A111Q3 0fi7Q^3

N/^UNSTOFSTANOABOS.a:S^C.

NBS SPECIAL PUBLICATION 400-11

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

Semiconductor Measurement Technology:

M BASIC Program for Calculating

Dopant Density Profiles from

Capacitance -Voltage Data
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1 9 1975

'30

Semiconductor Measurement Technology:

iril A BASIC Program for Calculating Dopant Density Profiles

from Capacitance-Voltage Data

Richard L. Mattis and

Martin G. Buehler

Electronic Technology Division

Institute for Applied Technology

' National Bureau of Standards

' ' ' Washington, D.C. 20234

This activity was supported by

The Defense Advanced Research Projects Agency

under ARPA Order 2397, Program Code 4D10

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued June 1975
Library of Congress Cataloging in Publication Data

Mattis, Richard L. A BASIC Program for Calculating Dopant Density Profiles from Capacitance -Voltage Data.

(Semiconductor Measurement Technology) (National Bureau

of Standards Special Publication; 400-11)

Supt. of Docs. No.: C 13.10:400-11

1. Electronic Data Processing—Ion Implantation. 2. Electronic Data Processing—Diodes, Semiconductor. 3. Electronic Data

Processing—Electrdc Measurements. 4. BASIC (Computer Pro- gram Language) 1. Buehler, Martin G., joint author. II. United

States. National Bureau of Standards. III. Title. IV. Series. V.

Series: United States. National Bureau of Standards. Special PubHcation; 400-11. OC100.U57 No. 400-11 [TK7871.85] 389'.08s [621.3815'.2'028] 75-619089

National Bureau of Standards Special Publication 400-11

Nat. Bur. Stand. (U.S.), Spec. Publ. 400-11, 39 pages (June 1975) CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1975

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.10:400-ll). Price $1.00 (Add 25 percent additional for other than U.S. mailing.)
TABLE OF CONTENTS

Page

1. Introduction 1

2. Equations 2

2.1. The Peripheral Correction 2

2.2. The Back Depletion Correction 2

2.3. The Complementary Error Function 3

2.4. The Inverse Complementary Error Function 5

3. Program Description

...

8

3.1. Data Input 8

3.2. Data Output 8

3.3. The ERF Subroutine 8

3.4. The INERF Subroutine 9

3.5. The TABLE Data File 9

3.6. The PLOT Subroutine 9

3.7. The Main Program 13

4. Modifications and Trouble-Shooting 15

4.1. Limitation on Program Length 15

4.2. Formation of Subprograms 15

4.3. Rectangular Diodes 15

4.4. LOG ER Errors 16

4.5. Program CV2 16

Appendix A. Listing of Program CVl 18

Appendix B. Some Comments on BASIC 24

Appendix C. Sample Calculation Using Program CVl 25

Appendix D. Listing of Program CV2 28

Appendix E. Sample Calculation Using Program CV2 30

References 33

iii
LIST OF FIGURES

Page

Figure 1. Schematic representation of the depletion region of a p-n junction diode

diffused in an epitaxial semiconductor 4

Figure 2. Semilog plot of the function x = erfc(y) showing the transformed variable

z 6

Figure 3. Calculation of y = erfc~"'"(x) by means of a parabolic fit 7

Figure 4. Flow chart of the PLOT subroutine 10

Figure 5. A plot artificially constructed to show the six types of printed output of

the PLOT subroutine 12

Figure 6. Summary flow chart of program CVl 13

iv
PREFACE

This work was carried out as a part of the Semiconductor Technology Program in the Electronic Technology Division at the National Bureau of Standards. The Semiconductor Technology

Program serves to focus NBS efforts to enhance the performance, interchangeability , and re- liability 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

Program receives direct financial support principally from three major sponsors: The

Defense Advanced Research Projects Agency (ARPA) , The Defense Nuclear Agency (DNA) and the

National Bureau of Standards. The specific work reported herein was supported by ARPA.*

The computer program CVl, the subject of this report, is derived from a program reported by

D. B. DeVries, G. Lee, and S. Watelski in Integrated-Circuit Process Control and Development, Technical Report AFAL-TR-73-268 , August 1973. The present program contains improvements in the peripheral capacitance correction, the error function calculations, the numerical integration, the plot routine, and data input/output. The present report is intended

as a guide for persons using the program described herein. It is not intended to provide a detailed comparison of the present and the original programs.

The authors are indebted to several persons who assisted in the editing and preparation of

this report. Gerard N. Stenbakken performed a critical and constructive reading of the

text. The several figures were prepared by Edgar C. Watts and Leo R. Williams. The typing

of the final draft was done by Frances C. Butler.

Through ARPA Order 2397, Program Code 4D10.

V

A BASIC Program for Calculating Dopant Density

Profiles from Capacitance-Voltage Data

by

Richard L. Mattis and Martin G. Buehler

Abstract: A computer program is presented which is suitable for calculating

dopant density vs. depth profiles from capacitance-voltage data for the case of a Gaussian-diffused p-n junction diode. The program includes corrections for

peripheral capacitance of round or rectangular diodes and back depletion of the

space-charge region into the diffused layer. Inputs to the program consist of

the surface dopant density, the junction depth, the background dopant density in

the diffused layer, the junction diameter, three scaling parameters, and the

capacitance-voltage (fata pairs. Output from the program is in the form of a plot

and an optional listing of dopant density as a function of depth. The equations

underlying the program are given and are related to the program whose operation

is described in detail. A second program, for generating idealized capacitancevoltage data for a Gaussian-diffused diode on material with a constant dopant

density is also included.

Key Words: BASIC; capacitance-voltage measurements; computer programs;

dopant profiles; error function; Gaussian diffusion; plotting, computer; semiconductors; silicon.

1. INTRODUCTION

The capacitance-voltage (C-V) method is widely used to measure dopant density versus depth

profiles of semiconductor specimens [1-4]. The basic equations for calculating dopant

density N(W) as a function of depletion width W were derived by Schottky [5] and are suitable for the case of a large area one-sided abrupt junction diode under reverse bias conditions. However, in many cases the dimensions of the diode are not large compared with the

depletion width, so the peripheral capacitance can cause a significant error in the calculated dopant density profile. Similarly, when the diffused layer dopant density is not

large compared to the dopant density of the region to be profiled, back depletion into the

diffused layer can cause significant error in the calculated dopant density profile [6].

A computer program, henceforth denoted CVl for convenience and listed in Appendix A, is

presented. It is suitable for calculating dopant density versus depth profiles from C-V

data for the case of a Gaussian-diffused p-n junction diode. The case of a Gaussian

diffusion is treated because of its common usage in the semiconductor industry. Program CVl

is not intended for profiling junctions which are part of transistors or other multijunction structures. The program has not yet been satisfactorily tested on diodes diffused

in epitaxial material in which the layer and substrate are of opposite conductivity type;

the program has been proven, however, on diodes diffused in epitaxial material in which the

layer and substrate are of the same conductivity type and on diodes diffused in bulk material. Program CVl is not intended to take into account the effects of diffusion capacitance

which occur under heavy forward bias conditions; it is recommended that caution be exercised

in interpreting any data taken in forward bias conditions. The program includes corrections

for peripheral capacitance of round and rectangular diodes and back depletion of the spacecharge region into the diffused layer. Inputs to the program consist of the surface dopant

density, the junction depth, the background dopant density in the diffused layer, the

junction diameter, three scaling parameters, and the C-V data pairs. Output from the program

is in the form of a plot and an optional listing of dopant density as a function of depth.

The equations underlying program CVl are given in section 2 along with a somewhat expanded

discussion relating to the calculation of the complementary error function and its inverse.

The program is described in detail in section 3. In section 4, program modifications and

check-out are presented, including the discussion of a second computer program which generates idealized C-V data for the case of a Gaussian-diffused junction diode fabricated in

material of constant background dopant density. For convenience, this second program is

henceforth denoted CV2

.

1
The programs described in this report are written in the BASIC language. A description of

the BASIC language can be found in several books [7-9]. However, when using the programs

described below the reader must be alert to the particular characteristics of the BASIC he

may be using. The particular type of BASIC employed in the programs described in this

report is applicable to a time-sharing system, has a six decimal place precision, can handle

positive and negative numbers in the range 10^^ to 10~^^, and can accoimnodate programs as long as 256 lines plus comment statements. This particular BASIC is compatible with most of

the BASIC in use. However, some of its characteristics are worthy of comment to avoid possi

ble confusion. These are described in Appendix B.

2. EQUATIONS

In this section, the equations which are employed to calculate the dopant density profile

from the experimental C-V data are given. These equations relate to the peripheral correction, the back depletion correction and the calculation of the complementary error function

and its inverse.

2.1. The Peripheral Correction

The Schottky equations for calculating dopant density N(W) and depletion width W have been

referred to above and are given below as eqs (1) and (2),

N(W) = qKeoA

_d_

dV

-1

(1)

W = r-J- (2)

where q is the electronic charge, k is the relative dielectric constant of the test specimen

eg is the permittivity of free space. A, is the area of the diode, C is the measured capacitance and V is the applied voltage. lA program CVl, the peripheral capacitance is first

substracted from the measured capacitance [10-13]. The peripheral capacitance calculation

for a circular diode can be written as

St

where D is the diode diameter and x. is the junction depth. The corrected or plane capacitance, C, is then given by

C = C - C . (4) m pt

Equation (3) was derived by assuming that the peripheral region is a one sided junction.

After the plane capacitances have been determined, an apparent profile N(W) vs. W is calculated using eqs (1) and (2).

