NIST Standard Reference Database 71 

____________________________________________________________________________________________ 

NIST Electron Inelastic-Mean-Free-Path Database

Version 1.2 

Users' Guide 

____________________________________________________________________________________________ 

Prepared by: 

C. J. Powell, Surface and Microanalysis Science Division 

National Institute of Standards and Technology 

Gaithersburg, MD, USA 

A. Jablonski, Institute of Physical Chemistry, 

Polish Academy of Sciences, Warsaw, Poland 

December 2010 

U.S. Department of Commerce

National Institute of Standards and Technology 

Standard Reference Data Program 

Gaithersburg, Maryland 20899 
 

 ________________________ 

The National Institute of Standards and Technology (NIST) uses its best efforts to deliver a high 

quality copy of the database and to verify that the data contained therein have been selected on 

the basis of sound scientific judgment. However, NIST makes no warranties to that effect, and 

NIST shall not be liable for any damage that may result from errors or omissions in the database. 

 ________________________ 

 

For a literature citation, the database should be viewed as a book published by NIST. The 

citation would therefore be: 

C. J. Powell and A. Jablonski, NIST Electron Inelastic-Mean-Free-Path Database - Version 1.2, 

National Institute of Standards and Technology, Gaithersburg, MD (2010). 

 ________________________ 

©2010 copyright by the U.S. Secretary of Commerce on behalf of the United States of America. 

All rights reserved. No part of this database may be reproduced, stored in a retrieval system, or 

transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or 

otherwise, without the prior written permission of the distributor. 

Certain trade names and other commercial designations are used in this work for the purpose of 

clarity. In no case does such identification imply endorsement by the National Institute of 

Standards and Technology nor does it imply that the products or services so identified are 

necessarily the best available for the purpose. 

Microsoft, MS-DOS, Windows® 95, Windows® 98, Windows® NT, Windows® 2000, 

Windows® ME, Windows® XP, Windows® Vista, and Windows® 7 are registered trademarks 

of Microsoft Corporation. 

ii 
 

ACKNOWLEDGMENTS 

The authors wish to thank Mrs. Cheryl W. Levey for testing the database and for editorial 

assistance. 

iii 
 

TABLE OF CONTENTS 

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

II. GETTING STARTED................................................................................................................2 

 Packet Content ..........................................................................................................................2 

 System Requirements................................................................................................................2 

 Installation.................................................................................................................................3 

 Removal of the Database ..........................................................................................................3 

III. STRUCTURE OF THE PROGRAM.........................................................................................4 

 Main Menu................................................................................................................................4 

IV. RUNNING THE DATABASE PROGRAM ...........................................................................10 

 Starting the Database..............................................................................................................10 

 Database (first option of the main menu)...............................................................................10 

 Elements.............................................................................................................................10 

 Inorganic Compounds........................................................................................................15

 Organic Compounds ..........................................................................................................17

 File Management (second option of the main menu).............................................................18 

 Save Created Files .............................................................................................................19 

 Delete Files ........................................................................................................................20 

 Print Files...........................................................................................................................20 

 Print Figures.......................................................................................................................21 

 Load Files ..........................................................................................................................22 

 Comparisons (third option of the main menu) .......................................................................23 

 Inelastic Mean Free Paths from the Database Only...........................................................24 

 Inelastic Mean Free Paths from other Sources and the 

 Database ........................................................................................................................25 

V. UNCERTAINTIES OF CALCULATED, MEASURED, AND PREDICTED 

 INELASTIC MEAN FREE PATHS........................................................................................27 

 Consistency of Calculated Inelastic Mean Free Paths ...........................................................27 

 Consistency of Measured Inelastic Mean Free Paths.............................................................27 

 Consistency of Calculated and Measured Inelastic 

 Mean Free Paths.................................................................................................................27 

 Recommended Inelastic Mean Free Paths..............................................................................28 

 Uncertainties of Calculated and Measured Inelastic 

 Mean Free Paths.................................................................................................................28 

 Uncertainties of Inelastic Mean Free Paths from 

 Predictive Formulae...........................................................................................................29 

 TPP-2M Equation of Tanuma, Powell, and Penn..............................................................29 

 G-1 Equation of Gries........................................................................................................30 

VI. REFERENCES ........................................................................................................................31 

iv 
 

v 

APPENDIX A: PREDICTIVE FORMULAE FOR ELECTRON INELASTIC MEAN 

FREE PATHS ................................................................................................................................32 

 TPP-2M Equation of Tanuma, Powell, and Penn ..................................................................32 

 G-1 Equation of Gries ............................................................................................................36 

 Atomic Weight and Density Data ..........................................................................................37 

APPENDIX B: EXAMPLE OF A FILE CONTAINING INELASTIC MEAN 

FREE PATHS ................................................................................................................................40 

APPENDIX C: CONTACTS .............................................................................................................................42
 

I. INTRODUCTION 

This database provides values of electron inelastic mean free paths (IMFPs) in solid elements 

and compounds at selected electron energies between 50 eV and 10,000 eV (although most of 

the available data are for energies less than 2,000 eV). 

The database was designed mainly to provide IMFPs for applications in surface analysis by 

Auger-electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). For these 

applications, IMFPs are needed for quantitative surface analyses (to correct elemental sensitivity 

factors for variations of IMFP with chemical state), for defining the surface sensitivity, and in 

calculations of the transport of signal electrons in solids. The IMFPs are also useful for defining 

the surface sensitivity of other surface-characterization methods in which electron beams are 

employed and for applications in which knowledge of the transport of low-energy electrons in 

solids is needed. 

In AES and XPS, a user often needs IMFP values at one or more specified electron energies or 

wishes to display IMFPs as a function of energy. The database can provide IMFP information 

from up to three types of sources: calculated IMFPs from experimental optical data for a limited 

number of materials, IMFPs measured by elastic-peak electron spectroscopy (EPES) for some 

elemental solids, and IMFPs from predictive formulae for all materials. The calculated and 

measured IMFPs were generally reported in journal papers at specified electron energies, and it 

was convenient to fit these IMFPs with appropriate functions so that IMFPs could be found by 

interpolation for intermediate energies [1]. 

A user of this database can obtain and display IMFP values for elements, inorganic compounds, 

and organic compounds at specified electron energies or energy ranges. For a selected material 

in each class, the user can specify a source of IMFPs (calculations, measurements, or predictive 

formulae) and then choose from a number of options for the IMFP units (nanometers, 

Ångstroms, or milligrams per square meter) and the type of display (linear, logarithmic, or 

linear/logarithmic coordinates). 

The user can display the IMFP results graphically (that is, a plot of IMFP versus electron 

energy), obtain an IMFP for a selected electron energy, obtain IMFPs for a number of specified 

energies, and create an IMFP Table for regularly spaced electron energies. The IMFPs from the 

latter two options can be stored in files for later processing (e.g., on-screen comparisons of 

IMFPs from different sources for the same material or comparisons of IMFPs for different 

materials), printing, or permanent storage. Finally, graphical displays can be saved in Windows 

bitmap format for easy incorporation into other documents. 

NIST released version 1.0 of the Electron Inelastic-Mean-Free-Path Database (SRD 71) in 

September, 1999. Version 1.0 was designed to operate under the DOS operating system. Version 

1.1 was designed to operate under the Windows 95, Windows 98, or Windows NT operating 

systems, and was released in December, 2000. The database screens were redesigned to make 

use of the database easier and more convenient. There were no changes or additions to the data 

in the database although there were some changes to the Nv parameter values listed in Table A.1. 

IMFP 1 
 

The installation program for Version 1.2 was changed so that it would operate on newer versions 

of the Windows operating system; Version 1.2 was released in December, 2010. There were no 

changes or additions to the data in the database although a new About box was added to the main 

menu. This box shows three references, a 1999 critical review [1] and two recent reviews [2,3] 

that discuss evaluations of the compiled data, methods of determination, and uncertainty. 

