Reference

NBS

PUBLICATIONS

NAT L INST. OF STAND & TECH 5-3145

All

CorV. : A FORTRAN Program for

Charge-Sheet Model Fitting of

MOSFET Data

L.C. Witte

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Semiconductor Electronics Division

Gaithersburg, MD 20899

November 1985

Pp“oared for

r ense Nuclear Agency

UL shington, DC 20305

100

U56

85-3145

1985

NBSIR 85-3145

CSFIT: A FORTRAN PROGRAM FOR

CHARGE-SHEET MODEL FITTING OF

MOSFET DATA

L.C. Witte

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Semiconductor Electronics Division

Gaithersburg, MD 20899

November 1985

Prepared for Defense Nuclear Agency

Washington, DC 20305

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

Table of Contents

Page

Abstract 1

1. Introduction 1

2. Theory 2

3. Computer Implementation 4

A. Software Modules 4

B. Limitations 7

4. Example Execution 7

5. Conclusions 8

6. Acknowledgments 17

7. References 17

Appendix A: Definition of Parameters 18

Appendix B: Example Execution Files 19

List of Figures

1. CSFIT computer program sections and subroutine flow diagram 5

2. CSFIT results compared to measured data for an unirradiated transistor

Vd = 0.25 V 9

3. CSFIT results compared to measured data for a 10 krad(Si) dose,

Vd = 0.25 V 10

4. CSFIT results compared to measured data for a 50 krad(Si) dose,

Vd = 0.25 V 11

5. CSFIT results compared to measured data for a 100 krad(Si) dose,

Vd = 0.25 V 12

6. CSFIT results compared to measured data for a 500 krad(Si) dose,

Vd = 0.25 V 13

iii
7. The linear region characteristics from the charge-sheet model and the

fitted values of mobility and flatband voltage, as a function of dose,

compared to measured data, Vj = 0.25 V 14

8. Charge-sheet model characteristics in the saturated region using the

fitted parameter compared to measured data for an unirradiated transistor ... 15

9. Charge-sheet model characteristics in the saturated region using the

fitted parameter compared to measured data for a 100 krad(Si) dose 16

IV
CSFIT: A FORTRAN Program

for Charge-Sheet Model Fitting of MOSFET Data

L. C. Witte

Semiconductor Electronics Division

National Bureau of Standards

Gaithersburg, MD 20899

ABSTRACT

A FORTRAN program, CSFIT, has been developed for fitting an expression

for the current-voltage (I-V) characteristics of a long-channel MOSFET to

experimental I-V curves. The one-dimensional charge-sheet model developed

by Brews provides the basis for the I-V characteristics. The I-V characteristics given by this model are optimized with respect to a set of experimental

data using the flatband voltage and the mobility as the only adjustable parameters. The program is written so that multiple sets of I-V data can be

fit simultaneously if desired. The user must supply, in specified formats, a

current-voltage data file, a device parameter file, and a starting value file. KEY WORDS: charge-sheet model; flatband voltage; I-V characteristics;

mobility; MOSFET; parameter extraction

1. INTRODUCTION

A FORTRAN program, CSFIT, has been developed for fitting an expression for the

current-voltage (I-V) characteristics of a long-channel metal-oxide-semiconductor fieldeffect transistor (MOSFET) to experimental I-V curves. The sign convention adopted is appropriate for n-channel enhancement-mode devices. The one-dimensional charge-sheet

model developed by Brews [1] provides the basis for the I-V characteristics. The I-V characteristics given by this model are optimized with respect to a set of experimental data

using the flatband voltage and the mobility as the only adjustable parameters.

The program CSFIT executes the optimization according to the least squares criterion us- ing a subroutine STEPIT, developed by J.P. Chandler [2]. STEPIT finds a local minimum

of any given smooth function of several parameters. CSFIT reads in dc MOSFET I-V data

and physical device parameters and then calls the subroutine STSET for the initialization

of the STEPIT input parameters. STEPIT performs the minimization of the specified

current model. The subroutine MODEL, called by STEPIT, uses the current equation

derived by Brews [1]. The MODEL routine then calls the subroutine CSO. The CSO and

FUNCTION subroutines, developed by C. L. Wilson [3], solve for the potential along the

oxide-silicon surface at the drain and source end of the channel needed to determine the

drain current. The subroutine FUNCTION is called by CSO to determine the actual drain

current once the potential at the drain and source has been determined.

1
In section 2, a brief discussion of the formulation of the charge-sheet model is presented. In

particular, the current equation is given along with a discussion of the method of solving

for the boundary conditions of the potential along the oxide-silicon surface for a given gate

voltage and drain voltage. The current equation and the boundary conditions are precisely

what the CSO computer code solves.

In section 3, the specific procedures needed to implement CSFIT are discussed. The

function of each of the principal subroutines is outlined. Limitations of the program are

discussed.

In section 4, verification of CSFIT is presented. An example of usage is demonstrated

by optimizing the flatband voltage and mobility when radiation-induced interface effects are present. The optimized values are then used to generate current-voltage curves in the

subthreshold, linear, and saturated regions of MOSFET operation. The input files used

to obtain the optimized parameters and the output file results are given in Appendix B.

A print-out of the CSFIT computer program is given in Appendix C.

2. THEORY

The charge-sheet model of the MOSFET assumes that the carrier density in the inversion

layer is contained in a charge sheet of zero thickness. Thus, the current is constrained to

flow along the oxide-silicon interface and there is no voltage drop across the inversion layer.

For long-channel devices* it can be assumed that Poisson’s equation must be solved in one

dimension only because the potential variations along the channel are gradual compared to

those normal to the channel. The discontinuity condition across the oxide-silicon interface

is then applied, implying that the carrier density per unit area N(y) is contained in a charge

sheet of zero thickness. The coordinate system used measures “y” along the channel of a MOSFET from the source toward the drain, “z” along the width of the drawn gate, and

“x” perpendicular to the plane of the gate.

Using an arbitrary potential along the oxide-silicon surface <f>{x = 0, y), Poisson’s equation

for the potential in the oxide and the semiconductor can be solved. Then, with a derived

equation for N(y) (refer to Brews for details [l]), an integral equation for the surface

potential is obtained. This equation is then solved, with the resulting drain current given

by

I = (^j

{ Cox (1 + PVG) [<t>SL - <£so) - ^Cox (05L “ <^5o)

- qNALs [Wsl - 1)

3/2 ~ Wso ~ 1)

3//2

] + qNaLb V® [(/?<£sl - 1)

1//2 - [P<t>so — 1)

1/,2

J },

2
where <(>sl = <f>s{L) and 050 = <^,s(0). This is eq (11) in the paper by Brews [l]. Definitions

of the parameters used in eq (11) are given in Appendix A. The value of <j>so and 4>sl for a given gate voltage Vq and drain voltage VB must be known before the current eq (11) can be solved.