2.2. The Back Depletion Correction

The back depletion correction [10] is based on eqs (5) through (10) below:

N(A) = No exp [ - ( ^~

) . ] - (5)

2
/x. - A\ /X. - A + W\

:fc (^L_j =erfc (^L_

j

N W

N(W) N(A) N(B)

W A

I = y N(w)dw = y N(a)da (9)

N(a)da = -y— erfc [-^) - erfc ^-^j

0 ^ -J

- K A (10)

D

As shown in figure 1, A is the depletion width on the heavily-doped side of the junction, B

is the depletion width on the lightly-doped side of the junction, N(A) and N(B) are the

respective net dopant densities at distances A and B from the junction, Ng is the dopant

density at the surface of the diffused layer, and N is the estimated background dopant

density in the diffused layer. The characteristic length of the Gaussian diffusion is

represented by L, and I is the area of either of the two shaded regions in figure 1. The

lower case w and a are used as variables of integration; whereas, upper case W and A represent specific values of w and a. The quantities W, A and B are related by eq (11).

W = A + B (11)

In computer program CVl, the integral on the left in eq (9) is calculated by numerical

integration of the N(W) vs. W data. Equation (7) is used in calculating the first step in

the numerical integration and the trapezoidal approximation is used in subsequent steps.

The value of this integral, I, is used to solve eq (10) for A. Knowing A, N(A) is calculated from eq (5), N(B) is calculated from eq (8) and B is calculated from eq (11). The

desired profile is a plot or listing of N(B) vs. B.

Equation (12) below is used to calculate a true Gaussian profile for comparison with the

experimentally determined profile.

N(B) = - No exp I - \ j j (12)

Experimental profiles sometimes show a decrease in N(B) for small B. A plot of the true

Gaussian profile can be helpful in determining whether such an experimental observation is

caused by the diffusion tail or by some other phenomenon. The true Gaussian plot is also

helpful in evaluating the adequacy of the assumed value. If the experimental plot and

the true Gaussian plot do not asymptotically approach the same background density, the calculation should perhaps by repeated using a different assumed N value.

b

2.3. The Complementary Error Function

The solution of eqs (7) and (10) calls for calculating the complementary error function and

its inverse. The calculation of the complementary error function employs equations given by

Stegun and Zucker [14] as

erf (x) = e-^' E ....[^.tl ^ .^ (13)

N

A nTo l-3---(2N-+l)

erfc(x) = 1 - erf(x) (14)

3
Figure 1. Schematic representation of the depletion region of a p-n

jimction diode diffused in an epitaxial semiconductor. (The distances A

and B have their origins at the junction. Note that the actual background dopant density, represented by the irregular line to the right of

the junction, is assumed to be constant within the diffused layer to the

left of the junction.)

4
erfc(x)

/IT

2x

Zx-^ + 1 - 1-2

2x2 + 5 - 3-4

2x^ + 9--

(15)

The reader is advised that eqs (13) to (15) and the software that implements them (see sec. 3.3.) have been thoroughly proven within the range of applicability. Other approximations

to the error function and its complement should be used only with extreme caution. In program CVl, the power series representation of eq (13) is used when x <_ 1, and the continued

fraction of eq (15) is used when x > 1.

2.4. The Inverse Complementary Error Function

The inverse complementary error function is calculated by interpolation in a table of values.

The equation to be solved is

y = erf c"-^ (x) or (16) X = erfc(y)

where x is given and y is to be determined. The given variable x is first transformed using

z = -100 ^^^^^ + 100 (17)

to yield a value of z from 0 to 100 corresponding to a value of x from 10"^ to 1. The transformation is illustrated in figure 2. The 10"^ lower limit was chosen so that eq (10) could

be solved for all practical ratios of Nq to . The table of values (see listing in lines

150 to 188 of Appendix A) lists those values of y corresponding to integer values of z from

1 to 100. For example, the first value in the table y = 3.74580, corresponds to z = 1 or

X = 1.17490 X 10"^. To calculate y from a given x, z is first calculated and three data

pairs (zi, yi), (z2, 72)* snd (Z3, y^) are chosen from the table such that

Z3 > z >_ Z2 > Zj

and (18)

73 < y 1 72 < Yl

This is illustrated in figure 3. A parabolic fit to these three data pairs is made by

simultaneously solving the equations

Yl = azi + hzi + c

y2 = az2^ + bz2 + c (19)

73 = azg^ + bZ3 + c

to yield the coefficients

(73 - yi)(z2 - zi) - (72 - 7l)(z3 - zi)

(z3 - zi)(z2 - zi)(z3 - Z2) (20)

72 - 71

b =

^ _ - a(z2 + zi) (21)

c = 71 - azf - bzj (22)

Equations (20) and (21) can be simplified since Z2-Zi=l, Z3-zi=2, and Z3 - Z2 = 1. The simplified equations are

71 + 73 - 272

a = ^ (23)

5
0 1 2 3 4

y

Figure 2. Semilog plot of the function x = erfc (y) showing the transformed variable

z. (The discontinuity which occurs at z = 2 , and the fact that y = 3.76656 for 0 <_ z

< 2 reflect the value of y calculated by the INERF subroutine rather than the true

value of y as explained in sec. 3.4.)

6
Figure 3. Calculation of y = erfc~ (x) by means of a parabolic fit. (The fit is made in terms of the variable

z which is calculated from the given x by eq (17).)
b = (72 - Yi) - a(z2 + zi) (24)

Thus knowing a, b, and c, y can be calculated from z, the transformed value of x, by

y = az2 + bz + c (25)

3. PROGRAM DESCRIPTION

3.1. Data Input

Two forms of data input are employed. The C-V data are read from a file which is titled

CVIN. The file CVIN is entered into the computer before CVl is executed. Each line of

CVIN consists of a line number, the capacitance in picofarads, and the applied voltage in

volts, where reverse bias is considered positive. Data are listed in order of decreasing

capacitance. A sample CVIN file, based on data reported in [10], is given in Appendix C.

The second form of data input involves entry of scaling and diffused layer parameters as called for by INPUT statements. The program statements which request these data are lines

2514 to 2585 (see listing in Appendix A). The relevant parameters are (1) Gl or 1ST LOG,

the minimum value of dopant density which is within the range of the plot (that is, the

dopant density at the origin of the plot), (2) G2 or CHAR/DEC, the number of teletypewriter

carriage spaces between decades of dopant density (the plot is semi-log), (3) G3 or LINES/UM,

the number of teletypewriter line feeds to represent 1 ym on the plot (all positive values

are permitted), (4) D or DIAMETER, the diameter of the diode in mils, (5) X5 or JCT DEPTH,

the junction depth of the diffused layer, in micrometres, (6) NO or SURFACE DENS, the density

of diffusant atoms at the surface of the diffused layer (as measured for instance by junction

depth and sheet resistivity on a pilot slice [15]) in (centimetres) ^, and (7) N3 or ESTIMATED NB, the backgroimd dopant density within the diffused layer in (centimetres)"^. An

example of such data input is given in the sample calculation of Appendix C.

3.2. Data Output

Data output is in the form of a plot of dopant density versus distance from the junction,

N(B) vs. B. Following this plot, final values of A and N(A) representing the maximum penetration of the depletion region into the diffused layer and the net dopant density at that

point, are printed out (lines 3990 to 3992) along with the percent peripheral capacitance

correction at the last data point (i.e., the maximum peripheral capacitance correction), and

an indication of whether the range of the INERF subroutine has been exceeded (see sec. 3.4.).

Finally a true Gaussian profile is calculated and plotted for comparison with the experimental

plot. The experimental N(B) vs. B values are written into a file named NBVSB, and the numerical values of the true Gaussian plot are written into a file named IDEAL. These can be

listed if desired after the program has run as is done in Appendix C.

3.3. The ERF Subroutine

The ERF subroutine consists of lines 1400 to 1565 in the listing of Appendix A. When this

subroutine is called it operates on the variable E, calculating El = erf(E) and Jl = erfc(E)

where E corresponds to x in eqs (13) through (15). If E < 10"^^, El and Jl are set equal to

0 and 1 respectively (lines 1400 to 1406). If E > 9, El and Jl are set to equal 1 and 0 respectively (lines 1410 to 1416). If 10"^^ £ ^ ^ 1> ^1 calculated from eqs (13)

and (14). In lines 1430 to 1434 the first 10 terms (to N = 9) of the power series are summed.

Additional terms would contribute to the seventh and higher significant figures which is

beyond the range of BASIC. In line 1440 the series is multiplied by the pre-factor indicated in eq (13) to get El = erf(E).

If 9 >_ E > 1, Jl = erfc(E) is calculated from eq (15). The first approximation to the con- tinued fraction is of the form 2x/(2x^ +1), as calculated in lines 1500 to 1508 and represented by F5. A second approximation to the continued fraction includes the term 2x^ + 5 in

eq (15) and is calculated in lines 1510, 1512, and 1520 to 1526 and represented by F9 . The

first and second approximations are compared in lines 1528 and 1530. If the first and second

approximations differ by 1 part in 10^ or more, a third approximation is calculated in lines

1538 to 1546 and 1520 to 1526 to include the term 2x^ + 9 in eq (15). The second and third

approximations are then compared to determine whether the continued fraction has converged.

8
Continued iterations are made, each time comparing the present with the previous approximation,

until a relative difference of less than 1 part in 10^ is obtained. In line 1550 the con- tinued fraction is multiplied by the pre-factor indicated in eq (15) to get Jl = erfc(E).

Each approximation of the continued fraction is expressed as a quotient of two expressions

(line 1526). As the order of the approximation increases, the number of terms which are multiplied together to construct the two expressions increases. The two expressions could

become excessively large and cause overflow. This is prevented by dividing several terms by

E3 = 10^^ whenever the denominator of this quotient exceeds 10^^. This is done in lines 1532

to 1537. The division by this scale factor does not affect the result since it is applied to both numerator and denominator of the quotient.

3.4. The INEEF Subroutine

The INERF subroutine consists of lines 1000 to 1080 in the listing of Appendix A. When this

subroutine is called, it operates on the variable H9 and calculates E = erfc~^(H9) by a table

look-up approach. Note that H9 in the program corresponds to x in eq (16) and E corresponds

to y. If H9 > 1 (x > 1 in figure 2) the inverse complementary error function is not defined;

E is set equal to zero and the flag Z5 (which is printed when the main program is run) is set equal to 2 (lines 1000 to 1003). If H9 = 1, E is set equal to zero (lines 1004 to 1007).

