NAT L INST. OF STAND & TECH

A 11 ID 5 Tfl357D

NBS

REFERENCE Publications

IMBSIR 84-2874R

CSIR: A Two-Dimensional Finite

Element Charge-Sheet Model of

MOSFET's Including Radiation-Induced

Interface and Oxide Charge

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Semiconductor Devices and Circuits Division

Washington, DC 20234

May 1984

Prepared for

, Defense Nuclear Agency

QC Washington, DC

100

U06

34-2374R

1034

NATIONAL BUREAU OF STANDARDS

_ LIBRARY ^

NBSIR 84-2874R

CSIR: A TWO-DIMENSIONAL FINITE

ELEMENT CHARGE-SHEET MODEL OF

MOSFET'S INCLUDING RADIATION-INDUCED

INTERFACE AND OXIDE CHARGE

C L. Wilson and J. L. Blue

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Semiconductor Devices and Circuits Division

Washington, DC 20234

May 1984

Prepared for Defense Nuclear Agency

Washington, DC

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

I \

*
List of Figures

1. Geometry of the charge-sheet model 4

2. A subthreshold region simulation compared to measured data for an

unirradiated transistor 15

3. A subthreshold region simulation compared to measured data for a

10 Krad(Si) dose 16

4. A subthreshold region simulation compared to measured data for a 50 Krad(Si) dose 17

5. A subthreshold region simulation compared to measured data for a 100 Krad(Si) dose 18

6. A subthreshold region simulation compared to measured data for a 500 Krad(Si) dose 19

7. A subthreshold region simulation compared to measured data for a 500 Krad(Si) dose, trap distribution peaked near the valence band .... 20

8. A saturation region simulation compared to measured data for an

unirradiated transistor 21

9. A saturation region simulation compared to measured data for a 500

Krad(Si) dose 22

10. The triode region characteristics, as a function of dose, compared to

measured data 23

IV
CS1R: A Two-Dimensional Finite Element Charge-Sheet Model

of MOSFETs Including Radiation- Induced Interface

and Oxide Charge

C, L. Wilson^ and J. L. Blue

National Bureau of Standards

Washington, DC 20234

Abstract

A two-dimensional charge-sheet model including radiation-induced interface and

oxide effects in short-channel MOS transistors has been developed. The unique

feature of the model is that the effects of channel inversion layer charge, interface

charge, and oxide charge are included as a nonlinear integral boundary condition on

the two-dimensional electrostatic field in the transistor. The average inversion layer

charge density and source-drain current are obtained directly from the model rather

than from the electron density or electron quasi-Fermi level. The model retains all of the physical detail of more complex two-dimensional models such as sensitivity

to source-drain profile shape, channel profile, and oxide field shape. This allows

the model to represent the changes in drain current associated with short-channel

effects while still allowing simple comparison with long-channel models.

The numerical solutions were obtained using general-purpose software for solving

elliptic partial differential equations. Problems with exact solutions have been solved

to test the correctness and accuracy of the codes. Also, the physics included in this

model and the geometry of the transistor can be easily changed. The finite element

method used allows refinement of oblique triangles which is important in achieving

computational efficiency.

Key words: finite elements; interactive graphics; MOS transistors; radiation effects.

1. Introduction

A two-dimensional formulation of a charge-sheet model of an MOS transistor and

an associated computer program are presented. This formulation differs from tin' formulation of De La Moncda [1] in that it includes the effects of source-drain

channel shape and arbitrary channel doping profile shape. The formulation <ii!W

from the formulation proposed by Brews [2] in that strong two-dime nsional elect n>-

t The work of the first author sponsored by the Defense Nuclear Agency under Task

X99QAXVX, Work Unit 00076.

1
static effects are included by solving Poisson's equation using adaptive finite element

techniques in the bulk semiconductor. In this formulation, a new approach that

differs from both [1] and [2] is used to couple the one-dimensional current to the

two-dimensional potential. The effects of the charge in the inverted channel of the

transistor are included as a nonlinear boundary condition at the interface between

the semiconductor and the gate oxide.

The principal modification of the program, from the original GS1 [3,4] program,

is accomplished by modifying the surface boundary condition. The primary effect

of ionizing radiation on MOSFETs is the introduction of oxide trapped charge

(OTC), interface trapped charge (ITG), and the reduction of channel mobility

caused by scattering from charge in interface traps. Both of the charge effects must

be included in the oxide interface boundary condition. The OTC is independent

of device operating voltage after irradiation, while the charge state of the ITC is dependent on gate bias in the subthreshold and weak inversion regions since the

probability of these traps being occupied is a function of the local surface potential

in the two-dimensional model. Inclusion of these two charge components in device

models introduces a nonscalable component into the calculation of the total effective

channel charge in short-channel transistors.

The charge-sheet formulation allows the two-dimensional electrostatic field and

drain current to be calculated without the inclusion of a two-dimensional current

continuity equation. This results in a great improvement in computational efficiency

which allows finite element model calculations to be performed on a minicomputer.

This model is accurate in all regions of inverted transistor operation and works

well even in regions of operation where the channel current produces large changes

in the electrostatic potential in the channel. The model retains the computational

efficiency of single equation models [5] without imposing the computer requirements

of coupled equation models [6,7,8]. The complexity and cost of the model lie between

the long-channel one-dimensional model of Brews, which runs well on a desk top calculator, and the coupled equation models, which are best suited to large computers.

Unlike previous single equation models [5], the two-dimensional charge-sheet model

works in all regions of inverted transistor operation including weak inversion. Use of

the finite-element method also allows the adaptive mesh procedures [9] previously

applied to MESFETs [10] to be applied to MOSFETs.

In section two, the formulation of the two-dimensional charge-sheet model and

the effect of ITC and OTC at the semiconductor-oxide interface are discussed. In

this formulation, the total channel current is computed as a function of the twodimensional electrostatic potential. The computation of total channel current allows

the effects of these mobile and fixed charges to be treated as an effective surface

2
charge and to be included in subsequent calculations of the electrostatic potential

as a nonlinear integral boundary condition.

In section two, the numerical procedures used to calculate the electrostatic potential in two dimensions with a nonlinear boundary condition are also discussed. The

partial differential equation is transformed into a system of nonlinear equations us- ing adaptive, computer-generated, finite elements. The nonlinear field equations are solved using a damped Newton’s method. The resultant system of linear equations

is solved either by direct methods or by a multilevel iteration.

In section three, the specific procedures used to implement the model are discussed.

The structure of the computer program is discussed and the function of each of

the principal modules is outlined. The installation requirements of the program are discussed as are the sources of the software components which were developed by

other authors. The physical limitations of the model are then discussed.

In section four, the modeling of a set of irradiated MOS transistors is discussed.

2. Theory

A. Two-Dimensional Charge-Sheet Model

The two-dimensional charge-sheet model used in this work couples the effects of

the interface trapped charge and the oxide trapped charge to short-channel effects seen in unsealed MOSFETs. In this work, a two-dimensional finite element model

of short-channel MOSFETs is applied which allows the effects of ITC and OTC,

as well as radiation-induced channel mobility degradation, to be included in a twodimensional short-channel MOSFET model. The basic formulation of the model

includes a two-dimensional calculation of the electrostatic potential in the channel

region and in the oxide and a one-dimensional calculation of the channel inversion

layer current. This simplification is achieved by making assumptions based on the

basic semiconductor equations:

V •(/cVfl = — —(p — n + N)

eo

( 1)

V -(p n n V0re ) dn

dt

+ R (o\

3
Gate ip = ipg

7 /Ty-/ / ZZZZZZZEZZZZZZZZZZ

p -

zz&yrsr.

T Source

x h>

= ips

ZZZZZ2IZZZ

\

Qss

/S//J/S/S//S

Drain

ip = ipd

7-r/ /777/7^

p

= N(j + e

* — e

*

< *’ n

/ / //zz/ / / / / vzznzjis^z^z^rzrrr/ sz/

Figure 1. Geometry of the charge-sheet model.

4
( 3 ^’{ftpP^fip) R) )

where the electron density, n, and the hole density, p, are:

n = rii exp - <f> n )/ kT) (4)

p = n{ exp{q{<f>p -i))/kT), (5)

and where Shockley-Read-Hall recombination is given by:

R= iPn ~ nl)

r„0 (n + ni) + T

po(p + pi).

The symbols have their usual meaning as defined in [12].

The simplification to a single two-dimensional equation and one-dimensional current

flow is achieved by assuming that R = 0, which eliminates (6), and that the hole

quasi-Fermi potential is pinned at the substrate potential, <j) p = Vaub. This is then

used to replace (5) and eliminate (3). If in addition the channel current is assumed

to flow only in a one-dimensional sheet at the surface, the problem is reduced to

solving (1) and:

( 6)

»(y) = dx exp 1 + (exp{-(3Vd ) - 1)

dyo

/o°° dx exp(/?V>)/i„

dyo

/0°° dxcxp{pip)pn _

( 7 )

Equation (7) then replaces (2). The effects of OTC and ITC are included in the

oxide solution and in the interface boundary condition connecting the oxide field

solution to the solution in the bulk semiconductor. One of the advantages of flit' finite element formulation of the model is that the interfacial charge can be treated

exactly in the calculation of the finite element equations and in oxide boundary

conditions. If in addition the depletion in the source and drain regions is neglected,

the problem is reduced to the geometry shown in figure 1.