At the source end of the channel, 4>so is taken from the one-dimensional Poisson equation

for zero drain voltage with (/?05o — 1) » exp(—/?05o)» yielding

Cox {Vg — <f>so) = qNALB V2 P<t>so — 1 + ( 12)

which is eq (12) in Brews’ paper. Equation (12) can be rearranged to provide an algorithm

for 05o. The iterative form becomes

4

+

0

‘ = tso + i/»{ [0(Va - 4o)]

j

/ [1 + (Mo - 1)/ exp Wso - Wb)} }, (13)

where <f> lso is the tth trial value for 0so and the initial trial value is

050 = 20b — -pin ,V2qNALB

'ox

Once the iterative algorithm for the potential at the source has converged, the resulting

potential can be used in the current equation.

To determine the potential at the drain end of the channel, for a given VB and VG , eqs

(14), (16), and (17) from the paper by Brews [1] were used. These equations are as follows:

qN{o) = qNALB V2{ 0<t>so — 1 + - {04’so - l)

1 ^2 } (14)

04>sl = 04>SO + 0Vd + In

.mo).

(16)

qN(L) = COI(VG - ifisi) - qNALB V2(0<t>si - 1)

1/J

. (17)

Using eqs (14) and (17) in (16) results in a value for the potential at the drain end of the

channel. With the source and drain potentials, 05o and 4>sl-> the current eq (11) can be

solved. Equation (11) is the function used to be minimized in the optimization routine.

3
3. COMPUTER IMPLEMENTATION

A. SOFTWARE MODULES

In order to run the program, the user should carry out the following steps. The user needs

to obtain a copyrighted copy of STEPIT from the distributing organization* and create

three input files in the required format. After creating the three input files, the user will

need to link CSFIT to STEPIT. Once the routines are linked, the user may then proceed

to execute the optimization routine. The program will then prompt the user for the I-V

data file name, the device parameter file name, the initial starting value file name, and

finally, the desired output result file name. This sample set of linkage control statements

has been used to execute the CSFIT program on the DEC VAX 11/780 under the VMS

system.

The computer program, CSFIT, consists of three sections: a data input and initialization

section, a fitting program, STEPIT, developed by J.P. Chandler [2], and a model section, as shown in figure 1. In the following paragraphs of this section, a circled number refers

to an encircled step on the flow-diagram given in figure 1.

The input section of CSFIT consists of the input routine 0 and STSET (f). The input

routine reads in measured dc transistor data and known device parameters. This routine

normalizes device parameters. The STSET subroutine, developed by Chandler [2], reads

in constraints on the minimization process and sets controlling parameters for the fitting

routine STEPIT.

The fitting section uses STEPIT (3) to minimize the objective function subject to the

constraints imposed by the user. The method used in STEPIT is an accelerated version

of the ‘cyclic variation’ or ‘one-variable-at-artime’ method. First, each fitting parameter

x(j) is varied individually. If progress is made by finding a lower value of the objective

function, the step size is doubled. However, the number of steps in this phase is limited.

When a local minimum has been found, quadratic interpolation is used in an attempt to

refine the position of the minimum. The minimum point is never shifted unless a better

(lower) value of the objective function is found.

Once each of the x(j) has been varied, attempts are made to move along the resultant of all of these individual displacements. Doubling of the step size follows each successful step,

this time with no limit on the number of steps. Quadratic interpolation again follows.

STEPIT consists of several subprograms which are referenced in [2].

The model section consists of the subroutines MODEL 0, CSO 0, and FUNCTION ©.

The CSO subroutine solves the charge-sheet equations for the potentials at the drain and

source end of the channel, passing the values to FUNCTION which calculates the drain-to-

* STEPIT is available from the Quantum Chemistry Program Exchange, Indiana University,

Bloomington, IN 47401.

4
Figure 1. CSFIT computer program sections and subroutine flow diagram.

5
source current. The calculated current is passed via © and © to the MODEL subroutine,

which generates an objective function which is the sum of the squares of the differences

between the measured and charge-sheet model drain currents. The STEPIT subroutine

receives the objective function via © and proceeds to ® to determine if the convergence

tolerance on minimization is satisfied. When the convergence tolerance is satisfied, CSFIT

is finished. If the convergence tolerance is not satisfied, steps ® to ® are repeated.

The first file is the current-voltage (IV) data file. The data are read into an (npts) x 3

array, where npts is the total number of points in all of the data sets. CSFIT, without

any modifications, assumes that the measured source-to-drain voltage for each data set is in npts x 1, the measured drain current is in npts x 2, and the measured gate voltage is in

npts x 3. This specific format can easily be changed to meet the user’s needs if so desired.

Thus, the required I-V data file would be as follows:

npts = the total number of data points

vds(i) vg(i) id(i)

vds(j) vg(j) id(j)

vds(k) vg(k) id(k)

The second file is the device parameter file. The following format is required:

nvds = the number of data sets

vds(l) = source-to-drain voltages for each data set

vds(i) i=l,nvds

npset(l) = number of data points in each set

npset(i) i=l,nvds

nch = average channel doping (cm3

) tox = oxide thickness (cm)

ljun = lateral source and drain diffusion under the gate (cm)

lch = drawn length of polysilicon (cm)

z = width of channel (cm)

The third file is the initial starting value file, with the following required format:

initial fbv(l)

initial mob(l)

initial fbv(2)

initial mob(2)

initial fbv(nvds)

initial mob(nvds)

The initial values of flatband voltage (fbv(i)) must be equal to or less than zero. The subroutine STSET is an initialization subroutine for the actual optimization routine STEPIT.

STSET allows the user to set the following controlling parameters:

x(i) = initial values of the fitting parameter, on which the function to be

minimized depends.

6
xmax(i)

xmin(i)

deltx(i)

delmn(i)

mask(i)

ntrac

the upper limit on the value of x(i)

the lower limit on the value of x(i).

the initial step by which x(i) is varied.

the lower limit (convergence tolerance) on the step size for x(i)

set nonzero if x(i) is not to be varied, but rather is to be held at its initial value.

determines the amount of printout from STEPIT.

ntrac=1 to obtain trace during the minimization process

ntrac=0 for initial and file output only

ntrac=-l for no output except error messages

STSET will set all the above to default value except ntrac; i.e., ntrac must be set by

the user. Without modification, CSFIT is written with the above parameters set to the

following values:

*(i)

xmax(i)

xmin(i)

deltx(i)

delmn(i)

mask(i)

ntrac

initial starting value file default value of +1.0E+35

default value of -1.0E-35

default value of x(i)/10

1.0E-04

default value of 0

1

The user need not be concerned with modification of the controlling parameters unless a fitting parameter is desired to be held constant (mask(i)=l), or a fitting parameter is desired to be held within a smaller range of values.

