtering yield S, a measurable quantity. The stopping power effect in

Haff's model is inherent in the sputtering yield.

Our derivation is based on the assumption that an atom in the bombarded solid

undergoes a number of random collisions N and is detected immediately prior to or after

its escape from the surface. In an ASP experiment, this assumption is valid if the escape

32
depth L is small C^O.S nm) or is much less than the ion broadening parameter W. In a SIMS

experiment, atcms are detected after their escape. We describe the path of the atom by a randan walk as illustrated in Fig. 25. Monte Carlo calculations [32] confirm that the

assumption of randan collisions at low and moderate ion energies is reasonable. The net

distance R traveled by the atom is given by

2 ~2

R = Na (63)

where a is the mean square step length.

In order to determine N, we again make use of the Kinchin-Pease formula, Eq.

(36) , which states that the number of atomic displacements occurring in the solid per incident ion is E/2E(j. The number of collisions which occur is twice the number of displacements since two atoms collide with each other in a displacement event. Suppose now that the

specimen of interest has been sputtered for a time sufficient to reach equilibrium. N, the

number of collisions suffered by an escaping atom, is simply the total number of collisions

which have occurred, divided by the total number of escaping atoms. If we normalize to the

number of incident ions, we obtain

e/e

# collisions/ion d N = T 1 T- ~ — — • (64)

# escaping atoms/ion S

S, of course, is the sputtering yield

In diffusion theory, a bro

We now define an analogous broadening parameter

2 In diffusion theory, a broadening parameter Dt is defined as Dt = (1/6) Na .

1 2 Ea

6 = 6iT (65)

For low ion energies (Eq < 1 keV) , most collisions occur at energies of several E^. a should then be roughly the nearest neighbor distance d in the solid (0.3 nm)

.

At higher energies, a2 is given by

-y {9} (e) N (e) de

a = -r (66)

/

N(e) de

where N(e) de is the number of collisions occurring in the interval de about and £

is the mean free path from Section 5.2. We will discuss higher energy considerations later

in this section.

W can be determined experimentally by observing the broadening of a step function profile, i.e., an abrupt change in concentration. The step function broadens into an erf profile with a 10% to 90% width of 3.6 W, as illustrated in Fig. 26.

From diffusion theory, we also know that, if the original profile is a Gaussian

or an erf described by Dtg/ the diffused profile is also a Gaussian or erf described by

Dt{4 = Dtg + Dt. Similarly, in a sputter profiling experiment, if the original profile is

described by the parameter Wq, the measured profile will be described by W^^ = /w~fw2.

Thus, the profile broadens in rms fashion.

5.4.3 Experiment

We have performed ASP experiments [19] to examine the broadening of the Si-Si02

interface as a function of ion energy for Ne+ and Xe+ bombardment. The experimental setup

will be discussed in Section 6. The measured sputtering yields of Si02 are shown in Fig.

27. The solid curves are obtained from our sputtering model with Si02 treated as a lattice

of Ne atoms and with E^ = 25 eV. Neon, with an atomic mass of 20, has a suitable average

33
0 —H3.6W K- DEPTH

Fig. 25. Schematic illustration

of a random walk with N steps

of lengths a^^ tance traveledand a net disR. r2 = Na2.

mass for Si02. The sputtering curve

for Ne"*" bombardment fits the data quite

well. This may be due to the fact that

the incorporation of Ne atoms into the

Si02 lattice does not affect its average mass. The measured yields for Ar"*" and Xe"*" are larger than predicted by

the model at low energies. This may

result from a larger incorporation of

noble gas atoms at low sputtering

yields, which makes the lattice effectively heavier. The range of the incoming ions is thereby reduced, more

energy is released near the specimen

surface, and the sputtering yield

increases

.

Fig. 26. A step function concentration

profile is broadened by ion knock-on mixing

into an erf profile with a 10% to 90% width

of 3.6 W,

1 2 ION ENERGY (keV)

Fig. 27. Average and standard deviation of

sputtering yields (atoms/ion) in thermal Si02 as

a function of ion energy for Ne+, Ar+, and Xe+

bombardment. Solid curves are the predictions

of our sputtering model for a lattice of Ne atoms (similar mass)

.

