Assessing Temperature Dependence of Drift. Mobility in Methylammonium Lead Iodide

Transcription

1 Supporting Information Assessing Temperature Dependence of Drift Mobility in Methylammonium Lead Iodide Perovskite Single Crystals Shreetu Shrestha, Gebhard J. Matt*, Andres Osvet, Daniel Niesner, Rainer Hock # and Christoph J. Brabec Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Institute of Materials for Electronics and Energy Technology (i-meet), Martensstrasse 7, Erlangen, Germany. Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Erlangen Graduate School of Advanced Optical Technologies (SAOT), Paul-Gordan-Strasse 6, Erlangen, Germany. Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Institute of Solid State Physics, Staudtstrasse 7, Erlangen, Germany. # Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Institute for Crystallography and Structural Physics, Staudtstrasse 3, Erlangen, Germany. *G.J.M. gebhard.matt@fau.de, Tel S1

2 (a) (b) Figure S1 MAPbI 3 single crystal. (a) Optical picture of the crystal. (b) Crystal Morphology simulated with the program WinXMorph. All crystal face indexations are indicated. Citation for WinXMorph: W. Kaminsky From CIF to virtual morphology using the WinXMorph program, J. Appl. Cryst. (2007). 40, S2

3 Electron TOF transient (a) (b) Figure S2 TOF transient from electrons in (a) linear scale and (b) double logarithmic scale at room temperature. MAPbI 3 crystal was 2.36 mm thick. S3

4 Low mobility feature (a) (b) Figure S3 Low mobility feature. (a) Electric field dependence at 150 K. (b) Peak photocurrent amplitude of the high and low mobility features. MAPbI 3 crystal was 1.48 mm thick. S4

5 Warming and cooling (a) (b) Figure S4 Starting from room temperature, the samples were first cooled to low temperatures and then warmed again. (a) Hole transient during heating and cooling. (b) Electric field dependence. MAPbI 3 crystal was 1.48 mm thick. S5

6 Electric field dependence (a) (b) Figure S5 Field dependence of (a) electron and (b) hole mobility at different temperature. S6

7 The mobility value at each temperature shown in Figure 4 is an average of 6 to 9 measurements at different electric fields (SI Figure 5). Determining transit time from a TOF transient can be inaccurate when the position of the kink is not clear. This typically is the biggest cause of uncertainty in TOF spectroscopy. At low electric fields, the transition from the plateau to the tail is rather washed out and the transit time is difficult to determine reliably. If the distance a carrier diffuses (L diff ) is equal to the device thickness (d) at a certain voltage V 1, the ratio of distance a carrier diffuses (L diff ) to the distance it drifts (L drift ) can be estimated as L diff /L drift = (kt/ev 1 ) 0.5 [1]. At room temperature, using the value kt/e = V, L diff /L drift 1/(6.3*V ). Therefore, a high bias is necessary to minimize ambiguities. S7

8 Fit to polar optical phonon scattering Figure S6 Temperature dependence of hole and electron mobility of MAPbI 3 in the tetragonal phase for phonon energy of 20 mev. The red line indicates fit to Equation S4. Equation S2 describing the relation between mobility and momentum relaxation time (τ m ): (2) Equation S3 from [2] [3]. The full equation was derived by Callen [4] : Where, (3) Using a parabolic band approximation S8

9 Equation S4: (4) S9

10 Mobilit-lifetime product Figure S7 Electric filed dependence of holes extracted. MAPbI 3 crystal was 1.48 mm thick. By fitting the extracted charge as a function of electric field to the Hecht equation (SI Figure 4), a tentative hole mobility-lifetime product (µτ) in the range 5*10-4 cm 2 /V is obtained. Using the relation for diffusion length, L D = (µ*kt/e *τ) 0.5 where k is the Boltzmann s constant, T is the temperature, e is the elementary charge, gives a diffusion length of approximately 35 µm. S10

11 XRD (a) (b) Fig S8 X-ray diffraction patterns measured on the (100) face of (a) the single crystal and (b) measured on powder crushed from a single crystal proofing phase purity. XRD patterns were measured with a Panalytical X Pert powder diffractometer. The wavelength used is Ni filtered Cu Kα 1,2 radiation. The X-Ray tube was operated at 40 KV and 35 ma tube current. The scan step size was degree. The single crystal was mounted on the sample stage with (100) facet facing up and a theattheta scan was measured. The MAPbI 3 powder was crushed from a single crystal in a agate mortar and mounted on a low backgroung sample holder. S11

12 Field perturbed currents Figure S9 Overshoot in hole transient signal Current overshoot was seen in some transients. After the initial spike the current did not plateau but continues to increase to a peak value before decaying. The drifting charge carrier front has a finite width (due to finite duration of the laser pulse and finite absorption depth of light in the crystal) and the leading edge of the carrier wave experiences a higher electric field than the trailing edge. As the sheet propagates, it experiences an increasing electric field resulting in an overshoot. S12

13 Electron-Temperature dependence Figure S10 Temperature dependence of electron transients. MAPbI 3 crystal was 2.76 mm thick. Reference (1) Haynes, J. R.; Shockley, W. The Mobility and Life of Injected Holes and Electrons in Germanium. Phys. Rev. 1951, 295. (2) Ridley, B. K. Quantum Processes in Semiconductors, 4th ed, Oxford University Press, Oxford, (3) Yu, P.Y.; Cardona, M. Fundamentals of Semiconductors, 4th ed.; Springer, Berlin, (4) Callen, H. B. Electric Breakdown in Ionic Crystals. Phys. Rev. 1949, 76, S13