In this formulation of the problem, the OTC and ITC are given by:

5
Qite = {{Done) (8)

Qotc = g(Dose)Vipox ( 9)

where:

Qitc((j>s)

Q(Ed )dEd

1 + gd exv({<f>s — Ed )/kT)

Q(Ea )dEa

1 + g- 1 exp((Eg - (f> s )/kT)

( 10)

n (a \ Q(Ed)kEd

Qitcifis)

^

/ , 1 // , x I ,rr>\ j-£l + gd exp{{<f>s - Ed)/kT)

_ v- Q(Ea)AEg

1 + 971 exp{{Eg - (/>s)/kT)

( 11 ) The specific relationships between dose and these charge components in (8) and (9) are very technology specific and must be determined by the program user.

B. Numerical Procedures

An important feature of this work is that the numerical solutions were obtained us- ing general-purpose software for solving elliptic partial differential equations (PDEs).

Although some efficiency is sacrificed, the benefits obtained by using the generalpurpose software far outweigh the loss in efficiency. Problems with exact solutions

have been solved to test the correctness and accuracy of the codes and to determine

optimal strategics and optimal values for parameters in the code. The physics included in the model and the geometry of the problem can be easily changed. The

numerical software was inspired by finite-element software of Bank and Sherman

[9] and retains most of their philosophy.

This version of the package solves the PDE

V • [ a(z , y, u)Vu] = f(x, y, u, du/dx , du/dy) (12)

6
in a region bounded by straight line segments and circular arc segments. On each

segment of the boundary, u must obey one of two types of boundary conditions (1):

g(x,y,u) = 0 (13)

or (2)

du/dn + g(x, y, u) =

0. (14)

This is a fairly general example of a PDE arising from conservation of a flux and

includes both Poisson’s equation and the hole and electron continuity equations (in

the multiple-PDE version).

At the heart of the package is a module which solves a linear elliptic PDE using linear

finite elements on a mesh of triangles. (Boundary “triangles” may have one curved

side.) The initial triangulation is an input to the package; succeeding triangulations

are calculated adaptively by the package.

For a given triangulation with M vertices, the calculation proceeds as follows.

The M finite-element basis functions {&m} are linear on each triangle; b m is 1 at

vertex m and 0 at all other vertices. The set of vertices on type 1 boundaries

is denoted by D (for Dirichlet). The solution is approximated by a sum of basis

functions

M

U{x,y)= ^ arnl>m(x,y)- ( 15 ) 771=1

The coefficients are determined by a Galerkin method [13]; the error in the PDF is made orthogonal to each of the basis functions except those in D:

-V • (flVu) + f)b m = 0].

771 = 1 , 2 ,..., M

m not ill D

( 10 )

7
The remaining conditions on the b’s are that the type 1 boundary conditions hold

exactly [13]:

g(xm, Vm, u{x m, yTO )) = 0, m in D. (17)

Equation (16) is integrated by parts to yield

/ /

(oVu •V6m + fbm) + J^agbm = 0, (18)

where the single integral is over the type- 2 parts of the boundary only. Equations

(17) and (18) comprise M nonlinear equations in M unknowns, the coefficients {aTO }.

The M nonlinear equations are solved by an iterative process, a damped Newton’s

method. Let v be the Newton step and use a fraction of v as a correction to u; v has the same form as u,

M

vi x,y) = X]

m=

1

(19)

To calculate v, replace u by u + v in eqs (17) and (18) and linearize in v. The

linearization of eq (17) yields

g{ x m) Vm

i

^m) d"

l/mt Mto ) du

/3m = 0,m in D , ( 20)

and the linearization of eq (18) yields

8
{

aVv • V6m + • V6m + b m

Oil

(

d

J-v

df dv df dv

+ a

da

g Yu

+

\du d(duldx)dx d(duldy)dy

“fu)

6 ”1 = ~ / /

( aVu S7l>m + /4 ”*) - J2 agbTM =

(21)

Substituting for u and v from eqs (15) and (19) and doing the integrals numerically

gives a set of M linear equations for the correction coefficients {/Sm}. These linear

equations are sparse; there are typically only nine nonzero elements per row, on

average, and M can be a few hundred or a few thousand. A satisfactory way to

solve these equations is directly, with Gaussian Elimination, using the Yale Sparse

Matrix Package [14].

Unless u is close to a solution of the nonlinear finite-element equations, u + v may

be worse than u. A damped Newton’s method is used: replace u by u -1- \v, where

X is chosen so that max^lr^it + v)| < maxTO |r rre (u)|. This avoids divergence of the

iterative process.

In practice, the initial triangulation may be too coarse to give the desired accuracy

or may need local refinement to represent the solution accurately in a region of

high curvature. After the package has converged to an approximate solution on the

initial triangulation, the approximate solution may be used to estimate the error and produce a new and finer triangulation adaptively. There are various ways to

approximate the error in each triangle. For the present work, a simple method is used. In the silicon, the PDE is

( 22 )

Since if) is linear in each triangle, V

2

ip = 0. We estimate the relative error in each

triangle by

/ /

triangle

P(*,V) (23)

The refined triangulation is obtained by dividing the triangles wit h the largest

9
estimated errors, such as all triangles with estimated error larger than 1/4 of the

largest error.

For the refined triangulation, the previously calculated u is a good guess at the new

u, so that few Newton iterations should be necessary. The hardest work is done on

the initial triangulation, the one with the fewest vertices.

If there are two or more triangulations, the linear equations on the finest triangulation may be solved by a multilevel iteration [15,9], saving both time and storage

space. However, for the present problem, sufficient accuracy could be obtained with

M of only a few hundred, so that a direct solution using the Yale Sparse Matrix

Package was quite adequate.

Using this procedure, the solution of eqs (1) and (7) is started by first obtaining a

trial solution for the linearized form of eq (1), using the solution of eq (7) obtained

from the one-dimensional charge-sheet model with the total charge as a boundary

condition. The Jacobian of g required for the solution of eq (20) contains the

Jacobian of eq (1). This Jacobian is approximated by

— = qP(n[y) + Qitc + Qotc )• (24)

Once the surface charge and approximate local field term are obtained from the

one-dimensional model and a local-field condition, the field term associated with

the oxide is obtained using a fast Poisson solver [16]. The trial solution is then

used to obtain a solution for eq (7) by quadrature and an additional fast Poisson

solution in the oxide. This iterative procedure is repeated for each Newton step until

the requested convergence is obtained or the specified maximum iteration count is reached.

3. Computer Implementation

A. Software Modules

The distributed source of the CS1R program is divided into four files: CS1R.FOR,

SYSTEM.FOR, PDESUB.FOR, and DEVLIB.FOR. These four files conform to

ANSI 66 FORTRAN IV and can be compiled on any FORTRAN compiler which

meets this standard. The files CS1R.IILP, CS1R.EXP, and CS1R.LNK are also

provided. CS1R.IILP provides a set of user instructions identical to Appendix A

of this report. CS1R.EXP contains an example set of program input and output

10
which is identical to Appendix B of this report. The file CS1R.LNK is a sample set

of linkage control statements which have been used to link the program on the DEC

VAX 11/780* under the VMS* system.

The file CS1R.FOR is the actual charge-sheet model program. This file contains the

subroutines which control input and output, model initial approximations, find the

oxide field solution, and contain the calls to the subroutines which solve the partial

differential equation. The starting approximation is identical to the charge-sheet

model originally developed by Brews [2]. The output of this long-channel model is printed at the beginning of each CS1R calculation. The oxide solution is calculated

using the fast methods discussed in reference [16]; these subroutines are in the file DEVLIB.FOR. A complete copy of the Swarztrauber and Sweet package [16] is not

included. Only those parts of the package that are used by CS1R are included.

The CS1R module of the program contains parameters TOL and IP(6) which

are used to control the accuracy of the solution. The parameter TOL is used

to control the iteration accuracy at each multigrid level. The parameter IP(6)

is used to control the number of muitigrid levels. These parameters are set to

yield very accurate solutions in the version of the program which is distributed.

This level of accuracy greatly exceeds that required for most applications, but is necessary, during installation and testing, to verify that the program has been

correctly installed. Resetting these parameters to lower accuracy by increasing the

iteration tolerance and/or decreasing the number of multigrid levels will greatly

improve run times.

The file SYSTEM.FOR contains subroutines which are used in the other three

program files but which are system dependent. The subroutines FOPEN and FCLOSE

are used to open and close input and output files. In the VAX VMS version supplied

on the tape, the file FCLOSE is a dummy subroutine. The subroutines ISTIME

and IFTIME are used to start and stop clocks which are used to measure the

execution times of the parts of the partial differential solution process. If these

routines are not used and dummy subroutines are substituted, ISTIME must be

less than, NOT equal to, IFTIME. If these subroutines are dummy routines, then

the timing information in the output summary will be incorrect.

The subroutines PLTUTL, CURVEA, and ISCALE contain calls to vector graphic s subroutines. The calls in the supplied program can be used with the TOS soft ware

* Certain commercial equipment, instruments, or materials are identified in tin

paper in order to adequately specify the experimental procedure. Such idenl ifiral am

does not imply recommendation or endorsement by the National Bureau of Si andai nor does it imply that the materials or equipment identi lied are necessaril v i L

best available for the purpose.

11
supplied by Tektronix* and can be used to drive either Tektronix or HewlettPackard* terminals. Other graphics packages can easily be substituted if the neces- sary initialization, absolute motion, and absolute vector drawing primitives are

available in either software or terminal firmware. If these subroutines are made into

dummy subroutines, graphics output will not be available from the program except

through the plot output file. The data written into the plot output file, file 2, are a sequence of non-negative x- and y-coordinate pairs. The first line of the file contains

the minimum and maximum values of the x- and y-coordinates. Each plot is terminated by a set (or sets) of negative coordinate pairs. The subroutines R1MACH,

D1MACH, and I1MACH are used to set machine constants which are used in the

other program modules to set machine-dependent quantities. The original versions

of the functions are discussed in reference [17] as are the procedures used to generate

these constants for a type of computer which is not presently included in the present

list. The conversion of the program from one computer type to another should not

require modification of any part of the program which is not in the SYSTEM.FOR

module. This assumes that some plotting package is available and that timing subroutines are available on the target computer system.