B. LIMITATIONS

Often, the error subroutines in STEPIT cannot be computed. The error routines sometimes

start with poor initial starting values for the CSO algorithm, resulting in the square root

of a negative number. If this occurs, the computed results should be considered valid.

If the CSFIT routine is given poor initial starting values for the fitting parameters, the

CSO algorithm will result in a square root of a negative number, and hence, the user must

correct initial starting values.

4. EXAMPLE EXECUTION

In this section, CSFIT is demonstrated using results obtained with an irradiated n-channel

enhancement-mode MOSFET. Prior to irradiation and after irradiation exposure to 10, 50,

100, and 500 krad(Si), the current-voltage characteristics of the transistor were measured.

All devices were biased with -1-9 V on the gate and source, drain, and substrate grounded.

The parameters used in the simulation are given in Table 1 . Techniques for determining

these parameters have been discussed in the literature [4].

7
Table 1

Device Parameters

Lch 6.42/xm

VG,VD 0.5 to 5.0 V, 0.25 V

tox 0.056/xm

neh 1 x 1016/cm3

Ljun 0.70jum

z 16.96/^m

Fitted values for the flatband voltage and mobility were obtained simultaneously for the

0, 10, 50, 100, and 500 krad(Si) doses, and then were used in the charge-sheet model to

generate model I-V curves.

Comparison of the charge-sheet model fitted values with measured data shows good agreement in the subthreshold region, the linear region, and the saturation region. Figure 2

compares the fit to measured data for an unirradiated sample. In figure 3, the fit after a

10 krad(Si) dose is compared to measured data. In figure 4, the fit after a 50 krad(Si) dose

is compared to measured data. As the dose is increased above 50 krad(Si), the effects of. the interface trapped charge energy distribution become important. As shown in figures 5

and 6, for devices irradiated at 100 krad(Si) and 500 krad(Si), respectively, the accuracy

of the model degrades with increased irradiation dose.

The linear region I-V characteristics generated from the charge-sheet model and the fitted

values of mobility and flatband voltage are compared to measured data as a function of

dose in figure 7. Linear region results obtained are in good agreement with measured

results.

Charge-sheet model I-V curves in the saturation region using the fitted parameters are compared to measured data in figure 8 for an unirradiated sample. Figure 9 gives a similar

plot after a 100 krad(Si) dose.

5. CONCLUSIONS

A fitting program has been developed to provide an optimum set of parameter values

for flatband voltage and mobility for a long-channel MOSFET based on the charge-sheet

model formulated by Brews [l]. This fitting procedure has been demonstrated using data

from an n-channel enhancement-mode MOSFET exposed to ionizing radiation.

6. ACKNOWLEDGMENTS

The author would like to thank C. L. Wilson and K. F. Galloway for their assistance and

guidance in preparing this work. Also, I would like to thank M. Gaitan, P. Roitman, and

8
Id

(A)

Vg (V)

Figure 2. CSFIT results compared to measured data for an unirradiated transistor,

Vd=0.25 V.

9
Id

(A)

10
Id

(A)

11
Id

(A)

Vg (V)

Figure 5. CSFIT results compared to measured data for a 100 krad(Si) dose, Vd—0.25 V.

12
Id

(A)

Vg (V)

Figure 6. CSFIT results compared to measured data for a 500 krad(Si) dose, V^=0.25 V.

13
0.6 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 4.2

Vg (V)

Figure 7. The linear region characteristics from the charge-sheet model and the fitted

values of mobility and fiatband voltage, as a function of dose, compared to measured data,

Vd=0.25 V.

14
Id

(pA)

150

Figure 8. Charge-sheet model characteristics in the saturated region using the fitted parameter compared to measured data for an unirradiated transistor.

15
Figure 9. Charge-sheet model characteristics in the saturated region using the fitted parameter compared to measured data for a 100 krad(Si) dose.

16
T. J. Russell for the experimental I-V data and the physical data used in this report.

Special thanks go to E. J. Walters for preparing the manuscript.

7. REFERENCES

1. Brews, J. R., A Charge-Sheet Model of the MOSFET, Solid-State Electronics 21,

345-355 (1978).

2. Chandler, J. P., STEPIT: Minimizing or Maximizing a Function, Department of Computing and Information Sciences, Oklahoma State University, Stillwater, OK 74074.

3. CSO is used to provide an initial guess in the CS1 program. CSO is reproduced here

as part of CSFIT. See: C. L. Wilson and J. L. Blue, CS1: A Two-Dimensional Finite

Element Charge-Sheet Model of a Short-Channel MOS Transistor, NBSIR 82-2471

(April 1982).

4. Wilson, C. L., Roitman, P., and Blue, J. L., High Accuracy Physical Modeling of

Submicron MOSFETs, IEEE Trans. Electron Devices ED-32, 1246-1258 (July 1985).

17
Appendix A: Definition of Parameters

<f>SL = 4>s[L) = the potential at the drain end of the channel

<f>so = ^s(O) = the potential at the source end of the channel

nch = average channel doping

Q = JL p kT

rii — intrinsic carrier concentration

<f>B = 0ln = bulk Fermi potential

Lb — (Debye Length) =

Cox = oxide capacitance per unit area

tox = oxide thickness

Leh = channel length = Lpoiy — 2Ljun

Lpoiy = gate poly length

Ljun = lateral junction depth

Z = channel width

fj.* = effective mobility (fitting parameter)

Vfb = flatband voltage (fitting parameter)

Vq = gate voltage

Vd — drain voltage

18
APPENDIX B: Example Execution Files

The following three required files, (1) I-V data file, (2) parameter file, and (3) initial starting

value file, were used to obtain the verification results, with the (4) resulting output file included. The I-V data file used consisted of 403 points. There was a total of five data

sets, one set for each radiation dose. The files were as follows:

(1) I-V data file

403

0.27147 8.597500E-01 1.299160E-08 vd V, Id

0.25198 7.079650E-01 1.428790E-09

0.25165 6.080440E-01 1.564180E-09

0.25048 4.591630E-01 1.422954E-09

0.25079 9.345300E-01 3.364700E-09
(2) parameter file

5

0.10

0.25

0.5

1.0

2.0

64

67

69

82

121

1.0E+16

Vd(0

mpts(i)