II. GETTING STARTED 

Packet Content 

CD-ROM 

Users’ Guide 

 

Alternatively, the files on the CD-ROM and a PDF file with the Users’ Guide can be 

downloaded from NIST (http://www.nist.gov/srd/surface.cfm). 

 

System Requirements 

1. Personal computer with Windows 95, Windows 98, Windows NT, Windows 2000, Windows 

ME, Windows XP, Windows Vista, or Windows 7 operating system 

2. CD-ROM drive 

3. Screen resolution: 1024 by 768 pixels. 

4. System font size: small fonts. 

5. Printer: Laser printer supporting the PCL 6 printer language. 

6. Hard disk space: 720 kilobytes minimum. Larger amounts of storage are required if numerous 

files are created with the database. It is suggested that 30 Megabytes be available, particularly 

if graphic files are created. 

The database has been designed to operate optimally at the screen resolution given above. 

However, it can also be operated at a lower screen resolution, e.g., 640 by 480 pixels, or 800 by 

600 pixels. At higher resolutions, the database will operate correctly but there may be difficulty 

in reading text on the screen. For all resolutions, small system fonts must be selected. 

 

To change the screen resolution or the system font size, follow these steps: 

1. Double click the My Computer icon on the desktop. 

2. Click the Control panel icon. 

3. Double click the Display icon. 

4. Click on the Settings tab. 

5. Set a given resolution by moving the slider. 

 

To change the system font size, proceed as follows depending on the operating system in use: 

For Windows 95 or NT, select Small Fonts in the Font Size box. 

For Windows 98, click on the Advanced... button, select the General tab, and then select the 

Small Fonts option in the Display box. 

 

IMFP 2 
 

For Windows XP, click on the Advanced... button, and then select the Normal size (96 DPI) 

option in the Display box. 

For Windows Vista, click on Appearance and Personalization, Personalization, Adjust font 

size (DPI) in the left pane, and select Default scale (96 DPI).

For Windows 7, click on Appearance and Personalization, Display, and select Small - 100 % 

(default option). 

Installation 

 

1. Insert the CD-ROM into the disk drive of the computer. 

2. Click the Start button on the task bar. 

3. Click the Run command. 

4. Type D:\SETUP (if D: is the drive letter for the disk drive) and click OK. 

5. Follow instructions on the screen. 

 

Alternatively, the following procedure can be used: 

1. Insert the disk into the disk drive of the computer. 

2. Double-click My Computer on the desktop. 

3. Double-click the icon corresponding to the disk drive. 

4. Double-click the Setup icon (showing the computer). 

5. Follow instructions on the screen. 

If files have been downloaded into a directory on the user’s personal computer, double-click the 

Setup icon (i.e., setup.exe). 

Should difficulty be encountered in installing the database as described above (e.g., due to 

security settings on the computer), the database can be launched by double-clicking on 

IMFPWIN.exe located in the Program Files directory. 

By default, the database is installed in the directory C:\PROGRAM FILES\NIST\IMFPWIN. 

Furthermore, an IMFPWIN icon is created. This icon appears after clicking the Start button and 

choosing Programs. 

 

Removal of the Database 

 

1. Double click My Computer on the desktop. 

2. Double click the Control panel icon. 

3. Double click the Add/Remove Programs icon. 

4. Select Install/Uninstall. 

5. In the list of programs, click Imfpwin. 

6. Click the button Add/Remove. 

IMFP 3 
 

III. STRUCTURE OF THE PROGRAM 

Main Menu

Figure 1. The title screen and main menu. 

The five options of the Main Menu are listed in the upper part of the title screen (Fig. 1), and the 

submenus corresponding to the first three options are shown in Figs. 2, 4 and 5. 

IMFP 4 
 

The functions of the five main menu options are as follows: 

1. Database (Figure 2) 

Figure 2. First option of the main menu (Database) 

With this option, IMFPs can be obtained for elements, inorganic compounds, and organic 

compounds. For each of these three classes of materials, submenus (Figs. 3(a)-(c)) enable the 

selection of data sources and the types of data to be obtained. These submenus are described in 

Section IV. Operation of the database can be terminated by choosing End the session. 

IMFP 5 
 

Figure 3(a). Elements submenu for the Database menu of Figure 2. 

Figure 3(b). Inorganic Compounds submenu for the Database menu of Figure 2. 

IMFP 6 
 

Figure 3(c). Organic compounds submenu for the Database menu of Figure 2. 

2. File Management (Figure 4) 

Figure 4. Second option of the main menu (File Management). 

This option allows the user to save files created in the present session to another directory for 

permanent storage, to delete files from the database directory, to print files containing IMFP 

IMFP 7 
 

data, to print figures showing displays of IMFP data as a function of electron energy, and to load 

files containing IMFP data or figures that were created in earlier sessions and stored in another 

directory. 

3. Comparisons (Figure 5) 

Figure 5. Third option of the main menu (Comparisons). 

With this option, IMFP data for different materials and/or from different sources can be 

graphically compared. 

4. Disclaimer (Figure 6) 

The NIST disclaimer is stated. 

IMFP 8 
 

Figure 6. NIST disclaimer. 

6. About box (Figure 7) 

The About box gives information on the release date of this version of the database, how the 

database should be cited in publications, and references to evaluations of the compiled data, 

methods of determination, and uncertainties [1-3]. 

Figure 7. The About box. 

IMFP 9 
 

V. RUNNING THE DATABASE PROGRAM 

Starting the Database

The database can be started by any of the following means: 

1. Click the Start button, choose Programs, and then the IMFPWIN icon. 

2. Click the Start button, choose Run, and type: 

 C:\PROGRA~1\NIST\IMFPWIN\IMFPWIN, 

 and then click OK. 

3. Double-click the My Computer icon on the desktop, select the C:\PROGRAM 

FILES\NIST\IMFPWIN directory, and double-click on the IMFPWIN icon. 

Database 

(First option of the main menu) 

Elements 

(First option of the Database option on the main menu) 

The user will initially select an element and a source of data (Figure 3(a)). 

The Periodic Table of the elements will then appear (Figure 8), and an element can be selected 

by clicking on the button for the element of interest. A selection is indicated by a change of color 

from black to red. 

An element can be deselected by clicking again on another button. After a selection has been 

made (Cu in the case shown in Figure 8), the OK button should be clicked. Clicking on the 

Cancel button returns control to the opening screen and the main menu. Note that it is not 

possible to select an element shown in bold letters. 

After an element has been selected, a screen will appear showing the IMFP data sources 

available for that element. For example, if copper (Cu) had been chosen, the screen shown in 

Figure 9 would be displayed. 

IMFP 10 
 

Figure 8. Screen for selecting an element (here Cu). 

Figure 9. Sources of IMFP data for copper. 

One of the data sources should then be selected. If experimental IMFP values are desired (i.e., 

IMFPs measured by elastic peak electron spectroscopy), an additional selection of a data source 

should be made in the bottom box of the screen. Further information concerning the selection(s) 

(the reference, the electron energy range for the IMFP data, and how the IMFP data were 

IMFP 11 
 

obtained) appears in the status box. The user should also select the preferred IMFP units 

(Ångstroms, nanometers, or milligrams per square meter) in the box in the upper right of the 

screen (although units can be changed on later screens). The OK button should then be clicked. 

Four types of data sources have been utilized to provide the IMFPs in the database: 

 

1. IMFPs calculated from experimental optical data (for a group of elements and a small 

number of compounds). An analytic function has been fitted to calculated IMFPs for a 

particular material and data source to allow convenient interpolation [1,4]. 

2. IMFPs measured by elastic-peak electron spectroscopy (EPES) and the use of either Monte 

Carlo calculations or analytical theory (for a group of elements). An analytic function has 

been fitted to measured IMFPs for a particular material and data source to allow convenient 

interpolation [1,4]. 

