Transcript Document

4. The Semiconducting Phase:
Undoped Conjugated Materials
This chapter is based on the review paper by V. Coropceanu et al., Chem. Rev. 107, 926 (2007)
A. Polymers with chromophoric pendant groups
 Microscopic disorder
B. Molecular crystals
poly(N-vinylcarbazole)
C. Conjugated polymers
1
Figures by G. Horowitz, Université Denis-Diderot, France
4.1. Organic semiconductors among other solids
σ = electrical conductivity
Eg = Band gap
1 S (Siemens)=1/ Ω
For Eg> ~2eV
 Insulator
For 0< Eg < 2eV  Semiconductor
For Eg0
 Metal
 σRT < 10-10 Ω-1cm-1= 10-10 S/cm
 10-10 S/cm < σ RT < 102 S/cm
 σRT > 102 S/cm
2
4.1.1. Definitions
 The mobility  of the charge carriers is the average speed of diffusion ||,
or net drift velocity, of the charge carrier (cm/s) as a function of applied electric
field (V/cm)
 = ||/E

in cm2/Vs
 is positive even though e- and h+ travel
in opposite direction.
||
E
 The electrical conductivity σ can be defined as a sum of two terms:
σ = (ne e + pe h )
in 1/Ωcm
n and p = density of charge carriers (n for electrons and p for holes) in cm-3
e = unitary charge (C)
3
4.1.2. Temperature dependence
The behavior of the electrical conductivity () vs. In a simplified manner, the
temperature (T) of solids is one criterion used to classify them as:
 metal:  decreases as T is raised
 semiconductor:  increases as T is raised
Note that an insulator appears as a semiconductor with very low conductivity.
Metals
 The excitation energy can be provided via an
chem/kT
increase of temperature. The population of the orbitals is
given by the Fermi-Dirac distribution:
P
1
e  E  chem  / kT  1
chem is the electron chemical potential, that is -EF for metals (T=0)
 When T increases, the charge carrier density increases…. However the
conductivity decreases because there are more collisions between the
transported electrons and the nuclei (phonon scattering)  less efficient
4
transport.
Semiconductors
In order to have a net electrical current: electrons must jump
from filled levels to empty levels across the band gap
If Eg is not too large, upon applying an external electric field, few
electrons at room T have the necessary energy to jump from
valence band to conduction band
Thermal energy: kT; at 300K, kT~0.025 eV~0.6 kcal/mol
 In crystals of intrinsic inorganic semiconductors, the band gap
can be small, thermal excitations promote e- to the conduction
band. The concentration in charge carriers produced is
proportional to exp(-Eg/2kBT), leading to an increase of σ with T.
The delocalized electrons/holes are not strongly bound to each
other because of the high dielectric constant and participate
efficiently to the electrical current.
 In undoped conjugated polymers, Eg is large. So, the thermal
excitation are negligible, i.e the concentration of carrier does not
increase with T. However, the conductivity increases with T like in
organic crystals. This is the subject of this chapter.
5
4.1.3. Undoped Conjugated Polymers
From the order of magnitude of the
band gap and the conductivity, most
undoped conjugated polymers are
rather like ”insulators”.
 However, these organic polymers
do have a conjugated π-system. The
formation of occupied π-valence
band and π*-conduction band results
in a lower band gap.
 As a result, they have a low ionization potential (IP) (usually lower than ~6eV) and/or
a high electron affinity (EA) (lower that ~2eV)
 They will be easily oxidized by electron accepting molecules (I2, AsF5, SbF5,…)
and/or easily reduced by electron donors (alkali metals: Li, Na, K)
