Computer simulation study of the effect of semiconductor deep bulk levels on the capacitance-voltage characteristics of InSb MIS structures

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Computer simulation study of the effect of semiconductor deep bulk levels on the

capacitance-voltage characteristics of InSb MIS structures

K.G. Germanova, E.P. Valcheva

To cite this version:

K.G. Germanova, E.P. Valcheva. Computer simulation study of the effect of semiconductor deep bulk levels on the capacitance-voltage characteristics of InSb MIS structures. Revue de Physique Appliquée, Société française de physique / EDP, 1987, 22 (9), pp.985-989. �10.1051/rphysap:01987002209098500�.

�jpa-00245658�

Computer simulation study of the effect of semiconductor deep ^bulk

levels on the capacitance-voltage characteristics of InSb MIS structures

K. G. Germanova and E. P. Valcheva

Solid State

Physics Department,

^Sofia

University,

¹¹²⁶

Sofia, Bulgaria

(Reçu

^{le 9}

février

1987, ^{révisé le 4 mai} 1987,

accepté

^{le 2}

juin 1987)

Résumé. ²⁰¹⁴ Dans cet

article,

^{on étudie} l’influence des niveaux

profonds

en ^{volume sur les}

propriétés

^{de la}

couche de

charge d’espace

^{dans les} structures MIS InSb. Les

dépendances

^{avec le}

potentiel

de surface de la

charge

^{totale et de la}

capacité

de la couche de

charge d’espace, respectivement Qsc(03C8s)

^et

Csc(03C8s),

^{y sont}

traitées. Les

caractéristiques

^{obtenues sont} fortement influencées par la

présence

de niveaux

profonds.

L’analyse

effectuée dans la

présente

^étude permet ^{d’avoir une meilleure}

compréhension

des états d’interface dans les structures MIS InSb,

lesquels pourraient

^être

probablement

^{confondus avec} les niveaux

profonds

^en

volume.

Abstract. ²⁰¹⁴ The influence of semiconductor

deep

bulk levels on the

space-charge layer (SCL) properties

ⁱⁿ

InSb MIS structures is

investigated. Computed

^{are the}

dependences

^on the surface

potential

of the total

charge

and the

capacitance

^{of SCL}

Qsc(03C8s)

^and

Csc(03C8s) respectively.

The characteristics obtained are found to be

strongly

^affected

by

the existence of

deep

levels. An

analysis

^is

performed

that could aid in a better

understanding

of interface states in InSb MIS structures which

might

^have

probably

been confused with

deep

bulk levels.

Classification

Physics

^Abstracts 73-40Q

1. Introduction.

The

properties

^of

deep

bulk levels in semiconductors

are

receiving

^a

great

^deal of attention

partly

^because

they

^{are a}

limiting

^factor

affecting

^device

perfor-

mance and

reliability.

^In fact surface space

charge layers

^{that are}

major parts

^of

semiconductor

^devices

and their electrical characteristics are most of all influenced

by

the existence of levels

lying deep

^{in the}

band-gap

in semiconductor bulk.

Study

^{of this}

influence is a

problem

^of

prime importance [1, 2].

^In

this field of

investigation

^the attainments are little

yet, especially

^with

respect

^to structures and devices based on

A3 B5

semiconductors since the

deep

^levels

have rather

complex

^{character there and are still}

poorly

understood.

In InSb

variety

^of

deep

^{levels are} observed and

investigated [3-5].

The purpose of ^our work is to

investigate

^{what sort of influence on} the space-

charge layer

characteristics in InSb MIS structures

they

^{cause. Such}

investigations

^{have not been}

conducted to our

knowledge

^{so far.}

Analysis

^of

capacitance-voltage (C-V)

^behaviour

of a MIS device is a convenient method for

investiga-

tion of the electrical

properties

of interfacial

region

between the semiconductor and the dielectric

layer.