1/2

The measured interface

widths are plotted in Fig. 28. The

solid curves are calculated from the

mixing model with an assumed original

10% to 90% interface width of 3.6 Wq = 2.0 nm and with {a^)^' " = aj-ms - 0.33 nm. The

divergence of the solid curves from the data at high energies is due to the increase of a^-j^g with energy. The dashed curves are a higher energy approximation which we discuss in the

next section. If the value of 3 . 6 Wg is increased beyond 2.0 nm, the curves in Fig. 28

will move closer together. Thus, at a particular ion energy, the different broadening parameters obtained for Ne"^ , Ar"*", and Xe"*" provide good evidence for the actual interface

width. Figure 28 illustrates that the mixing model is entirely consistent with the measured

interface widths.

5.4.4 Extension to Higher Energies

At energies greater than 1 keV, Eq. (66) must be used to evaluate a^ . In that

equation, 2.(e) is the mean free path between collisions which we discussed in the second

section of this chapter. We determined there, in Eqs . (22) and (26), that, as a first approximation , £(e) = yke = kg (67)

where y a-nd k are as defi-ned in Eqs. (23) and (27). Note that y a.nd k refer to the

atom of interest, a dopant atom, for example, striking a lattice atom and do not depend on the incident ion.

34
ION ENERGY (keV)

Fig. 28. Average and standard deviation of the measured 10% to 90% Si-Si02 interface widths as a function of ion energy

for Ne"*" , Ar"*", and Xe+ bombardment. Solid curves are the low

energy predictions of our mixing model for an original interface width of 2 nm. Dashed curves are predicted by the high

energy formula for W.

N{e) de , the number of collisions occurring between e and e + de , may be

roughly approximated as follows. Suppose that an ion of energy Eg collides with a lattice

atom, producing two atoms of energy Eq/2 which then collide to produce four atoms of en- ergy Eo/4 and so on. For such a process, N(e) °^ l/e^. Eventually, there will be Eo/2E(j

atoms with average energy 2E(j (recall the Kinchin-Pease formula) at which point no further

displacements occur. In Eq. (66) , we will use 2E(j as the lower limit of integration. We will also use YiEq as the upper limit since Y^Eq is the maximum energy that can be

transferred to a lattice atom by the incident ion. We now choose

N(e) = 2E^/e^ (68) so that

Y.E 2E E^

rN(e) de ^ [ ^ ° ^de ^

2E_, e" ^d

a

(69)

Recall that Eq/E^j is the number of collisions that occurred in the solid. Equation (66)

may now be written as follows:

^=i^/'''° i^^)'^'^^~= VVo • ^''^ 0 2E^ e d

Substituting this value of a^ into Eq. (65) , we obtain the following appealing result:

2 ^i^^^O^

" = ^3i^ • ''''

Ejj has cancelled out of the equation. Ishitani and Shimizu [32] point out that, at these

higher ion energies, the parameter does not affect the broadening since low energy

collisions (a few E,) become unimportant,

a

35
At this point, we pause to consider the applicability of this equation. Clearly,

the assumptions made above are of a very approximate nature. As the ion energy increases,

the form of N(e) , which we have used/ becomes inaccurate. The number of high energy

collisions is exaggerated due, in part, to the electronic energy losses at higher energies.

We see that Eq. (71) is only applicable when the electronic energy loss is small. We may,

as a further simplification, let the energy of the ion Eg equal the nuclear energy loss E in Eq. (71) . Thus,

2 Y- (KE)^

Our assumptions also break down when the mass of the dopant atom of interest differs significantly from the mass of a lattice atom.

Equation (72) can only be expected to indicate trends with energy or sputtering

yield and to roughly predict the broadening. We will demonstrate that Eq. (72) yields rea- sonable agreement with Monte Carlo calculations and experimental data. As a zeroeth-order

approximation, then, Eq. (72) is justified by its utility and its simplicity.

Table 3a

COMPARISON OF MONTE CARLO CALCULATIONS [32] OF THE BROADENING INDUCED BY Ar"*" BOMBARDMENT OF Si

WITH THE PREDICTIONS OF THE PRESENT MODEL

+ Ar Si

Broadening Parameters (nm)