Charge transfer between the polymer chain and dopant molecules is easy
6
P- versus n-type organic semiconductors
• p-type [n-type] most often does not reflect the intrinsic ability of the material to
transport holes [or electrons]; it rather translates the ease with which holes
[electrons] can be injected into HOMO [LUMO] of the material from the
electrodes. The energy of the HOMO [LUMO] determines to a first approximation the
ionization potential IP [electron affinity EA] of the material.
fBh= hole injection barrier
fBe= electron injection barrier
EA=~LUMO
e-
fBe
FITO + V
IP=~HOMO
EF
fBh
FAl - V FITO = workfunction of ITO
FAl = workfunction of Al
EF
V= applied voltage
EF= Fermi level
h+
7
In many organic semiconductors, the electron and hole mobilities
are expected to be comparable
8
• The experimental observation of a low n-type mobility in organic material is generally
the consequence of extrinsic effects, such as the presence of specific traps for electrons
(due to photo-oxidation of the ð-conjugated backbone) or the instability of radical-anions with
respect to water, hydroxyl groups (see example below in an OFET), or oxygen.
Example: The silanol SiOH groups present at the SiO2 surface quench
the n-channel FET activity of organic semiconductors that do not have
sufficiently large electron affinities (EA) (<3.85 eV). Materials with EAs
only larger than this have shown n-FET behaviour on pristine SiO2
interfaces, albeit with generally very high threshold voltages (due to
electron trapping).
S
D
semiconductor
SAM
SiO2
Gate doped SI
Transfer characteristics with drain voltage Vds = 60
V are plotted for the second gate-voltage (Vgs)
sweep (after filling some traps). The current below
threshold is from gate leakage.
L. L. Chua et al. Nature 434, 194 (2005)
For the untreated SiO2 interface, charge trapping is so severe that no ntype behaviour can be found. The addition of an self-assembled
monolayer (SAM) between the SiO2 surface and the organic
semiconductor allows recovering partially the n-channel FET activity. With
the
SAM
passivation
(HMDS,
hexamethyldisilazane;
DTS,
decyltrichlorosilane; OTS, octadecyltrichorosilane), n-channel activity can
be observed. However, the devices still exhibit a considerable Vgs
threshold shift with sweep number, which is particularly severe for the
shorter SAMs. For polyethylene as buffer dielectric, stable n-FET
conduction is observed, as for BCB as dielectric.
9
4.2. Experimental measurments of carrier mobilities
4.2.1. Time of Flight (TOF)
For TOF measurements, the sample consists of
a layer of the photoconducting material
sandwiched between two electrodes that are
blocking carrier injection into the sample. At
least one of the electrodes must be
semitransparent to permit the photoexcitation of
free carriers in the material just beyond the
illuminated contact by a strongly absorbed light
flash. Depending on the polarity of the electric
field applied across the sample, either electrons
or holes will then be drifted through the sample.
At their arrival at the back contact, the current
will drop since the blocking contact ensures that
only the primary photocurrent is measured.
From the transit time tT (the time needed for the
charge sheet to cross the sample), the drift
mobility μ can be calculated according to
μ = L/tTE = L2/tTV
where L is the sample length and E the applied
electric field. The essential elements of a TOF
Obtaining a true value of μ requires that the
field E be uniform and constant during the
carrier transit, which means that E should