The module PDESUB.FOR contains the subroutines used to solve the partial differential equations. The theory of these subroutines has been discussed in section 2B

above.

The module DEVLIB.FOR contains subroutines used by the other three modules.

These subroutines have been obtained from several sources. The error-handling software, memory management software, and machine-independent constant software

were obtained from [17]. The fast elliptic solver was obtained from [16]. In the initial

approximation, quadrature from [16] and root finding routines from [19] are used.

In the PDESIJB module, the Yale Sparse Matrix Package is used [14].

B. Physical Restrictions

Two physical restrictions have been imposed in the present implementation of the

CS1R program. First, the two-dimensional electric field dependence of the mobility

has not been included. Second, the detailed slopes of the source- and-drain doping

profiles have not been included in the model.

The first limitation is more serious. In circuit models and in some two-dimensional

device simulation programs, the field dependence of the mobility is empirically

included using an expression of the form a/( 1

-1- bE) where a and b are empirically

determined parameters and E is the magnitude of the electric field. Recent work

by Cooper and Nelson [201 suggests that this model is not adequate to characterize

12
the field dependence of the mobility. On the other hand, the Cooper and Nelson

data do not include several effects which are known to affect the low field value of

the mobility; these are the effects of bulk doping and oxide interface charge. Since

no definitive model for the two-dimensional dependence of the mobility is available,

none has been included.

The details of the two-dimensional source-and-drain profiles are included in the

model only as two elliptic abrupt junctions. This allows the details of the majority

carrier quasi-Fermi level to be neglected and greatly simplifies the program, making

the charge-sheet calculation much more efficient. On the other hand, at high sourcedrain-voltages, this approximation can lead to convergence problems and/or to

inaccurate modeling of the potential near the drain. In addition, this model places

the burden of specifying lateral and vertical junction depths on the program user. Other available two-dimensional device simulation programs, such as MINIMOS [6],

attempt to include simple two-dimensional process models in the device modeling

programs. These simplified models do not agree with more complex two-dimensional

models [21] or with experimental measurement of two-dimensional junction shape

[20]. If the user of the program wishes to use these simplified models, then the

work of Kennedy and O’Brien can be used [23]. If more complicated models [21] or experimental data are available, then these can be used.

4. Device Model Verification

The model is verified by comparing the results obtained with the model to n-channel

MOSFETs of the type discussed in [24] for doses of 0, 10, 50, 100, and 500 Krad(Si).

Prior to irradiation and after each irradiation, the current-voltage characteristics of

the transistor were measured. Capacitance data were also taken on a MOS capacitor

adjacent to the transistors. All devices were biased with -1-9 V on the gate or capacitor polysilicon electrode and the source, drain, and substrate grounded. The

device used for model verification was chosen with a channel length of 7.8 /im to

allow the effects of radiation to be separated from short-channel effects. In this

model, the interface traps are treated as a continuous distribution of traps which

are populated and depopulated as the surface potential is varied. At doses below

50 Krad(Si), the effect of the energy distribution of the traps is small. Above 50

Krad(8i), the energy distribution becomes important. At a dose of 500 Krad(Si), tin*

effect of energy distribution on subthreshold current is most sensitive to the trap

energy distribution. Two-dimensional simulations were then carried out which us<>d

fixed oxide charge, a variable distribution of interface traps and channel mobility

degradation to model the effects of the radiation.

All of the transistors studied were modeled in the subthreshold region, the triodc

13
region, and the saturation region. The parameters used in these simulations are given in table 1.

Table 1. Simulation Parameters

Lch 7.8 /im

Qitc 0.0 to 1.75 Xio12 cm

-2

VG ,VD 0.5 V to 4.0 V, 0.25 V

tox 0.0523 /im

Nch 1.5 XlO16 cm

-3

Ljun 0.710 /im

Djun 0.875 /im

Detailed comparison of the model with measured data shows excellent agreement

between the model and measured current-voltage characteristics in the subthreshold

region, the triode region, and the saturation region. A typical subthreshold region

simulation is compared to measured data in figure 2 for an unirradiated sample.

A typical subthreshold region simulation is compared to measured data in figure

3 for a 10 Krad(Si) dose. A typical subthreshold region simulation is compared to

measured data in figure 4 for a 50 Krad(Si) dose. A typical subthreshold region

simulation is compared to measured data in figure 5 for a 100 Krad(Si) dose.

As the dose is increased above 50 Krad(Si), the effects of the interface trapped

charge energy distribution become increasingly important. This effect is illustrated

in figures 6 and 7. In figure 6, the subthreshold characteristic of a device irradiated

at 500 Krad(Si) is simulated with a uniform energy distribution of traps in the band.

In figure 7, the subthreshold characteristic of a device irradiated at 500 Krad(Si)

is simulated with an energy distribution of traps in the band that is peaked on

the valence band side of the band gap. In both simulations, a total trap density of

1.75 X 10 12 cm~2 was used. In the uniform case, the traps are populated continuously

as the channel is inverted. In the second case, the populated trap density increases

more rapidly as the transistor enters strong inversion.

A typical saturation region simulation is compared to measured data in figure 8

for an unirradiated sample. A typical saturation region simulation is compared to

measured data in figure (J for a 500 Krad(Si) dose. The triode region characteristics, as a function of dose, are compared to measured data in figure 10. In the

radiation-hardened n-channel transistor modeled here, the effects of oxide charge

and interface charge both increase linearly with dose. These two charges cancel to

14
10

"

>N-^O)

>

(V) PI

15

Figure

2.

A

subthreshold

region

simulation

compared

to

measured

data

for

an

unirradiated

transistor,

V^=().

25V.
10

'

(V) PI

16

Figure

3.

A

subthreshold

region

simulation

compared

to

measured

data

for

Krad(Si)

dose,

Vd=

0.25

V.
10

"

o

>

O)

>

oLO

03

(V) PI

17

Figure

4

. A

subthreshold

region

simulation

compared

to

measured

data

for

Krad(Si)

dose,

Vj=0.25

V.
10

"

o

>

o> >

(V) PI

18

Figure

5.

A

subthreshold

region

simulation

compared

to

measured

data

for

a

100

Krad(Si)

dose,

Vj=

0.25

V.
10

"

(V) PI

19

Figure

6.

A

subthreshold

region

simulation

compared

to

measured

data

for

a

500

Krad(Si)

dose,

Vj=0.25

V,

uniform

trap

distribution.
10

"

o

O O O o

>

o> >

(V) PI

20

Figure

7.

A

subthreshold

region

simulation

compared

to

measured

data

for

a

500

Krad(Si)

dose,

V^=0.25

V,

trap

distribution

peaked

near

the

valence

band.
150

o

O 10

(Vrl) p|

21

Figure

8.

A

saturation

region

simulation

compared

to

measured

data

for

an

unirradiated

transistor.
Measured

data

Vg

=

3.0V

>

o

>

(Vri) PI

22

Figure

9.

A

saturation

region

simulation

compared

to

measured

data

for

a

500

Krad(Si)

dose.
(Vrt) PI

23

Figure

10.

The

triodc

region

characteristics,

asa

function

of

dose,

compared

to

measured

data,

Vj=0.25

V.
produce a total threshold shift of « 0.25 V at 500 Krad(Si). The resulting increase

in interface charge causes a decrease in channel mobility from 760 cm2 /V-sec. in

the unirradiated device to 257 cm2 /V-sec. at 500 Krad(Si). The increase in interface charge also results in an increase in subthreshold current and a decrease in

subthreshold slope. Simple linear relationships between dose and both oxide charge

and interface charge are sufficient to account for all of these device characteristics.

The model shows that the I-V characteristics of the heavily irradiated device are

similar to those of an unirradiated device of much shorter channel length. In the

short-channel device, the subthreshold characteristic is degraded by the drain field.

In the irradiated device, this subthreshold degradation is caused by the charge in

the radiation-induced interface traps.

5. Conclusions

A two-dimensional charge-sheet model of a surface-channel MOS transistor has been

developed. When this model is implemented using adaptive finite element methods,

an efficient high-accuracy transistor simulation program is possible. The inclusion

of interface trap energy distribution allows the characteristics to be modeled for

n-channel transistors for doses of up to 500 Krad(Si).

Acknowledgments

The authors would like to thank M. Gaitan and T. J. Russell for the data used to

verify the model.

References

1. De La Moneda, F., Threshold Voltage from Numerical Solutions of the TwoDimensional MOS Transistor, IEEE Trans. Circuit Theory CT-20, 666-673 (1973).

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

345-355 (1978).

3. Wilson, C. L., and Blue, J. L. Two-Dimensional Finite Element Charge-Sheet

Model of a Short-Channel MOS Transistor, Solid-State Electronics 25, 461-477

(1982).

4. Wilson, C. L., and Blue, J. L., Two-Dimensional Finite Element Charge-Sheet

Model of a Short-Channel MOS Transistor, National Bureau of Standards report

NBSIR 82-2471 (1982).

24
5. Greenfield, J. A., and Dutton, R. W., Nonplanar VLSI Device Analysis Using the

Solution of Poissons’s Equation, IEEE Trans. Electron Devices ED-27, 1520-1532

(1980).