3. IMFPs obtained from predictive formulae. 

4. Recommended IMFPs (only for Ni, Cu, Ag, and Au) [1]. 

Further information on the sources of calculated, measured, and recommended IMFPs and the 

uncertainty of the IMFP data has been published elsewhere [1-4]. These references also contain 

a description of the procedures used to fit IMFPs that were calculated or measured at specific 

energies so that convenient interpolations can be made. The predictive formulae are described in 

Appendix A; for most applications, use of the TPP-2M equation of Tanuma et al. [5] is 

recommended. 

For the example of Cu, seven separate data sources are shown in the screen of Figure 9. The first 

four of these are calculated IMFPs based on the work of the authors shown at the left of each 

line. For IMFPs from the work of Tanuma, Powell, and Penn [6], IMFPs are provided based on 

specific IMFP calculations for a selected element, if available, or otherwise from the predictive 

IMFP formula TPP-2M proposed by these authors [5]. If this formula has been utilized, 

information to this effect will be given on the screen for that element. 

The following source in Figure 9 allows IMFPs to be calculated from the predictive IMFP 

equation (G-1 formula) of Gries [7]. 

The next line on the screen of Figure 9 indicates that measured IMFPs are available for Cu from 

EPES measurements and Monte Carlo calculations; selection of this line will lead to the 

appearance of six sources of data in the lowest box of Figure 8 from which the user should make 

a selection. 

The last line on the screen of Figure 9 indicates that recommended IMFP values [1] are available 

for copper. The following screen (Figure 10) shows a graphical plot of calculated IMFPs for 

copper from Tanuma et al. [6] versus electron energy. 

IMFP 12 
 

Figure 10. Graphical display of calculated IMFPs for copper (from Tanuma et al. [6]) as a 

function of electron energy. 

The energy dependence of the cross section can be displayed in linear, semilogarithmic, or 

logarithmic coordinate systems; these coordinates are chosen with the buttons in the upper-right 

part of the screen. The IMFP units can be changed by clicking the Change Units button at the 

bottom-right of the screen, and the line type can be changed by clicking the Line Type button at 

the bottom of the screen. This plot provides a convenient means for showing the energy 

dependence of the IMFP. If it is desired to store or print a graphical plot such as that shown in 

Figure 10, a file with the IMFP data should be created with the Table with IMFP values option to 

be described shortly and then the Comparisons option of the main menu should be used to 

prepare a graphical display of the data in the file; this latter display can be printed and a file can 

be created for transfer to other applications. 

An IMFP value for a particular energy can be found by clicking the cursor inside the plot at a 

position close to the desired energy. The IMFP and the chosen energy appear in the upper-left 

corner of the screen. The selected energy can be changed by clicking on the Increase energy or 

Decrease energy buttons; these changes will occur in steps of 1 eV, 10 eV, or 100 eV depending 

on the choice of button selected in the upper part of the screen. In this way, numerical IMFP 

values for particular electron energies of interest can be quickly found. 

There are two additional methods by which numerical IMFP values for a particular material can 

be found and also stored. First, by clicking on the Multiple IMFPs button of the screen in Figure 

10, the user can obtain IMFPs for specified electron energies. As an example, Figure 11 shows 

the screen that would appear if the silicon IMFP measurements of Gergely et al. [8] had been 

selected earlier; these IMFPs are derived from an analytic function fitted to the IMFP 

measurements [1]. 

IMFP 13 
 

Figure 11. Example of multiple IMFP values from the measured IMFPs for silicon of 

Gergely et al. [8]. 

A series of electron energies can be entered into the box on the lower-left of the screen and the 

Add button clicked after each entry. These energies and the corresponding IMFPs will then 

appear in the center box of the screen. Entries in this box can be removed by selecting the 

relevant line(s) and clicking the Delete button. Similarly, new entries can be inserted above a 

selected line using the Insert button. The status box in the upper-right of the screen indicates the 

energy range of the original data; IMFPs can be obtained only for energies within this range. The 

IMFP units can be changed by clicking on the Change units button. Finally, a file can be created 

containing the indicated energies and IMFPs by entering a suitable file name in the box of the 

right-side of the screen and clicking the Create button. Such a file will be given the .MFP 

extension. A window will then appear on the screen indicating that the file has been successfully 

created; this window would show a diagnostic if, for example, an unsuitable file name had been 

chosen. This option is a convenient means of storing IMFPs at user-specified electron energies 

for a selected material and data source. 

Second, a Table can be created containing IMFPs for regularly spaced electron energies within 

the energy range of the original data source. Figure 12 shows the screen that would appear if the 

Table with IMFPs button in Figure 10 had been clicked and if measured IMFPs for silicon from 

Gergely et al. [8] had been previously selected. 

IMFP 14 
 

Figure 12. Table with IMFP values derived from the measured IMFPs for silicon of 

Gergely et al. [8]. 

The number of IMFP values in the Table can be selected by the user in the box at the upper-right 

of the screen; the default value is 401 (the maximum number). The user can also choose to have 

the energy values in the Table distributed uniformly on either linear or logarithmic scales by 

selecting the appropriate button on the lower part of the screen. Clicking on the Create button in 

the upper-right of the screen will then create the Table in the center of the screen. The IMFP 

units can be changed as before by clicking on the Change units button. Finally, a file can be 

created containing the Table of energies and IMFPs by entering a suitable file name and clicking 

on the Create button in the lower-right of the screen. Files of this type are given extensions of 

.ANG, .NAN, or .MGM depending on whether the IMFP units are Ångstroms, nanometers, or 

milligrams per square meter, respectively. This option is a convenient means of storing IMFP 

data for a selected material and data source over the energy range of the original data (shown at 

the upper-right of the screen). This file can be later used to create a graphical display of the 

IMFP data (e.g., for comparisons, printing, or transfer to other applications). 

Clicking on the Close button in Figs. 11 and 12 will return the user to the main menu. It is then 

possible to go directly to screens for obtaining a single IMFP value (Figure 10), multiple IMFP 

values (Figure 11), or a Table with IMFP values (Figure 12) for the previously selected element 

and data source using the submenu shown in Figure 3(a). 

Inorganic Compounds 

(Second option of the Database option on the main menu) 

The user can choose to obtain calculated IMFPs for a limited number of inorganic compounds or 

to derive IMFPs from predictive formulae (Figure 3(b)). If the first choice is made, the screen of 

IMFP 15 
 

Figure 13 appears in which four sources of calculated IMFPs are shown in the center part of the 

screen. 

Figure 13. Screen to select source and compound to obtain calculated IMFPs for inorganic 

compounds. 

If one of those sources is selected, the compounds for which calculated IMFPs are available 

appear in the lower part of the screen. After a compound is selected (and, if desired, the IMFP 

units changed using the box at the upper-right of the screen), the OK button is clicked and a 

series of screens similar to Figs. 10, 11, and 12 will then appear depending on whether the user 

wishes to obtain an IMFP value for a single electron energy, multiple IMFP values, or a Table of 

IMFP values as described for Elements in the previous section. 

If the second choice is made, a Periodic Table of the elements similar to Figure 8 appears (but 

now the gaseous elements are not shown in bold). At least two elements should be selected by 

clicking on the appropriate boxes. After clicking the OK button, a screen similar to Figure 14 

appears. 

The name of the compound should be entered in the box in the upper-left of the screen. The 

stoichiometry coefficients for each element in the compound should then be entered in the next 

lower box. 

IMFP 16 
 

Figure 14. Screen used to obtain IMFPs from predictive formulae for inorganic compounds. 

The user can choose to obtain IMFP values from the predictive TPP-2M equation of Tanuma et 

al. [5] or the predictive G-1 equation of Gries [7] using one of the buttons in the top-right of the 

screen; these equations are described in Appendix A. If the TPP-2M equation is selected, values 

for the density, number of valence electrons per molecule, and bandgap energy should be entered 

into the appropriate boxes; information on the latter two parameters is given in Appendix A. If 

the G-1 equation is selected, only the density value should be entered. The IMFP units can be 

changed, if desired, using the buttons on the right side of the screen. After clicking OK, screens 

similar to Figs. 10, 11, and 12 will appear. It is possible to go directly to the desired screens from 

the main menu after a data source and compound have been selected using the submenu options 

shown in Figure 3(b). 