5 keV 10 keV

Angle

e Potential

Monte

Carlo

2.4 /w Monte

Carlo

2.4 /w

0° LJ 14.0 9.1 26.0 16.4

0° TF 8.0 6.9 14.0 12.3

60° LJ 9.0 5.5 15.0 8.9

60° TF 6.0 4.0 10.0 7.6

Table 3b

Ratios

Monte

Carlo 2.4 ^^^

10 keV

0° LJ

60°

1.9

1.7

1.8

1.6

5 keV 0° TF

60°

1.8

1.7

1.8

1.9

60°

60°

5 keV LJ

10 keV

1.6

1.7

1.7

1.8

5 keV TF

10 keV

1.3

1.4

1.7

1.6

36
Ishitani and Shimizu [32] have performed Monte Carlo calculations for 5 and 10

keV Ar"*" bombardment of silicon at 0° and 60° incidence. In their paper, they tabulate the

nuclear energy loss E, the sputtering yield S, and the damage yield which conforms

fairly well to the Kinchin-Pease formula. They also examine the broadening of a step function profile of tagged Si atoms and tabulate the 20% to 80% width of the broadened profile.

Their results are ideally suited for a comparison with Eq. (72).

For the interaction of lattice atoms, the expression for K from Eqs. (27) and

(67) reduces to

K = 0^ nm eV-1 . (73) nZ

For Si, K = 0.012. y = 0.97 for Ar+ incident on Si. The 20% to 80% width of an erf profile is 2.4 W. Results are shown in Table 3a for the two potentials, Lenz-Jensen (LJ) and

Thomas-Fermi, considered in the Monte Carlo calculations [32] . The magnitudes of broadening

compare favorably. In particular, the trends with energy and angle predicted by Eq. (72)

agree well with the Monte Carlo calculations, as shown in Table 3b.

Finally, we return again to our Si-Si02 data from Fig. 28. We apply Eq. (72)

with the value of K = 0.012 previously calculated for Si. We also use the measured sputtering yields of Fig. 27 and again assume that the original interface width is 2.0 nm. The

results are shown as dashed lines in Fig. 28. The energy and ion dependence is quite reasonable. The accurate prediction of the magnitude of the broadening is somewhat fortuitous.

5.4.5 Summary

We have developed a simple model of ion ]<.nock-on broadening based on an analogy

to thermal diffusion theory. Broadening occurs in rms fashion, i.e.,

where is an unperturbed width and W is the broadening parameter.

At low energies, (E < 1 keV) , we obtained

2 W = Ea6E^S

d

(75)

where a is the nearest neighbor distance in the solid. The energy dependence of W is seen to be quite weak (as E increases, so does S) . The sputtering yield dependence indicates that, for two different bombarding ions of the same energy.

(76)

At higher energies (1 keV < E < 10 keV) , provided that the electronic energy

losses of the incident ion and of the lattice or dopant atoms are small, we used the following semi -empirical formula:

2 Y.(KE)^

W = -^3^ . (77)

Comparisons with Monte Carlo calculations and with an ASP experiment performed on the SiSiO interface produced reasonable agreement.

37
6. EXPERIMENTAL METHODS IN ASP STUDIES OF THE Si-SiO_ INTERFACE

6 . 1 Introduction

We have referred throughout this report to ASP studies of the Si-Si02 interface

performed in our laboratory. In this chapter, we examine the experimental technique used in

these studies.

In Section 6.2, we reiterate the , various physical mechanisms affecting the measurement

and describe how these are dealt with experimentally. In Section 6.3, electron stimulated

desorption of oxygen from Si02 is discussed. In Section 6.4, the specific experimental procedure for the Si-Si02 interface studies is outlined. Finally, the crater-edge profiling

technique is briefly described in Section 5.5.

6 . 2 Experimental Suppression of Profile Broadening

We have mentioned, in the previous chapters, several mechanisms which affect the

measured Auger profile. The most important mechanisms that broaden the profiles are listed

here. An experimental response to each of these mechanisms is then presented in sequence.

(1) electron escape depth (5) preferential sputtering

(2) ion knock-on mixing (6) ion-induced roughness

(3) electron stimulated desorption (7) charging

(4) gas readsorption

(1) Electron escape depth : We dealt with this effect in Chapter 4. Optimum depth resolution is obtained if the escape depth is minimized. The Sij^YV eV) peak is conveniently located at the minimum of escape depth.

(2) Ion knock-on mixing : We examined this effect in Chapter 5. Broadening is minimized by

using low energy ions striking the specimen at acute angles of incidence.

(3) Electron stimulated desorption : As we discuss in the next section, the electron flux

must be kept at an appropriately low level so that the oxygen level in Si02 does not

decrease perceptibly. The use of electron energies above about 3 keV is necessary to do this.