The transformed variable HO which corresponds to z is calculated in line 1010 by eq (17).

If HO is less than 2 (corresponding to H9 less than 1.39 x 10"^) E is set equal to 3.76656

and flag Z5 is set equal to 1 in lines 1012 to 1018. This lower limit arises because (1) the

transformation of eq (17) was defined to be applicable for x in the range 10~^ to 1, (2) the

value of X corresponding to z = 0 does not appear in the data table which runs form z = 1 to

100, and (3) the parabolic fit requires that z not be less than Z2 (eq (18)) so that interpolation cannot be performed for values of x (H9) for which z (HO) is less than 2. Factors

(2) and (3) therefore serve to make the lower limit of H9 be 1.39 x 10~^ rather than 10 ^.

In lines 1020 to 1045, z^, Z2, Z3, yj, y2, and y3 are defined as HI, H2 , H3, H5 , H6, and H7,

respectively (see figure 3). The coefficients of the parabolic fit a, b, and c or II, 13,

and 14 are calculated by means of eqs (23), (24), and (22), respectively in lines 1050 to

1065. The unknown E (y) is then calculated in line 1070 as in eq (25).

3.5. The TABLE Data File

The TABLE data file consists of lines 150 to 188 in the listing of Appendix A. As discussed

in sections 2.4. and 3.4. and referring to eqs (16) and (17), TABLE is a list of y (E) values

which correspond to integer values of z (HO) from 1 to 100 inclusive and which facilitate the

computation of the function E = erfc"^ (H9) for H9 values from 1.39 x 10 ^ to 1.

3.6. The PLOT Subroutine

The PLOT subroutine consists of lines 2150 to 2460 in the listing of Appendix A. The purpose of the PLOT subroutine is to produce a semilog plot of dopant density N(B) across the

paper of the teletypewriter printout versus distance from the junction B down the paper.

The subroutine is also used to plot the true Gaussian profile for comparison with the experimental profile.

The PLOT subroutine can be understood with the help of the flow chart of figure 4 and the

partial table of symbols in table 1. Some of the line numbers in the main program are also

found in table 1. The flags Z3, Z6, and Z7 are all initially zero. The PLOT subroutine

operates on the quantities XI and Yl which are calculated from B and N2 (where N2 corresponds

to N(B)) in lines 3240 and 3270. These in turn are derived from the C-V data (lines 3000 to

3230) in the first plot and calculated values (lines 4010 to 4050) in the second plot. The

first XI, Yl pair (Z6 = 0) is stored as X2 , Y2. The Yl values of succeeding XI, Yl pairs are accumulated in Y2 until an XI, Yl pair is input for which X2 > XI, that is, which should be

plotted at a farther position along the depth axis. When this occurs Y2 is averaged and

integerized. If no data points have yet been plotted (XO = 0) , + signs are printed at decade

intervals along the dopant density axis and XO is set equal to 1 before proceeding further.

The depth X2 is compared with the line space on the plot XO. If X2 > XO, a series of tick

marks in the form of + signs are printed along the depth axis until XO is advanced to X2

(where the data point is to be plotted) . The origin of the depth axis is the first of these

9
Y2=V2/I

Y2=IIIT IY2+J.9I 2200-2209

X0=X0+1

2380

Figure 4. Flow chart of the PLOT subroutine.

10
Table 1 — Symbols Used in PLOT Subroutine

B distance from junction into the specimen, ym

Gl minimum value of dopant density to be plotted, cm"^

G2 scale factor for N(B); number of carriage spaces to represent one decade of dopant density

G3 scale factor for B; number of lines (line feeds) to represent 1 ym

XO line number along the depth axis; initial value 0

XI scaled value of B integerized for plotting purposes

(line 3270)

X2 temporary storage of XI value as further XI values

are being calculated

Yl scaled value of N2 (N(B))

Y2 accumulated, averaged and integerized value of Yl

;

accumulated as further XI values are being calculated, averaged and integerized for plotting purposes (lines 2180, 2200 and 2205)

Z number of data points plotted at same depth position

Z3 flag for last data point; Z3 = 1 after last data

point (lines 3001, 3290, 2385), otherwise 0 Z6 flag for first data pair; Z6 = 0 for the first (XI,

Yl ) pai r , otherwise 1 Z7 flag for experimental or true Gaussian plot; Z7 = 0 if experimental data is being plotted, 1 if true

Gaussian is being plotted

tick marks and not the set of tick marks denoting the scale on the dopant density axis as shown in figure 5. There are six possible ways in which the data point may appear in the

plot. (1) If Y2 < 3, the data point is off scale at the low end (dopant density too small);

this is represented by the symbol < to the left of the tick mark preceded by the value of Z to indicate how many data points are off scale at that depth value (lines 2260 and 2310).

(2) If Y2 > 71, the data point is off scale at the high end (dopant density too large); this

is represented by the symbol > to the left of the tick mark preceded again by the value of Z (lines 2300 and 2370). (3) If a single XI, Yl pair (for which Z = 1) falls on the depth

axis, an asterisk * is printed on the axis at that depth value in place of the usual + sign

(lines 2270 and 2330). (4) If an average of several XI, Yl pairs (Z > 1) falls on the depth

axis, a 0 is printed on the depth axis at that depth value in place of the usual + sign and

the value of Z is printed to the left of the 0 (lines 2270, 2329, and 2342). (5) If a single

XI, Yl pair (Z = 1) falls within the range of the plot but not on the depth axis, a * is

printed at the proper number of carriage spaces at the proper depth position (lines 2290 and

2350). (6) If more than one XI, Yl pair (Z > 1) falls at the same position along the depth

axis and Y2 is such that it is within the range of the plot but not on the depth axis, a 0

is printed at the proper number of carriage spaces at the proper depth position, and the

value of Z is printed to the left of the tick mark (lines 2290, 2349, and 2362). After the

point is plotted XO is incremented (that is, the depth axis is advanced one line), Z is

reset to 1, XI and Yl are changed to X2 and Y2 , and a new XI, Yl pair is sought (lines 2380

to 2406) . The process continues until either all the C-V data have been processed (lines

3001, 3290, 2155, 2385) or the true Gaussian plot has been completed. Note that the quantities Z3, Z6, and XO are reset to zero before the start of the second plot (lines 4000 to 4002). The flag Z7 at line 3282 determines whether experimental or calculated values of XI

and Yl are sent to the PLOT subroutine.

An example plot, showing the six possible print-outs discussed above, is shown in figure 5. In practice it is desirable to choose Gl and G2 so that as few points as possible are off

scale. It is also desirable to choose G3 so that no more XI, Yl pairs than necessary are

11
averaged and represented by a single data point on the plot. Averaged points mean reduced

resolution.

It should be noted that the PLOT subroutine breaks down when 10 or more XI, Yl pairs are averaged to produce one printed data point. Because Z is printed in 12 format (line 2312),

and because one of those two spaces is reserved for the sign (even though the sign is positive and not printed), a two-digit number cannot be represented, and the print-out reverts

to exponential format. The data point may or may not be plotted properly depending on whether it lies outside or inside the field of the exponential number and tick mark. This

problem could be resolved by printing Z in 13 format and adjusting the TAB(x) arguments

accordingly. A carriage space otherwise available for plotting would be sacrificed, however.

As one further comment, it is possible to nearly disable the PLOT subroutine by a proper

choice of scale factor G3 when plots are not desired. If G3 is made sufficiently small, for

example, 0.01, all dopant density values corresponding to distances of less than 50 ym are averaged and plotted as a single point. In addition the true Gaussian plot will probably

not appear at all since, for such small values of G3, XI is always 1 (line 3270). The FORNEXT loop (lines 4010 to 4050) is therefore completed for all necessary B values before any

points are plotted, and the program advances to line 4060 and exists.

DOPANT DENSITY (CVT-S)

Figure 5. A plot artificially constructed to show the six types of printed output of the PLOT subroutine. (The points which are off-scale to the left appear

as the first and last plotted symbols in the direction of the depth axis. The

points which lie on the depth axis appear as the second and next to last plotted

symbols. The points which are off-scale to the right appear near the center of

the plot between the increasing and decreasing sections. The remaining majority

of the points appear within the bounds of the plot. The tick marks on the dopant

density axis are one decade apart; the dopant density at the origin is entered as Gl in line 2515 of Appendix A, and the number of carriage spaces representing one decade is entered as G2 in line 2525. The number of tick marks on the depth axis

representing one micrometre is entered as G3 in line 2540.)

12
3.7. The Main Program

The main portion of the program consists of lines 098 to 100, 210 to 570, and 2500 to 4060

as listed in Appendix A. A summary flow chart is given in figure 6,

In lines 210 to 220, the values stored in TABLE are read for later use by the INERF subroutine. Flags and other quantities are assigned initial values in lines 2500 to 2508. Input

of scaling and diffused layer parameters occurs in lines 2514 to 2585 as discussed in section

3.1.

In lines 2589 to 2682, several constants are entered or calculated for later use. The constants are (1) K, the dielectric constant of silicon, (2) P, the circumference of the diode

in mils, (3) L, the characteristic length of the diffused layer, as defined in eq (6) and

used in several equations, (4) K3, equal to erfc(x-/L), and used to solve eq (10), (5) Kl,

the coefficient of W in the second term on the rignt-hand side of eq (7), (6) K5 , which has

the value kcqA^ where A. = itD^/4, used in solving eq (2), where the factor 4.48649E-03 includes the conversion or D from mils to micrometres and assumes eg = 8.8542 x lO"-^** F/cm,

START

'COMPLETE PLOt\

& PRINT DATA ) 3290-3992/

CALCULATE

TRUE GAUSSIAN

4000-4050

PLOT TRUE \

GAUSSIAN

Figure 6. Summary flow chart of program CVl.