One must take into account

however,

that there are

variety

of factors that may introduce error into determination of interface characteristics. One of these can be the utilization of incorrect ideal C-V characteristics for

comparison

^with

experimental

^C-

V data if

possible

^{existence of}

deep

^{bulk levels is not}

assumed when

calculating

^{the ideal curve. We have}

developed

^a theoretical model of a MIS structure based on InSb

assuming

all basic semiconductor features

including deep

bulk levels. The model

might

^most

nearly

match the real structure and differ from it

through

^{the absence of interface states}

only.-

The model

developed

^is

applied

^{to the}

computation

of basic

characteristics

of the

space-charge layer Qsc(03C8s)

^and

Csc(03C8s).

^The characteristics

obtained

are

strongly

^affected

by

^{the existence of}

deep

^bulk

levels in the semiconductor. The

analysis performed

could aid in a better

understanding

of interface states in InSb MIS structures which

might

^have

probably

been confused with

deep

bulk levels.

2. Basic considerations.

For the evaluation a

p-type

^{InSb material is chosen}

possessing

shallow donor and

acceptor

^{levels as well}

as

deep acceptor

^{level. The shallow}

doping impuri-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:01987002209098500

986

ties are

compensated

^{to some}

degree

^{so that the}

deep

^{level is not masked}

[5, 6].

^The

dependences

^on

the surface

potential

^{of the total}

charge

^{in the SCL}

Qsc(03C8s)

^{and the}

capacitance

^{of the SCL}

Csc(tb,)

^are

calculated

observing equilibrium

conditions. Consi-

dered

is the occasion of uniform distribution of a

single deep

level into the semiconductor. The values of material

parameters

^{used were} chosen from the

experimentally

^{observed data available} in the litera- ture

[5].

^All calculations are carried out at a

tempera-

ture of 77 K.

The

computer-simulation study

^of

Qsc(03C8s)

^and

Qsc(03C8s) dependences

^{is carried out}

through

^the

solution of the one-dimensional Poisson’s

equation

for the case of semiconductor

containing deep

^level

in the bulk

[7]

where _p

(x )

^{is the}

charge density

^{in the} semiconduc-

tor

space-charge region,

Es is the semiconductor

permittivity, 03C8(x)

^{is the} normalized electrostatic

potential

^{in kT} units. The

charge density

p

(x )

^{in the}

presence of shallow donors and

acceptors

^with concentrations

Nsd

^and

Nsa, respectively

^and

deep

acceptors

with concentration

Nda

^is

In order to most

nearly

match the real situation the

following

^{features are} taken into account. Fermi- Dirac statistics is used

throughout

^the

computation

accounting

^{for the}

incomplete

ionization and rechar-

ging

^of shallow and

deep

^{levels in} SCI of InSb at low

temperatures.

^{The use of} Fermi-Dirac statistics is necessary also since

owing

^{to the}

special

^conduction

band structure of narrowgap semiconductors

degene-

ration

begins

^{at moderate surface} and bulk electron concentrations. Further conduction band

dispersion

law

nonparabolicity

^{of InSb is} considered in Kane

approximation.

^{So the} free carrier concentrations in the SCL are

where

EF

^is

Fermi-level, 03A61/2

^is

Fermi-integral

^of

order 1/2 ^..

F,,

^is

generalized Fermi-integral

^{of order n =}

3/2 [8]

where ~g ⁼

E

_{is the}

band-gap.

After the first

intégration

^{of Poisson’s}

équation

^we

obtain

where

and.

~sd and ~sa ^are the shallow donor and

acceptor

energy

levels and E da is the

deep acceptor

^{level in kT}

units. g

^{is the}

degeneracy

factor. All energy

positions

are counted from the

band-gap

^middle.

The

equilibrium Csc(03C8s)

curves were

computed

under the

assumption

^that

minority

carriers contri- bute

fully

^{to the}

capacity

A convenient

algorithm

^and

computer

program

were elaborated to conduct the calculations.

3. Results and discussion.

In

figure

^{1 are shown}

Qsc(03C8s) dependences

^{with the}

concentration of the

deep

^{levels as a}

parameter.