(4) Gas readsorption : In our sputtering experiments, the chamber is backfilled with the

sputtering gas with the ion pump off. Sputtered atoms may continue to circulate in the

chamber, and desorption from other parts of the chamber occurs. These background con- stituents may then be readsorbed. Oxygen, for example, sticks to a free Si surface but

not to Si02- Thus, broadening of the Si-Si02 interface width may occur if the rate of

O readsorption is significant in comparison to the sputtering rate. This effect is

countered by using a large sputtering rate and by sputtering with Ne in conjunction

with a liquid nitrogen cryopanel. Xe and Ar will condense on the cryopanel and,

therefore, cannot be used.

(5) Preferential sputtering : In a multicomponent specimen, one species may sputter preferentially, thereby altering the relative surface concentrations. This effect m^y depend

on the energy and mass of the incident ion. Experimental evidence indicates that preferential sputtering does not occur in thermal SiO^

.

(6) Ion-induced roughness : This effect was examined in Chapter 4. The ion beam is ras- tered to ensure that the crater is virtually flat over the width of the electron beam. A TV raster could produce unwanted ridges; therefore, a pseudorandom raster was used at

energies <3 keV. At 5 keV, a broad beam with slight TV rastering was used. When the

width of the beam is much greater than the raster spacing, roughness is minimized.

38
(7) Charging ; We find that thin Si02 layers, although they are insulating, do not charge

significantly (<1 eV) if good contact is made to the surface by copper clips and to the

back surface by a metallic tray. Specimens in which charging did occur due to poor

contact were abandoned.

6. 3 Electron Stimulated Desorption [13]

It is well known that Si02 decomposes under prolonged electron irradiation [43]. The

most pronounced beam interaction effect is dissociation and subsequent desorption of oxygen.

This results in time-dependent changes in the amplitudes of the Auger spectra of oxygen, as shown in Fig. 29. In the upper part of Fig. 29, we show how oxygen is depleted from the

0 2 4 6 8 10 12 14 16 ELECTRON EXPOSURE TIME (min)

Fig. 29. The effect of ESD on the Oj^^^ ^^LW

lines from Si02 and SiO^^ (x = 1.4) shown as a function of

irradiation time for an electron beam flux larger than

2 X IqI'^ cm~2 s"^ at 2 keV.

surface of Si02 and SiOjj, where x = 1.4. Note that the initial rate is the same for the two

specimens but that more oxygen is desorbed from the unsaturated oxide (x = 1.4) at long

irradiation times. This is a general feature. The smaller the stoichiometry factor x, the more volatile the specimen appears to be under electron irradiation, provided the specimen

has been exposed to normal atmosphere (e.g., "as-received" virgin sample). Depletion of

oxygen from the surface of the specimens is accompanied by a growth of the elemental silicon

LW line at 92 eV, as shown in the lower part of Fig. 29. Prior to electron irradiation of

the specimens (t = 0) , there is no "free" silicon even though we know that there is excess

silicon in unsaturated oxides [44] . The reason for this is, of course, that the specimens

have been exposed to atmosphere, and hence the specimens are oxidized to a depth sufficient

to mask their bulk stoichiometry. Figure 29 is a typical example of excess irradiation at a primary electron flux larger than 2 x 10^7 cm"^ sec~l at 2^keV. We have investigated the

effect of primary beam flux and energy on the interaction with silicon oxide surfaces in

39
terms of a desorption cross section of oxygen. The desorption cross section a is related

to the primary electron flux $ (cm~2 s~l) and defined by

ptp

(79)

t=0

where ^ptp -"-^ ^KLL peak-to-peak height and t is the irradiation time. Both $ and

Vptp are experimentally obtainable quantities. The flux has been varied by rastering the

beam over a known sample area. The rastering is done at a vertical frequency of 60 Hz and

a horizontal frequency of 15750 Hz. In Fig. 30, we show how the cross section of Eq. (79)

depends on the electron flux at 2 keV. Below 2 x 10-'-^ cm~^ s"-'-, the cross section appears

to be a well-defined quantity. At larger values of the cross section increases rapidly, probably due to thermal enhancement of the desorption process. The magnitude of the

total desorption cross section we observed, 2 x 10~21 cm^ for oxygen, is in reasonable

agreement with oxygen desorption from metal oxides such as SrO and MgO [45] where dissociation is a part of the process. The desorption cross section is also a function of the primary beam energy as shown in the upper part of Fig. 31. The linear relation is probably

fortuitous. However, the important thing to note is that o' decreases with increasing

energy to a small but finite value at higher energies. The reason for this energy dependence is to be found in the energy dependence of the secondary electron energy distribution.