13
(7) K7, which is 2 times K5 and is used to solve eq (2) for a single W value from two suc- cessive capacitance values (line 3090), (8) K6, which has the value 2/qKeQA? where Aj =

ttD^/A, used in solving eq (1), where the factor 5.49166E+18 includes the conversion of D from mils to centimetres, and assumes q = 1.602 x 10 '•^ C, (9) K8, which is it times 25.4,

the conversion factor for converting mils to micrometres, used in eq (3), and (10) K9,

which has the value keqix^T)/! , including the appropriate conversion factor from mils to centimetres, and used to solve eq (3). These relationships are summarized in table 2.

Table 2 — Derivation of Constants Found

in Program Lines 2660 to 2682

K5 ( 25^) 2

X JX 8.8542 x IQ-e

^ . K ^

\ 1 mi 1 / 4 pm

where D is given in mils

K7 = 2 X K5

K6

/ 1 mil \ ^ /4\ 2 2

\ 0.00254 cm/ u) 1.602 x 10"^^ coul x 8.8542 x 10"^^ F/ cm

where D is given in mils

I/O 25.4 pm

K8 = -^j X TT 1 mil

K9 = 8.8542 x 10"2 x 0.00254

^ x x K x D cm mil 2 where D is given in mils

After these constants are calculated, the program number Z9^, values of P, K and L, and a heading to the plot are printed in lines 2690 to 2750.

The C-V data are read from file CVIN in line 3000. The peripheral correction is implemented

in lines 3005 to 3014. The measured capacitance C3 is separated into its plane and peripheral components by the iterative loop in lines 3006 to 3014. In line 3005, a first estimate

WO of the depletion width W is calculated from eq (2). The peripheral capacitance C5 is

calculated from eq (3) in line 3006, and a new value of depletion width Wl is calculated

from eqs (4) and (2). The new value Wl is renamed WO and is inserted into eq (3). Successive iterations are made until the relative difference between Wl and WO is 10"^ or less.

The plane capacitance CI is then used in subsequent calculations.

In lines 3030 to 3070, a second C-V pair is read if the previous C-V pair was the first.

Two C-V pairs are required to calculate the derivative in eq (1). The quantities C2 and V2

thenceforth denote the previous C-V pair (see also lines 3100 and 3110). Flag Z2 is zero when the first data pair is read in line 3000; thereafter Z2 = 1.

An apparent profile N(W) versus W is calculated in lines 3080 and 3090 by eqs (1) and (2)

where plane capacitances rather than measured capacitances are operated on. The taking of

the absolute value in line 3080 permits the voltage VI to be measured with either polarity,

although reverse bias is generally assigned positive values for convenience.

The back depletion correction is performed in lines 3120 to 3230. The heart of the calculation is the iteration which computes A in lines 3140 to 3175. A numerical integration is

performed to evaluate the integral of eq (9). Although the trapezoidal approximation is

employed after the first step (line 3130), the first step is calculated assuming that the

Gaussian form of the diffusion continues past the junction to the depth represented by the

first N(W) versus W point.

•^Any value of Z9 can be entered in line 098. The authors find it helpful to increment Z9 by

0.01 each time the program is altered.

14
The first step numerical itegration is carried out in lines 500 to 570. Referring to eq (7) a first estimate AO = 0 is made for A in line 500. The right-hand side of eq (7) is calculated in lines 505 to 515. A second estimate Al is found by calculating A on the left-hand

side of eq (7) in lines 520 to 525. The second estimate is compared with the first estimate;

if the relative difference is greater than 10"^ further estimates are calculated by repeatedly placing the value of Al calculated in line 525 back into the right-hand side of eq (7)

(lines 530 to 545). When a suitable value of Al is obtained, it is used in eq (10) to calculate the desired integral (line 550 to 560).

Having thus calculated the integral in eq. (10) , the same equation is effectively rearranged

in lines 3135 and 3145 so that the expression erfc(x.! - A)/L is on the left-hand side of the

equation and everything else is on the right-hand side. An initial value of A, AO, is placed

in the right-hand side and a corrected value Al is calculated on the left-hand side in lines

3140 to 3155. The values Al and AO are compared in line 3160; if their relative difference

is greater than 10 ^, the value Al becomes the initial value AO and a new corrected value Al

is calculated (lines 3165 and 3170) . The iteration continues until sufficient agreement

between AO and Al is achieved, and A is set equal to Al , Using eqs (5), (8), and (11), N(A),

N(B) and B are calculated in lines 3190 to 3210. The N(B) versus B pairs are written into

file NBVSB in line 3215 for later listing if desired. The values of N(W) and W are saved' as N7 and X7 in lines 3220 and 3230 for subsequent use in the trapezoidal numerical integration.

Scaling and plotting is then done in lines 3240 to 3280.

After all the C-V data have been processed and the print-out of line 3990 is completed, a true Gaussian dopant density profile is generated in lines 4010 to 4050. Equation (12) is

solved in line 4020 for a set of B values given in line 4010. The N(B) versus B values are written into IDEAL for later listing if desired in line 4025 and plotted in line 4040. This

represents the profile that would be calculated if (1) the diffused layer were a pure

Gaussian having parameters Nq , and x, which were accurately known, (2) the dopant density

of the specimen were uniform at a level^'N^, and (3) various assumptions such as zero diffusion capacitance and abrupt space charge region boundaries were valid.

A sample calculation using program CVl is given in Appendix C.

4. MODIFICATIONS AND TROUBLE- SHOOTING

4.1. Limitation on Program Length

Program CVl contains 249 statements (exclusive of comment statements). As stated in section

1, the maximum number of statements permitted by BASIC is 256. The user must therefore exercise caution in attempting to expand the program to meet his individual needs. Additional

space could be created by compressing the TABLE data file to more than five entries per line.

Even more space could be made available by removing statements relating to the true Gaussian

plot if that is not needed. This could be done by deleting lines 2504, 3282 and 4000 through

4050 and deleting IDEAL from line 099.

4.2. Formation of Subprograms

The problem of program length discussed above can be solved and other advantages can be

gained by separating one or all of the ERF, INERF and PLOT subroutines and the TABLE data

file from the main program and creating each as an independent program or file. These subprograms can then be executed by the main program using CALL statements in place of the

present GOSUB statements. When this is done, substantial additions can be made to the main

program before the limit on program length is reached. This procedure has the advantage of

making the subprograms available to be called by other programs. The authors have employed

the ERF subroutine in this manner. If the INERF subroutine is to be set up as an independent subprogram, a means for reading in the TABLE values , presently done in lines 100 and

210 to 220, must be included in the program which calls INERF. In all such subprograms, an

END statement must be included as the last statement.

4.3. Rectangular Diodes

In some applications it may be desirable or necessary to measure dopant density profiles

using rectangular rather than circular diodes. The equation for the peripheral correction

15
in such a diode is given in [12]. This equation can be coded to solve for the plane

capacitance in place of the existing lines 3005 to 3014 using a similar approach (only line

3006 need actually be changed) . It is then necessary to enter the dimensions of the rectangle in place of the circular diameter in the present lines 2550 and 2555. Other lines which

need to be altered are 2590 and 2660 to 2682. The changes which are necessary are given in

table 3. The statements in table 3 should be inserted into the listing of Appendix A in

place of the existing statements. No statement appears after line number 2681 in table 3 indicating that for rectangular diodes that line should be deleted from the listing of

Appendix A.

Table 3 — Statements to be Modified in CVl

for the Case of Rectangular Junctions

2550 PRINT "WIDTH (MILS) = "%

2552 INPUT SI

2555 PRINT "LENGTH (MILS) = "I

2557 INPUT 52

2590 P=2*(S1+S2)

2660 K5=5.7I238E-03*K*S1*S2

2670 K6=3.38753E+18/(K*SJ*SI*S2*S2)

2680 K7=l . J4248E-02*K*S1*S2

2681

2682 K9=5.563 26E-d5*K

3006 C5=K9* I 2. 7* ( S 1 +S 2) /LOG( I +W0/X5 ) +K9*X5* (X5+W0 ) /WO

4.4. LOG ER Errors

On occasion program CVl produced a LOG ER statement indicating that it was attempting to compute the logarithm of a negative number. The log computation is performed in line 3240.

The negative number originates in line 3200 and may be produced if the input parameters D,

, Ng and (lines 2550 to 2585) are not sufficiently accurate.

4.5. Program CV2

A second BASIC computer program, titled CV2, has been written which generates idealized C-V

data for a Gaussian diffused p-n junction diode. Such data can be used for checking program

CVl. For example, when ideal data are generated for the case Ng = 10^^ cm~^ , = 3 x 10^^

cm~^, Xj = 1.0 pm and D = 6 mils and are entered as CVIN into program CVl, a profile corre- sponding to a true Guassian which asymptotically approaches N(B) = 3 x 10-'^^ cm ^ should be

calculated. If it is not, there is an error in either program CVl or CV2.

Program CV2 is listed in Appendix D. Input parameters are entered from the teletypewriter

in lines 100 to 127. The built-in voltage is entered as the constant VO; it does not take

account of the dependence of built-in voltage on the applied bias [10]; the agreement of a profile calculated via CV2-CV1 with the originally assumed profile is independent of the

choice of built-in voltage. The C-V data, however, are more in agreement with experimental

data if an appropriate choice of built-in voltage is entered. The calculation begins with a set of A (represented in CV2 as Al) values given in line 150. The initial and final capacitance values and the capacitance interval are determined by the coefficients of X5 in line

150 which can be altered as needed. Given the set of A values, the corresponding B (represented as Bl) values are calculated from eq (7), modified by letting W = B - A so that B is

given as an implicit function of A. This modified eq (7) is solved in lines 160 to 260.

The voltage VI is calculated using eq (12) of [10] in lines 320 to 350, and the plane capacitance is calculated in line 360 by eq (2) of this report. The peripheral capacitance is

added in lines 370 to 380 using eqs (3) and (4). The C-V pairs are printed out in line 390

and written into file GAUSCV in line 395. By renaming GAUSCV as CVIN, the C-V data file can be made compatible with the input required for program CVl. The subroutine for calculating

the complementary error function in lines 1400 to 1565 is identical with that subroutine in

CVl. The constants in lines 142 to 144 are analogous to the constants in lines 2640, 2681

and 2682 of CVl and are derived from the same values of eg and q. A sample calculation using

program CV2 is performed in Appendix E.