Further information on the sources of calculated IMFPs for the inorganic compounds and on their 

uncertainties has been published elsewhere [1-4]. 

Organic Compounds 

(Third option of the Database option on the main menu)

Similar choices are made to obtain IMFPs for organic compounds as described above for 

inorganic compounds, as in Figure 3(c). Figure 15 shows the screen that indicates sources of 

calculated IMFPs for organic compounds and, for the selected source, the compounds for which 

IMFPs are available. 

IMFP 17 
 

Figure 15. Screen to select source and compound to obtain calculated IMFPs for organic 

compounds. 

File Management

(Second option of the main menu)

With this option, a user can save files created in the present session to another directory for 

permanent storage, delete files from the database directory, print files containing IMFP data, 

print figures showing displays of IMFP data as a function of electron energy, and load files 

containing IMFP data or figures that were created in earlier sessions and stored in another 

directory (Figure 4). These options will be described in turn. 

IMFP 18 
 

Save Created Files 

(First option of the File Management option on the main menu)

Files containing IMFP values are created by the database (as described above) as text files in the 

directory in which the database is located (default C:\PROGRAM FILES\NIST\IMFPWIN). The 

files created by the Table with the IMFP values option have extensions of .ANG, .NAN, or 

.MGM (for which the IMFPs are in units of Ångstroms, nanometers, or milligrams per square 

meter, respectively) while the files created by the Multiple IMFP values option have the .MFP 

extension. Files containing IMFP figures are created by the Comparisons option (see below) and 

have the .BMP extension. 

The Save files option allows the user to save files in the database directory to any other directory 

for permanent storage. Figure 16 shows an example of a screen for this option. 

Figure 16. Example of saving three files from the database directory to the C:\FILES directory. 

The center panel shows illustrative data files in the database directory; if desired, files with 

particular extensions can be selected for display using the box on the right side of the screen. The 

file(s) to be saved should be selected by clicking on the file name(s) (and simultaneously 

pressing the Shift key or the Ctrl key if multiple selections are desired). The destination directory 

for the saved files is selected in the panel located in the lower-left corner of the screen; in Figure 

16, the directory C:\FILES has been selected as the destination directory for three selected files. 

The user then selects one of the three buttons in the lower-right corner of the screen to indicate 

whether the selected files should also be retained in the database directory after the Save files 

operation, whether these files should be removed from this directory, or whether all data files in 

the directory should be removed. The OK button should then be clicked to save the designated 

files. Appendix B gives an example of the content and format of a saved text file. 

IMFP 19 
 

Delete Files 

(Second option of the File Management option on the main menu)

Data files created during the present session or during previous sessions can be deleted with this 

option. Figure 17 shows an example of this option. 

Figure 17. Screen illustrating deletion of a file from the database directory. 

The user should initially select the directory from which files are to be removed; by default, the 

database directory is selected, as shown in Figure 17. It is possible to display files with selected 

extensions using the middle box on the left of the screen. The user then selects one or more files 

for deletion from the list. If desired, all data files in the database directory can be deleted by 

choosing the second button in the lower-right of the screen. Deletion of the selected files occurs 

after the OK button is clicked. 

Print Files

(Third option of the File Management option on the main menu)

IMFP files created by the database (i.e., those with .ANG, NAN, MGM, and MFP extensions) 

are text files and can be opened and printed by common word-processing software. These files 

can also be printed with this option of the database. A screen similar to Figure 18 appears and, if 

desired, the user can select files with a particular extension for listing. 

IMFP 20 
 

Figure 18. Screen illustrating selection of an IMFP file from the database directory for printing. 

Unlike the previous file-management options, the user can only select a single file for printing at 

a time. Printing is initiated by clicking the Print button. If a user wishes to print files stored in 

other directories, these files can be loaded into the database directory using the Load files option 

described below. Appendix B contains an example of a printed file. 

Print Figures

(Fourth option of the File Management option on the main menu)

Files with figures created by the Comparisons option of the database (see below) have the .BMP 

extension and can be inserted into documents produced by common word-processing software. 

These files can also be printed with this option of the database. A screen similar to Figure 19 

appears that lists files with the .BMP extension in the database directory on the right side of the 

screen. 

IMFP 21 
 

Figure 19. Screen illustrating selection of a figure from the database directory for printing. 

A file can be selected and, after clicking the Load image button, the figure appears in the center 

of the screen. This figure can be printed in one of eight sizes by moving the pointer in the lower 

part of the screen with the mouse. The printed sizes are approximately 5 cm x 4 cm, 7 cm x 5 cm, 

8.5 cm x 6.5 cm, 10 cm x 7.5 cm, 11.5 cm x 9 cm, 13 cm x 10 cm, 14.5 cm x 11 cm, and 16 cm x 

12 cm for pointer positions 1, 2, 3, 4, 5, 6, 7, and 8, respectively. Clicking the Print button 

initiates printing. Files with figures that are stored in other directories can be loaded into the 

database directory using the Load files option. 

Load Files 

(Fifth option of the File Management option on the main menu)

With this option, it is possible to transfer files to the current database directory (default: 

C:\PROGRAM FILES\NIST\IMFPWIN) that had been saved previously to other directories. An 

example of this option is shown in Figure 20. 

In this example, the directory C:\FILES has been selected as the source directory in the upperleft box on the screen. It is possible to load files with the .ANG, .NAN, .MGM, .MFP, and .BMP 

extensions, and listings of files with selected extensions can be chosen using the box in the 

lower-right of the screen. One or more of the files listed in the upper part of the screen can be 

selected and then loaded into the database directory by clicking OK. 

IMFP 22 
 

Figure 20. Example of loading a file from the C:\FILES directory to the database directory; in 

this example, files with a .BMP extension are listed. 

Comparisons

(Third option of the main menu)

This option is useful for making graphical comparisons of IMFP data from different sources for 

the same material or for comparing IMFP data from different materials. The option is also useful 

for creating a graphical display with a single set of IMFP data. These graphical displays can be 

stored or printed for later use. 

Files containing IMFP data are needed for use of this option. These files can be created from 

IMFPs provided by the database for any material using the Multiple IMFP values or Table with 

IMFP values options described above for the Elements option of the Database option in the main 

menu. The IMFP data to be compared must be in the same units; that is, the IMFPs to be 

compared will be in files with extensions of .ANG, .NAN, and .MGM for IMFPs expressed in 

Ångstroms, nanometers, and milligrams per square meter, respectively. Alternatively, files with 

these extensions that were created in previous sessions and stored in other directories can be 

loaded into the database directory using the Load files option described above. 

On selection of this option, the user will choose to compare IMFPs only from the database or to 

compare IMFPs from the database and other sources (Figure 5). In the latter case, comparisons 

are made with IMFP data from other sources (e.g., recent publications) that are entered by the 

user. These two options will now be described. 

IMFP 23 
 

Inelastic Mean Free Paths from the Database Only

Figure 21 shows an example of a screen that appears when this option is chosen. 

Figure 21. Screen showing selection of two files from the database directory with IMFP data to 

be compared. 

Files with IMFPs in the desired units can be listed according to their extensions using the box in 

the middle-left of the screen. Up to four files can be selected for comparison at a time. The OK

button should then be clicked. Figure 22 is an example of a graphical comparison of IMFPs 

calculated for silicon by Tanuma et al. [6] and of IMFPs measured for silicon by Gergely et al.

[8]. 

Linear, logarithmic, or semi-logarithmic display coordinates can be selected using buttons on the 

upper-right of the screen. The line type on the display can be varied by clicking the Line type

button, and the display can be printed by clicking the Print button. A file containing the display 

can be created by clicking the Create file button; a window will then appear in which the user 

can enter a suitable file name. This file will have the .BMP extension. 