6. Selberherr, S., Schutz, A., and Potzl, H. W., MINIMOS - A Two-Dimensional

MOS Transistor Analyzer, IEEE Trans. Electron Devices ED-27, 1540-1549 (1980).

7. Buturla, E. M., and Cottrell, P. E., Two-Dimensional Finite-Element Analysis

of Semiconductor Steady-State Transport Equations, Int. Conf. on Computational

Methods in Nonlinear Mechanics, Austin, Texas, 1974.

8. Fichtner, W., and Rose, D. J., On the Numerical Solution of Nonlinear Elliptic

PDE’s Arising from Semiconductor Device Modeling, Elliptic Problem Solvers, M.

Schultz, Ed. (Academic Press, New York, 1981), pp. 277-284.

9. Bank, R. E., and Sherman, A. H., PLTMG User’s Guide, CNA-152, Center for

Numerical Analysis, University of Texas at Austin, September 1979.

10. Laux, S. E., and Lomax, R. I., Numerical Investigation of Mesh Size Convergence

Rate of Finite Element Method in MESFET Simulation, Solid-State Electronics 24,

485-493 (1981).

11. Brews, J. R., Fichtner, W., Nicollian, E. H., and Sze, S. M., Generalized Guide

for MOSFET Miniaturization, Electron Device Letters EDL-1, 2-4 (1980).

12. Wilson, C. L., and Blue, J. L., Semiconductor Device Simulation, Elliptic Problem

Solvers, M. Schultz, Ed. (Academic Press, New York, 1981), pp. 435-439.

13. Strang, G., and Fix, G. J., An Analysis of the Finite Element Method (PrenticeHall, Englewood Cliffs, N.J., 1973).

14. Eisenstat, S. C., Gursky, M. C., Schultz, M. A. and Sherman, A. II., Yale Sparse

Matrix Package I. The Symmetric Codes, Research Report #112, Department of

Computer Science, Yale University, 1970.

15. Brandt, A., Multi-Level Adaptive Solutions to Boundary-Value Problems, Math.

Comp. 31, 333-390 (1977).

16. Swarztrauber, P., and Sweet, R., Efficient FORTRAN Subprograms for the

Solution of Elliptic Partial Differential Equations, NGAR Technical Note, NCARTN/IA-109, 1975.

17. Fox, P. A., Hall, A. D., and Schryer, N. L., The PORT Mathematical Subroutine

25
Library, ACM Trans. Mathematical Software 2, 104-126 (1978).

18. Blue, J. L., Automatic Numerical Quadrature - DQUAD, Bell Labs Comput. Sci.

Tech. Rep. 25, February 1975; also, Automatic Numerical Quadrature, Bell Syst.

Tech. J. 59, 1651-1678 (1977).

19. Brent, R. P., Algorithms for Minimization Without Derivatives (Prentice-Hall,

Englewood Cliffs, N.J., 1973), pp. 188-189.

20. Cooper, J. A., Jr., and Nelson, D. F., Measurement of High-Field Drift Velocity

of Electrons in Inversion Layers on Silicon, IEEE Electron Device Letters EDL-2,

171-173 (1981).

21. Warner, D. D., and Wilson, C. L., Two-Dimensional Concentration Dependent

Diffusion, Bell Syst. Tech. J. 59, 1-41 (1980).

22. Wilson, C. L., Scanning Electron Microscope Measurements on Short Channel

MOS Transistors, Solid-State Electronics 23, 345-356 (1980).

23. Kennedy, D. P., and O’Brien, R. R., Analysis of the Impurity Atom Distribution

Near the Diffusion Mask for a Planar p-n Junction, IBM J. Res. Dev. 9, 179-186

(1965).

24. Dressendorfer, P. V., Sodcn, J. M., Harrington, J. J., and Nordstrom, T. V.,

The Effects of Test Conditions on MOS Radiation-Hardness Results, IEEE Trans.

Nucl. Sci. NS-28, 4281-4287 (1981).

26
Appendix A

File CS1R.HLP

1. Interactive Execution

On a VAX 11/780 the program is executed by entering:

RUN CS1R.EXE

A prompt will appear for the next input; enter a file name

after each prompt, followed by a carriage return (denoted <cr>)

FILENAMEl<cr>

FILENAME2<cr>

FILENAME3<cr>

FILENAME4<cr>

FILENAMES <cr>

FILENAME6<cr>

The first and third files must have been created prior to this

execution. They contain input data used by the program. The

second file may be created during execution. The FILENAMES

must be legal VMS file names; they are limited to eight

characters by an internal buffer in CS1R.

A. FILES

1) Filel contains data for each point to be

calculated. The file format is shown below.

2) File2 is an empty file for output of plotting

data if the plots are to be saved. This file name

must be entered when if no plotting is to be done.

VMS will create the file if plotting data are to

be stored; other operating systems may require the file to be created before the run begins.

3) File3 contains a table of channel doping profiles.

4) File4 contains a table of acceptor trap density vs energy.

5) FileG contains a table of donor trap density vs energy.

6) FileO contains a table of oxide charge density vs distance.

B. Examples of FILE FORMATS.

Each point to be calculated requires G lines of input.

Data on a given line are frce-format. Comments may appear

after all required data fields. After each point

27
is calculated, the program will look for additional data

until a source doping of zero is found (first line of input),

after which the program will terminate.

EXAMPLE OF Filel: Data are in units given.

Line 1: Source doping/cm* *3

3.0el9

Line 2: Vertical junction depth(um),Lateral junction depth(um),Poly-Si length(um)

note: Channel length = Poly-Si length-2 ^Lateral junction depths

0.55 0.84 5.00

Line 3:

Drain(volts),Gate(volts),Substrate(volts)

note: Source voltage = 0.0.

0.15 +1.158 0.0

Line 4: Oxide thickness(um), Oxide dielectric constant,Interface charge(cm**2)

0.057 4.0 0.0

Line 5: Channel mobility(cm**2/V-sec),Channel width(um),Flatband voltage(V)

400.0 20.0 -.580

Line 6: Line 6 may contain 0.0 for stopping program, or may be

first line of data for next point to be calculated. Last line in

data file must be zero. EXAMPLE of File3: Data for doping density.

Line 1: Contains integer, Ndop, denoting the length of the profile table.

2

Lines 2 through Ndop+1:

Each contains an x (um) and the doping density at x (l/cm**3)

0.0 3.el5

100.0 3.el5

EXAMPLE of File4: Data for acceptor trap density.

Line 1: Contains integer, Nqa, denoting the length of the table and a scale factor.

28
4 0.144

Lines 2 through Nqa-t-1:

Each contains an energy referred to mid-band (Ey) and the density l/(Ev-cm xx

2)

-0.500 0.0

-0.499 l.Oell

0.499 l.Oell

0.500 0.0

EXAMPLE of File5: Data for donor trap density.

Line 1: Contains integer, Nqd, denoting the length of the table and a scale factor.

4 0.144

Lines 2 through Nqd+1:

Each contains an energy referred to mid-band (Ey) and the density l/(Ev-cm x *2)

-0.500 0.0

-0.499 l.Oell

0.499 l.Oell

0.500 0.0

EXAMPLE of File6: Data for oxide charge density.

Line 1: Contains integer, Nqox, denoting the length of the table and a scale factor.

4 1.00

Lines 2 through Nqox+l:

Each contains a distance referred to the source (um) and the density l/(cm“2).

0.000 0.0

0.100 l.Oell

5.000 l.Oell

5.500 0.0

C. OUTPUT DISPLAY

All outputs (except the drain current) are in intrinsic Debye

lengths (33um) and thermal volts (25mV), or units derived from

these such as, Thermal volts/Debye length.

29
1. After program execution, the following prompts appear on

the display:

ENTER 0, 1,2,3 FOR CURRENT AND NEXT POINT, 2D PRINTING,

2D PLOTTING, CURRENT AND STOPPING.

0 - print current. Continue to next point in data file, if any.

1 - print additional information about point just calculated.

2 - plot additional information about point just calculated.

3 - print current and terminate execution. Do not continue

to next data point in data file, if any.

If response 1 or 2 is given, further prompts will be furnished.

2. OPTIONS for printing (response 1)

The prompt is ENTER SUMMARY,NX,NY

SUMMARY - for a summary of the number of mesh points and triangles

created, how much memory allocated, and how much time

used, enter 1. If not desired, enter 0.

NX NY - how many points along X and Y are to be printed in the

print matrix. If NX and NY are both negative, a

scaled integer printer plot of the potential will result.

If NX and NY are both positive, a rectangular grid is placed on the region; at each point X, Y, U (the

potential), UX, and UY (the derivatives of U in the

X and Y directions) will be printed. At grid points outside

the region, large numbers will be printed.

3. OPTIONS for plotting (response 2)

The prompt is liTRIANCLES, 2:CONTOURS, 3:SURFACE, 4:PROFILES

Enter 1, 2, 3, or 4, to plot on screen. Enter 101, 102, 103, or 104, to save plot data on File2.

Enter 0 to terminate plotting.

30
Each plot mode will furnish one or more further prompts. In every

screen-plotting case, the final prompt before drawing the plot is

Enter g or G to when ready to plot

This gives the user time to clear the screen or to do any work

necessary to put the terminal in plotting mode.

After each plot is drawn on the screen, the program will wait for a carriage return, and then re-issue the above prompt. This gives

the user time to clear the screen or to do any work necessary to

change the terminal out of plotting mode.

1: TRIANGLE PLOTS

The prompt is ENTER LEVEL

Enter level number (1, 2, ...) to plot the mesh of that level.

Enter 0 to terminate triangle plotting.