16
As was the case with CVl (sec. 4.3.)> program CV2 can be modified if necessary to make it

applicable to rectangular diodes. The alterations which need to be made are given in table

4. The statements in table 4 replace the statements having the same line number in the

listing given in Appendix D. The statement with line number 143 should be deleted from the

listing given above for the case of rectangular diodes.

Table 4 — Statements to be Modified in CV2

for the Case of Rectangular Junctions

105 PRINT "WIDTH (MILS) = » 106 INPUT SI

107 PRINT "LENGTH (MILS) = "?

108 INPUT S2

143

144 K9=5.56326E-05*K

360 CI =5.71 238E-03*K*S1*S2/(A1+BI

)

375 C2=K9*( 12.7*(S1+S2)/L()G( 1 +W/X5 ) + ( X5+W) *X5/W)

17
APPHMDIX A: LISTING OF PROGRAM CVl

050 * PROGRAM CVl — CALCULATES A DOPANT

051 * DENSITY PROFILE FROM C-V DATA PAIRS

052 * FOR A GAUSSIAN DIFFUSED P-N JUNCTIf)M

053 * 098 Z9=10.52

099 FILES CVIN,NBVSB, IDEAL

100 DIM H(I05)

120 *

121 * "TABLE" DATA FILE

122 *

1 50 DATA 3.74580 , 3.7 249 2 , 3. 70394 , 3.68285 , 3 .661 64

152 DATA 3.64031 , 3.6 1887 , 3. 59731 , 3.57562 , 3 .55382

154 DATA 3.53189 , 3.50982 , 3. 48 763 , 3.46531 , 3 .44 286

156 DATA 3.42026 ,, 3.39753 , 3. 37465 , 3.35163 , 3 .32847

1 58 DATA 3.30515 , 3.28168 , 3. 25805 , 3.23427 , 3 .21032

160 DATA 3. 18620 , 3. 16192 , 3. 13747 , 3. 1 1 283 ,, 3 .08802

162 DATA 3.06303 , 3.03785 , 3. 01247 , 2.08690 , 2.96 1 1 3

164 DATA 2.93515 , 2.90896 , 2. 88 256 , 2.85593 , 2 .8 2908

166 DATA 2.80200 , 2.77467 , 2. 74711 , 2.71920 , 2.691 22

168 DATA 2.66288 ., 2.63427 , 2. 60539 , 2.57621 , 2 .54674

1 70 DATA 2.51696 ,, 2.48687 , 2. 45645 , 2.42570 , 2.39460

1 72 DATA 2.36315 ,

, 2.33133 , 2. 299 1 3 , 2.26653 , 2 .2 3352

1 74 DATA 2 . 20009 , ?..\66?J , 2. 13 188 , 2.09 707 , 2 .061 76

176 DATA 2.02594 , 1.98957 , 95265 , 1.91513 ,1 .87699

1 78 DATA 1.8382 1

,,

1 .79875 ,1 « 75857 ,

I .71764 ,

1 .67592

130 DATA I .63335 , 1 .58990 ,

1 • 54550 ,1 .50009 ,1 .45360

182 DATA 1 .40597 ,1 .35710 ,

1 • 3069 1

, 1.25528 , 1 . 202 1 0

184 DATA 1 .14722 , 1 .09049 ,

1 • 03172 , .97069 , .90715

1 86 DATA .84078 ,

, .77121 , • 69798 I

,

.62052 , .53808

1 88 DATA .449681

,

, .35403 , • 24928 , . 1 32 7 , 0

200 *

201 * READ VALUES FROM "TABLE"

202 * FOR "INERF" SUBROUTINE

203 * 210 FOR H0=1 TO 100

215 READ H(HO)

21 7 IF H0=1 00 THEN 2500

2 20 NEXT HO

495 * 496 * CALCULATE FIRST VALUE OF INTEGRAL I 497 * 500 A0=0

505 E=(X5-A0+X)/L

510 GOSUB 1400

515 H9=Jl+( 1 . 1 2838*N3*X)/(N0*L)

520 GOSUB I 000

525 A1=X5-E*L

530 IF ABS( ( Al -A0)/A1 )<=1 .OE-05 THEM 550

540 A0=A1

545 GO TO 505

550 E=(X5-A1 )/L

555 GOSUB 1400

560 I = (L*N0/1 . 1 2838)*( J1-K3)-N3*A1

570 GO TO 3135

18
090 * 991 "INHRF" SUBROUTINE

993 * 1000 IF H9<=1 THEN 1004

1001 E=0

1002 Z5=2

1003 GO TO 1080

1004 IF H9<I THEN 1010

1 005 E=0

1007 GO TO 108 0

1010 H0=(-1 00*L0G(H9)/L()G( 1 . OOOOOE-07 ) ) + 1 00

1012 IF H0>=2 THEN 1020

1014 E=3. 76656

1016 Z5=l

1018 GO TO 1080

1020 H 2= I NT (HO)

1025 H3=H2+1

1030 H1=H2-1

1035 H5=H(H1

)

1040 H6=H(H2)

1045 H7=H(H3)

1050 I l=(H7+H5-2*H6)/2

1060 I3=H6-H5-I 1*(H2+H1

)

1065 I4=H5-I 1 *HI *H I -I3*H

I

1070 £=I 1 H0*H0+I3*H0+I4

1080 RETURN

1 390 *

I 391 * "ERF" SUBROUTINE

1393

1400 IF E>=1 .OOOOOE-3 2 THEN 1410

1402 E1=0

1404 J 1=1

1406 GO TO 1565

1410 IF E<=9 THEN 1420

141 2 El=l

1414 J 1=0

1416 GO TO 1565

1420 IF E>1 THEN 1500

1 430 El =1 + .666667*E"2+.266667*E''4+7.6I905E-02*E'^6

1432 E1=E1 + 1 .6931 2E-02*E'^8 + 3 . 07840E-03*E'' 1 0+4 . 73600E-04*E" 1 2 1434 E1=E1+6.3I467E-05*E"14+7.42903E-06*E'^16+7.8 2003E-07*E''18

1440 E1=I . 1 2838*E*E1*EXP(-(E''2))

1445 J1=1-E1

1450 GO TO 1565

1500 F2=0

1502 F4=l

1504 FI=2*E

1506 F3=2*E*E+1

1508 F5=F1/F3

1510 F6=l

1512 F8=F3+4

1514 E2=l .OE-06

1516 E3=I .OE+25

1 520 F7=-F6*(F6+1

)

19
1522 E4=F8*F1+F7*F2

1524 E5=FS*F3+F7*F4

Id 26 F9=E4/E5

1528 E6=ARS(1-(F9/F5))-E2

1530 IF E6<=0 THEN 1550

1 531 IF F5>F9 THEN 1 548

1532 IF E5<E3 THEi^l 1538

1534 E4=E4/E3

1535 E5=E5/E3

1536 FI=F1/E3

1537 F3=F3/E3

1538 F2=Fi

1539 F4=F3

1540 F1=E4

1541 F3=E5

1543 F6=F6+2

1544 F8=F8+4

1545 Fd=F9

1546 GO TO 152 0

1548 F9=F5

1550 J1=.56419*F9*EXP(-(E''2))

1 555 El=l -Jl

1565 RETURN

2 140 * 2141 * "PLOT" SUBROUTINE

2142 *

21 50 IF Z6=0 THEN 2390

21 55 IF Z3=l THEN 2 200

21 60 IF X 1 >X2 THEN 2200

2 I 70 Z=Z+

1

2180 Y2=Y1+Y2

2190 GO TO 2406

P200 Y2=Y2/Z

2205 Y2=IN1 (Y2+3.5)

2210 IF X0=0 THEN 2410

2220 IF X2=X0 THEN 2 260

2230 PRINT TAR(3)"+"

2240 XO=XO+1

2250 GO TO 2 220

2260 IF Y2<3 THEN 2310

2270 IF Y2=3 THEN 2329

2290 IF Y2<=71 THEN 2349

2300 IF Y2>71 THEN 2370

2310 PRINT, 231 2,Z, "< + " 2312 FMT 12

2320 GO TO 2380

2329 IF Z>1 THEN 2342

2330 PRINT TAB (3)"*"

2340 GO TO 2380

2342 PRINT, 231 2,Z, " 0"

2344 GO TO 2380

2349 IF Z>1 THEN 2362

2350 PRINT TAR(3)"+";TAB( Y2) "*" 2360 GO TO 2 380

2362 PRINT, 231 2, Z, TA B( 3

) " + " ; TAB( Y2 ) "0"

20
2364 GO TO 2380

2370 PRINT, 23 1 2,Z, ">+"

2360 X0=X0+1

2385 IF Z3=I THEiJ 2406

2390 Y2=Y1

2 394 X2=X1

2398 Z=l

2402 Z6 = l 2406 RETURN

2410 FOR Y0=3 TO 71 STEP G2

2420 PRINT TAR( YO) "+"

;

2430 NEXT YO

2440 PRINT

2450 XO=l

2460 GO TO 222 0

2490 * 2491 * SEl INITIAL VALUES

2492 * 2500 Z2=0

2501 Z3=0

2502 Z5=0

2503 Z6=0

2504 Z7=0

2505 X0=0

2d06 X7=0

2507 N7=0

2508 1=0

2510 * 25 1 1 * ENTER SCALING AND

2512 * DIFFUSED LAYER PARAMETERS

251 3 * 2514 PRINT " 1 ST LOG = "

;