IMFP 24 
 

Figure 22. Screen showing comparison of IMFPs for silicon from two data files. The dotted line 

shows IMFPs calculated by Tanuma et al. [6] and the solid line shows IMFPs measured by 

Gergely et al. [8]. 

Inelastic Mean Free Paths from Other Sources and the Database

If this option is chosen, a screen similar to Figure 23 appears. With this screen, one or more files 

in the database directory can be selected as in Figure 21. In addition, the user can enter electron 

energies (in eV) and corresponding IMFP values (in the same units as the IMFP data in the 

selected files) in the boxes on the right side of the screen; on clicking the Add button, these 

entries will be transferred to the summary box above. If desired, a line on this box can be 

selected and then removed by clicking the Delete button. When data entry is complete, the OK 

button should be clicked, and a screen similar to Figure 24 will appear. This screen shows IMFPs 

for silicon from the same sources as in Figure 22. The open circles in Figure 24 are effective 

attenuation length (EAL) values for silicon that were measured by Ebel et al. [7] (and which 

were entered on the screen of Figure 23). As expected, the EALs are smaller than the 

corresponding IMFPs [8]. 

IMFP 25 
 

Figure 23. Example of selection of files for comparison of IMFP data from the selected files with 

IMFP data entered by the user. 

Figure 24. Screen showing IMFPs for silicon from the two data files shown in Figure 23. The 

dotted line shows IMFPs calculated by Tanuma et al. [6] and the solid line shows IMFPs 

measured by Gergely et al. [8]. The open circles show effective attenuation lengths for silicon 

measured by Ebel et al. [10]. 

IMFP 26 
 

V. UNCERTAINTIES OF CALCULATED, MEASURED, AND PREDICTED 

INELASTIC MEAN FREE PATHS 

Detailed evaluations of the uncertainties of IMFPs calculated from experimental optical data, 

IMFPs measured by elastic-peak electron spectroscopy (EPES), and IMFPs obtained from 

predictive formulae have been published [1-4,11]. We will give here a brief summary of 

information from these evaluations. The most detailed analysis was of calculated and measured 

IMFPs for seven elemental solids (Al, Si, Ni, Cu, Ge, Ag, and Au) for which there were 

calculated IMFPs from at least two independent sources and measured IMFPs from at least two 

independent sources [1]. 

Consistency of Calculated Inelastic Mean Free Paths 

It was convenient to compare calculated IMFPs for a particular material from a particular source 

over the available energy range with IMFP values obtained from a function fitted to calculated 

IMFPs from all available sources for that material [1]. Two measures of deviation of individual 

IMFP values from the fitted IMFPs were employed. First, the average root-mean-square 

deviation RMS of the individual IMFPs from the fitted IMFPs was found to be 0.89 Å for the 

group of seven elemental solids [1]. Second, the average of the mean percentage deviations R for 

each element of the individual IMFPs from the fitted IMFPs was found to be 4.4 % [1]. Similar 

values of RMS and R were found in similar evaluations of calculated IMFPs for Fe, Al2O3, SiO2, 

KCl, poly(butene-1-sulfone), polyethylene, and polystyrene [4]. The values of RMS and R for the 

seven elements indicate the variability in IMFPs that can be found from the use of different sets 

of optical data and different technical approaches [1]. 

Consistency of Measured Inelastic Mean Free Paths 

For the same group of seven elemental solids, a similar comparison was made of measured 

IMFPs for a particular material from a particular source over the available energy range with 

IMFP values obtained from a function fitted to measured IMFPs from all available sources for 

that material [1]. Values of RMS and R were again computed to describe the variability of the 

measured IMFPs for each solid with respect to the fitted IMFPs. For the seven elemental solids, 

the average value of RMS was 3.00 Å and the average value of R was 13.2 % [1]; these values 

are about three times larger than the corresponding values for the calculated IMFPs. Similar 

values of RMS and R were found in comparisons of measured IMFPs for Fe, Mo, W, and Pt [4]. 

The values of RMS and R for the seven elements are a measure of the uncertainties of IMFP 

measurements by EPES [1]. 

Consistency of Calculated and Measured Inelastic Mean Free Paths 

A similar comparison has been made of the measured IMFPs for the seven elemental solids with 

the corresponding calculated IMFPs [1]. It was convenient to compare the measured IMFPs for 

each element to a function fitted to all of the calculated IMFPs for that element. Values of RMS

and R were again calculated to describe the deviations of the measured IMFPs about the fitted 

IMFPs. For the seven elemental solids, the average value of RMS was 4.56 Å and the average 

value of R was 17.4 % [1]. Similar values of RMS and R were found in comparisons of measured 

IMFPs for Fe, Mo, W, and Pt with functions fitted to the calculated IMFPs for these elements 

[2]. Although the values of RMS and R found in the comparisons of measured and calculated 

IMFPs are much greater than the corresponding values found in the comparison of calculated 

IMFP 27 
 

IMFPs from different sources, the precision of IMFP measurement in a particular laboratory is 

generally sufficient to show that the energy dependence of the measured IMFPs is close to that 

expected from the IMFP calculations [1,4]. 

Recommended Inelastic Mean Free Paths 

In the comparisons of the calculated IMFPs for each of the seven elements, comparisons of the 

measured IMFPs for those elements, and comparisons of the calculated and measured IMFPs for 

the same elements, it was found that the values of RMS and R for Ni, Cu, Ag, and Au were 

appreciably less than the corresponding average values for the group of seven elements [1]. The 

database contains “recommended IMFPs” for Ni, Cu, Ag, and Au that were derived from a 

function fitted to the calculated IMFPs for each element [1]. 

Uncertainties of Calculated and Measured Inelastic Mean Free Paths 

In the comparisons of calculated and measured IMFPs described above for the group of seven 

elements, the values of RMS and R are considered to be indications of the uncertainties in the 

calculations and measurements, respectively. These values of RMS and R, however, should be 

considered as lower limits to the uncertainty because it has not been possible to quantify 

potential sources of systematic error in the calculations and measurements [1-3]. In the absence 

of more detailed knowledge of the systematic errors in the IMFP calculations and measurements, 

the average value of RMS = 4.56 Å found in the comparison of measured IMFPs with the 

function fitted to the calculated IMFPs for each of the seven elements and the corresponding 

average value of R = 17.4 % will be considered as reasonable estimates of the IMFP standard 

uncertainty. 

This discussion of uncertainties has been based on an evaluation of calculated and measured 

IMFPs for seven solid elements [1]. There is no known reason for the uncertainties in IMFPs of 

other materials to be substantially different. Measured IMFPs for non-elemental solids, 

however, may have additional uncertainty due to the need to determine the surface composition 

over the depth probed by EPES if there is reason to believe that this could be different from the 

bulk composition [1]. 

For some elements and compounds, the database contains more than one source of calculated or 

measured IMFPs. In general, it has not been possible to quantify the uncertainties in individual 

IMFP measurements or calculations. Until this can be done, no guidance can be given to a 

preferred source of data. The “recommended IMFPs” should nevertheless be used for Ni, Cu, 

Ag, and Au. For these four elements, calculated and measured IMFPs from other sources are 

also provided so that users can access these data if they wish to (or if future analyses show that 

IMFPs from particular sources have a lower uncertainty). 

There is an additional source of uncertainty in IMFPs from the database arising from the use of 

analytical functions to fit the calculated and measured IMFPs from each source so that 

interpolations could be made. Information on this uncertainty is given elsewhere [1,4]. 

IMFP 28 
 

Uncertainties of Inelastic Mean Free Paths from Predictive Formulae 

IMFPs can be obtained conveniently from two predictive formulae in the database, the TPP-2M 

equation of Tanuma et al. [5] and the G-1 equation of Gries [7]. These formulae can be used to 

obtain IMFPs in materials for which no IMFP calculations or measurements have been made. 

These two equations are described in Appendix A. 

Information on uncertainties of IMFPs from the two equations will now be presented. 