556E-08 0.7E-04 6.416E-04 16.956E-04 nch tox Ljun Lpoiy Z

(3) initial starting value file

0.1 500 Vfb (i) n{i)

0.1 500

0.1 500

0.1 500

20
(4) The resulting output file

Vfb * -7.59070E-01 Mu = Id

0 . 2205E-08

0 . 5492E-08

0 . 1168E-07

0.3415E-07

0.7210E-07

0 . 1960E-06

0 . 4269E-06

0.8419E-06

0 . 1389E-05

0 . 2331E-05

0 . 3363E-05

0 . 4518E-05

0 . 5754E-05

0 . 7036E-05

0 . 8341E-05

0.9659E-05

0 . 1098E-04

0 . 1229E-04

0 . 1359E-04

0 . 1489E-04

0 . 1617E-04

0 . 1744E-04

0 . 1857E-04

0 . 1994E-04

0 . 2116E-04

0 . 2237E-04

0 . 2357E-04

0 . 2476E-04

0 . 2593E-04

0 . 2709E-04

0 . 2823E-04

0 . 2936E-04

0 . 3048E-04

0.3159E-04

0 . 3268E-04

0 . 3377E-04

0 . 3484E-04

0 . 3590E-04

0.3695E-04

0 . 3799E-04

0 . 3902E-04

0 . 4004E-04

0 . 4105E-04

0 . 4205E-04

0 . 4304E-04

0 . 4403E-04

0 . 4500E-04

0 . 4597E-04

0 . 4693E-04

0 . 4787E-04

0 . 4882E-04

0 . 4975E-04

0 . 5068E-04

0 . 5160E-04

0 . 5251E-04

0 . 5342E-04

0 . 5432E-04

448.10 Vd = 0.05 Set 1

Ideal

0 . 8265E-09

0 . 3088E-08

0 . 1068E-07

0 . 3064E-07

0 . 8757E-07

0 . 2345E-06

0 . 5594E-06

0 . 1163E-05

0 . 1415E-05

0 . 2091E-05

0 . 2845E-05

0.3655E-05

0 . 4504E-05

0 . 5382E-05

0 . 6281E-05

0.7198E-05

0.8128E-05

0 . 9070E-05

0 . 1002E-04

0 . 1098E-04

0 . 1195E-04

0 . 1292E-04

0 . 1389E-04

0 . 1487E-04

0 . 1586E-04

0 . 1685E-04

0 . 1784E-04

0 . 1883E-04

0 . 1983E-04

0 . 2083E-04

0 . 2183E-04

0 . 2283E-04

0 . 2384E-04

0 . 2485E-04

0 . 2586E-04

0 . 2687E-04

0 . 2788E-04

0 . 2889E-04

0 . 2991E-04

0 . 3092E-04

0 . 3194E-04

0 . 3296E-04

0 . 3398E-04

0 . 3500E-04

0 . 3602E-04

0.3704E-04

0 . 3806E-04

0.3908E-04

0 . 4011E-04

0 . 4113E-04

0 . 4216E-04

0 . 4318E-04

0 . 4421E-04

0 . 4523E-04

0 . 4626E-04

0 . 4729E-04

0 . 4832E-04

Vg

0.7OOOE+OO

0.75OOE+OO

0 . 8000E+00

0.85OOE+OO

0 . 9000E+00

0.95OOE+OO

0. 1000E+01

0. 1050E+01

0. 1100E+01

0. 1150E+01

0. 1200E+01

0. 1250E+01

0.1300E+01

0.1350E+01

0. 1400E+01

0.1450E+01

0.1500E-t-01

0.1550E+01

0.1600E+01

0.1850E+01

0.1700E+01

0.1750E+01

0.1800E+01

0.1850E+01

0.1900E+01

0.1950E+01

0.2000E+01

0.2050E+01

0.2100E+01

0.2150E+01

0.2200E+01

0.2250E+01

0.2300E+01

0.2350E+01

0.2400E+01

0.2450E+01

0.2500E+01

0.2550E+01

0.2600E+01

0.2650E+01

0.2700E+01

0.2750E+01

0.2800E+01

0.2850E+01

0.2900E+01

0.2950E+01

0.3000E+01

0.3O5OE+O1

0.31OOE+O1

0.315OE+O1

0.32OOE+O1

0.325OE+O1

0.33OOE+O1

0.335OE+O1

0.34OOE+O1

0.345OE+O1

0 . 3500E+0

1
0.3550E+01

0.3600E+01

0.3650E+01

0.3700E+01

0 . 3750E+01

0 . 3800E+01

0.3850E+01

0.3900E+01

0 . 3950E+01

0 . 4000E+01

0.4050E+01

0 . 4100E+01

0.4150E+01

0 . 4200E+01

0 . 4250E+01

0.4300E+01

0.4350E+01

0 . 4400E+01

0 . 4450E+01

0.4500E+01

0.4550E+01

0.4600E+01

0 . 4650E+01

0 . 4700E+01

0.4750E+01

0 . 4800E+01

0.4850E+01

0.4900E+01

0.4950E+01

0 . 5000E+01

0 . 5050E+01

0.5100E+01

0.5150E+01

0 . 5200E+01

0.5250E+01

0 . 5300E+01

0 . 5350E+01

0 . 5400E+01

0 . 5450E+01

0.5500E+01

0.5550E+01

0 . 5600E+01

0 . 5650E+01

0 . 5700E+01

0 . 5750E+01

0 . 5800E+01

0 . 5850E+01

0 . 5900E+01

0 . 5950E+01

0 . 6000E+01

0 . 6050E+01

0.6100E+01

0 . 6150E+01

0 . 6200E+01

0 . 6250E+01

0 . 6300E+01

0.6350E+01

0 . 6400E+01

0 . 6450E+01

22 0 . 6500E+01

0 . 5521E-04

0 . 5609E-04

0 . 5697E-04

0 . 5785E-04

0 . 5872E-04

0 . 5957E-04

0 . 6043E-04

0 . 6128E-04

0 . 6212E-04

0 . 6296E-04

0 . 6379E-04

0 . 6461E-04

0 . 6543E-04

0 . 6625E-04

0 . 6706E-04

0 . 6786E-04

0 . 6867E-04

0 . 6946E-04

0.7025E-04

0.7104E-04

0.7182E-04

0 . 7259E-04

0 . 7337E-04

0 . 7414E-04

0.7490E-04

0.7565E-04

0 . 7641E-04

0.7716E-04

0 . 7790E-04

0 . 7864E-04

0 . 7938E-04

0.8012E-04

0 . 8085E-04

0.8157E-04

0 . 8229E-04

0 . 8301E-04

0 . 8372E-04

0 . 8443E-04

0 . 8514E-04

0 . 8584E-04

0 . 8654E-04

0 . 8723E-04

0 . 8792E-04

0.8861E-04

0 . 8929E-04

0 . 8997E-04

0 . 9065E-04

0.9132E-04

0 . 9199E-04

0 . 9265E-04

0 . 9332E-04

0 . 9398E-04

0 . 9463E-04

0.9529E-04

0.9594E-04

0 . 9658E-04

0.9723E-04

0 . 9786E-04

0 . 9850E-04

0 . 9914E-04

0 . 4935E-04

0 . 5038E-04

0 . 5141E-04

0 . 5244E-04

0 . 5347E-04

0 . 5450E-04

0 . 5553E-04

0 . 5656E-04

0 . 5760E-04

0 . 5863E-04

0 . 5966E-04

0 . 6070E-04