^The

corresponding

^{curve for the case of} semiconductor without

deep

levels is also

given

^{for a}

comparison (curve A).

^{The curves} reveal the well known three

regions

^of accumulation

(03C8s 0), depletion (03C8s > 0)

^{and inversion}

(03C8s > 0, 03C8s 2|ub|,

^,

1 ub | = |(Ei - EF ) |/kT, ^{Ei being the}

intrinsic Fermi-

level)

^{for a}

p-type

semiconductor. In accumulation

Qsc(03C8s)

^{curves almost}

entirely

^{coincide. In}

depletion

and inversion

regions

^{however curves B-F differ}

considerably compared

^{to curve A.}

Increasing

^{of the}

total

charge

^{in the SCL} is observed with

increasing

the

deep

^level concentration. Moreover in

depletion region

the normal

slope

^of

Qsc proportional

^to

03C81/2s

^is disturbed. The

change

^{of the}

slope

appears around the energy

position

^{of the}

deep

level in the

band-gap.

^{The onset of}

strong

^{inversion shifts to}

higher ^values

^of

lis

^with

increasing

^the

deep

^level

concentration.

Fig.

^{1. -}

Space-charge density Qsc

^{as a} function of the surface

potential afrs

ⁱⁿ p-type ^InSb

space-charge layer.

Nsa - Nsd = 5 1012 m-3 . Nda m-3 = (A: 0; B:1019;

C: 5 x

10’9; D: 1020;

^{E: 5 x}

102°; F:1021).

All the observations discussed are better manifes- ted in the calculated

Csc(03C8s) plots

^{shown in}

figure

^2.

The characteristic minimum in the standard

equili-

REVUE DE PHYSIQUE APPLIQUÉE. - T. 22, N° 9, SEPTEMBRE 1987

Fig.

^{2. -}

Capacitance

^of

space-charge layer

^{as a function}

of surface

potential Csc(03C8s) · Nsa - N sd

^and

Nda (curves

^A-

F)

^{have the same values as in}

figure

^{1. ,}

brium

Csc(03C8s)

^curve is absent and on its

place

appears ^a

bump.

^Its

magnitude

increases with the

deep

^level concentration.

Comparing

^{with curve A}

the

capacitance

in inversion is

larger

^{in the} presence of

deep

^level and increases with

increasing

^its

concentration.

The behaviour of

Qsc(03C8s)

^and

Csc(03C8s)

^curves

might

^be

explained

^{in the}

following

^{manner. Fermi-}

level

position

in the bulk calculated from the

charge neutrality equation

for different concentrations

Nda

^{is not affected}

by

^the

deep

^level concentration variation. This fact shows that the

deep

^{level does}

not contribute to the free carriers concentration in the occasion under consideration. The

deep

^{level is}

neutral in this case. In accumulation

charge

^{state of}

the

deep ^level

remains the same as in the bulk ^- the

deep ^level

^{is far from the} Fermi-level. That’s

why Qsc(03C8s)

^{curves coincide} in accumulation.

Let us consider the

band-diagram

^{of the structure}

at a

given

^reverse bias for the case of a

deep acceptor

in the substrate

(Fig. 3).

^The

region signed by (a)

^is

totaly depleted

^of mobile carriers and the

trap

occupation

^{in it is} controlled

only through

^emission

processes. ^{In the}

region (b-a) generation-recombina-

tion processes ^are active in

determining the equili-

brium

occupation

of the level.

So,

ⁱⁿ

depletion,

66

988

V

Fig.

^{3. -}

Energy

^band

diagram

^{for a} p-type ^{InSb MIS}

structure

containing deep

level in semiconductor

bulk,

under conditions of

depletion.

when the

deep

^level

approaches Fermi-level,

^the ionization

probability

^for

^the deep

^{level increases}

and it takes

part

in the formation of the total

charge

in SCL

together

with the ionized shallow

impurities

i. e.

