CC BY
13
DOI: 10.17277/amt.2020.04.pp.058-066
The I-V Characteristics of M-BaxSr1-xTiO3-M Thin Film Structures
with Oxygen Vacancies. Part 2
V.V. Buniatyan*, H.R. Dashtoyan, A.A. Davtyan
National Polytechnic University of Armenia (NPUA), 105 Teryan Str., 0009, Yerevan, Armenia * Corresponding author. Tel. +3 749 131 16 39. E-mail: vbuniat@seua.am, vbuniat@yahoo.com
Abstract
In Part 2 of the paper, based on the results and assumptions pointed in Part 1, analytical expressions were derived for Schottky barrier thermal/field assisted and Poole-Frenkel emission currents. The computer modeling theoretical dependencies of the I-V characteristics has been compared with the experimental measured results and obtained good agreements.
Keywords
Ferroelectric; trapping center; Schottky barrier; Poole-Frenkel emission; oxygen vacancy.
© V.V. Buniatyan, H.R. Dashtoyan, A.A. Davtyan, 2020
Hole currents due to thermo-ionic emission
The hole current is associated with the thermo-ionic emission of the holes from the contact 2 [2-5]. For small bias, the effective barrier for holes at contact 2 is (Op2 -V2) . The hole current is given by [2-4]:
Jp2 = A*T2 exp(- P(O p2 +91))(exp(pV2)-1), (1) for the V > VRT :
i. XEm1 j(|V - VfB I)
(V + VFB)
91 - V2 =-
qNA
2h
\h -
Em1h]
' ; Em1 = '
( - VFB\)
h
91 - V2 =■
2h
2h - h ™} (V - Vfb )
9l - V2 =■
h
4h
[ - h(V + Vfb )](V - VFB )!
4h2
Jp1 = A*T 2exp(-pO p 2 )x
x{exp(-P^1 )exp(P V2 ) - exp(- P91)} =
= ApT 2exp(-pO p2 )x
x { exp(- P(91 - V2)) - exp(- P^1)}. In the neutral region, before the reach-through condition takes place, V << VRT, the steady-state continuity equation for holes is given by [4]:
d 2 P P - P„
dx
2
Dp T p
= 0,
(2)
where Pc is the equilibrium hole density, Dp is the diffusion coefficient, and Tp the lifetime. The solution to (2) is:
P - Pc = Aexp
f \ x
V p
+ Bexp
v p /
(3)
where LP is the diffusion constant of the holes
(Lp = V DpTp ). The boundary conditions
are:
x = dfi, P = Pc expl -
(9 f1 + Vi) ^
kT
and at x = df 2 one
has J p2 = Ap exp(-ß(0
p2
+ 9i - V2)), where df 1 and
df 2 are the depletion regions width in the core before the reach-through condition.
x
2
— AM&T
The hole current density Jp\ is then given by the gradient at df 1 and the thermal equilibrium condition (V = 0) [2-4]:
dp
JP\ = qDp—
dx
qDpPo tanh[(df - dfx )Lp ]
L„
A*nT 2exp(-B(0 _ 2 +®,)) x(l - exp(- p Vi + PV p2
cosh
(df 2 - df 1)
L,
x (exp(pV2) -1), Jpi = A*T 2exp(-pO f 2 )x
(4)
(
x<! exp
-P
(V - Vfb ) b(V2 - V}B )
2
4^2
- exp(-p9i) f
At V = Vfb, the factor in {•} bracket approaches unity and hole current density is given by:
Jpi = ApT 2exp(-pO p2 ).
(6)
For the large voltages, when V > VFB, the barrier lowering effect at contact 2 has to be considered due to the applied field and defect caused field (as it was done for the contact 1), and the hole current is now expressed as
Jpi = A*pT 2exp(-pO p2 )exp(pAO p2), (7)
where
A9 p 2 =
q(Em2 - E )
4nX5
Total current due to thermo-ionic emission
The total current density is found by adding up the contributions of electron current and hole currents. Here the following definitions are used:
Electron saturation current density
(
hole saturation current
Jns = ApT 2exp
kT
density Jps = ApT exp
qO >
p2
kT
flat-band voltage
L2
VFB = — y, reach-through voltage VRT = VFB - 2A52y . For small voltage V < VRT, from [1, see (Eq. (7)]:
Jni = AnT exp(-
p(-PO n1 )
x exp(p(AOn1 +aiEm1 ))(l - exp(-PVi )), and from (ii) [i]:
J = JnS exp(pAOn )(i-exp(-pVi)) +
qDpPo tanh
+-
(df2 - dfi)
Lr
Lr
(i - exp(-pVi ))-
+ -
Jps exp(-p9i)
cosh
df2 - dfi L„
(exp(pV2 )-i).
