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Charge Transport and Observation of Persistent Photoconductivity in Tl6SeI4 Single Crystals Sanjib Das,† John A. Peters,†,‡ Wenwen Lin,§ Svetlana S. Kostina,† Pice Chen,† Joon-Il Kim,† Mercouri G. Kanatzidis,†,§ and Bruce W. Wessels*,† †

Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States Department of Chemistry and Physics, Chicago State University, Chicago, Illinois 60628, United States § Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States ‡

S Supporting Information *

ABSTRACT: The chalcohalide compound Tl6SeI4 is a promising wide-bandgap semiconductor for efficient hard radiation detection at room temperature due to its high density, average atomic number and mobility-lifetime product. However, the nature of its charge transport kinetics, especially the role of defects in recombination, has not been examined in detail. To determine the charge transport kinetics in Tl6SeI4 single crystals, electrical conductivity and photoinduced current transient spectroscopy were measured over the temperature range 105−330 K. These measurements reveal the existence of multiple defect states with energy levels in the range 0.10−0.90 eV, within the bandgap of Tl6SeI4. Large persistent photoconductivity (PPC) is observed at low temperature that shows strong thermal quenching at 160 K. The quenching of PPC is described using a configuration coordinate model involving a deep level donor state, which is tentatively attributed to the presence of iodine vacancies or Si interstitial impurities.

T

recombination centers and PICTS measures deep trapping states.11,12 The PL spectra of Tl6SeI4 crystals showed a broad emission band centered around 1.63 eV, below its energy gap of 1.86 eV. This was tentatively attributed to a bound exciton emission.11 PICTS measurements revealed a series of relatively shallow acceptor levels with ionization energies at ∼80 and ∼180 meV attributed to Tl-vacancy and I-interstitial, respectively, as well as donor levels with ionization energies of ∼60 and 100 meV attributed to I−Se antisite and I-vacancy, respectively.12 No deeper levels were observed by PICTS over the temperature range 77−325 K. However, Biswas et al., who investigated the electronic defect structure of Tl6SeI4 using density functional theory (DFT) calculations indicated that the presence of deep donors could result in electron trapping and/ or enhanced recombination, both detrimental to detector performance.13 Recently, we observed PL fatigue in Tl6SeI4, whereby there is a reduction in PL intensity under prolonged photoexcitation. The fatigue was attributed to the formation of photoinduced defects.11 These defects introduce additional radiative and nonradiative recombination channels that lead to a decrease in the PL intensity under prolonged laser irradiation. These photoinduced defects are presumed to be analogous to the DX centers observed in II−VI and III−V semiconductor com-

here is an increasing demand for widegap semiconductor hard radiation detectors for X- and γ-rays that operate at room temperature in medical imaging, security, and space applications. 1,2 Currently, pseudobinary semiconducting CdxZn1−xTe (CZT) compound is the benchmark material due to its excellent radiation detection performance at room temperature.3,4 However, synthesis of high-quality CZT singlecrystals remains challenging due to precipitate formation that degrades its spectral response.5 Consequently, new semiconductors are sought that can detect X-ray and γ-ray radiation at room temperature. These semiconductors require optimal bandgaps, high electrical resistivity, and excellent charge transport with large charge carrier mobility-lifetime (μτ) products. Among the compounds that simultaneously satisfy these requirements are heavy metal binary halides such as HgI2, PbI2, and BiI3.6−8 Their μτ products, however, are much smaller than that of CZT.4,9 Previously, the ternary compound Tl6SeI4 was reported by Johnsen et al. as a promising detector material with an appropriate bandgap, high electrical resistivity, and excellent μτ products.10 In addition to these properties, this compound also enables low-cost purification/growth because of its low melting point. Since the mobility-lifetime products of most semiconductors are often affected by electron and hole trapping states and recombination centers, it is essential to obtain detailed information about their origin and effect on charge transport of Tl6SeI4 single crystals. Our group previously investigated its native defects using photoluminescence (PL) and photoinduced current transient spectroscopy (PICTS), where PL is sensitive to radiative © XXXX American Chemical Society

Received: February 11, 2017 Accepted: March 16, 2017 Published: March 16, 2017 1538

