shoulder at ~790 nm in the PL of MAPbI3 single
crystals is in agreement with the PL from thin
films (5), with the main PL peaking at 820 nm
attributed to the intrinsic PL from the MAPbI3
crystal lattice. A more structured PL spectrum
was observed for polycrystalline MAPbBr3 thin
films (fig. S2) (9).
We investigated the key quantities that directly affect a material’s potential for application
in PSCs: carrier lifetime t, carrier mobility m,
and carrier diffusion length LD. In addition, we
estimated the in-gap trap density ntraps in order
to correlate the trap density with the observed
diffusion length. For MAPbBr3 single crystals, we
first measured carrier mobility using the time-of-flight technique (11). The transient current was
measured for various driving voltages (V), and
the corresponding traces are shown in Fig. 3A on
a bilogarithmic scale. The transit time tt, defined
as the position of the kink in the time traces, is
marked by the blue squares, and the corresponding values are plotted in Fig. 3B as a function of
V –1. The mobility m [m = mp ≈ mn, where mp and mn
are the hole and electron mobility, respectively
(12, 13)] can be directly estimated from the
transit time tt, sample thickness d, and applied
voltage V as m = d2/Vtt (Fig. 3B) (9). Estimating
mobility via a linear fit of tt versus V–1 led to an
estimate of 115 cm2 V–1 s–1. Complementary Hall
effect measurements at room temperature confirmed a carrier (holes) concentration of between
5 × 109 and 5 × 1010 cm–3, and provided a mobility
estimate in the range from 20 to 60 cm2 V–1 s–1.
Slightly lower mobilities obtained via the Hall
effect may be ascribed to surface effects that are
negligible for time-of-flight, which constitutes a
bulk probe.
For MAPbI3 single crystals, we estimated the
carrier mobility using the space-charge-limited
current (SCLC) technique. We measured the
current-voltage (I-V) trace for the crystals and
observed a region showing a clear quadratic dependency of the current on the applied voltage at
300 K (see fig. S8 for details). From this region,
we could conservatively estimate the carrier mobility, obtaining the value m = 2.5 cm2 V–1 s–1.
From the linear ohmic region, we also identified
the conductivity of the crystal to be s = 1 × 10−8
(ohm·cm)–1. Combining the information on mobility and conductivity, we estimated a carrier
concentration of nc = s/em ≈ 2 × 1010 cm−3 (where
e is the electronic charge).
We estimated the carrier lifetime t from transient absorption (TA) and PL spectra. Nanosecond pump-probe TA spectroscopy was carried
out over a window covering the nanosecond-to-microsecond time scales in order to evaluate the
fast (t ≈ 74 ns) as well as the slow (t ≈ 978 ns)
carrier dynamics, as determined from biexponential fits. Time (t)– and wavelength (l)–resolved
PL maps IPP(t, l) (Fig. 3D) of single-crystalline
MAPbBr3 were acquired in the wavelength region around the main band-to-band recombination peak at 580 nm (l = 500 to 680 nm). The
time-dependent PL signals in single-crystalline
samples of MAPbBr3 and MAPbI3 are shown in
Fig. 3, E and F, respectively; the data were measured at the wavelength of the main PL peak—i.e.,
l = 580 nm and l = 820 nm for MAPbBr3 and
MAPbI3, respectively (see insets).
The time-resolved traces are representative
of the transient evolution of the electron-hole
population after impulsive (Dt ≈ 0.7 ns) photoexcitation. Biexponential fits were performed
to quantify the carrier dynamics (fig. S4, blue
traces) (9). Both the bromide- and iodide-based
perovskite crystals exhibited a superposition of
fast and slow dynamics: t ≈ 41 and 357 ns for
MAPbBr3, and t ≈ 22 and 1032 ns for MAPbI3.