2515 INPUT Gl

2520 PRINT "CHAR/DEC = " ;

• 2525 INPUT 02

2530 PRINT "LINES/UM = "; 2540 liJPUT 03

2550 PRINT "DIAf.'ETER (MILS) = "? 2555 INPUT n 2560 PRINT "JCT DEPTH (UM) = 2565 INPUT X5

2570 PRINT "SURFACE DENS (C^r -3) = "; 25 75 INPUT NO

2580 PRINT "ESTIMATED NP (CM" -3) = "; 2585 INPUT N3

2586

2587 CALCULATE SEVERAL CONSTANTS

2588 * 2589 K=1 1 .7

2590 P=3. 141 59*D

2600 L=X5/S0R(L()G(N0/N3))

2610 E=X5/L

2620 GOSUP 1400

2630 K3=J1

2640 Kl=l . 1 2838*N3/NO/L

21
2660 K5=4.48649E-03*K*n*D

2670 K6='j.49166E+18/(K*n'"4)

2680 K7=8 .97298E-03*K*D*n

2681 K8=79.796b

2682 K9=l . 1 no82E-03*!<*D

2685 * 2686 * PRINT OUT SEVERAL CONSTANTS

268 7 * AMD PLOT HEAD IMG

2688 * 2690 PRINT "CV N(8) VS. R PROFILE, PROGRAM # ";Z9

2730 PRINT, 2735,P,L,K

2735 FMT "P(MILS) =",F7.3," L(UM) =",F6.3," DIEL. CONST. =",F7.3

2740 PRINT, 2750

2750 FMT /X22, "Dr)PANT DENSITY (CM'^-3)"//

2990 * 2991 * READ IN C-V DATA AND

2992 CORRECT FOR PERIPHERY

2993

3000 READ # 1 ,C3, VI 3001 IF END #1 THEN 3 290

3005 W0=K5/C3

3006 C5=K9/L0G(( I+iN0/X5)/( l+4*W0/( K8*D+4*X5 )) ) 3008 CI=C3-C5

3009 i^l=K5/Ci

3010 IF APS((^^1-W0)/W1 XI .OE-06 THEN 3030

3012 W0=-^I1 3014 GO TO 3006

3030 IF Z2=l THEN 3080

3040 C2=C1

3050 V2=V1

3060 Z2=l

3070 GO TO 3000

3074

3075 CALCULATE APPARENT

3076 * PROFILE IH'i) VS. W 30 77

3080 N=ABS(K6*(V2-V1 )/( ( 1/(C2*C2) ) -( I /( C I *C I ) ) )

)

3090 X=K7/(C1+C2)

3094 * 3095 * PERFORM DIFFUSED LAYER CORRECTION

3096 * AND GENERATE CORRECTED PROFILE

3097 * 3100 C2=CI

3110 V2=V1

3120 IF 1=0 THEN 500

3130 I=I+(N7+N)*(X-X7)/2

3135 K2=l .12338*I/N0/L

3140 A0=0

3145 H9=K1*A0+K3+K2

31 50 GOSUB 1 000

3155 A1=X5-E*L

3160 IF ARS((A 1 -AO)/A I )<1 .OOOOOF-05 THEN 3175

3165 AO=AI

31 70 GO TO 3145

3175 A=AI

22
3190 NI=NO*EXP(-( (X5-A)/L)"2)-N3

3200 N2=l/( ( l/N)-( 1/Nl )

)

3210 B=X-A

3215 WRITE #2,N2,R

3220 N7=M

3230 X7=X

3235 * 3236 * CALCULATE SCALING PARAMETERS

3237

3240 YI=G2*L0G(N2/Gi )/L()G( 10)

3270 X 1=INT(G3*R+1 .5)

3280 GOSUB 2150

3282 IF Z7=l THEN 4050

3284 GO TO 3000

3 290 Z3=l

3300 GOSUB 2150

3980 * 3981 * PRINT OUT P ARAAIETERS

3982 * RELATING TO CORRECTIONS

3983 * 3990 PRINT, 3992, A, Nl , 1 00*C5/( C 1 +C5 ) ,Z5

3992 FMT /"A(UM) =",F9.6," N(A) =",EI2.6," %C()RR =",F8.4," Z5 = 'M2//

3995 * 3996 * PLOT TRUE GAUSSIAN PROFILE

3997

4000 Z3=0

4001 Z6=0

4002 X0=0

4010 FOR B=.I*L TO 2*L STEP .

1 *L

4020 N2=N3-NO*EXP(-((X5 + B)/L)'"2)

4025 WRITE #3,N2,B

4030 Z7=l

4040 GO TO 3240

4050 NEXT B 4060 END

23
APPENDIX B: SOME COMMENTS ON BASIC

As discussed in section 1, the particular type of BASIC employed in this program is compatible with most of the BASIC language family. In the interest of clarification, however,

some of the program statements and system commands are now discussed.

The use of external files is employed by use of READ # and WRITE # statements in conjunction

with a FILES statement. For instance if a file titled ABC consists of a set of ten numbers

to be used as input data, and if these numbers are to be multiplied by 2 and written into a new file titled DEF which is created at the time of program execution, the statements for

doing this would be

10 FILES ABC, DEF

20 FOR I = 1 TO 10

30 READ # 1, A

40 B = 2 * A

50 WRITE // 2, B

60 NEXT I 70 END

The number following the // sign in lines 30 and 50 indicates which file named in the FILES

statement of line 10 is to be read from or written into. If program CVl is to be run on a system which cannot access external files, the C-V data can be entered in DATA statements

anywhere in the program after line 188 and read by a READ statement (no # symbol). In place of the WRITE # statement, N(B) and B values can be stored in an array to be called

out later in the program by a PRINT statement.

The LET statement has been abbreviated to omit the word LET. For example, in line 505 of

Appendix A the statements

505 E = (X5 - AO + X)/L and

505 LET E = (X5 - AO + X) /L are equivalent. If program CVl is to be run on a system which requires that LET be present,

it should be inserted in all the necessary lines.

The IF END #n statement in line 3001 of Appendix A provides a means for branching in the

program if no more data are found in file number n. The end of the C-V data could alternately be signaled by inserting a dummy C-V pair with a negative capacitance after the final

actual C-V data pair. Line 3001 could then be

3001 IF C3 < 0 THEN 3290.

The formatted PRINT statement permits printed outputs to be formatted according to the FMT

statement in the line number given following the first comma in the PRINT statement. For

example, the formatted PRINT statement in line 3990 of Appendix A refers to the FMT statement in line 3992. The FMT statement dictates that after a line feed (denoted by /) the

characters A(UM) = are printed, then the current value of A in F9.6 format, and so on. The use of FMT statements is not necessary, and on systems not having this capability they can

be deleted and unformatted PRINT statements used for data output.

Comment statements are introduced by an asterisk (*) as the first printed character following

the line number. In some types of BASIC, REM rather than * is used for comment statements.

These statements may be deleted without affecting the operation of the program.

System commands are more dependent on the system being used. For the system on which program CVl was run, the program is entered by the command CREATE CVl, listed by the command

LIST CVl, and executed by the command BASIC CVl. These system commands are given to the

computer as indicated in the sample calculations of Appendices C and E. Other systems may

have different but analogous sets of system commands.

24
APPENDIX C: SAMPLE CALCULATION USING PROGRAM CVl

A sample calculation using the C-V data given in [10] is shown below. The calculation,

which occupies three pages in this report, consists of four parts, each part being introduced by a system command entered from the teletypewriter keyboard following the printing

of a question mark (?) by the computer. In the first part, following CREATE CVIN, the C-V

data are entered from the teletypewriter or from punched paper tape in the format described

in section 3.1. In the second part, following BASIC CVl, the actual calculations are performed and the plots are printed. Note that the numbers following exclamation points (!) are entered by the operator from the keyboard. The scaling is such that the dopant density

along the depth axis is 5 x 10 cm" 3; the tick marks on the dopant density axis are one decade apart. The depth axis scale of 5 lines/ym means that there is 0.2 ym between tick

marks. The origin of the depth axis is the second tick mark on that axis as shown in figure

5. In the third part, following LIST NBVSB, the values of N(B) in (centimetres)"^ and B in

micrometres calculated from the experimental data are listed in two columns (three columns

including the line number). In the fourth part, following LIST IDEAL, the values of N(B) in

(centimetres) ^ and B in micrometres calculated for a true Gaussian profile are listed in two columns.

?CWEArE

BEGIN

0010

0020

0030

0040

00^0

0060

0070

0080

0090

01 00

0110

01 20

01 30

01 40

01 50

01 60

01 70

01 80

01 90

0200

02 1 0

02 20

0230

0240

0250

0260

02 70

0280

0290

CVIN

36. 1 2

27.07

22.09

20. M

1 8.07

1 o . 1 3

15.13

13.16

1 2.08

11.12

10.14

9. 1 02

8.2

7.507

6.806

6. 21 3

5.918

5.609

5.356

5.113

4.QIQ

4.714

4.522

4.32

4. 1 1 3.911

3.764

3.614

3.524

-.3502

-. 1 649

.0903

.2561

.5034

.8387

1 .073

1 .703

2.2

2.782

3.558

4.686

6.059

7.489

9 .424

1 1 .64

12.99

14.66

1 6.25

10

19.59

2 1 .48

23.49

25.87

28.79

32.7

39.25

58.2

34 .99

?BASIC CVl

RUN

1 5T LOG = ! 5.0L->1 4 CHAR/DEC = ! 40

LINES/Ur! = ! 5

niAMETER (iaLS) = ! JCT DEPTH (UM) = ! 2.