TPP-2M Equation of Tanuma, Powell, and Penn

Tanuma et al. [5] derived their TPP-2M equation from an analysis of their calculated IMFPs for 

electrons of 50 eV to 2000 eV energy in a group of 27 elements [6] and a group of 14 organic 

compounds [5]. This equation is based on the Bethe equation [12] for inelastic electron 

scattering in matter but with modifications suggested by Inokuti [13] and Ashley [14] to describe 

the IMFP dependence on energy for energies less than 200 eV. 

Comparison of IMFPs from the TPP-2M equation with those directly calculated from optical 

data showed average RMS deviations of 10.2% for the group of 27 elements, 8.5 % for the group 

of 14 organic compounds, and 18.9% for the group of 15 inorganic compounds [5]. These 

deviations were considered to be satisfactorily small on account of the similar uncertainty of the 

optical data used in the IMFP calculations and the empirical nature of the modifications to the 

Bethe equation. The larger deviations found for the inorganic compounds was expected because 

the optical data for these compounds had greater sum-rule errors than for the other materials 

[5,15]. 

Comparisons of IMFPs calculated from the TPP-2M equation for Ni, Cu, Ag, and Au with the 

corresponding recommended IMFPs for these elements show satisfactory agreement [4]. The 

average value of RMS between IMFPs from the TPP-2M equation and the corresponding 

recommended IMFPs was 0.90 Å and the corresponding value of R was 10.9 % [4]. 

The uncertainties of IMFPs obtained from the TPP-2M equation can be expressed in two ways 

depending on the intended application of the data. If, for example, IMFPs for two materials are 

to be compared, then the standard uncertainty of each is estimated from the comparison with the 

recommended IMFPs to be 0.90 Å or 10.9 %. If absolute values of IMFPs are required, the 

standard uncertainty will be the quadrature sum of one of these values and the corresponding 

uncertainty found in the comparison of measured and calculated IMFPs (4.56 Å and 17.4% for 

RMS and R, respectively). This combined standard uncertainty is thus estimated to be 4.7 Å or 

20.5 %. 

There is one additional source of uncertainty in the use of the TPP-2M equation. For some 

elements, it is not clear whether the parameter Nv should be simply the number of valence 

electrons, as defined in Appendix A, or whether this number should be increased to include the 

number of core electrons with binding energies of less than about 30 eV [6,16]. For some 

elements (listed in Table A.1), Nv has been increased to include these shallow core electrons but 

for others the core electrons have been excluded. In some cases, the inclusion or exclusion of the 

shallow core electrons does not lead to changes of more than 20 % in the IMFPs calculated from 

the TPP-2M equation but larger changes can be found for other elements [17]. 

IMFP 29 
 

G-1 Equation of Gries 

Gries [7] developed his G-1 equation from an analysis of the calculated IMFPs of Tanuma et al.

[5,6,15] over the 200 eV to 2000 eV range and an atomistic model of inelastic electron 

scattering. The G-1 equation has a different dependence on material parameters than the TPP2M equation of Tanuma et al. At an energy of 2 keV, the average deviations between IMFPs 

from the G-1 equation and IMFPs of Tanuma et al. were similar in magnitude to those reported 

by Tanuma et al. [5] for their TPP-2M equation (although it should be noted that the 

comparisons of Tanuma et al. were made over the 50 eV to 2000 eV energy range). 

Tanuma et al. [11] have analyzed the Gries model and have pointed out some important 

limitations. Although the G-1 equation provides useful estimates of IMFPs for many elements 

and compounds, there can be substantial deviations (of up to about 50%) for a few of the 

materials that have been examined to date. Since there is presently no explanation for these 

deviations, it is believed that the TPP-2M equation has greater general reliability [11]. Although 

use of the G-1 equation requires knowledge of just one material parameter (the specimen 

density), it is recommended that IMFPs be determined from this equation only if a user has 

reason to believe that the TPP-2M equation will not give satisfactory results.

IMFP 30 
 

REFERENCES 

1. Powell, C. J., and Jablonski, A., J. Phys. Chem. Ref. Data 28, 19 (1999). 

2. Nucl. Instr. Meth. Phys. Res. A 601, 54 (2009). 

3. Powell, C. J., and Jablonski, A., J. Electron Spectrosc. Rel. Phenom. 178-179, 331 (2010). 

4. Powell, C. J., and Jablonski, A., Surf. Interface Anal. 29, 108 (2000). 

5. Tanuma, S, Powell, C. J., and Penn, D. R., Surf. Interface Anal. 21, 165 (1994). 

6. Tanuma, S, Powell, C. J., and Penn, D. R., Surf. Interface Anal. 17, 911 (1991). 

7. Gries, W. H., Surf. Interface Anal. 24, 38 (1996). 

8. Gergely, G., Konkol, A., Menyhard, M., Lesiak, B., Jablonski, A., Varga, D., and Toth, J., 

Vacuum 48, 621 (1997). 

9. Ebel, M. F., Ebel, H., Hofmann, A., and Svagera, R., Surf. Interface Anal. 22, 51 (1994). 

10. Jablonski, A., and Powell, C. J., J. Electron Spectrosc. Relat. Phenom. 100, 137 (1999); ibid. 

107, 201 (2000). 

11. Tanuma, S, Powell, C. J., and Penn, D. R., Surf. Interface Anal. 25, 25 (1997). 

12. Bethe, H., Ann. der Physik 5, 325 (1930). 

13. Inokuti, M., Rev. Mod. Phys. 43, 297 (1971). 

14. Ashley, J. C., J. Electron Spectrosc. Relat. Phenom. 46, 199 (1988). 

15. Tanuma, S, Powell, C. J., and Penn, D. R., Surf. Interface Anal. 17, 927 (1991). 

16. Tanuma, S, Powell, C. J., and Penn, D. R., Surf. Interface Anal. 11, 577 (1988). 

17. Tanuma, S, Powell, C. J., and Penn, D. R. (to be published). 

18. Seah, M. P., and Gilmore, I. S., Surf. Interface Anal. 26, 908 (1998). 

19. Seah, M. P. (private communication). 

20. Smith, D. M., Gallon, T. E., and Matthew, J. A. D., J. Phys. B 7, 1255 (1974). 

21. Netzer, F. P., and Matthew, J. A. D., Rep. Prog. Phys. 49, 621 (1986). 

22. American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1963), 

p. 9-22. 

23. Ashcroft, N. W., and Mermin, N. D., Solid State Physics (Holt, Rinehart and Winston, 1976), 

p. 566. 

24. Kittel, C., Introduction to Solid State Physics, sixth edition (John Wiley, New York, 1986), 

p. 185. 

25. Wolfe, C. M., Holonyak, J., and Stillman, G. E., Physical Properties of Semiconductors

(Prentice-Hall, Englewood Cliffs, 1989). 

26. CRC Handbook of Chemistry and Physics, 77th edition, D. R. Lide, ed. (CRC Press, Boca 

Raton, 1996), pp. 12-94–12-98. 

27. Tanuma, S, Powell, C. J., and Penn, D. R., Surf. Interface Anal. 20, 77 (1993). 

28. Coplen, T. B., Pure Appl. Chem. 68, 2339 (1996). 

29. CRC Handbook of Chemistry and Physics, 77th edition, D. R. Lide, ed. (CRC Press, Boca 

Raton, 1996), pp 4-37–4-98. 

30. CRC Handbook of Chemistry and Physics, 77th edition, D. R. Lide, ed. (CRC Press, Boca 

Raton, 1996), pp 3-3–3-330. 

IMFP 31 
 

Appendix A 

PREDICTIVE FORMULAE FOR ELECTRON INELASTIC MEAN FREE PATHS 

IMFPs can be obtained conveniently from two predictive formulae in the database, the TPP-2M 

equation of Tanuma et al. [5] and the G-1 equation of Gries [7]. These formulae can be used to 

obtain IMFPs in materials for which no IMFP calculations or measurements have been made. 

Information on the uncertainties of IMFPs from these two formulae is given in Section V. 

