Nature - 2019.08.29

Letter reSeArCH

described by Marcus theory, thus allowing further improvement of
molecular doping levels through optimization of ionic interactions.

The remarkable enhancement in doping levels achieved by anion-ex-
change doping suggests that the additional anion (such as TFSI−) is

incorporated into the host polymer thin film to achieve charge neutral-
ity. We verified this solid-state intercalation by X-ray diffraction (XRD)

analyses. Figure 4a shows out-of-plane XRD profiles for various PBTTT
thin-film specimens. Here, the first-order (h00) diffractions assigned to

lamellar spacing (d-spacing) are plotted against the scattering vector, q.
As in the conductivity measurements (Fig. 3c), the samples consisted

of pristine PBTTT (black), PBTTT doped with F4TCNQ (orange), and
PBTTT doped via anion exchange with EMIM-TFSI (light blue) or

with Li-TFSI (red). We determined the d-spacing and full width at half
maximum (FWHM) values by Gaussian peak fitting, with the results

summarized in Fig. 4b. These data show that the conductivity of the
doped PBTTT thin films increased (Fig. 3c) along with the d-spacing.

The increases in the lamellar spacing suggest that the counteranions
(F4TCNQ•− or TFSI−) were incorporated into the zones occupied

by alkyl side chains, which is consistent with previous reports^11 ,^15 ,^16.
It is also evident that the FWHM values decrease as the doping level

increases. Thus, it appears that the extent of lattice disorder decreases
dramatically. We note here that the relaxation of torsion, tension and/

or bending along the polymer backbones may result in crystal rear-
rangement (Supplementary Information section 1.3).

We assessed two-dimensional, coherent charge transport in the

polymer thin film by magnetotransport analyses, in which we meas-

ured both the longitudinal and the transverse electromotive forces

while applying an external magnetic field using a standard Hall bar

geometry. The Hall voltage is observable only when the charge car-

riers are equivalent to a free electron—that is, when the wavenumber

is definable in the charge-transport system^17 –^19. Here, we observed a

clear Hall voltage over a wide range of temperatures from 300  K down

to 2  K, with the symmetry and sign of the voltage corresponding to

the hole carrier conduction (Extended Data Fig. 9). Figure 4c, d plots

Hall mobility, μHall, and Hall carrier density, nHall, determined from a

standard expression of the Hall effect. A remarkably high carrier con-

centration of more than 1  ×  1021  cm−^3 (Fig. 4d) was achieved, together

with a reasonably high Hall mobility of 2  cm^2  V−^1  s−^1 (Fig. 4c). This

concentration is equivalent to one hole per monomer unit (representing

a half-filled state), and is also approximately three times larger than that

obtained with conventional F4TCNQ doping^11. Surprisingly, the Hall

mobility was almost completely unaffected by temperature. Although

a finite fraction of localized carriers hinders a truly metallic signature,

the temperature-invariant Hall mobility indicates that the obtained

half-filled state in highly conductive PBTTT thin films is close to the

onset of metallicity^20.

Figure 4e summarizes the magnetic-field dependence of the differ-

ential sheet conductivity of a film (Δσ = σ(B) − σ(0), where σ is the

Area-normalized intensity (a.u.)

0.20 0.25 0.30 0.35 0.40

q (Å–1)

Pristine

F4TCNQ

EMIM-TFSI

Li-TFSI

F4TCNQ

EMIM-TFSI

Li-TFSI

24

23

22

21

20

19

18

FWHM (10

–3

Å

)–1

28

26

24

22

20

d-spacing (Å)

F4TCNQEMIM-TF

SI

Pristine Li-TFSI

a

b

c

d

e

f

Oφ

(nm)

1.2

1.0

0.8

0.6

0.4

0.2

0.0

PHall

(T

) /

PHall

(300 K) (cm

2 V

–1

s

–1

)

10 100

Temperature (K)

F4TCNQ

EMIM-TFSI

Li-TFSI

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

nHall

(×

10

21

cm

–3

)

10 100

Temperature (K)

F4TCNQ

EMIM-TFSI

Li-TFSI

35

30

25

20

15

10

5

0

10 100

Temperature (K)

(μ

S)

Δσ

20 μS

2 K

10 K

50 K

100 K

200 K

300 K

Li-TFSI

–10 –5 0 5 10

Magnetic eld (T)

Fig. 4 | Highly ordered structures and coherent charge transport in
doped PBTTT. a, Area-normalized X-ray diffraction profiles along the
out-of-plane direction for PBTTT thin films (black, pristine; orange,
F4TCNQ-doped; blue, anion-exchange-doped with EMIM-TFSI; and
red, anion-exchange-doped with Li-TFSI). b, Variations in the
d-spacing and FWHM values of (100) scattering peaks. The error bars in
FWHM stem from compound errors that result from propagation of the
uncertainties in fitting of the diffraction peak, and represent one standard
deviation. c, Temperature dependence of the normalized Hall mobility
μHall (T)/ μHall (300 K). From the Hall effect measurements in Extended
Data Fig. 9, we determined the Hall mobilities at 300  K (μHall (300 K))

to be 1.9, 2.4 and 2.0 cm^2  V−^1 s−^1 for F4TCNQ-doped PBTTT thin film

(orange) and films anion-exchange-doped with EMIM-TFSI (blue) and

with Li-TFSI (red), respectively. d, Temperature dependence of the Hall

carrier density, nHall. e, Effects of the magnetic field (B) on differential

sheet conductivity (Δσ = σ(B) − σ(0)) for Li-TFSI-doped film at various

temperatures, with B applied perpendicular to the substrate plane.

f, Ef fects of temperature on the phase-coherent length (λφ). The error

bars in Hall mobility, Hall carrier density and λφ were determined from

uncertainty in the extraction of electromotive force from the fitting, and

represent one standard deviation.

29 AUGUSt 2019 | VOL 572 | NAtUre | 637