We assign these two very different time scales
to the presence of a surface component (fast)
together with a bulk component (slow), which
reveals the lifetime of carriers propagating deeper
in the material. The relative contribution of these
two terms to the static PL can be readily evaluated by integrating the respective exponential
traces (the integral is equal to the product of the
amplitude A and the decay time t), which shows
that the fast (tentatively surface) component
amounts to only 3.6% of the total TA signal in
MAPbBr3, and to 12% and 7% of the total PL
signal in MAPbBr3 and MAPbI3, respectively.
Ultimately, by combining the longer (bulk) carrier lifetimes with the higher measured bulk mobility, we obtained a best-case carrier diffusion
length LD = (kBT/e · m · t)1/2 (where kB is Boltzmann’s
constant and T is the sample temperature) of
~17 mm in MAPbBr3; use of the shorter lifetime
and lower mobility led to an estimate of ~3 mm.
The same considerations were applied for the
MAPbI3 crystals to obtain a best-case diffusion
length of ~8 mm and a worst-case length of ~2 mm.
For comparison, we also investigated the PL
decay of solution-processed thin films of MAPbBr3
(fig. S5). We again found two dynamics: a fast
decay (t ≈ 13 ns) and a longer-lived component
(t ≈ 168 ns), in both cases faster than the single
crystals. This result suggests a larger trap-induced
recombination rate in the thin films, which are
expected to possess a much higher trap density
than the single crystals. Previous studies on
non–Cl-doped MAPbI3 nanostructured thin films
also corroborate this trend, revealing a PL lifetime of ~10 ns and a carrier diffusion length
of ~100 nm (3, 5).
Crystalline MAPbX3 is characterized by a charge
transport efficiency that outperforms thin film–
based materials in mobility, lifetime, and diffusion length. To unveil the physical origins of this
difference, we investigated the concentration of
in-gap deep electronic trap states. We measured
the I-V response of the crystals in the SCLC regime (Fig. 4). Three regions were evident in the
experimental data. At low voltages, the I-V response was ohmic (i.e., linear), as confirmed by
the fit to an I ≈ V functional dependence (blue
line). At intermediate voltages, the current exhibited a rapid nonlinear rise (set in at VTFL = 4.6 V
for MAPbBr3 and 24.2 V for MAPbI3) and signaled the transition onto the trap-filled limit
(TFL)—a regime in which all the available trap
states were filled by the injected carriers (14).
The onset voltage VTFL is linearly proportional
to the density of trap states ntraps (Fig. 4A). Correspondingly, we found for MAPbBr3 single
crystals a remarkably low trap density ntraps =
5.8 × 109 cm–3, which, together with the extremely
clean absorption and PL profiles (see again
Fig. 2A), points to a nearly defect-free electronic
structure. At high fields, the current showed a
quadratic voltage dependence in the Child’s regime.
In this region, we extracted the value for the trap-free mobility m. We found m = 38 cm2 V–1 s–1 (Fig.
4A), a value in good agreement with the mobility
extracted using time-of-flight and Hall effect measurements (fig. S7) (9). We determined a comparable low trap density ntraps = 3.3 × 1010 cm–3
for MAPbI3 single crystals using the same method (Fig. 4B).
The defect density measured for the room
temperature–grown MAPbX3 crystals was superior to a wide array of established and emerging
optoelectronic inorganic semiconductors including polycrystalline Si (ntraps ≈ 1013 to 1014 cm–3) (15,
16), Cd Te/CdS (ntraps ≈ 1011 to 1013 cm–3) (17), and
copper indium gallium selenide (CIGS) (ntraps ≈ 1013
cm–3) thin films (18), as well as organic materials
such as single-crystal rubrene (ntraps ≈ 1016 cm–3) (19)
and pentacene (ntraps ≈ 1014 to 1015 cm–3) (20). Only
Fig. 4. Current-voltage traces and trap density. Characteristic I-V trace (purple markers) showing
three different regimes for (A) MAPbBr3 (at 300 K) and (B) MAPbI3 (at 225 K). A linear ohmic regime (I V V,
blue line) is followed by the trap-filled regime, marked by a steep increase in current (I V Vn>3, green line). The
MAPbBr3 trace shows a trap-free Child’s regime (I V V2, green line) at high voltages.