For Vrt< V< Vfb from [i, Eq. (7)] and (2): J = JnS exp(3AOni )+
f r(V-Vfb) -VJ^B
(5) + Jps 1exp
-p
FB
2
4L2
- exp(-p9i )f.
For very large DC bias voltages, V > VFB, from Eq. (7) and Eq. (5) [1],
J = J«s exp(pAOW1)+ JpS exp(pAOp2). (8)
Two cases have to be considered:
1) Jns << Jps electron barrier height 0„1 is much larger than the hole barrier height Op2. In this case, for the small voltages (V < Vrt), the hole current is smaller than the electron current. However, for voltages larger than Vrt (V > Vrt< Vfb), the hole current dominates;
2) for the Jns >> Jps case, the hole current will be always be smaller than electron current. So that the total current essentially is given by the first term in (8).
Poole-Frenkel mechanism
If the ferroelectric film contains traps for electron and holes, at high temperature and in the presence of an applied high field some of these trapped electrons (holes) will be excited into shallow traps or conduction levels, either thermally or due to the action of the field [1-5, 6-14]. In case the applied field in thin film is up to 1 MV/cm, the Poole-Frenkel emission becomes dominant for the charge separation both in the surface layers [14] and in the core (middle part) of the ferroelectric film. Thus, traps for electrons are assumed to be neutral when occupied and positive charged when empty (i.e., they are donors). Traps for holes are assumed to be neutral when emptied of an electron. For trap states with Coulomb potential, the charge transport is governed by the Poole-Frenkel emission
d
x
a) b)
Fig. 1. Lowering of the barriers by A®„ for electrons and AOp for holes under the applied high field [14] (a), energy diagram of the trapping center in the presence of the electric field (b) [15-17]
which is very similar to the Schottky emission [2-4, 13, 14]. Fig. 1 helps to analyze the relationship between trapped electrons and holes due to Poole-Frenkel effect [14, 15-17]. Arrows indicate the possible mechanisms of electron emission: thermal ionization over the lowered barrier (PF effect), direct tunneling (DT) into the conduction band (CB), and phonon assisted tunneling (PAT) [15-17].
We assume that ferroelectric film contains traps for electron and for holes, which have and Etp energy levels below the conductance and above the valence bands, respectively. The electron and hole trap densities are denoted by Ntn and Ntp respectively, Fig. 2. It is assumed that the density of the donor like impurities, particularly the oxygen vacancies, is smaller than that of acceptor like impurities, Ntp > Ntn, i.e. the core (middle part) of the ferroelectric film has poor p-type conductivity.
Therefore, if there is no injection of free charge carriers from the contacts and no applied field, it is reasonable to assume, that the for concentration of the holes in the core of ferroelectric will is (pto - nto),
where nto and pto are the equilibrium concentrations of the trapped electrons and holes. Let the trap densities are given be [15, 18]:
Ntn = Atn exp
E,
tn
bkT
Ntp = Atp exp
tp'
E ^
tp
bkT
where the constants Atn, Atp and b 1 define the shape of the distribution of traps in energy. Using the Shockley-Read-Hall formulation, one may write:
n dt
= r1n - r
2n->
dt
= r1 p - r2 p,
nc
{
Ec EFn
Ntn
EFn
'Np.