only be applied a short time before the
optical excitation and that the transit time
should be short with respect to the dielectric
relaxation time in the material.
10
Explanation based on the Handbook of Electronic and Photonic Materials by
Safa Kasap and Peter Capper
The transit time can be measured
directly on the current trace, in
which case it is variously defined as
the time at which the current has
dropped by values ranging from
10% to 50% (the latter one being
most commonly used), or it can be
obtained by integrating the current
and using the time at which the
collected charge saturates.
D. Hertel, et al., J. Imag.Sci. Technol. 43, 220 (1999)
In materials with a wide distribution
of localized gap states, as is
generally the case in disordered
photoconductors, the drifting charge
package spreads out along the
length of the sample, and a
representative transit time can only
be discerned as a change of slope in
a double-logarithmic plot of current
versus time.
11
4.2.2. Field effect transistor configuration
In the linear region:
Qinv WL
ID  
tr
tr 
L
v
and v  E  
Qinv  Ci (VGS  VT )
S W
L
D
VDS
L
I D  Ci
I D  Q inv
W
VDS
L
W
(VGS  VT )VDS
L
Qinv = Charge per unit area in inversion layer
tr = Transit time for charge between source and drain
VT = Threshold Voltage (Qinv = 0 if VGS < VT)
Ci = Gate insulator capacitance per unit area
In the saturated region:
I D,sat  Cox
W (VGS  VT )
(1  VDS )
L
2
2
Empirically derived
12
1) If Vd small, the charge is nearly constant over the channel and the drain current is :
ID 
Linear
W
Ci  VG  VT VD
L
•The channel conductance gd can be expanded to first order:
W
T
The extracted mobility increases and then decreases with gate voltage, which has no physical
meaning (for the corresponding charge carrier densities). This is due to the presence of a
potential drop at the contact (contact resistance) that is not taken into consideration. This
contact potential is also gate dependent.
2) A further step of the method consists
of introducing a contact series resistance
Rs, which leads to
W
T
13
4.2.3. Diode Configuration
Two high
workfunction
electrodes to prevent
electron injection
LUMO
low p, high E
HOMO
Collecting contact
Au
+
Injeting contact
ITO
injection/collection no problem
study of intrinsic conduction!
0
t
x
(i)
For the sake of simplicity, the device is described in one dimension and only single carrier
devices are considered (i.e. either holes or electrons).
(ii)
A potential V is applied at the injecting contact (i.e. at x = 0) and that the opposite contact is
grounded. Given that the device thickness is L these two boundary conditions can
be expressed as: Ψ(0) = V (BV.1); Ψ(L) = 0 (BV.2), where Ψ is the electrical potential at
position x.
(iii)
The injecting contact is assumed to be ohmic, i.e. no barrier for injection, implying that the
electric field, E, vanishes at the injecting contact due to built up of a very high
charge concentration, p. This can be expressed in two ways: E(0) = 0 (BV.3a); p(0) = p0
(BV.3b), where p0 is large enough so that p(x) is independent of p0 for any x larger 14
than a
few nm.
Determination of the J-V behavior
•
The diffusion current, i.e. current originating from a gradient of
concentration of charge carrier in space, is neglected
•
The current density is then given by the drift equation (Ohm law)
generalized with a mobility u depending on the charge carrier density p(x)
and the electric field E(x):
J  eu px, Ex pxEx
•
(1)
The charge carrier density distribution across the device is given by the
Poisson equation:
d  x 
e