SURFACE DhMS (C/r-3)

ESTI,MATEO NR (C,vr-3)

CV N(-i) 75. B PROEILE

P(MILS) = 62.832 L(U

20

.460

= I 3.2F+18

1 .4E+15

PROGRAM #

) = .885 n I EL

0.52

, CONST. 1 1 .700

25
DOPANT DEMSITY (C,vr-3)

+

+

+

+ 'k + •k 2 + 0

2 + 0

+

2 + 0 + •k + •kX

1T

+ K + ic + •k +

2 + 0

+ if +

+

+ * +

+ *

+ * +

+

+

++

A(UM) = .702d96 ;(^) = .603B0«P 17 .xCnii-H = 5.859^ 0

+ +

+ X

2 + 0

2 + 0

2 + 0

3 + 0

2 + . 0

2 + 0

2 + 0

4060 HXIT

26
?LIST NBVSR

00)0 .i040Q2E

0020 .122829E

0030 .128460E

0040 .r31b33E

OObO .1341537E

0060 .I37963E

0070 .136185E

0080 .138005E

0090 . 1 39834E

0100 .138794E

Olio .13938bE

0120 .140371E

0130 .14 1 149E

0140 .141358E

0150 .142793E

0160 .140783E

0170 . 141941

E

0180 .14139IE

0190 .1403 22E

0 200 .139964E

0210 .13876yE

0220 . I 382 98

E

0230 .136869E

0240 .I38375E

0 2bO .168B42E

0260 .3473bOE

0270 .96'/007E

0280 .239498E

16, .447257

16, .60875 2

16, . 730555

16, .823065

16, .938722

16, 1 .04371

16, 1 . 1 7367

16, 1 .341 41 16, 1 .47976

16, 1 .63754

16, 1 .83752

16, 2 .0762

1

1 6, 2.31893

16, 2. 57758

16, 2.8696

1

16, 3 . 1 0 777

16, 3 . 29 1 69

16, 3.46 1 79

16, 3.66729

16, 3.8466

16, 4.02515

16, 4.21 878

16, 4.4 2891

16, 4 .6704O

16, 4,93474

1 % 5.1 7544

16, 5.38478

1 5.54458

VLISr I HEAL

0010 .605266E

0020 .957787E

0030 .11588 IE 0040 .127106E

0050 .133 243E

0060 . 1 36529E

0070 .138 253E

0080 .139 133E

0090 .139583E

0100 .1 39802

E

0110 .1 39908

E

0120 .139958E

0130 .13998 IE

0140 .13990 2E

0150 .139906E

0160 .139999E

01/0 . 1 39999E

0180 .I40000E

0100 .140000E

15, .884547E-01

15, . 1 76O09

16, . 265364

16, .35381

9

16, .442 27 3

16, .530728

16, .619 183

16, .7076 38

16, .796092

16, .884547

16, .973002

16, 1 .06 1 46

16, 1 . 1 4991

16, 1 . 23'^ 3 7

1'^, 1 . 3268 2 16, 1 . 4 1 5 28

16, 1 .50373

16, 1 .592 1

8

16, 1 .68064
APPHMPTX Hi LTSTTNC5 OF PP.Onu ^!^ ?.

080 FILES GAUSCV

090 HRINT "VEH 16, 3/11/75"

100 PRINT "JOT DEPTH (UM) = "; 102 INPUT X5

10b PRINT "DIAMETER (MILS) = "; 10b INPUT D

110 PRINT "SURFACE OE'^IS (CM"-3) = "»

1 1 2 INPUT UO

120 PRINT "RACKGROUND DENS (CM"-3) = 12b INPUT N3

126 PRIITf "RUILT-IN VOLTAGE = "; 127 INPUT VO

130 K= 1 1 . 7 140 L=Xb/SuR(L()G(N0/N3) )

i 42 K2=N3*1 . 1 2838/NO/L

143 K8=79.7065

144 K9=l . 1 0982E-03*K*D

1 46 PR INT, 1 47

147 FMT /X6,"C3",X 12, "VI "/

1'j.O FOh Ar=0.10*X5 TO 0.'^6*X5 STEP 0.02*X5

1 60 E=(Xb-Al )/L

16b J3=E

1 10 (30SUR 1400

1 /b J2=J1

190 R0=0

200 E=(X5+H0)/L

210 GOSUR 1400

220 B2 = ( ( J2-Ji )/i<2 )-Al

230 IF ABS ( (R2-R0)/B2)< 1 .OE-07 THEN 260

240 R0=R2

2dO go Tf) 200

260 R1=B2

3 20 Vb=(AI*Al )-(Rl*Bl ) - ( 2*X5* ( A 1 +R 1 )) 330 v6=(N0*L*L/N3)*EXP(-( (Xb-A 1 ) /L )"2)

340 V7=-(NO*L*L/N3)*EXP( -( (Xb + BI )/L)'^2)

3!d0 V 1 =9.04768E-1 b*N3*( Vb+V6+V7) /K

360 01 =4.48649E-0 3*K*D'fD/( A I+Rl ) 370 .•J=A1+BI

3 75 C2=K9/L0G( ( 1+ l/Xb)/(l+4*rt/(K8*D+4*X5) )) 380 C1=CI+C2

390 PRINT 01 , -VO-Vl

39b h'RITE #1,01 ,-VO-v 1 400 NEXT Al 490 STOP

1400 IF E>=1 .OOOOOE-32 THEN 1410

1 402 E 1 =0

1404 Jl=l

1406 GO TO lb6 5 14 10 IF E<=o THEN 14 20

1412 El=l

1414 J1=0

1416 GO TO Ib6b

1420 IF E>1 THElJ 1500

28
I 430 E I = 1 + . 666667*E'^2+.266667*E"4+7.6 1905H-02*E'^6

1432 E1=E1 + I .6931 2E-0 2*E''S + 3. 07840E-n3*E" 1 n+4. 7360nE-04*F''

1434 E1=£1+6.31467E-05*E"I 4+7.42903E-n6*F'^ I 6+7 .8 2003E-07*E

1440 El=l . 1 2838*E*E1*EXP(-(E"2))

1 445 J 1 = 1 -hi

1450 GO TO 1665

1500 F2=0

1502 F4=l

1504 Fl=2xE

1506 F3=2xE*E+l

1508 F5=F1/F3

1510 F6=l

1512 F8=F3+4

1514 E2=l .OE-06

1516 E3=l .OE+25

1520 F7=-F6*(F6+1

)

15 22 E4=F8*FI+F7*F2

1524 E5=FB*F3+F7*F4

1526 F9=E4/E5

1528 E6=ABS(1 -(F9/F5) )-E2

1 530 IF E6<=0 THEM 1 550

Id31 if F5>F9 THEN 1548

1532 IF E5<E3 THE:^i 1538

1534 E4=E4/E3

1535 E5=E5/E3

1536 F1=F1/E3

1537 F3=F3/E3

1538 F2=F1

1539 F4=F3

1540 F1=E4

1541 F3=E5

1543 p6=F6+2

lo44 F8=p8+4

1545 F5=F9

1546 GO TO 1520

1548 F9=F5

1550 J1=.564I9*F9*FXP(-(E"2))

1555 E1=1-J1

1565 RETURN

15 70 END

\ 29
APPENDIX E: SAMPLE CALCULATION USING PROGRAM CV2

A sample calculation using the diode parameters given in the first paragraph of section 4.5.

is performed below. The idealized C-V data thus generated by program CV2 are then entered

into program CVl to see if in fact the originally assumed profile is produced.

As in Appendix C, characters following a question mark (?) or exclamation point (!) are entered by the operator from the teletypewriter. The command BASIC CV2 initiates execution

of program CV2 and produces a tabulation of C-V pairs which are also written into file

GAUSCV. The command RENAME GAUSCV CVIN gives a new name to this file so that it is compatible with program CVl. The command BASIC CVl and subsequent commands have already been dealt

with in Appendix C. The fact that files NBVSB and IDEAL give plots which can be superimposed

means that CVl and CV2 are probably free of errors.

V3ASIC CV2

RUN

VEH 16, 3/1 1/75

JCT DEPTH (UM) = ! 1.0

DIAMETER (MILS) = ! 6

SURFACE OEMS (CM"-3) = ! 1.0E+I8

BACKGROUND DENS (CM"-3) = ! 3.0E+I6

BUILT-IN VOLTAGE = ! 0.7

C3 VI

6 .78502 -.402974

7 . 1 2055 -. 1 51 537

5 .9 2403 . 231 969

5 .02001 .79025

4 .31 095 1 .5765

3 .73864 2.6554

3 .2663 4. 1 0603

2 .86967 6.02497

2 .53223 8.53001

2 .24239 1 1 .7635

I .991 79 1 5.8967

1 .77412 21 . 1 343

1 .58445 27.7186

1 .41877 35.9334

400 EXIT

7RENAME GAUSCV CVIN

?BASIC

RUN

1ST LOG = ! 1 .OE+1

5

CHAR/DEC = ! 30

LINES/UM = ! 20

DIAMETER (MILS) = ! 6

JCT DEPTH (UM) = ! 1.0

SUf?FACE DENS (CM'^-3) = ! l.OE+18

ESTIMATED NB (Cf..r-3) = ! 3.0E+16

CV N(B) VS. B PROFILE, PROGRAM # 10.52

P(MILS) = 18.850 L(U'-.f) = .534 DIEL. CO;.|ST. = 11.700

I

I

30
nOPAMT DE'^ISITY (C/r-3)

+ +

+

++

2 + 0

+ X + *

+ *

+ *

++

+ *

+ Vc +

+ *

+

+ *

+

+ *

+

+

+ *

A(U,M) = .349707 lUA) = .IO708 2E IB :iCnUU = 6.2Q20

+ +

+

+ *

+ *

+ *

+ *

+ *

+

+ X +

+ *

+ *

+ *

+ *

+ *

+ *

+ *

+ X

+ *

+ *

+ * 4060 tXIT

31
?LIST MP.VSB

no 10 17, . ! 39570

0020 . 223280E 17, . i 741 32

0030 .244 271

E

17, .212609

0040 .26 1692E 17, .255602

0050 .275252E 17, .303834

0060 . 2851 90E 17, .3581 39

0070 . 291942E 17, .41 9452

OOHO . 296 I 57E I 7, .48879

0090 .298453E 17, .567187

0 1 00 .29955 1

E

I 7 .65569

Olio .299981

E

17, .755298

0120 .3001 lOE "7. ,866951

01 30 .3001 30E 17, .99 1 534

?L I ST IDEAL

00 1 0 .957664E 16, .5M02 2E-01

0020 . 1637I5E 17, . 1 06804

0030 . 21 0858E 17, . 1 60207

0040 . 242848E i 7, . 21 3609

0050 .264083E 17, .2670 1 1 0060 .277876E 17, .3 2041

3

00 70 . 28664 1

E

17, .3738 16

0080 . 2O2094E 17, .427218

0090 .295413E 17, .4806 2 01 00 .297392E 1 7, .5340 22

0110 .298546E 1 7, .587425

01 20 . 2 092 06

E

17, .64082 7 01 30 . 299575E 17, .604229

01 40 . 209777E 17, .747631

01 50 .2f59885E 1 7, .801033

01 60 .2 99042

E

1 7, .854436

01 70 .299971

E

17, .907837

01 80 . 20 9986E I 7, .96 1 24

01 90 .29 9903E 17, 1 .01 464

0200 .29 9997E 17, 1 .06804
REFERENCES

1. Hilibrand, J., and Gold, R. D. , Determination of the Impurity Distribution in Junction

Diodes from Capacitance-Voltage Measurements, RCA Review 21_, 245-252 (1960).