0 . 6173E-04

0.6276E-04

0 . 6380E-04

0 . 6484E-04

0 . 6587E-04

0 . 6691E-04

0 . 6794E-04

0 . 6898E-04

0 . 7001E-04

0 . 7105E-04

0 . 7209E-04

0.7313E-04

0 .7416E-04

0 . 7520E-04

0.7624E-04

0 . 7728E-04

0 . 7831E-04

0 . 7935E-04

0 . 8039E-04

0 . 8143E-04

0 . 8247E-04

0.8351E-04

0 . 8455E-04

0 . 8559E-04

0 . 8663E-04

0 .8767E-04

0 . 8871E-04

0 . 8975E-04

0 . 9079E-04

0 . 9183E-04

0 . 9287E-04

0.9391E-04

0 . 9495E-04

0 . 9599E-04

0 . 9703E-04

0 . 9808E-04

0 . 9912E-04

0 . 1002E-03

0 . 1012E-03

0 . 1022E-03

0 . 1033E-03

0 . 1043E-03

0 . 1054E-03

0 . 1064E-03

0 . 1075E-03

0 . 1085E-03

0 . 1095E-03

0 . 1106E-03
O.055OE+O1

0.66OOE+O1

0 . 6650E+01

0.67OOE+O1

O.075OE+O1

0.68OOE+O1

0.685OE+O1

O.09OOE+O1

0.695OE+O1

0.7OOOE+O1

0.7O5OE+O1

0.71OOE+O1

0.7150E+01

0.72OOE+O1

0.725OE+O1

0.73OOE+O1

0.735OE+O1.

0.7400E+01

0.745OE+O1

0.7500E+01

0.7550E+01

0.7600E+01

0.7650E+01

0.7700E+01

0.7750E+01

0.7800E+01

0.7850E+01

0.7900E+01

0.7950E+01

0.8000E+01

0 . 9976E-04

0 . 1004E-03

0 . 1010E-03

0 . 1016E-03

0 . 1022E-03

0 . 1029E-03

0 . 1035E-03

0 . 1041E-03

0 . 1047E-03

0 . 1053E-03

0 . 1059E-03

0 . 1065E-03

0 . 1071E-03

0 . 1077E-03

0 . 1083E-03

0 . 1088E-03

0 . 1094E-03

0 . 1100E-03

0 . 1106E-03

0 . 1111E-03

0 . 1117E-03

0 . 1123E-03

0 . 1129E-03

0 . 1134E-03

0 . 1140E-03

0 . 1145E-03

0 . 1151E-03

0 . 1156E-03

0 . 1162E-03

0 . 1167E-03

0. 1116E-03

0 . 1127E-03

0 . 1137E-03

0 . 1148E-03

0 . 1158E-03

0 . 1168E-03

0. 1179E-03

0 . 1189E-03

0 . 1200E-03

0 . 1210E-03

0 . 1221E-03

0 . 1231E-03

0 . 1242E-03

0 . 1252E-03

0 . 1262E-03

0 . 1273E-03

0 . 1283E-03

0 . 1294E-03

0 . 1304E-03

0 . 1315E-03

0 . 1325E-03

0 . 1336E-03

0 . 1346E-03

0 . 1357E-03

0 . 1367E-03

0 . 1378E-03

0 . 1388E-03

0 . 1398E-03

0 . 1409E-03

0 . 1419E-03
This main program executes a Curve Fit using:

STEPIT for the curve fitting

STSET for initialization of STEPIT input parameters

MODEL for minimizing the current equation derived

from a "Charge-Sheet Model"

CSO for main Charge-sheet program

FUNCTION for the current equation

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C* ** * ***** ******************** ***************** *afe * ***** **a|e *** ** ** * * * ***

The user must supply:

1. IV data file in required format

2. Parameter file in required format

3. Initial Starting value file for mobility

and flat band voltage in each data set.

c

c The user can request a copy of STEPIT from:

c

c Quantum Chemistry Program Exchange

c Indiana University

c Bloomington, Indiana 47401

c

c Authored by: J.P*. Chandler

c Department of Computing and Information Sciences

c Oklahoma State University

c Stillwater, Oklahoma 74074

c

c

c***********Sfc* afcsfc ** afe * * ****afcsfc ** * * * **** *sfc ***a(( aft * ****** **  a(t afe **  s(e *

24

c

c

c The program CSFIT assumes that the fitting parameters

c are flat band voltage and mobility with the flat band

c voltage=X(2i-l) and mobility=X(2i) where i=l,2,

c . . . nvds=the total number of data sets and 2*nvds=total

c number of fitting parameters. Thus, if 2 I-V data sets

c are used with X(l)=ul, X(2)=fbvl, X(3)=u2, and X(4)=fbv2

c the output file results would be as follows:

c

c

clSUBROUTINE STEPIT. COPYRIGHT (C) 1965 J. P. CHANDLER

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INITIAL VALUES

MASK

X

XMAX

XMIN

DELTX

0 0

0 . 10000E+00 0 . 50000E+03

0 . 10000E+36 0 . 10000E+36

-0 . 10000E+36 -0 . 10000E+36

0 . 10000E-02 0 . 50000E+01

0

0 . 10000E+00

0 . 10000E+36

-0 . 10000E+36

0 . 10000E-02

0

0 . 50000E+03

0 . 10000E+36

-0 . 10000E+36

0 . 50000E+01
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DELMN = 0 . 10000E-03 0.10000E-03 0.10000E-03

4 VARIABLES, 4 ACTIVE. MATRX =110

NFLAT = 1 RELAC = 0. 1000E-16

FOBJ = 0 . 5310057276E-08

BEGIN MINIMIZATION

0 . 10000E-03

NFMAX = 1000000

c TERMINATED WHEN THE STEP SIZES BECAME AS SMALL AS THE DELMN (J)

.

c

277 FUNCTION COMPUTATIONS

FINAL VALUE OF FOBJ = 0 . 136086974597773E-10

FINAL VALUES OF X(J)

0 . 897635003046762E+00 0 . 538229046900407E+03 0 . 903491922574461E+00

0 . 537289871078474E+03

1 SUBROUTINE STERR.

COMPUTE AN APPROXIMATE ERROR MATRIX USING FINITE DIFFERENCES

.