Qsc

increases. The

interpretation

^{in terms of}

ionization of the

deep

^level

Eda explains

^the

change

in the

slope

^of

Qsc(03C8s)

^{curves and}

respectively

^the

bump

ⁱⁿ

Csc(03C8s)

^{curves, too.} It appears around the energy

position

^{of the}

deep

^{level because the Fermi-}

level

approaches Eda

^{and crosses it with}

increasing t/I

^s value and the level

gradually

^ionizes. It is the

region (b-a)

^{that is}

responsible

^{for the finite}

equili-

brium

population probability

^{for the}

deep

^{level and}

where the discussed above features in

Qsc(03C8s)

^and

Csc(03C8s)

curves are manifested.

Inversion

begins

^at

larger 4rs ^values

because the effective condition

03C8s 2 |ub| 1

is fulfilled at

larger

ub. The ^reason is the inclusion of the

deep

^{level in}

the balance of

charges

and therefore

increasing

^of

Qsc in depletion

^and inversion. Hence the total

capacitance

in inversion is

larger

^too.

As it is observed

through

^the

computer-simulation study

^of

Qsc

^and

C,c characteristics,

^{similar behaviour}

is

expected

^to appear in ^an

experimental

^{C-V curve}

measured on MIS structure based on

p-type

^InSb

containing deep

level. We have taken the

computed Csc(03C8s)

^{curves when no}

deep

^{level is assumed as a}

theoretical one

(curve

^{A in}

Fig. 2)

^{and the corres-}

ponding Csc(03C8s)

^curves for different values of the

deep

^level concentraton

Nda

^as

experimental

^curves

(curves

^{B-F in}

Fig. 2). Utilizing

^{these curves we have}

simulated C-V

analysis [9]

^{and we} have obtained

apparent

^{interface state}

density

distributions shown in

figure

^{4. The}

peak

values of

N t

^r around the energy

corresponding

^{to the}

deep

^level

position

^are

of the order of

1010 - 1011 eV-1 cm-2

i. e. of the order of the interface state densities

normally

^obser-

ved in InSb MIS structures

[10, 11]. ^So,

if there is a

deep

level in the bulk of the

substrate,

^{it is}

going

^to

manifest itself as a

peak

^{in the interface state}

spectra

Fig.

^{4. -} Simulated interface state spectra.

N sa - Nsd

^and

Nda (curves A-D)

^{have the same values as in}

figure

^1.

as a real discrete interface state do. There exists a

real

possibility

^{for the surface states in the interface}

region

^{to be confused with}

deep

levels in the bulk.

4. Conclusion.

Using

the method of mathematical

modelling

^we

have conducted a

study

^on the influence of

deep

bulk levels on the

space-charge layer

characteristics in InSb MIS structures. We

have developed

^a

theoretical model of a MIS structure based on InSb

assuming

^{all basic} semiconductor features

including

deep

bulk levels. The model was

applied

^to

computa-

tion of basic characteristics of SCL - the

depen-

dence of the total

charge

^on the surface

potential Qsc(03C8s)

^and

capacitance

^on the surface

potential Csc(03C8s).

^The

problem

^as formulated is

applicable

^to

other narrow-gap semiconductors or other

tempera-

tures.

Comparing

^to the conventional case

(without deep levels) Qsc(03C8s)

^and

Csc(03C8s) dependences

^{were found}

to be

strongly

^affected

by

the existence of

deep

^bulk

levels in the semiconductor. It allowed us to simulate

a

density

distribution of InSb ^- dielectric interface

states in presence of

deep

levels and to estimate the

real

possibility

interface states to be confused with

deep

bulk levels. An

experimental Csc(03C8s)

^curve

was calculated

assuming

^{a MIS structure without}

interface states and the semiconductor

containing deep

^{bulk level. A} theoretical curve was calculated without interface states and without

deep

^{level. The}

simulated C-V

analysis

^revealed

apparent

^interface

state

spectrum.

^{Therefore the} theoretical C-V curve

necessary for the C-V

analysis

^{has to} consider the existence of the

deep

levels in the

semiconductor

bulk. It allows to eliminate the

apparent peaks

^due

to the

deep

^{levels and to} obtain the true interface state

spectrum.

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