where r2n, r2p are the rates of electron and hole release from traps, respectively; nn, r1p are the rates of electron capture to the conductance band and hole to valence band:
r1n = SnVtnncNtn (1 - fn ) ; r1p = spvtppcNtp (1 - fp)t
here Sn, Sp, Vtn, Vtp are the capture cross sections and the thermal velocity for the electrons and holes, respectively, nc and pc are the free electron and hole concentration in conductance and valence bands, fn and fp are the occupancy factor (distribution function) for the electrons and holes respectively. The rates r2n, r2p depends upon the concentration of centers occupied by electrons and holes, and on electron and hole relaxation times TXn and x^; Txn and xXp are given by [15, 18]:
pc
Fig. 2. Trap levels for electron and holes
Ev f 1 ' (E ^ c tn f 1 ' (E \ ^ tp
Tnx exp ; T px exp
V Vv n V I kT V lV p V 1 kT V
{
where vn, Vp are the "attempt to escape" frequencies for the electrons and holes respectively. Hence, for the r2n and r2p one has:
r2n = Ntn fnVn exp
r2p = Ntp fp V p exP
( E Л
tn
kT
( E Л ^tp
kT
dnt dpt
At the thermal equilibrium — = 0, — = 0, and
dt dt
from r1n = r2n, r1p = r2p one obtains the concentrations of free electrons and holes:
fnv n exP
( E Л
tn
kT
SnVtn (1 - fn )
In the equilibrium,
pc =•
E
fpV p exp| - — p p 1 kT
SpVtp (1 - fp )
fn )eq fp )eq =
1 + gn exP 1 + gp exP
( E Л
tn
kT
( E Л
( tp Л
kT
-1
-1
where gn = -
S V
n tn
% gp =■
SV
p tp
To use the same detailed balance principle, one can obtain the concentrations of the trapped electrons nto and holes pto in thermal equilibrium:
Nn
1 + gn exP
( E Л
kT
N
pto =-
tp
1+gp exP
( E Л Etp
kT
ncNtn
nc + n
pcNtp pc + p1
where n1 and p1 are the Shockley-Read state factors for the electron and hole respectively (i.e., the concentration of electrons and holes in conductance and valence bands, when the quasi-Fermi levels coincides with the trap levels). Consequently, in equilibrium the concentrations of ionized donors and ionized acceptors are:
n+= nd - nto; n-= na - pto,
nd and na are respectively the concentrations of the donors and acceptors.
Now the Poole-Frenkel emission will be considered assuming the contact 1 [1, see Fig. 3] being reverse biased and contact 2 forward biased. For V > Vpn the current density is given by:
J = JnS exp (ß s AO ni) + Jps exp (ß, AO p 2 ^
where ß ^ = \ —
I kT,
(
q
\
1/2
f
J = Jns exP(ß s (Em2 )1/2 )+ JpsexP( (Em2 )1/2 );
J = JoexP(ß s (Em (0))1/2 ).
(9)
When the Poole-Frenkel emission becomes dominant, the continuity of steady-state current inside the film requires that J is constant and independent of the position in the film. Thus, neglecting diffusion, since the electric field is high, J may be given by
J = —nc (xKE( x) + qpcpE( x)
(10)
where nc(x), pc(x), цp are correspondingly the free electron and hole concentrations due to Poole-Frenkel emission and mobilities.
Under the Poole-Frenkel emission the electric field distribution in the ferroelectric may be determined from the Poisson's equation:
dE
— = -—{Ntp (1 - Fp (x))-Nn (1 - Fn (x)) + pc + nc },
dx
X f
(11)
where Fn (x) and Fp (x) are the coordinate dependent trap occupations of the electrons and holes in the film; pc and nc are respectively the free hole and electron concentrations.
Let ntn(x) be the filled trap density of electrons and ptp(x) be the filled trap density of holes at position x. Then the Poisson's equation may be written as (direction of electric field is the negative x axis):
dE q r i
— =--[p (x) - ntn (x) + pc - nc ] . (12)
dx
X f
Let the electron capture rate from conduction band be r1n and electron release rate from traps be r2n and from the holes r1p and r2p, respectively. Considering an infinitesimal trap energy range between Et and Et + dEt the expressions for r1n, r1p can be written, respectively, as:
r1n = ncNtn (1 - fn (x))SnVtndEt;
1p = pcNtp (1 - fp (x))SpVtpdEt,
V
V
n
nto =