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c INCREMENTS IN X(J) TO BE USED

c

c 0 . 32000E+02 0.20000E+05 0.32000E+02 0.10000E+05

c

c

c SQUARE ROOT OF NEGATIVE NUMBER HAS OCCURRED:

c

c EITHER THE INITIAL STARTING VALUES ARE BAD AND NEED TO BE RESET OR

c

c THE ERROR MATRIX CAN NOT BE COMPUTED WITH THE CSO ALGORITHM,

c

c THUS IGNORE MESSAGE AND ASSUME FITTED VALUES ARE CORRECT

.

c

! c

! c

I c

c

c Note: The error matrix could not be computed and thus it is

I c disregarded. When an approximate error matrix is

• c attainable, a matrix of the second partial derivatives,

jc a standard errors matrix, and a lower triangle of the

I c correlation matrix is given.

| c

|| .

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25
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The final optimized values are given in corresponding order,

i.e. , vfb(l) ,mob (1) ,vfb(2) ,mob(2) vfb(i) ,mob(i) .

implicit real*8 (a-h,o-z)

external model

dimension a (1000, 3)

common /cstep/ x(20) ,xmax(20) ,xmin(20) ,deltx(20) ,delmn(20)

,

*err(20,21) ,fobj ,nv,ntrac,matrx,mask(20) ,nfmax,nf lat, j vary

,

*nxtra,kf lag, norep, kerf 1 ,kw

common /cmod/ xm(lOOO) ,y(1000) ,npts

common /input/ npset (20) ,vds (20) ,nvds

real *4 vds,beta

common /mshape/ djun, ljun, lch

real*4 djun, ljun, lch

common /dopant/ nsd , nch

real *4 nsd, nch

common /bias/ vd,vs,vg,vsub,vfb

real*4 vd,vs,vg,vsub,vfb

common /gate/ tox , qO , kox , ksi

real *4 tox, qO, kox, ksi

common /sheet/ mustar , z , psib , lb , cox,psis0, psisl ,n0, iO , id

reai*4 mustar , lb , nO , iO , id , psib , cox, psisO , psisl ,

z

COMMON /NORM/ VT , VN0RM , Q , NI , EPS0 , EPS , LN0RM , NN0RM , tnorm , muO

REAL*4 VT , VNORM , Q , NI , EPSO , EPS , LNORM , NNORM , tnorm , muO

character*40 f i 1 ini , f i 1 in2 , f i 1 in3 , f i lout

write (6,*) ’Enter XV Data file’

read (5,5) filinl

format (a)

write (6,*) ’Enter Parameter file’

read (5,5) filin2

write (6,*) ’Enter Initial Starting Value file’

read (5,5) filin3

write (6,*) ’Enter Output file’

read (5,5) filout

open (unit=10, f ile=f ilinl , status=’old ’

)

open (unit=ll ,f ile=f ilin2, status=’old’)

open (unit=12 , f ile=f ilin3 , status= ’ old ’

)

open (unit=16, file=fi lout, status=’ new’)

open (unit=17, f ile=’ plot.dat’ , status= ’ new ’

)

Read from the Data file. The following

format for the data file is required:

npts

a(j >1)

where

:

a(j .2) a(j,3)

npts=total number of iv points

a (j t l)=source-to-drain voltage

a (j>2)=gate voltage

a (j>3)=drain current

200

26 c

read (10,*) npts

do 200 j =1 , npts

read (10, *) a(j , 1) , a( j, 2) , a( j

, 3)

y(j)=a (j >3)

xm (j

)

=a ( j >2)

continue
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201

202

Read from the Parameter file. The following

format is required:

nvds

vds (1)

vds (i)

npset (1)

npset (i)

nch

tox

ljun

lch

zwhere: nvds=the number of data sets.

vds (i) =source-to-drain voltages for

each set.

npsets (i)=number of data points in

each set.

nch=average channel doping (cm-3)

tox=oxide thickness (cm)

lj unilateral source and drain

diffusion (cm)

lch=drawn length of polysilicon (cm)

z=width of channel (cm)

read (11,*) nvds

do 201 j 1=1 , nvds

read (11,*) vds(jl)

do 202 j 2=1 , nvds

read (11,*) npset (j 2)

read (11,*) nch , tox, 1 j un, lch,

z

q=l . 6E-19

ni=l . 5E+10

nch=nch/ni

kox=3 .

9

ksi=ll .8

eps0=8 . 854E-14

mu0=1000

q0=0

.

vt=.0259

beta=l .0/vt

lnorm=sqrt (ksi*epsO/q/ (beta*ni))

tox=tox/1norm

1 jun=ljun/lnorm

lch=lch/lnorm

z=z/lnorm

Call STSET to initialize starting values for STEPIT.

See STEPIT documentation for details.

Note: STEPIT allows the user to control the least

squares criterion by setting certain values

:

x(i)=initial values of the parameters, on whi
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203

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the function to be minimized depends

.

)=the upper limit on the value of x(i) . xmin(i)=the lower limit on the value of x(i)

.

deltx(i)=the initial step by which x(i) is varied, delmn

(

1 ) —the lower limit (convergence tolerance)

on the step size for x(i)

„

mask (i)=set nonzero if x(i) is not to be varied, but rather is to be held at its initial' value

.

ntrac=determines the amount of printout from STEPIT

ntrac=l to obtain trace during the

minimization process

ntrac=0 for initial and file output only

ntrac—1 for no output except error messages

STSET will set all the above to default values except ntrac

i

f

,

ca4ledthe inital starting values are read via the following format.

initial vfb(l)

initial mob(l)

initial vfb(2)

initial mob (2)

initial vfb(nvds)

initial mob (nvds)

call stset

nv=nvds*2

ntrac=0

do 203 j 3=1 , nv ,

2

read (12, ) x(j3) ,x(j3+l)

x (j 3 + 1) = -x(j3+l)

do 204 j 4=1 , nv

delmn ( j 4) =1 . 0E-04

matrx=110

call STEPIT for least squares fit.