We have measured the secondary electron yield in the energy range 15 to 150 eV and 15 to 500

eV, as a function of primary electron energy. The result is shown in the lower part of Fig.

31. The total incident current was kept constant at 5 \1A. The fact that the number of sec- ondary electrons in the given energy intervals decreases with increasing primary energy

leads to a smaller number of ionized oxygen atoms in the surface region of the sample and,

hence, to a yet smaller number of desorbed oxygen atoms. This desorption mechanism is

elaborated on in the literature [45]

.

8

Ep=2keV

PRIMARY ELECTRON FLUX DENSITY <I>p(IO"cm^s-')

Fig. 30. The total desorption cross section of oxygen

at 2 keV shown as a function of primary flux for a silicon oxide.

40
3<

O

UJ

a:<

o

zo

o

llJ cn

SECONDARY ELECTRONS

O 15- 500 eV

X 15- 150 eV

0 2 PRIMARY ELECTRON ENERGY E, (keV)

Fig. 31. The upper part shows the dependence of the cross section on primary

electron energy; the lower part shows how

the secondary electron density depends on primary electron energy. The secondary

electron energies are given in the figure.

We conclude that the primary electron

beam interactions in AES analysis depend on the chemical composition of the specimen

under investigation and its previous history. Beam interactions may be minimized by

a suitable choice of primary beam parameters

such as energy and flux. We have found that

at 2 keV a total electron exposure of less

than IQI^ cm~^ leaves the surface of silicon

oxides, practically speaking, virgin insofar

as the AES measurement is concerned.

In depth profiling work, we typically

have applied a 4.5 keV rastered primary

electron beam. The beam diameter is approximately 10 ym, and the scanned area is typically 10~4 cm2. with a total beam current

of 1 yA, we stay well below the exposure

level that gives rise to noticeable oxygen

desorption. We feel that the rastered primary electron beam is a necessary precaution

in high-resolution AES work. It provides a uniform cvurrent density without deteriorating the signal-to-noise ratio.

6 . 4 Experimental Procedure

The specimens used in our investigation

were pieces from a single lightly doped Si

(100) wafer oxidized at 1000°C for 40 min in

dry O2 with a 5 min preanneal and postanneal

in N2 . The oxide thickness was measured

ellipsometrically and determined to be 440 ±

2 nm.

The profiling experiments were performed in an Auger spectrometer at base

pressures of ~10~9 Torr. Electrons from the

integral gun of the cylindrical mirror ana- lyzer struck the specimen surface at an an- gle of 30° to the surface normal. The angle

of incidence of the ion beam was 49°.

Sputtering was performed with two different ion guns. For ion energies of 3 keV

or less, a Varian ion gun with a pseudorandom beam raster was used. The random raster minimized surface roughening. At 5 keV ion

energies, a 3M model 430 ion gun was used. A large spot size with little or no line rastering again minimized any surface roughening which might occur. Experimental comparisons

between the guns were made at 3 keV with consistent results. The chamber was backfilled to

a pressure of ~5 x io~5 Torr with either Ne, Ar, or Xe. In all cases, ion current densities

of 22.2 yA/cm^ were used. Ion beam profiles were measured with a Faraday probe.

When the sputtering rate is too low (<1 nm/min) , oxygen readsorption can affect the

measured interface width. Due to the low ionization probability for Xe , insufficient ion

current was obtained at 500 eV to establish a reasonable sputtering rate. The readsorption

effect was negligible in all other cases. A liquid nitrogen trap was used with the neon

runs to minimize the O2 partial pressure.

A 1-yA 4.5-keV electron beam rastered over a 200 ym by 200 ym square was directed to the center of the sputtered crater. With these parameters, electron stimulated desorption

of oxygen was negligible [13]. The ion beam was, in all cases, uniform to within 0.5% over

the 200 ym by 200 ym square.