After the triangle plot has been drawn, the program waits

for a carriage return, and then reissues the Triangle

Plot prompt.

2: CONTOUR PLOTS

The first prompt is l:FUNCTION, 2:ABS(GRADIENT)

Enter 1 to plot the function (potential), or 2 to plot the

absolute value of its gradient (absolute value of electric

field; units are thermal volts/Debye length).

Enter 0 to terminate contour plotting.

The next prompt is NUMBER OF CONTOURS

31
Enter the number of contour lines to be drawn. They will be

drawn equally-spaced between (and including) the minimum and

maximum values found.

After the contour plot has been drawn, the program waits

for a carriage return, and then reissues the first Contour

Plot prompt.

3: SURFACE PLOTS

The first prompt is l:FUNCTION, 2:ABS(GRADIENT)

Enter 1 to plot the function (potential), or 2 to plot the

absolute value of its gradient (absolute value of electric

field; units are thermal volts/Debye length).

Enter 0 to terminate surface plotting.

The next prompt is ENTER LEVEL

Enter level number (1, 2, ...) to make a plot of the surface

using the mesh of the given level.

Enter 0 to return to the First Surface Plot prompt

The next prompt is ENTER VIEWING DIRECTION-NX,NY,NZ

Enter three integers. The surface plot is a (parallel)

projection of the surface as seen from indicated direction.

Thus (0,0,1) will give a top view (like a Triangle Plot),

and (0,-l,0) will give a side view.

After the surface plot has been drawn, the program waits

for a carriage return, and then reissues the first Surface

Plot prompt.

4: PROFILE PLOTS

The first prompt is ENTER NUMBER OF PROFILES

Enter an integer, the number of profiles to be drawn.

32

/
Enter 0 to terminate profile plotting.

The next prompt is ENTER INDICES OF PROFILE PLANE(S), NX AND NY

Enter two integers. A profile plot is a slice through the

solution, perpendicular to the given direction. Thus (0,1)

will give a slice parallel to the X axis.

After the profile plot has been drawn, the program waits

for a carriage return, and then reissues the first Profile

Plot prompt.

2. BATCH EXECUTION (for VAX-VMS only)

A. Submit File

Create a submit file which contains:

$ RUN CS1R.EXE

FILENAME1

FILENAME2

FILENAME3

FILENAME4

FILENAMES

FILENAME6

(Any other input used for the the equivalent interactive

execution).

B. Output will be printed on the line printer.

3. SUMMARY OF MODEL

A two-dimensional charge sheet model of a surface-channel MOS

transistor has been developed. When this model is implemented

using adaptive finite element methods, an efficient high- accuracy

transistor simulation program is possible.

The primary effect of ionizing radiation on MOSFETs is the

33
introduction of oxide trapped charge (OTC) and interface trapped

charge (ITC). The OTC is independent of device operating voltage

after irradiation, while the charge state of the ITC is dependent

on gate bias in the subthreshold and weak inversion regions.

Inclusion of these two charge components in device models introduces

a nonscalable component into the calculation of the total effective

channel charge in short-channel transistors.

34
Appendix B

File CS1R.EXP

INPUT FILE NAME FOR INPUT DATA,

FILE specification MUST BE <= 40 CHARACTERS.

s8 . dat (user input)

INPUT FILE NAME FOR OUTPUT DATA PLOTTING

plot . dat (user input)

INPUT FILENAME FOR DOPING PROFILE DATA

dops8 . dat (user input)

INPUT FILENAME FOR tJIA ENERGY DATA

qa . dat (user input)

INPUT FILENAME FOR QID ENERGY DATA

qd . dat (user input)

INPUT FILE NAME FOR QOX VS DISTANCE DATA

qox . dat (user input)

BETA = 3 . 868472E+01

PSIB = 3 . 466497E-01

LB = 4 . 086666E-06

COX = 6

.

207734E-08

BPSO = 2 . 331486E+01

BPSI = 3 . 318985E+01

PS(O) = 8.579575E-01

NO = 1 . 106634E+12

PS (L) = 1

.

104439E+00

NL = 9 . 657040E+11

ID = 8.584329E-05

10 = 5 . 349826E+01

I... = 9 . 999379E+02

VG 1 . 547389E+02

VSD = 9 . 671180E+00

LCH = 2.481457E-01

level 1

1 dpsi -1 . 553E+01 a -2.540E+08 umax 4 . 639E+01

2 dpsi 9 . 854E+00 a -1..500E+08 umax 1 . 042E+01

3 dpsi 4 . 888E+00 a -1 . 088E+08 umax 1 .042E+01

4 dpsi 8 . 537E+00 a -9.717E+07 umax 8 . G93E+00

5 dpsi 8.361E-IQ0 a -1 . 199E+08 umax 8 . 676E+00

6 dpsi 4 . 273E+00 a -1 . 731E+08 umax 4 . 311E+00

7 dpsi 2 . 256E+00 a -2 . 395E+08 umax 2 . 277E+00

8 dpsi 1 . 012E+00 a -3.043E+08 umax 1 .016E+00

35
9 dpsi -8 . 973E-01 a -3.470E+08 umaz 9.037E-01

10 dpsi -8 . 854E-01 a -3. 421E+08 umax 8 . 919E-01

11 dpsi -8.539E-01 a -2. 968E+08 umax 8.614E-01

12 dpsi -7 . 848E-01 a -2.413E+08 umax 7.944E-01

13 dpsi -6.455E-01 a -1 . 945E+08 umax 6 . 582E-01

14 dpsi -4.437E-01 a -1 . 631E+08 umax 4 . 455E-01

15 dpsi 4.279E-01 a -1 . 638E+08 umax 4.455E-01

level

1

2

dpsi 7 . 609E-02 a -1 . 529E+08 umax 4.455E-01

2 dpsi 1 . 169E+00 a -1 . 408E+08 umax 2 . 663E+01

3 dpsi 1 . 234E+00 a -1 . 366E+08 umax 1 . 977E+01

4 dpsi 3 . 674E+00 a -1 . 372E+08 umax 1 . 429E+01

5 dpsi 2 . 572E+00 a -1.846E+08 umax 2 . 737E+00

6 dpsi 2.915E-01 a -1 . 920E+08 umax 1 . 188E+00

7 dpsi 2 . 092E-01 a -1.994E+08 umax 1 . 064E+00

8 dpsi 2 . 829E-03 a -1 . 996E+08 umax 1 . 057E+00

level

1

3

dpsi 4.082E-04 a -1 . 996E+08 umax 1 . 057E+00

2 dpsi 7 . 940E-01 a -2. 113E+08 umax 7 . 997E+00

3 dpsi 5.418E-01 a -2. 552E+08 umax 1 . 191E+00

4 dpsi -2 . 892E-01 a -2 . 826E+08 umax 9 . 930E-01

5 dpsi -2.685E-01 a -2 . 875E+08 umax 5 . 127E-01

6 dpsi -2.579E-01 a -2 . 772E+08 umax 2 . 583E-01

ENTER 0 FOR CURRENT AND NEXTPOINT

1 FOR 2D PRINTING

2 FOR 2D PLOTTING

3 FOR CURRENT AND STOPPING

4 FOR CHANNEL PRINTING

1 (user input)

enter summary , ni , ny

1 -6 -11 (user input)

3 MULTI-GRID LEVELS

VERTICES 146 340 517

TRIANGLES 322 852 1344

STORAGE ALLOCATION

36
ALLOCATED USED

MAXT 17655 1349

MAXV 6621 517

MAXVSM 8826 1006

MAXJA 35877 3766

MAXU 1099 1099

MAXJU 1099 1062

TOTAL 200000 19992

TIMING DISTRIBUTION

SECONDS PERCENT

GRID 0.540 0.298

ASMBLY 133.740 73.784

MG 38 . 620 21.306

ADAPT 8.360 4.612

TOTAL 181.260 100.000

scaled values from -1.410E+01 to 3.344E+01 scale 3.344E+01

9999 9999 -39 -41 -40 -38

9999 9999 -42 -41 -40 -38

100 -42 -42 -41 -40 -38

96 -42 -42 -41 -40 -38

92 -42 -42 -41 -40 -38

88 -42 -42 -41 -40 -38

85 -42 -42 -41 -40 -38

81 -42 -42 -41 -40 -38

77 -42 -42 -41 -40 -38

9999 9999 -42 -41 -40 -38

9999 9999 -41 -41 -40 -38

ENTER 0 FOR CURRENT AND NEXTPOINT

1 FOR 2D PRINTING

2 FOR 2D PLOTTING

3 FOR CURRENT AND STOPPING

4 FOR CHANNEL PRINTING

1 (user input)

enter summary , nz , ny

0 6 11 (user input)