px 
2
dx
 0 r
2
Ψ is the electrical potential.
e
 dEx 

px 
 dx
 0 r
 
 d x    E x 
 dx
(2)
15
• Assuming steady state, i.e. that the current density is the same in
all positions of the device,
dJ
0 
dx
dJ du
dp
dE  u dp u dE 
dp
dE
 pE  u


pE  u
E  up
 

E  up
dx dx
dx
dx  p dx E dx 
dx
dx

u  dp 
u  dE 
u  dp
e 
u  2
  u  p  E
 u  E
  u  p  E

p
u  E
p  0
p  dx 
E  dx 
p  dx  0 r 
E 


u  dp
e
  u  p  E

p  dx
 0 r

u  2

u

E

p
E 


dp
e

dx
 0 r
 u  E u E   p 2


(3)
 u  p u p  E
• There are three variables to the problem (p, E, Ψ) and three
equations. The system of differential equations to solve is:
 dp( x)
e  u  E ( x) u E  p( x) 2




 0 r  u  p( x) u p  E ( x)
 dx

e
 dE( x)

p ( x)

 0 r
 dx
 d ( x)
  E ( x)


 dx
(4)
16
Simple case : mobility independent of both E and p
The system of differential equations (4) is simplified with (i.e. ∂u/∂E = 0
and ∂u/∂p = 0) and it can be solved analytically using boundary conditions (BV.1),
(BV.2) and (BV.3a), resulting in:

x  V 1  x / L
E x   
p x  
32

(6a)


d
d
3V
32

V 1  x / L 

x/L
dx
dx
2L
 0 r dE
e
 0 r d  3 V
 3  0 r V

x/ L 

2
dx
e dx  2 L
 4 e L
(6b)
1
x/ L
(6c)
Resulting in the well-known Mott-Gurney law to describe space charge
limited current (SCLC):
V2
9
J   0 r u 3
8
L
(6d)
17
Mott-Gurney law valid for constant 
3 V
1

p
(
x
)

 J  p( x )eE ( x )


4 e L2 x / L


  dE( x )
 p( x )
 E( x)  3 V x / L

 e dx


9 V2
 J   3
8
L
At V=1Volt, log J
 log
2L
9
 log J  log 3  2 logV
8L
Slope 2
9
► Extraction of the mobility (valid only at low voltages)
8 L3
upturn caused mostly by pdependence of 
Mott-Gurney
J  V2
constant 
2
1
18
P.W.M. Blom et al., Phys. Rev. B 55, 656 (1997)
4.3. Factors influencing the charge carrier mobility
Efficient charge transport requires that the charges be able to move from molecule to
molecule and not be trapped or scattered. Therefore, charge carrier mobilities are
influenced by many factors including:
• molecular packing
• disorder
• presence of impurities
• temperature
• electric field
• charge-carrier density
• size/molecular weight
• pressure.
Those parameters are illustrated in the next sections.
19
4.3.1 Mobility vs. Molecular packing and disorder
A. Molecular Crystals
μ in the range [0.1-20] cm2V-1s-1
 Molecular order can be controlled via deposition conditions
 Charge carrier mobility depends strongly on the molecular order
pentacene
20
Dimitrakopoulos & Mascaro, IBM J. Res. Dev. (2001) 45 11
slow
transport
Anisotropy of the charge transport
Fast
transport
Lee, J. Y.et al. Appl. Phys. Lett. 2006, 88, 252106.
pentacene
Layered structure; thickness of a
monolayer = ~ 1 nm.

Charge carrier transport is 2D (within
molecular plane) and anisotropic (e.g.,
direction d1 is more favorable)