where fn(x) and fp(x) are occupancy factors for the electron and holes, respectively. They depend on the trap energy and position in the film [15, 18]:
Fn ( x) = •
\fn (x)NtndEt\ \fp ( x) NtpdEt\ -; Fp ( x) = *L__-
¡NndEt ¡NtpdEt
0 0
The electron and hole release rates r2„, r2p depend on the concentrations of centers which are occupied by electrons and holes and on the electron and hole relaxation times xn, Tp [15, 18]:
(Etn -AOn)
f 1 Y
exp
kT
T p =
Y r(( -aOtp ^
exp
kT
where vn, Vp are the attempt to escape frequencies, while A®^, AOpt represent the lowering of the tarp barrier heights assuming the Poole-Frenkel mechanism, i.e.,
AOtn =P PFkTE
1/2
AOtp = p PFkTE ?1/2
1/2
where Ppf is the slope of the log J ~ E plot when the Poole-Frenkel mechanism dominates the condition:
Ppf = 2P,, p, =
f q Y
kT
f \ q
1/2
nX f
The barrier lowering in the case of the Poole-Frenkel emission differs by a factor 2 from the one for the Schottky emission due to the immobility of the ionic centers emitting the charges [2-4]. Therefore, for the r2n and r2p take the form:
r2n = NtnfnV n exP
f e y
tn
kT
exp
(p pfE1/2 )dEt
r2 p = NtpfpV p exp
f E Y / \
exp(ppfE1/2 )dEt
kT J
assuming, that the trap densities are given by:
Ntn = kT Atn exp Ntp = kT Atp exp
f E Y
tn
V b1kT J
f E Y
tp
V b1kT J
As it was noted: J = Jns exp[PsErn1(0)1/2 ]+ Jps exp[PsErn1(0)1/2 ] (13)
Equating r1n to r2n, and r1p to r2p and using (10) and (13), for the occupancy factors fn and fp one arrives at:
fn H1 +
f Vn^nq Y
J S V
V n, n tn J
E(x) exp[ppf(E(x))1/2
x exp
fp H1 +
[ (E (0))
( \ V p ^ pq
J S V
V ps p tp J
1/2
exp
f E Y! -1
^tn 1
kT
(14)
E(x) exp[ppf(E(x))1/2
x exp
-P, (E (0))
1/2
exp
f Etp
v kT j
-1
Then the density of the trapped electrons and holes ntn(x) andptn(x) are:
Etn Etp
tn (x)= j fnNtndEt; ptp(x) = j fpNtpdEt. 0
Assuming Etn > b\kT, Etp > b\kT one may rewrite fn and fp as:
1
fn =-
fp =-
1 + Y o Y n exp 1
f E Y
tn
kT
1+ Y o Y p exp
with
Y n =
Y p =
f Vn^nq Y
J S V
V nskJn' tn J
f Y
V p ^ pq
J S V
V*7 ps^p tp j
f E Y' Etp
kT
exp[-p sE]l? ],
exp[-P,Elm12] .
For the ntn(x) andptp(x) one has:
Etn AtndEt exp
,( x) =
1 + YoYnexp
f E Y
tn
bkT
f E Y
tn
kT
or
n
, V
V v n J
1
V
n
ntn (x) =■
Atn\kT Y 0 Y n (bi - i)
-exp
AtvdEt exp
ptp( x) = f
Etp
i + Y0 Y p exp
, , AtpbikT Ftn( x) =-:—- exp
Etn (bi - i)
kTbi
( F \ ^tp
y bkT J
^tp p--—
{ kT J
Etp (bi " i)
kTbi
or
Y o Y n (bi -i) Y o = E( x) exp[p pf (E( x))i/2 ].
Now the Poisson's equation may be solved and the voltage drop across the film calculated:
V = f E(x)dx .
As it is evident from (ii) and (i2), E(x) depends on the concentrations of captured and free charge carriers, which, in turn, depend on E(x) via yn , Yp
exponentially. Hence the Poisson's equation is impossible to solve analytically. In this paper, for numerical simulations, an average value of electric field is used:
E fav (x) = "
V
f
h - 25
where Vf =
V -
( 2 + Vfb 2 ) .
2V
FB
is the voltage drop in the
core of the ferroelectric film.
If the concentration of the donor (vacancies) is n^, the concentration of ionized donors is n+= nd - ntn,
and at the same time n+ = nc (that is concentration of free electrons), then nc = nd - ntn,
Atnb1kTJnsSnVtn exp (ps (Em1)1/2 )
Y0VnVnq(bi- i)
x exp
Etn (bi - i)
bkT
and
Jns = '
(nd- nc) y ov n^nq (bi-i)
AtnbikTSnVtn exp( (Emi )i/2)
exp
En (b - i) bikT
J ps =
Similarly, for the Jps:
(na - pc) Y0VpM^ (bi - i)
ApbikTSpVp exp(Ps(Em2)i/2)
exp
Ep (bi - i)
bkT
Substituting for the Jns and Jps in (i3) on arrives
at:
r y0vnVnq(nd- nc )(bi- i) J =-exp
Atnbi kTSnVtn
+
Y0VpVpq(na - pc )(bi - i) Atpbi kTSpVp
-exp
(bi - i) Etp bikT
(bi -i) Etp ' bkT
+
. (i5)
Assuming Sn = Sp, Am = Atp = Ao, vn = Vp = Vo, Etn = Etp = Et, one can obtain
' = c,
where
a pf =-
J = apfE(x) exp {ppf[E(x)]i/2 }, (i6) qv o (bi- i)
bi kTAoSo
Vn (nd - nc ) ^p (na - pc ) -+ —-
V,
tn
vt
tp
x exp
(bi - i)Et
bikT
(i7)
Note, that the expression (15) is distinctive for the Poole-Frenkel emission [2-4, 8-10, 13-22].