DOI: 10.1021/acs.jpclett.7b00336 J. Phys. Chem. Lett. 2017, 8, 1538−1544

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The Journal of Physical Chemistry Letters pounds, where highly localized and ionized deep level defects undergo significant lattice relaxation.14−16 In this work, we investigated the effects of these deep level defects in Tl6SeI4 crystals by measuring the temperature dependence of both the dark electrical conductivity and photoconductivity as well as photoinduced current transient spectroscopy (PICTS). Large persistent photoconductivity (PPC) was observed in this compound at low temperature, which was quenched at a temperature of ∼160 K. We explain the PPC using a configuration coordinate model involving a deep donor defect level. To evaluate the sample quality, current−voltage (I−V) characteristics of a series of Tl6SeI4 single crystals were measured in the dark and under illumination of a 405 nm emission of a semiconductor laser with intensity range 0−4000 mW/cm2. The Tl6SeI4 crystals characterized in this study have undergone improved growth processes (as described in the Experimental Methods section), namely, the removal of oxygen impurities and the purification of precursor materials. The samples exhibited linear I−V dependence at room temperature, and over the bias ranges of −200 to +200 V, with no electrical breakdown (Supporting Information, Figure S1). The average dark electrical resistivity values are 1.28 × 1012 and 1.47 × 1012 Ω·cm under positive and negative biases, respectively. All samples showed excellent photosensitivity when illuminated by a 405 nm semiconductor laser, yielding average photoresponse (Δσ/σ) values of 89 and 170 under positive and negative biases, respectively. To determine the dominant current conduction mechanism as well as the nature of defects present in Tl6SeI4 crystals, steady-state conductivity measurements were carried out as a function of temperature in the range 120−330 K. Figure 1a shows the effect of temperature on the conductivity of a typical sample. The conductivity increased with increasing temperature in the range 250−330 K, which is attributed to the increase in total carrier density. The dark electrical conductivity depends on temperature according to the relation, σ = σ0 exp(−Eai/kT), where σ0 is the pre-exponential factor, Eai is the activation energy for conductivity in a given temperature range (denoted by the letter i), k is the Boltzmann constant, and T is the absolute temperature.17 The values of Eai were calculated from the slopes of the Arrhenius plot of ln(Idark) versus 1/kT, as shown in Figure 1b, where Idark is the dark current. The slopes of the fitted straight lines, in the temperature regions of 300− 330 K and 270−300 K are (0.88 ± 0.02) and (0.19 ± 0.01) eV, respectively. The level observed at high temperatures is close to midgap (room-temperature bandgap of Tl6SeI4 is ∼1.86 eV). The calculated activation energies for conductivity in all measured samples are summarized in Table 1. It should be noted here that the variation in activation energies among the samples is presumably due to differences in background impurities. To investigate the properties of trapping states in Tl6SeI4, photoinduced current transient spectroscopy (PICTS) was carried out on the sample WW2025SE2 over the temperature range 102−330 K. PICTS is a highly sensitive technique that can reveal deep levels in highly resistive materials.18,19 One of the major advantages of PICTS is its ability to identify both radiative and nonradiative transitions of trapped carriers to conduction and valence bands.20 By analyzing PICTS data, one can determine the trap type, activation energy, and capture cross section.21 At low temperatures (∼102−150 K), the sample showed large photoinduced current whose magnitude

Figure 1. (a) Dark current versus temperature in Tl6SeI4 single crystal (sample WW2002L) at applied bias of −25 V. (b) Arrhenius plot of the dark current, showing the activation energies.

decreased with increasing temperature (inset to Figure 2a) and completely quenched at around 170 K. Upon analyzing the transient current signals during the off-state of the laser using a two-gate technique (see Experimental Methods for details), two peaks were observed in the range 102−200 K, while no peaks were observed in the temperature range 200−330 K (Figure 2a). These two peaks indicate the presence of two defect levels in the temperature ranges of 105−120 and 130−150 K, labeled as traps A and B, respectively (Figure 2). The corresponding Arrhenius plots of ln(ei/T2) versus 1000/T reveal that the two levels have activation energies of 0.11 ± 0.01 (trap A) and 0.26 ± 0.06 eV (trap B) below the conduction band, with capture cross sections (σi) of 5.86 × 10−17 and 4.09 × 10−13 cm2, respectively (Figure 2b). The activation energy in the temperature range 130−150 K agrees well with the energy obtained from the temperature-dependent dark conductivity measurements in the same temperature range for the same sample (Figure S2 and Table 2). Neutral traps have σi values on the order of ∼10−15 cm2.22 Therefore, the relatively larger σi of trap B indicates a Coulombic attraction between the trap and the charge carriers making it an effective recombination center, while the value of σi for trap A is indicative of weak Coulombic repulsion.17,23,24 Thus, the carrier detrapping time in Tl6SeI4 is likely determined by trap B due to its large capture crosssection. To better understand the mechanisms by which defects can limit the photoresponse, the photoconductivity was measured with varying excitation intensity as a function of temperature. 1539