These predictive formulae will now be described in turn. Information on atomic weights and 

elemental densities is given in the final section. 

TPP-2M Equation of Tanuma, Powell, and Penn 

Tanuma et al. [5] proposed the following equations for the calculation of the IMFP λ (in 

Ångstroms) as a function of electron energy E (in eV) and various material parameters: 

)]/()/()ln([2 2 EDECEE

E

p   

 (A.1) 

where 

 = – 0.10 + 0.944/(Ep

2 + Eg2)

1/2 + 0.0690.1 (A.2) 

 = 0.191

–0.50 (A.3) 

C  91.097.1 U (A.4) 

D  8.204.53 U (A.5) 

U = Nv/ M = Ep

2 / 829.4 (A.6) 

and Ep = 28.8 (Nvρ/M)

1/2 is the free-electron plasmon energy (in eV), ρ is the density (in g cm-3), 

Nv is the number of valence electrons per atom (for an element) or molecule (for a compound), 

M is the atomic or molecular weight, and Eg is the bandgap energy (in eV). Equations (A.1) 

through (A.6) are collectively known as the TPP-2M equation. 

Table A.1 shows recommended elemental values for the parameter Nv in the TPP-2M equation. 

During the development of the TPP-2M equation, there was ambiguity in the choice of a value of 

Nv for elements in which there were core-levels with binding energies less than about 30 eV 

[6,16,17]. Measurements of Auger-electron yields for many solid elements by Seah and Gilmore 

[18], however, have given experimental guidance on the appropriate choice of Nv for many 

elements. For the rare-earth elements, these authors recommended that the 4f electrons should be 

excluded in the count for Nv. In more recent work from the same group, however, the 

IMFP 32 
 

recommended choices for the rare-earth elements have been revised [19] to include the 4f 

electrons but the details of the analysis have not been published. Comparisons of IMFPs 

calculated from optical data for Gd, Tb, and Dy with IMFPs obtained from the TPP-2M equation 

and various values of Nv nevertheless indicate that the 4f electrons should be excluded [17]. This 

conclusion is supported by an analysis of the energy-loss function for these three elements and 

the expectation that the 4f electrons do not contribute substantially to the energy-loss function 

for energy losses less than about 50 eV [20]. On this basis, values of Nv for the rare earths in 

Table A.1 have been computed from the sum of the chemical valence [21] and the 6 5p electrons 

that contribute strongly to the energy-loss spectrum [17]; these values of Nv are larger than those 

recommended in Version 1.0 of the database where Nv was equated to the valence. There is now 

a non-physical discontinuity, however, between the Nv values for the rare earths and those for 

Cs, Ba, and La. Further work is needed to establish the influence of 5p-electron excitations in the 

latter three elements and of similar core-electron excitations for other elements in groups IA, II, 

and III of the Periodic Table [17]. 

For compounds, Nv is calculated from the sum of contributions from each constituent element 

(i.e., Nv for each element multiplied by the chemical or estimated stoichiometric coefficient for 

that element). 

Values of the bandgap energy Eg for many compounds can be found in a number of books [22-

26]. Table A.2 contains values of Eg for some elements and representative compounds. If a 

value for the bandgap energy Eg cannot be found for the compound of interest, it is satisfactory 

to estimate this parameter because the IMFP is not a sensitive function of Eg [15,27]. For highly 

ionic compounds such as the alkali halides, Eg is generally between 6 eV and 11 eV. For oxides, 

Eg is often between 1 eV and 9 eV. 

Table A.1. Recommended values for the number of valence electrons per atom (the parameter 

Nv) for each element for which IMFPs can be computed in the database. 

____________________________________________ 

Z Element Nv

____________________________________________ 

1 H 1 

2 He 2 

3 Li 1 

4 Be 2 

5 B 3 

6 C 4 

7 N 5 

8 O 6 

9 F 7 

10 Ne 8 

11 Na 1 

12 Mg 2 

13 Al 3 

14 Si 4 

IMFP 33 
 

15 P 5 

16 S 6 

17 Cl 7 

18 Ar 8 

19 K 1 

20 Ca 2 

21 Sc 3 

22 Ti 4 

23 V 5 

24 Cr 6 

25 Mn 7 

26 Fe 8 

27 Co 9 

28 Ni 10 

29 Cu 11 

30 Zn 12 

31 Ga 3 

32 Ge 4 

33 As 5 

34 Se 6 

35 Br 7 

36 Kr 8 

37 Rb 1 

38 Sr 2 

39 Y 3 

40 Zr 4 

41 Nb 5 

42 Mo 6 

44 Ru 8 

45 Rh 9 

46 Pd 10 

47 Ag 11 

48 Cd 12 

49 In 3 

50 Sn 4 

51 Sb 5 

52 Te 6 

53 I 7 

54 Xe 8 

55 Cs 1 

56 Ba 2 

57 La 3 

58 Ce 9 

59 Pr 9 

60 Nd 9 

62 Sm 9 

IMFP 34 
 

63 Eu 8 

64 Gd 9 

65 Tb 9 

66 Dy 9 

67 Ho 9 

68 Er 9 

69 Tm 9 

70 Yb 8 

71 Lu 9 

72 Hf 4 

73 Ta 5 

74 W 6 

75 Re 7 

76 Os 8 

77 Ir 9 

78 Pt 10 

79 Au 11 

80 Hg 12 

81 Tl 3 

82 Pb 4 

83 Bi 5 

90 Th 4 

91 Pa 3 

92 U 3 

 ____________________________________________ 

Table A.2. Values of the band gap energy Eg for elements and selected compounds (at room 

temperature) from the indicated references. 

 __________________________________________________________ 

Material Eg Reference 

 (eV) 

 __________________________________________________________ 

B 1.55 24 

C (diamond) 5.4 24 

Ge 0.67 24 

Se (gray) 1.5 24 

Si 1.107 24 

Sn (alpha phase) 0.08 24 

Te 0.33 24 

AgBr 2.50 24 

AgCl 3.0 20 

AgI 2.63 24 

AlAs 2.16 24 

AlN 6.02 24 

AlP 2.5 20 

IMFP 35 
 

AlSb 1.60 24 

BN 4.6 24 

CdS 2.42 24 

CdSe 1.74 24 

CdTe 1.5 24 

Cu2O 2.2 20 

GaAs 1.35 24 

GaN 3.34 24 

GaP 2.24 24 

GaSb 0.67 24 

HgTe 0.2 20 

InAs 0.36 24 

InN 2.0 24 

InP 1.27 24 

InSb 0.16 24 

KCl 8.5 20 

MgO 7.3 20 

NaCl 8.6 20 

PbS 0.5 24 

PbSe 0.37 24 

PbTe 0.25 24 

SiC (alpha phase) 2.86 24 

TiO2 (rutile) 3.05 20 

ZnO 3.2 24 

ZnS 3.6 24 

ZnSb 0.56 20 

ZnSe 2.58 24 

ZnTe 2.26 24 

 __________________________________________________________ 

G-1 Equation of Gries

Gries [7] developed the following equation for the prediction of the IMFP λ (in Ångstroms): 

 = 10k1(Va / Z*)E/(log E  k2) (A.7) 

where Va = M/ρ is the atomic volume (in cm3

 mol-1), Z* is a parameter found empirically to be 

equal to Z1/2, Z is the atomic number (for an element), and k1 and k2 are parameters. Values of 

k1 and k2 were found from fits of Eq. (A.7) to the IMFPs calculated by Tanuma et al. [5,6,15] for 

groups of selected elements and compounds: 0.0020 and 1.30 for the 3d elements (Ti-Cu); 

0.0019 and 1.35 for the 4d elements (Zr-Ag); 0.0019 and 1.45 for the 5d elements (Hf-Au); 

0.0014 and 1.10 for the remaining elements (with which Y is included instead of the 4d 

elements; 0.0018 and 1.00 for organic compounds; and 0.0019 and 1.30 for inorganic 

compounds. The terms Va and Z* in Eq. (A.7) were generalized by Gries to apply to a 

compound ApBq, ...Cr, with corresponding atomic numbers ZA, ZB, ... ZC and atomic weights 

MA, MB, ... MC, as follows: 

IMFP 36 
 

Z*  (pZA

1/2  qZB1/2  ... + ZC1/2 )/( p  q  ... + r) (A.8) 

Va  (pMA  qMB  ... + rMC)/( p  q  ... + r) (A.9) 

Equations (A.7) through (A.9) constitute the G-1 equation. 