Experimental
The test capacitors are fabricated on high resistivity (> 5 kOhm-cm) silicon substrate [21]. The commercially available template used has Pt/TiO2/SiO2/Si( 100) structure. Pt (50 nm) / Au (500 nm) bottom electrode is deposited by e-beam evaporation at room temperature (Fig. 3). The 560 nm thick Ba0.25Sr0.75TiO3 (BSTO) film is deposited by pulsed laser ablation from a stoichiometric Ba0.25Sr0.75TiO3 target at 650 °C and 0.4 mBar oxygen pressure using a KrF examiner laser (A, = 248 nm, t = 30 ns) operating at 10 Hz with an energy density of
1.5 Jcm . After deposition, the sample is cooled down to room temperature at 950 mBar oxygen pressure. The Au (500 nm) / Pt (50 nm) top electrode are deposited by e-beam evaporation at room temperature and patterned with a lift-off process. The I-V performance is measured using HP415B semiconductor parameter analyzer (Fig. 4) [21].
x
n
a)
b)
Fig. 3. Structures of the test varactor with Au (a) and Pt (b) interfaces
Calculations and discussions
In this section the expressions of (1) - (17) are used to investigate the dependence of the I-V on various parameters, and more specifically on the parameters of the oxygen vacancies associated traps. Symmetrical structures [1, see Fig. 2], with contact 1 forward biased and contact 2 reverse biased are considered. The results of the numerical simulations using (8) are denoted as Sch and correspond to the Schottky barrier emission. The results of the simulations using (15) are denoted as PF and correspond to the Poole-Frenkel emission. The numerical calculations have been carried out for the following values of the parameters: cross section area So ~ (6 - 8)-10-6 cm2, thickness of the film: h = 550 nm, 30 ^m diameter [21, 22], the electron and
_2
hole mobilities are: ^no = 10 cm/Vs and ^po = _2
= 10 cm/Vs respectively [6-8, 13, 23], the barrier
heights: 4n1 -0.9 V, 4p2 -0.5 V [8, 9, 15, 24],
T = 300 K, the dielectric constant of the interface region with high density of oxygen vacancies: X§ -1.5 _ 5, the dielectric constant of the ferroelectric
film core: x f - 290 [6, 15, 21-23], - 10_1 _ 10_2,
Etn = 0.1_0.4 eV, Etp = 0.2 _ 1eV, b1 = 10, m*p /m0 = 10,
* _12 mn /m0 = 10, the conductivity of core: c0 -10 sm,
the concentration of free electrons and holes, respectively nc -1014 _ 1017 cm_3, np -1014 _1017 cm_3, the concentration of the trapped electrons and holes
the thermal
I, A
nt « 103 -106 cm-3, pt
TO3 -106 cm-3,
7
velocity of carriers vtp -10 cm/s , the capture cross 16 cm2, the attempt to escape
sections Sn = Sp = 10
12 —1
frequencies u = 10 s .
The results of the numerical simulations are shown
in Fig. 4 where the experimental results for comparison
are also presented.
The Richardson's constants have been calculated by:
U, V
Fig. 4. Experimental I-V dependence of a Pt/Ba025Sr0 75TiO3/Pt parallel-plate ferroelectric capacitor
(So ~ 7-106 cm2, sample: T21, 550 nm thick BST, 30 ^m diameter, xf - 290 [21, 22])
* 2 * 2 * 4nqmnk * 4nqmpk
A n- 3 ; A p- 3 ,
hp hp
where hp is the Plank's constant.