I X Y U UX UY

37
12

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

0 . 00000 0 . 00000 1 . 7Q141E+38 1.70141E+38 1 . 70141E+38

0.01716 0 . 00000 1 . 70141E+38 1.70141E+38 1 . 70141E+38

0.03432 0 . 00000 -1 . 37603E+01 -1.15893E+01 -1 . 00326E+02

0.05148 0 . 00000 -1 . 35980E+01 2 . 32617E+01 -2.00069E+00

0.06864 0 . 00000 -1 . 32181E+01 2 . 17328E+01 -3.08984E-01

0.08580 0 . 00000 -1 . 28544E+01 2 . 11106E+01 -2.26113E-01

0.00000 0.03333 1 . 70141E+38 1.70141E+38 1 . 70141E+38

0.01716 0 . 03333 1 . 70141E+38 1.70141E+38 1 . 70141E+38

0.03432 0 . 03333 -1 . 40133E+01 3.47357E+01 -2.64253E+00

0.05148 0 . 03333 -1 . 36049E+01 2.32352E+01 -3.97550E-02

0.06864 0 . 03333 -1 . 32227E+01 2 . 20039E+01 6 . 71393E-02

0.08580 0 . 03333 -1 . 28544E+01 2 . 13377E+01 0 . 00000E+00

0.00000 0.06665 2 . 56068E+01 -7 . 69545E+03 6 . 86773E+01

0.01716 0 . 06665 -1 . 41004E+01 -1.64209E+00 8.90639E-01

0.03432 0 . 06665 -1.40099E+01 2.69803E+01 -6.98656E-01

0.05148 0.06665 -1 . 36036E+01 2 . 29632E+01 1.84883E-02

0.06864 0.06665 -1.32223E+01 2 . 19542E+01 -1.14683E-02

0.08580 0 . 06665 -1 . 28545E+01 2 . 13854E+01 0 . 00000E+00

0 . 00000 0 . 09998 2 . 71429E+01 -7 .79302E+03 9 . 72625E+01

0.01716 0 . 09998 -1 . 40999E+01 4.87984E+00 -1.99454E-01

0.03432 0 . 09998 -1 . 39963E+01 1.53671E+01 1 . 52627E+00

0.05148 0 . 09998 -1.36035E+01 2 . 28412E+01 1 . 19908E-02

0.06864 0 . 09998 -1.32227E+01 2 . 19542E+01 -1.14683E-02

0.08580 0 . 09998 -1.28545E+01 2 . 13864E+01 0 . 00000E+00

0.00000 0.13330 2 . 83510E+01 -8 . 25570E+03 1 . 48578E+01

0.01716 0.13330 -1 . 40893E+01 -5.37798E+00 5.95635E-01

0.03432 0.13330 -1 . 39811E+01 1.67567E+01 -5 . 16155E+00

0.05148 0.13330 -1 . 36031E+01 2 . 28756E+01 1.81706E-02

0.06864 0.13330 -1.32229E+01 2 . 18015E+01 -1.84935E-02

0.08580 0.13330 -1 . 28544E+01 2 . 14624E+01 0 . 00000E+00

0.00000 0.16663 2 . 95216E+01 -8 . 13601E+03 4 . 19888E+01

0.01716 0.10663 -1.40986E+01 -6 .38180E+00 -4 . 97834E-01

0.03432 0.16663 -1.39721E+01 1.73758E+01 6 . 77656E+00

0.05148 0.10663 -1 . 36069E+01 2 . 38427E+01 -5.01812E-01

0.06864 0 . 16663 -1.32235E+01 2 . 18015E+01 -1.8493GE-02

0.08580 0 . 16663 -1.28544E+01 2 . 14624E+01 0 . 00000E+00

0.00000 0 . 19996 3 . 0G777E+01 -8 . 50732E+03 4 . 61548E+01

0.01716 0.19996 -1.40893E+01 -4.21487E+00 5 . 42349E-02

0.03432 0 . 19996 -1.39811E+01 1.07960E+01 5 . 21157E+00

0.05148 0 . 19996 -1 . 36031E+01 2.28729E+01 -1.87395E-02

0.06864 0.19996 -1.32229E+01 2 . 18015E+01 1 . 87087E-02

38
42 0.08580 0.19996 -1 . 28544E+01 2 . 14624E+01 0 . 00000E+00

43 0.00000 0.23328 3 . 19591E+01 -8 . 33355E+03 2 . 53904E+01

44 0.01716 0.23328 -1.41009E+01 1.41400E+01 1 . 46553E+00

45 0.03432 0.23328 -1 . 39964E+01 1 . 55038E+01 -1 . 51089E+00

46 0.05148 0.23328 -1 . 36036E+01 2 . 28469E+01 -1.40815E-02

47 0.06864 0.23328 -1 . 32227E+01 2 . 19575E+01 1 . 05458E-02

48 0.08580 0.23328 -1.28544E+01 2 . 13845E+01 0 . 00000E+00

49 0.00000 0.26661 3 . 34385E+01 -8 . 54575E+03 1 . 13276E+02

50 0.01716 0.26661 -1 . 40937E+01 -2.87519E+00 -7.03582E-01

51 0.03432 0.26661 -1.40099E+01 2.75868E+01 5 . 18849E-01

52 0.05148 0.26661 -1 . 36035E+01 2 . 29437E+01 -5.69664E-03

53 0.06864 0.26661 -1 . 32223E+01 2 . 19575E+01 1 . 05458E-02

54 0.08580 0.26661 -1.28544E+01 2 . 13845E+01 0 . 00000E+00

55 0.00000 0.29993 1 . 70141E+38 1.70141E+38 1.70141E+38

56 0.01716 0.29993 1.70141E+38 1.70141E+38 1 . 70141E+38

57 0.03432 0 . 29993 -1 . 40225E+01 4.93789E+01 7 . 53808E+00

58 0.05148 0.29993 -1 . 36073E+01 2.36961E+01 -2 . 07513E-02

59 0.06864 0.29993 -1 .32227E+01 2 . 19793E+01 -6.87528E-02

60 0.08580 0.29993 "1 . 28544E+01 2 . 13406E+01 0 . 00000E+00

61 0.00000 0.33326 1.70141E+38 1.70141E+38 1.70141E+38

62 0.01716 0.33326 1.70141E+38 1.70141E+38 1 . 70141E+38

63 0.03432 0.33326 -1 . 29086E+01 -3.49977E+02 2 . 29821E+02

64 0.05148 0.33326 -1 . 36006E+01 2.27103E+01 -3.52686E-01

65 0.06864 0.33326 -1 . 32178E+01 2 . 21573E+01 1 . 15992E-01

66 0.08580 0.33326 -1 . 28544E+01 2 . 10266E+01 2.88546E-01

ENTER 0 FOR CURRENT AND NEXTPOINT

1 FOR 2D PRINTING

2 FOR 2D PLOTTING

3 FOR CURRENT AND STOPPING

4 FOR CHANNEL PRINTING

2 (user input)

1: triangles, 2: contours, 3: surface, 4: profiles

101 (user input)

writing co-cordinates instead of plotting

enter level

1 (user input)

writing to file 21 (see figure B-l)

enter level

2 (user input)

writing to file 21 (see figure B-2)

enter level

39
3 (user input)

writing to file 21 (see figure B-3)

enter level

0 (user input)

1: triangles, 2: contours, 3: surface, 4: profiles

0 (user input)

writing co-cordinates instead of plotting

103 (user input)

1: function, 2 : abs (gradient)

1 (user input)

enter level

1 (user input)

enter viewing direction — nx,ny,nz

3-11 (user input)

writing to file 21 (see figure B-4)

1: function, 2: abs (gradient)

1 (user input)

enter level

2 (user input)

enter viewing direction — nx,ny,nz

3-11 (user input)

writing to file 21 (see figure B-5)

1: function, 2 : abs (gradient)

1 (user input)

enter level

3 (user input)

enter viewing direction — nx,ny,nz

3-11 (user input)

writing to file 21 (see figure B-6)

1: function, 2 : abs (gradient)

0 (user input)

1: triangles, 2: contours, 3: surface, 4: profiles

102 (user input)

writing co-cordinates instead of plotting

1: function, 2 : abs (gradient)

1 (user input)

number of contours

-8 (user input)

umin and umax

-10 25 (user input)

ulev

40
-1 . 000E+01 -5 . OOOE+OO O.OOOE+OO 5.000E+00

1 . 500E+01 2 . 000E+01 2.500E+01

writing to file 21 (see figure B-7)

1: function, 2 : abs (gradient)

0 (user input)

1: triangles, 2: contours, 3: surface, 4: profiles

0 (user input)

ENTER 0 FOR CURRENT AND NEXTPOINT

1 FOR 2D PRINTING

2 FOR 2D PLOTTING

3 FOR CURRENT AND STOPPING

4 FOR CHANNEL PRINTING

l.OOOE+Ol

0 (user input)