call stepit (model)

c print results

c

k=l

do

1002

2000 j=l,nvds

Vffit = -x(2*j -1) write (16, 1002) Vff it ,x(2*j ) , vds (j ) ,

j

format (’ Vfb = , ,lpel2.5,’ Mu = ’,0p ’Set ’ , i2, /

,

* Vg S

write (17, ) npset(j)

imax=npset ( j

)

vd=vds(j)/vt

Opf7 .2,

Id

Vd = \f7,

Ideal *

)

2 ,

28
vfb=-x(2*j -1) /vt

mustar=x (2* j ) /muO

do 1000 i=l , imax

vg=xm(k) /vt

o2#X X csO

write (16, 1001) xm(k) ,y (k) , id

1001 format (3el2.4)

write (17, 1001) vds (j ) ,xm(k) , id

k=k+l

1000 continue

2000 continue

207

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I1000

2000

continue

close (10)

close (11)

close (12)

close (16)

end

MODEL subroutine

subroutine model

implicit real*8 (a-h,o-z)

common /cstep/ x(20) ,xmax(20) ,xmin(20) ,deltx(20) ,delmn(20)

,

err (20, 21) , fobj ,nv,ntrac,matrx,mask(20) ,nfmax,nf lat, j vary

,

*nxtra,kf lag, norep, kerf 1 ,kw

common /cmod/ xm(lOOO) ,y(1000) ,npts

common /input/ npset(20) , vds (20) ,nvds

real*4 vds, beta

common /mshape/ djun, 1 jun, lch

real*4 djun, 1 jun, lch

COMMON /GATE/ T0X, QO,KOX,KSI

REAL*4 K0X,KSI, tox, qO

common /dopant/ nsd,nch

real*4 nsd,nch

COMMON /NORM/ VT , VN0RM , Q , NI , EPS0 , EPS , LNORM , NNORM , tnorm , muO

REAL*4 VT , VNORM , Q , NI , EPSO , EPS , LNORM , NNORM , tnorm , muO

common /bias/ vd,vs,vg, vsub,vfb

real*4 vd,vs,vg,vsub,vfb

common /sheet/ mustar , z , psib , lb , cox, psisO , psisl , nO , iO , id

real*4 mustar, lb,nO, iO, id, psib, cox, psisO , psisl ,

z

real*4 ifun,nl

f obj=0

.

k=l

do 2000 j=l,nvds

imsLX=npset ( j )

vd=vds (j ) /vt

vfb=-x(2* j -1) /vt

mustar=x(2*j ) /muO

do 1000 i=l , imax

vg=xm (k) /vt

oslX X csO

fobj=fobj + (id/y (k) -1 .0) **2

k=k+l

continue

continue

return

end 2V
CSO Subroutine

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12

30 13

subroutine csO

common /mshape/ djun, 1 jun, Ich

real*4 djun, 1 jun, Ich

COMMON /GATE/ TOX, QO,KOX,KSI

REAL*4 KOX, KSI , tox , qO

common /dopant/ nsd,nch

real *4 nsd nob.

COMMON /NORM/ VT , VNORM , Q , NI , EPSO , EPS , LNORM , NNORM , tnorm , muO

REAL*4 VT , VNORM , Q , NI , EPSO , EPS , LNORM , NNORM , tnorm , muO

common /bias/ vd, vs,vg, vsub,vfb

real *4 vd,vs,vg,vsub,vfb

common /sheet/ mustar , z,psib, lb, cox,psisO,psisl ,n0, iO, id

real*4 mustar , lb , nO , iO, id,psib, cox, psisO, psisl ,

z

real*4 ifun,ni

beta = 1.0/vt

psib = vt*alog(nch)

lb = sqrt (ksi*epsO/q/ (beta*nch*ni)

)

cox = kox*epsO/ (T0X*LN0RM)

vgl = vg-vfb+q*beta*QO/cox

bpsO = 2.0*beta*psib-2.0*alog(beta*sqrt(2.0)*q*nch*ni*lb/cox)

bpsi - bpsO

bpsis = XoOelQ

if (vgl . It .bpsO) bpsis = bpsO

if (vgl . le .bpsO) goto 11

do 10 i=l , 500

bpsi = bpsO+alog(abs ( (vgl-bpsi) **2/ (1 .+(bpsi-l .0) /exp (bpsi

1 -2 .0*psib*beta) ) )

)

if (abs (bpsi-bpsis) . It . 1 . e-4) goto 11

bpsis = bpsi

continue

psisO=bpsi/beta

nO=nch*ni*lb*sqrt (2 . ) * ( (bpsi-1 . 0+ (1 . /nch) **2*

1 exp (bpsi) ) 0. 5- (bpsi-1 . ) **0 . 5)

psisl = psisO+vd*vt

vO = (q*nch*ni*lb/cox) **2

IF (VG1.LT. 1.0) GO TO 5000

psiss=vgl*vt+vO*beta-sqrt ( (vO*beta) **2+2 . *v0* (vgl-1 . 0)

)

if (psisl . gt . psiss) psisl=psiss

nl = 0.0

if (psisl . eq. psiss) goto 13

h = 1.0

dpold = 1.0

do 12 i=l , 100

nl = cox* (vgl*vt-psisl) /q-ni*nch*lb*sqrt (2 . ) * (beta*psisl-l . ) **0 .

5

if (nl.lt.l.0e-25) nl=1.0e-25

psisi=psisO+vd*vt+alog (nl /nO) /beta

delpsi=psisi-psisl

if (abs(delpsi) .gt.vt) delpsi=vt*abs (delpsi) /delpsi

if (delpsi . eq. 0.0) goto 12

if (dpold/delpsi.lt.O.O) h=h/2.0

psisl=psisl+h*delpsi

if (abs (delpsi) . It . 1 . Oe-5) goto 13

dpold=delpsi

continue

id = ifun (psisl , lch)
xidot = id*beta**2/(mustar*mu0*z/(lch-2.0*ljun)*cox)

xlch = lch-2.0*ljun

c WRITE (6,90) BETA, PSIB , LB , COX, BPSO , BPSI , PSISO , NO

c 1 , PSISL, NL, ID, iO, xidot, vg,vd, xlch

90 FORMAT (’ BETA = ’,1PE15.6/

1

» PSIB = ’ , 1PE15 . 6/

1

* LB = ’ , 1PE15 . 6/

1

* COX = * , 1PE15 . 6/

1

’ BPSO = * , 1PE15 . 6/

1

’ BPSI = * ,1PE15. 6/

1 ’ PS(O) = ’,1PE15.6/

1

’ NO = * , 1PE15 . 6/

1

’ PS (L) = \1PE15 .6/

1

’ NL = * , 1PE15 . 6/

1

’ ID = * , 1PE15 . 6/

i

’ io = \ipei5.6/

1

’ I. .