2. Kennedy, D. P., Murley, P. C. , and Kleinfelder, W. , On the Measurement of Impurity

Atom Distributions in Silicon by the Differential Capacitance Technique, IBM Journal

of Research and Development 12_, 399-409 (1968).

3. Gupta, D. C. , Diode Voltage-Capacitance Method for Measuring Resistivity and Impurity

Profile in a Silicon Epitaxial Layer, Solid-State Technology 11, No. 2, 31-34 (1968).

4. Severin, P. J., and Poodt , G. J., Capacitance-Voltage Measurements with a MercurySilicon Diode, Journal of the Electrochemical Society 119 , 1384-1389 (1972).

5. Schottky, W. , Vereinfachte und erweiterte Theorie der Randschichtgleichrichter

,

Zeitschrift fur Physik 118, 539-592 (1942).

6. Mattis, R. L. , and Buehler, M. G., Semiconductor Measurement Technology, Quarterly

Report, July 1 to September 30, 1973, Bullis, W. M. , ed. , NBS Special Publication

400-1, pp. 7-9 (March 1974).

7. Farina, M. V., Programming in BASIC, The Time-Sharing Language (Prentice-Hall, Inc.,

Englewood Cliffs, New Jersey, 1968).

8. Kemeny, J. G. , and Kurtz, T. E. , BASIC Programming, Second Edition (John Wiley and

Sons, Inc., New York, 1971).

9. Farina, M. V., Elementary BASIC with Applications (Prentice-Hall, Inc., Englewood

Cliffs, New Jersey, 1970).

10. Buehler, M. G. , Peripheral and Diffused Layer Effects on Doping Profiles, IEEE Transactions on Electron Devices ED-19 , 1171-1178 (1972).

11. Wilson, P. R. , The Capacitance of Deep Diffused Planar Junctions, Solid-State Electronics 11, 381-382 (1968).

12. Wilson, P. R. , Depletion Layer and Capacitance Calculations for Gaussian Diffused

Junctions, Solid-State Electronics 12_, 1-12 (1969).

13. Wilson, P. R. , An Analysis of the Circular Approximation for Silicon Planar Junctions,

Solid-state Electronics 16, 1511-1515 (1973).

14. Stegun, I. A., and Zucker, R. , Automatic Computing Methods for Special Functions, J. Res. National Bureau of Standards (U. S.), 74 B (Math. Sci.) No. 3, 211-224 (197C).

15. Griffin, T. E. , and Buehler, M. G., in Semiconductor Measurement Technology, Quarterly

Report, July 1 to September 30, 1973, Bullis, W. M. , ed., NBS Special Publication 400-

1, pp. 11-15 (March 1974).

33
i

I

i
NBS-114A IREV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. Sp-cial Publication 400-112. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

SemiaonduatoT Measurement Technology: A BASIC Program for

Calculating Dopant Density Profiles from Capacitance-Voltage

Data

5. Publication Date June 1975

6. Performing Organization Code

7. AUTHOR{S)

Richard L. Matt is and Martin G. Buehler

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. See item 15

1 1. Contract/Grant No. ARPA

Order 2397, Program Cod^

4D10: DNA lACRO 74-811

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Jointly Sponsored by NBS, Washington, D. C. 20234,

Defense Nuclear Agency, Washington, D. C. 20305, and

Advanced Research Projects Agency, Arlington, Virginia 22209

13. Type of Report & Period Covered Final 9/72 to 9/74

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

4251126, 4251555, 4251522

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. If document includes a significant bibliography or literature survey, mention it here.) A computer program is presented which is suitable for calculating dopant density vs. depth profiles from capacitance-voltage data for the case of a Gaussian-diffused p-n

junction diode. The program includes corrections for peripheral capacitance of

round or rectangular diodes and back depletion of the space charge region into the

diffused layer. Inputs to the program consist of the surface dopant density, the

junction depth, the background dopant density in the diffused layer, the junction

diameter, three scaling parameters, and the capacitance-voltage data pairs. Output

from the program is in the form of a plot and an optional listing of dopant density

as a function of depth. The equations underlying the program are given and are related to the program whose operation is described in detail. A second program, for

generating idealized capacitance-voltage data for a Gaussian-diffused diode on material with a constant dopant density is also included.

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

)

BASIC; capacitance-voltage measurements; computer programs; dopant profiles; error

function; Gaussian diffusion; plotting, computer; semiconductors; silicon.

18. AVAILABILITY [X] Unlimited

1 ! For Official Distribution. Do Not Release to NTIS

|X 1 Order From Sup. of Doc, U.S. Government Rrijiti|ri« X)f£j<:e Washington, D.C. 20402. SD Cat. No. CI3» iU:4oU-il

1

! Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

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USCOMM-DC 29042-P74

Announcement of New Publications on Semiconductor Measurement Technology

Superintendent of Documents,

Government Printing Office,

Washington, D.C. 20402

Dear Sir:

Please add my name to the announcement list of new publications to be issued in the series: National Bureau of Standards Special Publication 400-O

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NBS TECHNICAL PUBLICATIONS

PERIODICALS JOURNAL OF RESEARCH reports National Bureau

of Standards research and development in physics,

mathematics, and chemistry. It is published in two sections, available separately:

• Physics and Chemistry (Section A)

Papers of interest primarily to scientists working in these fields. This section covers a broad range of physical and chemical research, with major emphasis on

standards of physical measurement, fundamental constants, and properties of matter. Issued six times a

year. Annual subscription: Domestic, $17.00; Foreign,

$21.25.

• Mathematical Sciences (Section B)

Studies and compilations designed mainly for the mathematician and theoretical physicist. Topics in mathematical statistics, theory of experiment design, numerical analysis, theoretical physics and chemistry, logical design and programming of computers and computer

systems. Short numerical tables. Issued quarterly. Annual subscription: Domestic, $9.00; Foreign, $11.25. DIMENSIONS/NBS (formerly Technical News Bulletin) —This monthly magazine is published to inform

scientists, engineers, businessmen, industry, teachers,

students, and consumers of the latest advances in science and technology, with primary emphasis on the work at NBS. The magazine highlights and reviews such

issues as energy research, fire protection, building tech- nology, metric conversion, pollution abatement, health and safety, and consumer product performance. In addition, it reports the results of Bureau programs in measurement standards and techniques, properties of matter and materials, engineering standards and services, instrumentation, and automatic data processing. Annual subscription: Domestic, $9.45; Foreign, $11.85.

NONPERIODICALS

Monographs—Major contributions to the technical liter- ature on various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and

industrial practice (including safety codes) developed

in cooperation with interested industries, professional

organizations, and regulatory bodies.

Special Publications—Include proceedings of confer- ences sponsored by NBS, NBS annual reports, and other

special publications appropriate to this grouping such

as wall charts, pocket cards, and bibliographies.

Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists, engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides

quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a world-wide

program coordinated by NBS. Program under authority

of National Standard Data Act (Public Law 90-396). NOTE: At present the principal publication outlet for

these data is the Journal of Physical and Chemical

Reference Data (JPCRD) published quarterly for NBS

by the American Chemical Society (ACS) and the American Institute of Physics (AIP). Subscriptions, reprints, and supplements available from ACS, 1155 Sixteenth

St. N. W., Wash. D. C. 20056.

Building Science Series—Disseminates technical infor- mation developed at the Bureau on building materials, components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental functions and the durability and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete

in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under pro- cedures published by the Department of Commerce in Part 10, Title 15, of the Code of Federal Regulations.

The purpose of the standards is to establish nationally

recognized requirements for products, and to provide

all concerned interests with a basis for common under- standing of the characteristics of the products. NBS

administers this program as a supplement to the activities of the private sector standardizing organizations. Federal Information Processing Standards Publications (FIPS PUBS)—Publications in this series collectively constitute the Federal Information Processing Standards Register. Register serves as the official source of information in the Federal Government regarding stand- ards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended,

Public Law 89-306 (79 Stat. 1127), and as implemented

by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations). Consumer Information Series—Practical information, based on NBS research and experience, covering areas

of interest to the consumer. Easily understandable language and illustrations provide useful background

knowledge for shopping in today'? technological

marketplace.

NBS Interagency Reports (NBSIR)—A special series of interim or final reports on work performed by NBS for

outside sponsors (both government and non-govern- ment). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service (Springfield, Va. 22161) in paper

copy or microfiche form.

Order NBS publications (except NBSIR's and Biblio- graphic Subscription Services) from: Superintendent of Documents, Government Printing Office, Washington,

D.C. 20402. BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey

bibliographies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service A literature survey issued biweekly. Annual subscription: Domestic, $20.00; foreign, $25.00.

Liquefied Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00. Superconducting Devices and Materials. A literature

survey issued quarterly. Annual subscription: $20.00. Send subscription orders and remittances for the pre- ceding bibliographic services to National Technical Information Service, Springfield, Va. 22161.

Electromagnetic Metrology Current Awareness Service Issued monthly. Annual subscription: $100.00 (Special rates for multi-subscriptions). Send subscription order and remittance to Electromagnetics Division, National Bureau of Standards, Boulder, Colo. 80302.
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