41
The Si, (92 eV) and O (502 eV) peak-to-peak heights were monitored during the expe- LW riments . The 92 eV Si peak appears only for Si atoms which are not bonded to oxygen . The

escape depth minimym of -0.5 nm occurs near 92 eV. In Chapter 4, we discussed an electron

escape depth deconvolution technique [49] and showed that, for the detector geometry in our apparatus, the escape depth broadening is less than 0.3 nm for measured interface widths

greater than 2.5 nm. Ten to ninety percent interface widths were measured for the Si 92 eV profi]

Further evidence for the absence of extraneous broadening effects comes from similar

experiments in our laboratory. We have shown that the effect of sputtering nonuniformities

on measured interface widths is less 0.5% of the oxide thickness for oxides as thick as 500 nm [46]. This corresponds in the present case to an error of less than 0.3 nm.

The interface width measurements assume a constant sputtering rate (nm/min) through the

interfacial region. Sputtering rates for Si02 were determined from the time taken to reach

the interface. The Si sputtering rate was measured for Ar"^ bombardment at 1 keV by masking

one side of the oxide specimen, sputtering the other side well onto the Si, and measuring

the sputtered depth with a Tencor Alpha-Step stylus apparatus. The Si sputtering rate

measured in this manner was 5% less than the corresponding rate for SiO_.

6.5 Crater-Edge Profiling [1]

Ideally, sputtering produces a crater on the specimen of interest which is flat in the

center and slopes upward away from the center. A crater formed on a thermal oxide of Si is

schematically illustrated [47] in Fig. 32. A depth profile may be obtained by scanning an electron beam across the surface of the crater edge. The slope of the crater depends on the

thickness of the oxide sputtered away. For a 100-nm thick oxide, a 5-nm depth profile may

be obtained by sweeping the electron beam over a width of '^'1 mm. The resolution of this

technique deteriorates if the electron beam is wider than the lateral distance corresponding

to an exposed depth of one escape depth. Escape depth considerations were discussed in Chapter 4. Escape depth deconvolution also proceeds as in Chapter 4.

5 nm

Imm

Fig. 32. Schematic illustration of the crater formed

by sputtering a thin layer of Si02 on Si. From W. E. Spicer et al. [47]

.

In the Varian 2730 Auger spectrometer, the electron beam is electronically swept along

the path of interest. This steady sweep of the intensely focused beam reduces electron

stimulated desorption problems.

The crater-edge technique bears a strong resemblance to conventional angle lapping

techniques; however, the angle involved is three orders of magnitude less. Once the crater

is formed, the experimenter can return to it at leisure and perform many sweeps, thereby

improving the signal-to-noise ratio.

The depth scale of the crater edge profile can be calibrated in two ways. If the ion

beam profile is accurately known, the slope of the crater can be calculated. Otherwise, a normal ASP profile can be obtained as the crater is formed. The crater edge profile can then be compared to the normal profile for depth scale calibration. Further experiments

can then be performed to investigate dopant distributions, etc. We have used this method

[8] to examine phosphorus pileup at the Si-SiO interface.

42
6 . 6 Experimental Results for the Width of the Si-SiO^ Interface [46]

As an example of the capabilities of the ASP technique, we will now discuss experimental measurements of elemental and chemical profiles of silicon and oxygen in passing through

the Si-Si02 interface. Specimens were prepared in a similar manner, as discussed in Section

6.4, except that growth times were varied to obtain specimens with thicknesses from 25 to 100 nm.

The strength of the elemental silicon LW transition at 92 eV and the oxygen KLL transition at 510 eV were measured during the sputter profiling experiment. The silicon 92 eV

transition is characteristic of silicon atoms bonded to other silicon atoms as in elemental

silicon. Silicon atoms coordinated differently, such as in Si02 with each silicon atom

bonded to four oxygen atoms, have different characteristic transition energies and line

shapes, (78 eV for Si02 , for example) so that by monitoring the 92 eV transition, an accu- rate profile of the elemental silicon can be obtained.

Table 4

OXIDE THICKNESS DEPENDENCE OF THE WIDTH OF THE Si-SiO^ TRANSITION REGION

60 70 80 90

KINETIC ENERGY (eV) 100

Fig. 33. Sequential Si-^^ spectra obtained

while sputtering through the Si-Si02 interface [46].