For the thermo-ionic field (Schottky) emission:
AnT2
exp(3AO n1 ) (
1 ps
A" VT 2
exp(PAO n 2 )
Ist = 4.9 -10-8 T 2 S 0
(
mn0 exP
4.64
(V + Vfb ^
1/2A
+ m
p0 exP
4.64
(V - Vfb ^
X50 h0
V
1/2 AA
X50h
0 J
+
J J
For the Poole-Frenkel emission:
IPF = S0Ï0a0 ; Y 0 = E( x)exp(3E1/2( x)),
Efav ( x) =■
V.
f
h - 25
5x10
2x10
Vf =
v -
(2 + v 2
FB
2V
FB
is the voltage drop in
ferroelectric core,
<<0 =-
qv(bx -1)
blkTAt„
M n (n j - nc ) ( (bi -1)E
~nV'J SnVtn
-exp
KT
+
M p (na - nc ) ( (b1 - 1)Etp ^
"p\"a c
+--exp
SpVtp
ipf = 12 -10-3 So & (m h
kT
nont +MpoPt jx
x exp
f /11 \1/2Y V * vf|
0.06
v h X f o y
The total current is taken as a sum of 1 = ISt + Ipf-
As it is evident from Fig. 5, there is a fairly good agreement between the experimental curves and theoretical calculations. For the bias voltages up to 12-13 V the I-V dependence may be explained by Schottky emission in punch-through (flat-band) regime. With the applied voltage increased, the Poole-Frenkel emissions from the trap levels begin to start and when V > (12-13) V, the leakage current is associated simultaneously by the Schottky barrier and the Poole-Frenkel emission. The small discrepancy between the theory and experiments may be explained, first of all, by the difference between the symmetric model used in the analysis, asymmetric Pt/BST/Pt structure used in the experiment. Furthermore, the electric field in the core of ferroelectric film was approximated by Efav = Vf /(h - 281). For accurate calculations one has
to take into account the x-coordinate dependence of the electric field according to the Poisson's equation. And finally, the mobility is not known exactly.
It is also necessary to note, that our analysis is based on the hydrogen model of impurities in crystalline dielectrics, i.e. in approximation of the Coulombic potential, which is valid for relatively shallow levels. The precise shape of potential wells corresponding to deep levels may different from the Coulombic form. The second point is follow: while in Schottky mechanism the lowering of the barrier occurs uniformly for all direction of carrier motion in the hemisphere centered on the direction of the field, i.e. the probability of escape is enhanced by the same factor
exp(^ Ell2/kT) forall attempted directions of escape,
i - 10, A
8 7
2.5 2
1.5 1
10
15
v, V
Fig. 5. Theoretical and experimental I-V characteristics of Pt/BST/Pt structure
(sample: T21: 550 nm thick, Ba0.25Sr0.75TiO3, 30 ^m
diameter, % f = 290 [21], X8 =5, the other parameters are chosen as: E,0 = ncJnp = 0.8, <pk « 0.7 eV, Etn = 0.2 eV , Etp = 0.36 eV, Vth = 107 cm/s, ^n = 0.01 cm2/Vs,
Vp = 0.005cm2/Vs, u = 1012 s-1, nc = 1.5-1015 cm-3, np = 1.0-1014 cm-3, nt = 106 cm-3, pt = 106 cm-3, Sn = Sp = 10-16 cm2, b1 = 10)
the situation for the Poole-Frenkel effect is more complicate. In this case it is necessary to take into account the effect of the angle between the direction of escape and the direction of the field E. The received expression (14) based the model, on which the
maximum barrier lowering {PF [E(x)]12 } occurs only in one particular direction in space, all other directions having to overcome a higher barrier. The measured I-V and the theoretical estimations of the emission process unambiguously indicate that the Poole-Frenkel emission is compatible with the Schottky field emission mechanism. The Poole-Frenkel emission takes place in the range of higher voltages. The analysis of the PF effect indicates that the active trapping centers are located in the region of very high electric field exceeding 105 V/cm. The field of such strength is concentrated at the middle part of ferroelectric film. The space charge is assumed to be related to deep trapping centers and oxygen vacancies. In the discussed applied voltage polarity case [1, see Fig. 2) the carrier injected mainly are holes [1, see Fig. 2, from
6
5
4
2
4
contacts 2]. According to the energy band diagram of the Pt/BST/Pt films, the hole injection is much more favorable than the electron injection.
From the practical point of view, the further understanding of the mechanism of the trapping/detrapping process may allow to characterize hysteresis effects and the noise in devices based on Pt/BST/Pt structures. And finally, the proposed theory may be useful for the analysis of similar structures based on other perovskite ferroelectrics.
Acknowledgments
The study was supported by RA MESCS Science Committee as part of the research project No. 19YR-2J050.
The authors would like to thank Prof. S. Gevorgian and Dr. Andrei Vorobiev from Department of Microtechnology and Nanoscience (Chalmers University of Technology, Gothenburg, Sweden), for stimulating discussions and providing experimental results.
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