21
B. Conjugated Polymers
Charge mobilities are small, in the range 10-6-10-3cm2V-1s-1. Mobilities
significantly increase when the polymer chains present self-assembling
properties that can be exploited to generate ordered structures.
The mobility is limited by the slowest steps (bottle neck):
 At the macroscopic scale: defects, grain boundaries and lack of
crystallinity are the limiting parameter.
 At the microscopic scale: the mobility is limited by π-π interchain rather
than intrachain transport, which is fast.
The challenge: to create order on the macroscopic scale and maximize
the interchain transport.
Mobilities significantly increase when the polymer chains present selfassembling properties that can be exploited to generate ordered
structures.
22
Self-Organized Polymer Thin Films
Direction of the current flow
measured in a FET
High regioregularity (96%)
Low regioregularity (81%)
Film formation
mechanisms are not
understood!
Poly-3-hexylthiophene (spin-coated on SiO2/Si substrates)
23
H. Sirringhaus et al., Nature 1999, 401, 685
Self-organization in discotic liquid crystals
HBC-C12
• Highly soluble
• Structural defects can be repaired
by the self-healing properties of liquid
crystal phases
• can be highly purified
• high
(supra)molecular
order
spontaneously achieved (over μm
thickness)
• high charge mobilities along the
columns (comparable to amorphous
silicon ~0.1 cm2/Vs)
24
Crystal phase
Liquid crystal mesophase
anneal
cool down
A qualitative illustration of the role
of order is given by the evolution
of charge carrier mobility in
discotic liquid crystalline materials.
The carrier mobility is observed to
drop significantly in going from the
crystalline phase (K) to the liquid
crystallin mesophases (H and D)
and eventually to the isotropic
phase (I=melted liquid phase).
Example of mobility variation with temperature for a
discotic liquid crystals (Warman, J. M.;et al. Chem.
Mater. 2004, 16, 4600.)
25
Printing Discotic liquid crystals for OFETs
A. Tracz et al, J. Am. Chem. Soc., 2003, 125, 1682
A. M. van de Craats et al, Adv. Mater., 2003, 15, 495
26
4.3.2 Temperature
 π-π intermolecular interactions due to the overlap between π-orbitals of adjacent
molecules  creation of a narrow π-band in the neutral ground state of the organic
crystal.
2tLUMO
W=4tLUMO  Electron mobility
2tHOMO
W=4tHOMO  Hole mobility
By J.Cornil et al., Adv. Mater. 2001, 13, 1053
 The strength of the interaction, i.e. the electronic coupling, is measured by the
transfer integral: t = <Psi/H/Psi>
 Band width in a solid can be estimated from the splitting of the frontier levels27“t” in a
dimer
Carrier residency time, τ, on a molecule:
τ ↔ 1/kET and W↔ 4t
W= full effective bandwidth
 If W > 0.1–0.2 eV, τ < time for a molecular vibration (10-14 s)
 the molecules do not have the time to geometrically relax and trap the charge:
This is a condition for a band like motion.
Temperature
Band regime
Hopping Regime
 Vibrations introduce a loss of coherence among the interacting units, leading to a
decrease of W upon temperature increases.
28
 Upon temperature increase, charge carriers can go from band motion to hopping
regime
Hopping Regime
μ ÷ f(T) exp(-Ea/kbT)
Ea = activation energy
Temperature
Band regime
(diffusion limited)
μ ÷ T-n , n>1.
Holstein’s theory for transport in
one dimension
29
Band motion regime in molecular crystals
The temperature dependence is markedly
different in single crystals and in disordered
materials. In single crystals, the hole and
electron mobilities generally decrease with
temperature according to a power law
evolution: T-n. This is illustrated in Figure 6 for
the case of electron and hole transport along a
crystal axis direction of naphthalene. Similar
evolution is observed along specific directions
for a large number of single crystals; the main
difference lies in the value of n, which typically
varies between 0.5 and 3. This decrease in
mobility with temperature is typical of band
transport and originates from enhanced
scattering processes by lattice phonons, as is
the case for metals.
30
Warta, W.; Karl, N. Phys. ReV. B 1985, 32, 1172.
4.3.3 Charge carrier density
At low voltages, i.e., for low charge carrier densities, the mobility can be extraced
from Mott-Gurney law in hole only diodes.
In polymer transistors (FETs), the gate voltage controls the density of charge
carriers in the channel, while the lateral electric field between source and drain
driving the drain current is low. Hence, the extracted mobility from FET will directly
display the p-dependence (E-independent) but for charge carrier densities much
larger than in diodes.
OC1C10PPV
FET
LED
31
Tanase, et al., PRB 70, 193202 (2004)
4.3.4 Impurities
Organic semiconductor