.

= ’ ,1PE15.6/

1

’ VG = ’ , 1PE15 . 6/

1

’ VSD = * , 1PE15 . 6/

i ’ lch = ’,ipeis.6/)

return

5000 id = 1.0e-20

c5000 write (16, 500)

500 FORMAT (//, ’SQUARE ROOT OF NEGATIVE NUMBER HAS’,

1* OCCURRED: ’//’ EITHER THE INITIAL STARTING’,

1’ VALUES ARE BAD AND NEED TO BE RESET OR’,

1//, ’THE ERROR MATRIX CAN NOT BE COMPUTED WITH’ , 1’ THE CSO ALGORITHM, ’//’THUS IGNORE MESSAGE’,

1’ AND ASSUME FITTED VALUES ARE CORRECT.’)

c STOP

return

end

Function Subroutine IFUN

real function ifun(ps,y)

common /mshape/ djun, ljun, lch

real*4 djun, ljun, lch

COMMON /GATE/ TOX, QO,KOX,KSI

REAL*4 KOX, KSI , tox , qO

common /dopant/ nsd,nch

real*4 nsd,nch

COMMON /NORM/ VT , VNORM , Q , NI , EPSO , EPS, LN0RM,NN0RM, tnorm, muO

REAL*4 VT , VNORM , Q , NI , EPSO , EPS , LNORM , NNORM , tnorm , muO

common /bias/ vd,vs,vg,vsub,vfb

real*4 vd, vs , vg, vsub, vfb

common /sheet/ mustar , z ,psib , lb , cox, psisO , psisl , nO , iO , id

real*4 mustar , lb , nO , iO, id, z ,psib, cox, psisO , psisl

real*4 iOO,fff

beta = l.O/vt

vgl = vg-vfb+q*beta*QO/cox

if ((y-2.0*ljun) .ne.O.O) iOO = 1 .0/beta*mustar*muO*z/ (y-2 . 0* 1

j

fff = cox* (1 .0+vgl) (ps-psisO) ~beta/2 . *cox* (psx*>*'2-psis0- -2)

f f f=f f f-q*ni*NCH*lb*sqrt (8 . ) /3 . * ( (beta*ps-l . 5- (beta- PS I SO

1 —1 . ) **1 . 5)

f f f=f f f +q*nch*ni*lb*sqrt (2 . ) * ( (beta*ps— 1 .)«•***». 5- (be ta*ps i sO- 1 . ) 1 ** . 5)

ifun = iOO*fff
if (ps . eq.psisl) iO=iOO

return

end
fiStl14A imv. a-«oi U.S. OtPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR-85/3145

2. Performing Organ. Report No. 3. Publication Date

November 1985

4. TITLE ANO SUBTITLE

CSFIT : A FORTRAN Program for Charge-Sheet Model Fitting of MOSFET Data

5. AUTHOR(S)

L. C. Witte

S. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No. Subtask X99QMXVA,

Work Unit 00059

S. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME ANO COMPLETE AODRESS (Street. City. State, ZIP)

Defense Nuclear Agency

Washington, DC 20305

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

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

bibliography or literature survey, mention it here)

A FORTRAN program, CSFIT, has been developed for fitting an expression for the

current-voltage (I-V) characteristics of a long-channel MOSFET to experimental

curves. The one-dimensional charge-sheet model developed by Brews provides the

basis for the I-V characteristics. The I-V characteristics given by this model

optimized with respect to a set of experimental data using the flatband voltage

the mobility as the only adjustable parameters. The program is written so that

multiple sets of I-V data can be fit simultaneously if desired. The user must

supply, in specified formats, a current-voltage data file, a device parameter £ and a starting value file.

I-V

are

and

He,

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate <ev ~ora: charge-sheet model; flatband voltage; I-V characteristics; mobility; MOSFET;

parameter extraction

13. AVAILABILITY

I ^

Unlimited

I | For Official Distribution. Do Not Release to NTIS

I I Order From Superintendent of Documents, U.S. Government Printing Office, Washington. D.C. 20402.

[^] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTEO PACE

38

15. P-
01. Summary date

Yr. Mo. Day

8 5 4 3

04. Software date

Yr. Mo. Day

8 5 4 3

FEDERAL INFORMATION PROCESSING STANDARD SOFTWARE SUMMARY

03. Summary action New Replacement Deletion a

Previous Internal Software ID

02. Summary prepared by (Name and Phone)

L. C. Witte (301) 921-3621

05. Software title CSFIT : A FORTRAN Program for Charge-Sheet Model

Fitting of MOSFET Data

06. Short title

07. Internal Software 10 CSFIT

08. Software type

Automated Data System

g Computer Program

|—

|

Subroutine/ Module

09. Processing mode

[^] Interactive g Batch

f~j Combination

10. GeneralApplication area

Computer Systems

|~| Support/Utility

g Scientific/ Engineering PI Bibliographic/Textual

Management/

Business g Process Control g Other

Specific

MOS Transistor

Modeling

11.

Submitting organization and address National Bureau of Standards

Gaithersburg, MD 20899

12.

Technical contact(s) and phone

C. L. Wilson (301) 921-3541

13.

Narrative A FORTRAN program, CSFIT, has been developed for fitting an expression for the currentvoltage (I-V) characteristics of a long-channel MOSFET to experimental I-V curves. The

one-dimensional charge-sheet model developed by Brews provides the basis for the I-V

characteristics. The I-V characteristics given by this model are optimized with respect

to a set of experimental data using the flatband voltage and the mobility as the only

adjustable parameters. The program is written so that multiple sets of I-V data can be

fit simultaneously if desired. The user must supply, in specified formats, a currentvoltage data file, a device parameter file, and a starting value file.

14.

Keywords

charge-sheet model; flatband voltage; I-V characteristics; mobility; MOSFET; parameter

extraction

15. Computer manufr and model 16. Computer operating system 17. Programing language(s) 18. Number of source program state- ments DEC 11/780 VMS FORTRAN 484

19. Computer memory requirements

40K

20. Tape drives

0

21. Disk/Drum units

1

22. Terminals

1

23. Other operational requirements

Requires local vector-oriented graphics

24. Software availability

Available Limited 0

C. L. Wilson (301) 921-3541

9- track magnetic tape

In-house only

25. Documentation availability

Available Inadequate

Title as in section 05

NBSIR-8 5/3145

In-house only

26. FOR SUBMITTING ORGANIZATION USE

Standard Form 1S5

1974 July

U.S. Oapt. of Commarce—NBS

(FIPS. Pub. 30)

185-101

*