Sample

"o W . Si

24 nm 3. 16 nm 2 .37 nm

24 nm 3. 90 nm 2 .74 nm

29.5 nm 3. 55 nm 2 . 50 nm

31.0 nm 3. 20 nm 2 .31 nm

31.0 nm 3. 20 nm 2 . 45 nm

58.5 nm 3. 30 nm 2 .42 nm

95.5 nm 3. 14 nm 2 .58 nm

Average

3.0. 35

25

+nm

20

.5 ± .15 nm Average

corrected 2. 9 1 2 .35 ± for escape 0. 5 nm 0 . 25 nm

depth

The width of the interface was taken

as that distance over which this silicon

92 eV transition increased from 10% to 90%

of its final value. For comparison purposes, the oxygen KLL profile was also

measured, with the interface width defined

in a similar way. Data from the silicon

KLL transition will not be discussed since,

with about a 3 nm escape depth, the minimum

interface width observable with this transition is about 5 nm.

A typical profile is shown in Fig. 7 (Chapter 4) where the peak-to-peak heights of the

Si LW and oxygen KLL transitions are shown as a function of depth for the 100 nm oxide

sample. A set of Si LW spectra corresponding to such a profile is shown in Fig. 33.

43
In Table 4, we show measured interface width as a function of oxide thickness for

oxides grown at 1000°C. The interface widths are remarkably similar, the average values

being shown in the bottom row.

The 10% to 90% width of the interface is about 2.5 nm as determined by the Si LW transition and 3.3 nm as detemined by the oxygen KLL transition. There are three factors that

may be responsible for the apparent discrepancy between the two values for interface width:

escape depth, preferential ion knock -on effects, and the presence of an oxygen-containing

phase of silicon at the interface other than SiO^.

Correcting the data for electron escape depth, we find that the values for interface

width are 2.35 nm for the Si LW and 2.9 nm for the oxygen KLL. Although escape depth is

certainly contributing to the discrepancy, the corrected values for interface width are outside the limits of experimental error. The difference in interface width is therefore

probably related to preferential knock-on effects or the presence of an additional oxygencontaining phase of silicon.

An estimate of the limit of any additional broadening contribution that might be proportional to thickness can be obtained by dividing the rms deviation, 0.15 nm, by the average oxide thickness of the samples, ~40 nm. This gives an upper limit of 0.4% for broadening proportional to oxide thickness. This value is the level at which contributions from

the nonflat sputtering crater bottom must be taken into consideration and probably represents the limit of present capabilities. (Note, however, this would give an ~4 nm interface

width for a 1-ym thick oxide and an abrupt interface.)

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.

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46

* U.S. GOVERMMENT PRINTING OFFICE : 1981—340-997/* 1798
NBS-n4A iREv. 2-8CI U.S. DEPT. OF COMM.

DID! inrRAPuir nflTA SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. SP 400-67

2. Performing Organ. Report No. 3. Publication Date September 1981

4. TITLE AND SUBTITLE

Semiconductor Measurement Technology : The Capabilities and Limitations of Auger

Sputter Profiling for Studies of Semiconductors

5. AUTHOR(S)

S. A. Schwarz, C. R. Helms, W. E. Spicer, and N. J. Taylor

6. PERFORMING ORGANIZATION (If jo/nt or other than NBS, see instructions)

Stanford University

Stanford, CA 94305

Varian Associates

Palo Alto, CA 94303

7. Contract/Grant No.

8. Type of Report & Period Covered Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State. ZIP)

Defense Advanced Research Projects Agency and the

1400 Wilson Boulevard National Bureau of Standards

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10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 81-600003

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or /ess (actual summary of most si gnificant information. If document includes a si gnificant

bi bl iography or literature survey, mention it here) Materials characterization is a critical area in current silicon integrated circuit

technology. Those techniques that are commonly used include Auger sputter profiling. X-ray photoelectron spectroscopy, secondary ion mass spectrometry, and Rutherford backscattering. All of these techniques have unique capabilities and limitations for studies of silicon device structures. In this paper, we describe the

capabilities and limitations of Auger sputter profiling especially with regard to

sensitivity, spatial resolution, depth resolution, and chemical state determination. Although much of the discussion centers on Auger sputter profiling, the results are also applicable to X-ray photoelectron spectroscopy and secondary ion mass spectrometry.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Auger electron spectroscopy (AES); metal-oxide-semiconductor (MOS), secondary ion mass spectrometry (SIMS); semiconductor devices; sputtering; X-ray photoelectron

spectroscopy (XPS, ESCA )

.

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Announcement of Semiconductor Measurement Technology

List of Publications 72 — 1962-1980

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