If the HOMO of the impurity (LUMO) is above (below) the HOMO (LUMO) of
the organic semiconductor, then the impurity site is energetically more
favorable, and in a device in thermal equilibrium, the latter has a higher
probability to be occupied than the organic semiconductor sites. The impurity
acts as a trap for the charge carriers.
VTFL
Current density
J-V behavior of diodes in the presence of traps
(i) the trap limited regime: for low voltages, i.e. when
the carrier concentration << trap concentration. The
traps are to a large extent empty and therefore the
transport is strongly limited by the traps. The current
density is low, the mobility is approximately constant and
J~V2.
(ii) the trap filling regime: at intermediate voltages, i.e.
when the carrier concentration is high enough to
increase significantly the occupancy of the traps. There
are fewer active trap states to limit the mobility.
Therefore the current density increases rapidly with J~Vβ
and β >> 2.
(iii) the trap free regime: when EF is shifted above the
energy level of the traps, all trap states are filled and the
mobility is no longer limited by trapping. The current
density acquires the familiar J~V2 behavior in the case
of an otherwise constant mobility (Mott-Gurney).
The voltage at which the J-V behavior transits from the
trap-filling to the trap-free behavior is traditionally called
the trap-filled limit, VTFL.
Impurity
Trap limited
2
J~V
Trap free
2
J~V
Trap-filling
T /T+1
J~V
r
Voltage
32
4.4. The fundamental events in Hopping transport
A. Electron-Phonon Coupling
R
E
H2C===CH2
LUMO= 2*
-1
Ionization
GS
2||
ReqGS Req-1
HOMO= 1
Relaxation
effects
R
An electron injected in the LUMO
introduces
antibonding
character
between the 2 carbon atoms the C=C
33
bond length increases. ReqGS < Req-1
B. Charge carriers: radical-cation or polarons
 Molecular crystal
Example
of
negative
polaron created after
electron injection from an
electrode
In the hopping regime,
the polaron is a localized
charge associated with a
structure distortion on
one molecule or part of
one conjugated chain
Screening of the surrounding electron density
 Conjugated polymer
Example
of
positive
polaron created after hole
injection from an electrode
+
34
C. The localized polaron hopping events
b)
E
 An electron
(Self-exchange) = polaron hop
a) transfer between two similar molecules
Charged
E
 In the self-exchange model, the electric
kET
field is neglected.
The presence of an electric field 
would
2
stabilize one of the potential well.
A+B
However, this model gives
the main
Neutral
molecular
parameters
governing
the
hopping transport.
AB+
Q
1
 At high temperature, the motion of the carriers can be modeled by a
sequence of uncorrelated hops, which gives a mobility:
Q
||
a = average spacing between molecules or chain
segments
E35
The rate for electron transfer kET is given by the semi-classical theory of electron
transfer (see previous chapter)
Two major parameters determine the self-exchange ET rate and ultimately the
charge mobility:
1)
The electronic coupling between adjacent molecules/segments represented by
the transfer integral t (or HRP), which needs to be maximized
2)
The reorganization energy, , which needs to be small for efficient transport
36
The transfer integral t
estimated from the splitting of the frontier levels in a dimer
2tLUMO
 kET for an negative polaron hop
electron mobility
2tHOMO
 kET for an positive polaron hop
hole mobility
Distance dependence of ”t”(HRP) is
exponential as demonstrated for
other ET (see previous chapter):
t=
37
By J.Cornil et al., Adv. Mater. 2001, 13, 1053
Example: pentacene
There are significant electronic splittings only along the a axis and the d1 and d2
axes. Interactions between molecules located in adjacent layers (along c) are
negligible  charge transport has a dominant two-dimensional character and
takes place within the layers in directions that are nearly perpendicular to the long
molecular axes.
38
J. Cornil et al (2001) J. Am. Chem. Soc. 123, 1250–1251.
The internal reorganization energy (i)
i reflects the geometric changes in the molecules when going from the neutral to
the ionized state or vice versa. (i ↔ electron-vibration coupling)
i= 1+ 2
i (defined in the ET theory)
corresponds to the polaron binding
energy (Epol= 2~ i/2) defined in
transport theory of solids
39
Internal reorganization energy vs. molecular size
For those three molecules, the polaron
(charge+
structure
distortion)
is
delocalized over the whole molecule.
To modify slightly many bond-lengths
cost less than modifying a lot few bondlengths (see the shape of the Morse
potential)
The larger the molecule, the lower
the reorganization energy
By V. Coropceanu et al. Theor Chem Acc (2003) 110:59–69
40