Atomic Weight and Density Data

Numerical data for atomic weights and material densities are needed for evaluation of the TPP2M equation of Tanuma et al. and the G-1 equation of Gries. 

The database makes use of atomic weights recommended by the International Union of Pure and 

Applied Chemistry in 1995 [28]. Elemental densities have been obtained from Ref. 29 and are 

shown in Table A.3. Other Handbooks containing density data were reviewed and numerous 

(generally small) discrepancies were found. Since the conditions of measurement in the various 

sources were not specified (and no references were provided), it was not possible to make a 

selection of data on scientific criteria. Instead, densities from Ref. 29 have been arbitrarily 

assumed to be “correct.” If more reliable density data becomes available for particular elements, 

suitable adjustments can be made to IMFPs or EALs obtained from the database using the 

equations given above. The calculated IMFPs of Tanuma et al. for carbon in the database are for 

glassy carbon with a density of 1.8 g cm-3 [6]; IMFPs can be calculated in the database with the 

Gries G-1 equation [Eqs. (A.7-A.9)] using either the density for graphite or for diamond in Table 

A.3. Densities for inorganic compounds and organic compounds can be obtained from Refs. 29 

and 30, respectively. 

Tanuma et al. developed an earlier predictive IMFP formula, designated TPP-2, based on 

calculated IMFPs for a group of 27 elements [6]; this predictive equation was later modified, in 

one parameter, to become the TPP-2M equation given above after consideration of calculated 

IMFPs for a group of 14 organic compounds [5]. The extent to which an IMFP calculated from 

the TPP-2 equation depends on material density has been analyzed for several representative 

elements and inorganic compounds [6,27]. Similar tests have not been made for the TPP-2M 

equation although it is thought that the earlier tests with the TPP-2 equation should provide 

general guidance. The database can, of course, be utilized to examine the variation of calculated 

IMFPs for a material of interest with different assumed densities in the TPP-2M and G-1 

equations. 

IMFP 37 
 

Table A.3. Densities of elemental solids at or near room temperature [29]. 

__________________________________________________________ 

Z Element Density 

 (g cm-3) 

__________________________________________________________ 

3 Li 0.534 

4 Be 1.85 

5 B 2.34 

6 C 2.2 (graphite) 

 3.513 (diamond) 

11 Na 0.97 

12 Mg 1.74 

13 Al 2.70 

14 Si 2.3290 

15 P 1.823 (white) 

 2.16 (red) 

 2.69 (black) 

16 S 2.07 

19 K 0.89 

20 Ca 1.54 

21 Sc 2.99 

22 Ti 4.506 

23 V 6.0 

24 Cr 7.15 

25 Mn 7.3 

26 Fe 7.87 

27 Co 8.90 

28 Ni 8.86 

29 Cu 8.96 

30 Zn 7.14 

31 Ga 5.91 

32 Ge 5.3234 

33 As 5.75 

34 Se 4.39 (alpha phase) 

 4.28 (vitreous phase) 

 4.81 (gray) 

37 Rb 1.53 

38 Sr 2.64 

39 Y 4.47 

40 Zr 6.52 

41 Nb 8.57 

42 Mo 10.2 

44 Ru 12.1 

45 Rh 12.4 

46 Pd 12.0 

IMFP 38 
 

47 Ag 10.5 

48 Cd 8.69 

49 In 7.31 

50 Sn 5.769 (gray) 

 7.265 (white) 

51 Sb 6.68 

52 Te 6.24 

55 Cs 1.93 

56 Ba 3.62 

57 La 6.15 

58 Ce 6.770 

59 Pr 6.77 

60 Nd 7.01 

62 Sm 7.52 

63 Eu 5.24 

64 Gd 7.90 

65 Tb 8.23 

66 Dy 8.55 

67 Ho 8.80 

68 Er 9.07 

69 Tm 9.32 

70 Yb 6.90 

71 Lu 9.84 

72 Hf 13.3 

73 Ta 16.4 

74 W 19.3 

75 Re 20.8 

76 Os 22.59 

77 Ir 22.5 

78 Pt 21.5 

79 Au 19.3 

80 Hg 13.5336 

81 Tl 11.8 

82 Pb 11.3 

83 Bi 9.79 

90 Th 11.7 

91 Pa 15.4 

92 U 19.1 

__________________________________________________________ 

IMFP 39 
 

Appendix B 

EXAMPLE OF A FILE CONTAINING INELASTIC MEAN FREE PATHS 

The listing shown below is an example of an IMFP data file produced by the database. This file 

was created using the Inorganic Compounds option of the Database option on the main menu, 

the option to calculate IMFPs from predictive formulae, the TPP-2M equation of Tanuma et al.

[5], and parameters for silicon nitride.

COMPOUND: SILICON NITRIDE 

SOURCE: 

 Tanuma, Powell & Penn 

 Surface Interface Anal. 21 (1994) 165 

 Values of IMFP obtained from TPP-2M equation 

 

MOLECULAR WEIGHT: 140.28346 

DENSITY: 3.4400 g/cm**3 

TABULATION: 

__________________________________________________________ 

 Energy IMFP 

 eV Angstroms 

__________________________________________________________ 

 50.000 5.83 

 100.000 6.26 

 150.000 7.10 

 200.000 8.10 

 250.000 9.13 

 300.000 10.17 

 350.000 11.19 

 400.000 12.21 

 450.000 13.22 

 500.000 14.21 

 550.000 15.19 

 600.000 16.16 

 650.000 17.12 

 700.000 18.07 

 750.000 19.01 

 800.000 19.94 

 850.000 20.86 

 900.000 21.78 

 950.000 22.69 

IMFP 40 
 

 1000.000 23.59 

 1050.000 24.49 

 1100.000 25.37 

 1150.000 26.26 

 1200.000 27.14 

 1250.000 28.01 

 1300.000 28.88 

 1350.000 29.74 

 1400.000 30.60 

 1450.000 31.46 

 1500.000 32.31 

 1550.000 33.15 

 1600.000 34.00 

 1650.000 34.84 

 1700.000 35.67 

 1750.000 36.50 

 1800.000 37.33 

 1850.000 38.16 

 1900.000 38.98 

 1950.000 39.80 

 2000.000 40.62 

__________________________________________________________ 

IMFP 41 
 

IMFP 42 

Appendix C 

CONTACTS 

If you have comments or questions about the database, the Standard Reference Data Program 

would like to hear from you. Also, if you have any problems with the diskette or installation, 

please let us know by contacting: 

Joan C. Sauerwein 

National Institute of Standards and Technology 

Standard Reference Data Program 

100 Bureau Drive, Stop 2310 

Gaithersburg, MD 20899-2310 

Internet: srdata@nist.gov 

Phone: (301) 975-2208 

FAX: (301) 926-0416 

If you have technical questions relating to the data, contact: 

Dr. C. J. Powell 

National Institute of Standards and Technology 

100 Bureau Dive, Stop 8370 

Gaithersburg, MD 20899-8370 

E-mail: cedric.powell@nist.gov 

Phone: (301) 975-2534 

FAX: (301) 216-1134 

Prof. Dr. A. Jablonski 

Institute of Physical Chemistry 

Polish Academy of Sciences 

ul. Kasprzaka 44/52 

01-224 Warsaw 

Poland 

E-mail: ajablonski@ichf.edu.pl 

Phone: (+48) 22-343-3331 

FAX: (+48) 22-343-3333