Vg = 4.000 Vd = 0.250 Vfb = -0.560

BETA —

3 . 868472E+01

PSIB = 3 . 466497E-01

LB -

4 . 086666E-06

COX = 6 . 207734E-08

BPSO = 2 . 331485E+01

BPSI = 3 . 252674E+01

PS(O) = 8.408164E-01

NO = 7 . 291709E+11

PS (L) = 1.085300E+00

NL - 5 . 889478E+11

ID = 5.458326E-05

10 = 5 . 349826E+01

I. . . = 6 . 358082E+02

VG = 1 . 160542E+02

VSD -9 . 671180E+00

LCH = 2.481457E-01

Q = O.OOOOE+OO current 9.7684E-05

level 1 1 dpsi -1 . 479E+01 a

2 dpsi 5 . 689E+00 a

3 dpsi 5.550E+00 a 4 dpsi 7 . 272E+0Q a

5 dpsi 5 . 560E-I-00 a

6 dpsi 1 . 788E-02 a 7 dpsi 1 . 779E-02 a

Q dpsi 1.768E-02 a

9 dpsi 1 . 759E-02 a

-2 . 528E+08 umax 4 . 639E+01

-1 . 356E+08 umax 7 . 711E+00

-8 . 503E+07 umax 7 . 711E+00

-6. 459E+07 umax 7 . 478E+00

-6.957E+07 umax 5 . 711E+00

-6 . 970E+07 umax 4 . 678E+00

-0.983E+07 umax 4 . 6G3E+00

-6.99GEH07 umax 4 . 828E+00

-7 . 009E+07 umax 4 . 603E+00

41
10 dpsi 1 . 749E-02 a -7.022E+07 umax 4 . 578E+00

11 dpsi 1.739E-02 a -7. 035E+07 umax 4 . 552E+00

12 dpsi 4 . 428E+00 a -9 . 768E+07 umax 4 . 527E+00

13 dpsi 2 . 440E+00 a -1 . 370E+08 umax 2 . 482E+00

14 dpsi 1 . 050E+00 a -1.765E+08 umax 1 . 058E+00

15 dpsi -5 . 859E-01 a -2.047E+08 umax 5.868E-01

level 2

1 dpsi 2.937E-02 a -2 . 033E+08 umax 5.868E-01

2 dpsi 3 . 419E-01 a -1 . 896E+08 umax 2 . 649E+01

3 dpsi 3.657E-01 a -1 . 829E+08 umax 1.966E+01

4 dpsi 3.425E-01 a -1.795E+08 umax 1 . 420E+01

5 dpsi 2.933E-01 a -1 . 777E+08 umax 9 . 663E+00

6 dpsi 9 . 516E-01 a -1 . 721E+08 umax 6.125E+00

7 dpsi -4.338E-01 a -1 . 653E+08 umax 1 . 003E+00

8 dpsi 3 . 321E-01 a -1 . 504E+08 umax 7.332E-01

9 dpsi 3 . 251E-01 a -1.405E+08 umax 3 . 254E-01

level 3

1 dpsi 1 . 507E-02 a -1 . 402E+08 umax 3.254E-01

2 dpsi 4 . 210E-01 a -1 . 275E+08 umax 8 . 837E+00

3 dpsi 4 . 559E-01 a -1 . 400E+08 umax 7 . 946E-01

4 dpsi 2 . 663E-01 a -1 . 507E+08 umax 2 . 676E-01

ENTER 0 FOR CURRENT AND NEXTPOINT

1 FOR 2D PRINTING

2 FOR 2D PLOTTING

3 FOR CURRENT AND STOPPING

4 FOR CHANNEL PRINTING

1 (user input)

enter summary , nx , ny

1 11 11 (user input)

