PROPERTJESOF PPTEOS
Chapter 5: DC ELECTRICAL PROPERTIES OF PPTEOS
5.2 DC electrical conduction mechanism
5.2.2 Poole-Fnmkel (PF) mechanism
The PF effect is the bulk analog of the Schottky effect at an interfacial barrier This effect is also known as field-assisted thermal ioni,alion process, The mecharusm of Poole-Frenkel emission is 500"11in Fig, 5.2. If an electron trapped in the energy gap of a dielectric is activated by the joinl effect of electric field and temperature over the coulomblc barrier of the neighbouring sne, the potential energy of an electron in a Coulombic field -e'/411Ex is four times that due to the image force effects, the PF attenuation of a Coulombic barrier 1I.<pPF' uniform electric field is twice that due to the SehoUky effect at aneutral bamer:
•
5,9
. ,
• •
Chapler5:DC ElectricalPropeltiesofPPTEOS 78
With Ihe applied field, Ihe Coulombic barrier heighl between electrode and the film is lowered, and !he carrier can escape more emal} giving rise to field assisled conductivily:
[p F''']
u=uoexp P~T 5.10
where F =Vld, is Ihe de applied field, k is Boltzmann constant, T ;s Ihe absolute
{ , ]'"
lemperalure, <:1"is the low field conductivity, fJpp = -'- =
2ft.
4""0"
field-lowering co-efficient The field dependent current density is gwen by JI'F= e~c expH'I'p; -A'I'PF )!2kTj
!s the PF
5. II
"
J
8<lIlom QrConduC"l;an Balld
Fig5,3 Poole-Frenkel effect at "donor center.
WhereJo =e~c exp(-'I'PF 12kT) is the low field current density and ('1'1'1,'"A'I'PF) is thc resultant pOlentia! barrier due to field lo",ering , !-'is the free electron mob!lil) and Nc is the effective density of stales in lhe conduction band. The I-V dependence corresponding to eq"(5.11) leads 10
looexp[b'Vli2] 5,]2
Where b'=
P
PF/2kTd1l2and f\P>=2j1..
,•
•
Chapter5: DC ElectricalPropertiesofPPTEOS 79
5.2.3 Space chargelimited (SeL) conduction mechanism
The mecl1arusm of electrical conduction in thin insulating films has been discussed by Lamb and several important theorctical modes have been pul fon-varded.
Dielectric malerials, which are basIcally insulators, are capable of carrying electric curren\5 by virtuc of carriers injected at one or both the electrodes According to the basic assumptions, if an orumc contact is made at the surface of an insulator, electrons flow from the melal 10the conduction band oftbe insulator.
l"lAf>-i'fi~E SOUARE L"-I\/
f(C 521
o.-L .•-,
•__
"fa lOG"
Fig. 5.4 Space charge hmited conduction mechanism.
Due to the injected charges near the electrodes, lhere is a generation of space charge near the electrodes, which affect the conduction mechanism. A!3 an effect, ohmic conduction changes into seL conduction as the applied electric field is increased.
When a bIas is applied to the system shown in Fig 5.41hat is, an insulator havmg two ohmic contacts on its surface. The result of the applied bias is to add positive charge to lhe anode and negative charge 10the calhode. As the voltage bias increases, the net positive charge on the anode increases and that on the cathode decreases then the current density would be
9 V'
J
=-titi /-i- S ' dl511
Cltapm 5: DC Electrical Properties ofPPTEOS 80
5.12 Where I! is the mobility of charge carriers, E IS dielectric constant, £" is the permittivity of free space, V 1$ the applied voltage, d is the thickness eqn 5,11 predicts that SCL current is directly proportumll1to V' and inversely proporlional to
d'.
Conduction Band
N,
E,
Fig 5.5. Energy dIagram sho\\ing shallow traps in an insulator.
Practically, the character and the magnitude or SCL conduction are modified d"e to the presence of localiLed trapping centers which try to immobilize the injected charge earners, If the insulator contains Nt shallow traps positioned an energy ~ below the conduction band and No is the number of charge carriers, shown in Fig. 5.5 then the rree component of the space charge
Pf=eN,eXP(-d)
and trapped component of the space charge
P =eNexJ_(EF-E,)]
I
'1.
kTthus the trapping factor, e is defined as
P, N [-EJ
'.-o-'e"p --'
N kJ'
p, ,
5.13
5.14
5.15 The SCL c"rrent density with traps is defined by:
9 V'
J= -6e ,,--8 8 .r d-'
For a shallow trap SCLC and trap-free SCLC, e =1. According to eqn 5.15, Jvaries as d" in the ohmic region and as d-3in the SCLC region except for the trap-filled
Chapter5, DC ElectricalPropertiesoFPPTEOS 81
SCLC part, In eqn 4.15 it can be seen /hat for a fixed V, the dependence of In J on In d should be linear with slope I ?:.3.
The voltage at which transition from the ohmic region to the shallow trap SCLC regl0n (v,,)occurs ISgiven by
5,16
where
no
is independent of both f' and J. TIlls value ",Ill be defined from the ex!Iapolated parts of the respective current region in the InJ - InV curves.5.3 Thermally activated conduction processes 5,3.1 Electronic conduction
The band theory of solids has been appl1ed to understand the electrical behavior of polymers. An important featured of the band system is /hat electrons are delocali7ed or spread over the lattice. Some delocaJization is e"pected ",nen an atomic orbital or any atom overlaps appreciably "ith those of more than one of its neighbors, but delocalizatJon reaches an e".-tremeform in the case of a regular 3-D lattice. The band theory assumes (hat the electrons are delocalizcd and can extend over the latllce.
When electrOniCconduction is conSIdered in polymers, band theory is not totally suitable because the atoms are covalently bonded to one another, forntlng polymeric chains that experience weak intermolecular interactions. But macroscopic oonduction will require electron movemenl, not only along Ihe chains but also from one chain 10 another.
The carrier mobihty in organic molecules IS usually very low. TIus is due to the fael that electrons, while jumping from one molecule to another, lose some energy But the mobihties of electrons arc found to increase with molecular si7c in such type of compounds, In polymer system, the conductivity is influenced by the factors such as dopant level, morphology of polymer, concentration of conduding species, temperature, etc. The temperature dependence of current density can be described by
an Arrhenius type of eqn
n
J=J,exp[-ABIkT] 5.17
Where, dE is the activation energy for carner generation. The plot of 10gJ
V51"(
must be Imear for thermally activated conduclJon.
',',
•
•
Chapter5, DC ElectricalPropertiesorpPTEOS 82