3 MULTI-GRID LEVELS

VERTICES 146 342

TRIANGLES 322 858

STORAGE ALLOCATION

ALLOCATED USED

MAXT 17655 1905

MAXV 6621 726

MAXVSU 8828 1217

MAXJA 35877 4595

42
MAXU

MAXJU

TOTAL

GRID

ASMBLY

MG

ADAPT

TOTAL

I

12

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

10

19

20

21

22

23

24

25

26

27

28

1099

1099

200000

1099

1062

25205

TIMING DISTRIBUTION

SECONDS PERCENT

0 500 0.330

108,,470 71.635

CO co .500 22.124

8 .950 5.911

151..420 100.000

X Y U UX

0 . 00000 0 . 00000 1 . 70141E+38 1.70141E+38

0.00858 0 . 00000 1 . 70141E+38 1.70141E+38

0.01716 0 . 00000 1 . 70141E+38 1.70141E+38

0.02574 0 . 00000 1 . 70141E+38 1.70141E+38

0.03432 0 . 00000 -1 . 37152E+01 -7.24994E+01

0.04290 0 . 00000 -1.37948E+01 2.27971E+01

0.05148 0 . 00000 -1 . 35992E+01 2.27971E+01

0.06006 0 . 00000 -1 . 34068E+01 2.20188E+01

0.06864 0 . 00000 -1 . 32178E+01 2 . 20188E+01

0.07722 0 . 00000 “1 . 30350E+01 2 . 10478E+01

0.08580 0 . 00000 -1.28544E+01 2.10478EH-01

0.00000 0 . 03333 1 . 70141E+38 1.70141E+38

0.00858 0 . 03333 1 . 70141E+38 1.70141E+38

0.01716 0 . 03333 1 . 70141E+38 1.70141E+38

0.02574 0 . 03333 -4 . 80514E+00 -3.49964E+03

0.03432 0 . 03333 -1 . 40162E+01 3 . 50974E+01

0.04290 0.03333 -1 . 38026E+01 2.26781E+01

0.05148 0 . 03333 -1 . 36063E+01 2 . 34576E+01

0.06006 0 . 03333 -1 . 34112E+01 2 . 19170E ' 01

0 . 06864 0.03333 -1.32227EKH 2 . 19800Eh 01

0.07722 0.03333 -1 . 30376E+01 2 . 14340E-* 01

0.00580 0.03333 -1 . 28544E+01 2 . 13398E+01

0 . 00000 0 . 06665 2 . 49507E+01 -7.58698E+03

0.00858 0.06665 -1 . 36085E i-Ol -1 . 4G060E i 02

0.01716 0.06665 -1.41009E+01 -1 . 58318E* 00

0.02574 0.06665 -1 . 41098E+01 1 . 00770E+01

0.03432 0.06665 -1 . 401Q0E+01 2 . 7012GE 1-01 0.04290 0.06665 -1.38036E+01 2 . 67176E+01

43

UY

1 . 70141E+38

1 . 70141E+38

1 . 70141E+38

1 . 70141E+38

9 . 86443E+01

1 . 43763E+00

1 . 43763E+00

1.99132E-01

1.99132E-01

2.70350E-01

2.70350E-01

1 . 70141E+30

1 . 70141E+38

1 . 70141E+38

2 . 41900E+03

6.71809E-02

1 .41791E-02

1 .62690E-02

1 .62705E-02

6.59292E-02

G.59292E-02

0 . OOOOOE+OO

5 . 04481E+01

3. 19051E+01

0.35297E-01

3.55419E-01

6.04067E-01

4.96515E-01
29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

0.05148 0.06665 -1 . 36036E+01 2 . 29500E+01 1.03107E-02

0 . 06006 0.06665 -1.34109E+01 2 . 19080E+01 -3.18217E-03

0 . 06864 0.06665 -1 . 32223E+01 2 . 19563E+01 -1.07920E-02

0.07722 0 . 06666 -1 . 30378E+01 2 . 13398E+01 -1.07920E-02

0.08580 0.06665 -1 . 28545E+01 2 . 13848E+01 0 . 00000E+00

0 . 00000 0 . 09998 2 . 62073E+01 -7.72841E+03 4 . 12046E+01

0.00858 0 . 09998 -1 . 34399E+01 -1 . 46998E+03 1 . 20562E+02

0.01716 0 . 09998 -1 . 40998E+01 3 . 50989E+00 2.51406E-01

0.02574 0.09998 -1 . 41165E+01 -3.06538E+00 -2.00862E-01

0.03432 0 . 09998 -1 . 39963E+01 1 . 63389E+01 1 . 53542E+00

0.04290 0 . 09998 -1 . 38064E+01 2 . 29145E+01 -5 .82507E-01

0.05148 0 . 09998 -1.36036E+01 2 . 28447E+01 1 . 29900E-02

0.06006 0 . 09998 -1 . 34111E+01 2 . 19563E+01 -1.07920E-02

0 . 06864 0 . 09998 -1.32227E+01 2 . 19563E+01 -1.07920E-02

0.07722 0 . 09998 -1 . 30379E+01 2 . 13848E+01 0 . 00000E+00

0.08580 0 . 09998 -1 . 28546E+01 2 . 13848E+01 0 . 00000E+00

0.00000 0.13330 2 . 75698E+01 -8.06315E+03 4 . 27771E+01

0.00858 0.13330 -1.32443E+01 -4.95397E+02 1 . 86663E+00

0.01716 0.13330 -1.40925E+01 -2 . 57716E+00 -6.32129E-01

0.02574 0.13330 -1.41251E+01 1.67888E+01 -5 . 20889E+00

0.03432 0.13330 -1.39811E+01 1.67888E+01 -5 . 20889E+00

0.04290 0.13330 -1.38154E+01 2.62370E+01 1 . 29900E-02

0.05148 0.13330 -1 . 36031E+01 2 . 28750E+01 1.84167E-02

0.06006 0.13330 -1.34106E+01 2 . 19563E+01 1 . 84166E-02

0.06864 0.13330 -1 . 32229E+01 2 . 18018E+01 -1.86626E-02

0.07722 0.13330 -1 . 30385E+01 2 . 13848E+01 -1 . 86626E-02

0.08580 0.13330 -1 . 28544E+01 2 . 14625E+01 0 . 00000E+00

0.00000 0.16663 2 . 90819E+01 -8 . 20106E+03 6 . 69754E+01

0.00850 0.16663 -1 . 32432E+01 -5.29061E+02 -2 . 71480E+01

0.01716 0.16663 -1.41034E+01 -2 . 96251E+00 -1 . 66998E+00

0.02574 0.16663 -1 . 41135E+01 -4.42005E-01 -3.11330E-01

0.03432 0.16663 -1.39724E+01 1.74443E+01 6 . 71829E+00

0.04290 0.16603 -1.30113E+01 2.38325E+01 -4.96427E-01

0.05148 0.16663 -1.360G9E+01 2.30326E+O1 -4.96427E-01

0.06006 0.16663 -1.3410GE+01 2 . 10O18E+O1 -1.06626E-02

0.06004 0.10663 -1.32235E+01 2.18018E+01 -1.06620E-02

0.07722 0.10063 -1.30306E+01 2 . 14025E+01 0 . 00000E+00

0.00580 0.16663 -1.28544E+01 2.14625E+01 0 . 00000E+00

0 . 00000 0.19996 3 . 04268E+01 -8.3G422E+03 4 . 10107E+01

0.00050 0.19996 -1.30226E+01 -6.30326E+02 7 . 11257E+00

0.01716 0.19996 -1 . 40915E+01 -2.04639E+00 9.05867E-01

44
70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

0.02574 0.19996 -1.41255E+01 1.68276E+01 5 . 25861E+00

0.03432 0.19996 -1.39811E+01 1.68276E+01 5 . 25861E+00

0.04290 0.19996 -1 .38153E+01 2.62277E+01 -1.37740E-02

0.06148 0.19996 -1.36031E+01 2 . 28749E+01 -1.85242E-02

0.06006 0.19996 -1.34106E+01 2 . 19569E+01 -1.85242E-02

0.06864 0.19996 -I . 32229E+01 2 . 18018E+01 1.87087E-02

0.07722 0.19996 -1 . 30385E+01 2 . 13846E+01 1.87087E-02

0.08580 0.19996 -1 . 28544E+01 2 . 14625E+01 0.00000E+00

0.00000 0.23328 3. 17745E+01 -8.37652E+03 3 . 19841E+01

0.00858 0.23328 -I .30848E+01 -2.02673E+03 -1 . 69270E+02

0.01716 0.23328 -1.41006E+01 1 . 12604E+01 8 . 60107E-01

0.02574 0.23328 -1.41169E+01 -3.41704E+00 2 . 02267E-01

0.03432 0.23328 -1.39964E+01 1 . 54589E+01 -1 . 52158E+00

0.04290 0.23328 -1 . 38064E+01 2 . 2S022E+01 5 . 82274E-01

0.05148 0.23328 -1.36036E+01 2 . 28484E+01 -1.37740E-02

0.06006 0.23328 -1.34111E+01 2 . 19569E+01 1.05765E-02

0.06864 0.23328 -1.32227E+01 2 . 19569E+01 1.05765E-02

0.07722 0.23328 -1 . 30379E+01 2 . 13846E+01 0.00000E+00

0.08580 0.23328 “1 . 28544E+01 2 . 13846E+01 0 . 00000E+00

0.00000 0.26661 3 . 30732E+01 -8 . 50807E+03 4 . 09423E+01

0.00858 0.26661 -1.31670E+01 -2.92030E+02 -6. 59520E+01

0.01716 0.26661 -1.40958E+01 -2 . 57167E+00 -7 . 99016E-01

0.02574 0.26661 -1.41124E+01 1.04042E+01 2.25980E-01

0.03432 0.26661 -1.40100E+01 2.75647E+01 5.13087E-01

0.04290 0.26661 -1.38035E+01 2.67078E+01 -4.94524E-01

0.05148 0.26661 -1 . 36035E+01 2 . 29433E+01 -6.04121E-03

0.06006 0.26661 -1.34108E+01 2 . 19811E+01 4 . 78094E-03

0.06864 0.26661 -1.32223E+01 2 . 19569E+01 1.05765E-02

0.07722 0.26661 -1.30378E+01 2 . 13405E+01 1.06765E-02

0.08580 0.26661 -1.28544E+01 2 . 13846E+01 0 . 00000E+00

0.00000 0 . 29993 1.70141E+38 1.70141E+38 1.70141E+38

0.00858 0 . 29993 1 . 70141E+38 1.70141E+38 1 . 70141E+30

0.01716 0 . 29993 1.70141E+38 1 . 70141E+38 1.70141E+38

0.02574 0 . 29993 -2.52721E-01 -4 . 59297E+03 3 . 12036E>03

0.03432 0 . 29993 -1.40262E+01 4.98050E+01 5 . 56810E+00

0.04290 0 . 29993 -1 . 38007E+01 2 . 20174E+01 -6.35175E-02

0.05148 0.29993 -1.36071E+01 2 . 38481E+01 -1 . 91027E-02

0.06006 0 . 29993 -1.34112E+01 2.19110E+01 -1 . 91827E-02

0 . 06864 0 . 29993 -1.32227E+01 2.19811E+01 -6 . 82150E-02

0.07722 0 . 29993 -1.30376E+01 2 . 14380E+01 -0.82160E-02

0.08580 0.29993 -1 . 28544E+01 2 . 13405E+01 0.00000E+00

45
111 0.00000 0.33326 1 . 70141E+38 1.70141E+38 1 . 70141E+38

112 0.00858 0.33326 1 . 70141E+38 1.70141E+38 1 . 70141E+38

113 0.01716 0.33326 1 . 70141E+38 1.70141E+38 1 . 70141E+38

114 0.02574 0 . 33326 1 . 70141E+38 1.70141E+38 1 . 70141E+3S

115 0.03432 0.33326 -1 . 29702E+01 -3 . 29089E+02 2 . 21887E+02

116 0.04290 0.33326 -1 . 37952E+01 2 . 27185E+01 -4.02840E-02

117 0.05148 0.33326 -1 . 36003E+01 2 . 27186E+01 -4.02840E-02

118 0.06006 0.33326 -1.34077E+01 2 . 21324E+01 1.30200E-01

119 0.06864 0.33326 -1 . 32178E+01 2.21324E+01 1 . 30200E-01

120 0.07722 0.33326 -1 . 30349E+01 2 . 10306E+01 2.86185E-01

121 0.08080 0 . 33326 -1 . 28544E+01 2 . 10306E+01 2.85185E-01

ENTER 0 FOR CURRENT AND NEXTPOINT

1 FOR 2D PRINTING

2 FOR 2D PLOTTING

3 FOR CURRENT AND STOPPING

4 FOR CHANNEL PRINTING

3 (user input)

Vg = 3.000 Vd = 0.250 Vfb = -0.560 Q = O.OOOOE+OO current 5.3089E-05

46
01. Summary date

Yr. Mo. Day

8 4 0 3 2 1

04. Software date

Yr. Mo. Day

8 4 0 3 2 1

FEDERAL INFORMATION PROCESSING STANDARD SOFTWARE SUMMARY

02. Summary prepared by (Name and Phone)

C. L. Wilson (301) 921-3541

05. Software title CS1R: A Two-Dimensional Finite Element Charge-Sheet

Model of MOSFETs Including Radiation-Induced Interface and Oxide Charge

06. Short title

03. Summary action New Replacement Deletion

Previous anInternal Software ID

07. Internal Software ID

08. Software type

Automated Data

| | System

f^| Computer Program

| | Subroutine/Module

09. Processing mode

[x] Interactive Batch

| [ Combination

10. General

Application area

Specific

Computer Systems

Q Support/Utility

|~^| Scientific/Engineering

Bibliographic/Textual

Management/

[—

|

Business P“ Process Control Other

11.

Submitting organization and address National Bureau of Standards

Washington, DC 20234

12.

Technical contact(s) and phone

C. L. Wilson 921-3541

J. L. Blue 921-3395

13. Narrative A two-dimensional charge-sheet model including radiation-induced interface and oxide

effects in short-channel MOS transistors has been developed. The primary effect of

ionizing radiation on MOSFETs is the introduction of oxide trapped charge (OTC)

,

interface trapped charge (ITC) , and the reduction of channel mobility caused by scattering from charge in interface traps.

14.

Keywords

Finite elements; MOS transistor; radiation effects

15.

Computer manuf’r and model VAX

16.

Computer operating system

VMS

17. Programing language(s)

FORTRAN

18. Number of source program state- ments

19. Computer memory requirements

200K

20. Tape drives

0

21. Disk/Drum units

0.

22. Terminals

23. Other operational requirements

Requires local interactive vector-oriented graphics

24. Software availability 25. Documentation availability

Available Limited In-house only Available Inadequate In house only

0 Q

C. L. Wilson 925-3541 Title as in section 05.

9-track 1600bpi ASCII

magnetic tape. DNA approved users only

26. FOR SUBMITTING ORGANIZATION USE

185-101 Standard Form IIS

1974 July U S. Dtp! of Commtrt#

NBI
NBS-114A (REV, 2-80

U.S. DEPT. OF COMM. 1 . BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

PUBLICATION OR 2 REPORT NO.

NBSIR 84-2874R

. Performing Organ. Report No. 3. Publication Date

May 1984

CS1R: A Two-Dimensional Finite Element Charge-Sheet Model of MOSFETs Including

Radiation-Induced Interface and Oxide Charge

5

6

. AUTHOR(S)

C. L. Wilson and J. L. Blue

. P ERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. Task No.

NATIONAL bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

X99QAXVX , Work Unit 00076

8.

Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

Defense Nuclear Agency

Washington, DC

10.

SUPPLEMENTARY NOTES

|~X] 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

bi bl iography or literature survey, mention it here) A two-dimensional charge-sheet model including radiation-induced interface and oxide

effects in short-channel MOS transistors has been developed. The unique feature of

the model is that the effects of channel inversion layer charge, interface charge,

and oxide charge are included as a nonlinear integral boundary condition on the twodimensional electrostatic field in the transistor. The average inversion layer charge

density and source-drain current are obtained directly from the model rather than from

the electron density or electron quasi-Fermi level. The model retains all of the

physical detail of more complex two-dimensional models such as sensitivity to sourcedrain profile shape, channel profile, and oxide field shape. This allows the model

to represent the changes in drain current associated with short-channel effects while

still allowing simple comparison with long-channel models.

The numerical solutions were obtained using general-purpose software for solving elliptic partial differential equations. Problems with exact solutions have been solved

to test the correctness and accuracy of the codes. Also, the physics included in this

model and the geometry of the transistor can be easily changed. The finite element

method used allows refinement of oblique triangles which is important in achieving

computational efficiency.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Finite elements; interactive graphics; MOS transistors; radiation effects.

13. AVAILABILITY

LD Unl imited |XJ For Official Distribution. Do Not Release to NTIS

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

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14. NO. OF

PRINTED PAGES

50

15. Price

USCOMM-DC 6043-P80