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Table 1. Measured Activation Energies under Dark (Ea1 and Ea2) and Laser Illumination of 1000 mW/cm2 (Ea3 and Ea4) at −25 V (+25 V in Parentheses) Applied Biasa sample code

Ea1 (dark, eV)

Ea2 (dark, eV)

Ea3 (laser, eV)

Ea4 (laser, eV)

WW2002S

0.65 ± 0.03 (--) 0.88 ± 0.02 (0.41 ± 0.02) 0.83 ± 0.03 (0.98 ± 0.05) 0.68 ± 0.01 (0.58 ± 0.02) 0.44 ± 0.01 (0.55 ± 0.01)

0.15 ± 0.01 (--) 0.19 ± 0.01 (0.21 ± 0.01) 0.25 ± 0.01 (0.49 ± 0.02) 0.15 ± 0.01 (0.36 ± 0.01) 0.26 ± 0.01 (--)

0.77 ± 0.02 (0.37 ± 0.03) 0. 76 ± 0.04 (0.21 ± 0.01) 0.49 ± 0.02 (0.20 ± 0.01) 0.26 ± 0.01 (0.45 ± 0.02) 0.21 ± 0.01 (0.26 ± 0.01)

0.11 ± 0.02 (--) 0.12 ± 0.01 (0.17 ± 0.01) 0.10 ± 0.01 (--) 0.16 ± 0.01 (0.17 ± 0.01) 0.12 ± 0.01 (0.12 ± 0.01)

WW2002L WW2025SE0 WW2025SE1 WW2025SE2 a

Dashes mean that accurate Ea values could not be obtained due to the large margin of error.

Table 2. Comparison of Activation Energies Calculated from PICTS and I−T Measurements for Tl6SeI4 Single Crystal (Sample WW2025SE2) activation energy, Ea (eV) temperature range (K)

PICTS

105−120 130−150 150−170 270−300 300−340

0.11 ± 0.01 0.26 ± 0.06 − − −

I−T 0.21 0.40 0.26 0.44

− ± ± ± ±

0.01 0.01 0.01 0.01

according to the relation Iph ∝ Fγ, where the values of the exponent γ depend on the recombination mechanism of the photoexcited carriers. The values of γ being greater than 1, equal to 1, or less than 1 indicate the dominance of supralinear (strong surface recombination), linear (monomolecular), and sublinear (bimolecular) recombination mechanisms, respectively.17 The variation of γ with temperature for two samples WW2002L and WW2025SE0is shown in Figure 3. The value

Figure 2. (a) Four representative two-gate PICTS signals for Tl6SeI4 sample WW2025SE2 between 102 and 200 K, under −25 V applied bias to the illuminated contact; t2/t1 = 2 in the two-gate technique used. The plots are vertically offset for clarity. The inset shows photoinduced current transient profiles recorded at temperatures between 102−200 K. (b) Arrhenius plots of ln(ei/T2) versus 1000/T for the observed defects; solid lines are the linear fits of the data.

Figure 3. Variation of γ with temperature for WW2002L and WW2025SE0 at applied bias voltages of −10 V. At room temperature, bimolecular recombination dominates the photocurrent.

of γ was ∼0.5 in the 250−330 K temperature range, indicating that photoexcited carriers undergo bimolecular recombination. In the intermediate temperature range 170−250 K, γ was in the range 0.5−1 indicating mixed kinetics determined by both monomolecular and bimolecular recombination of carriers. The observation of supralinear photoconductivity (γ > 1) in the temperature range 150−170 K may be attributed to the change in the behavior of the defect centers from traps to recombination centers.17,25 The carrier lifetime (τ) is a function of the light intensity (F) according to the relation, τ ∝ F(γ−1).17 For γ > 1, the carrier lifetime increases with increasing excitation rate showing supralinear behavior. A value of γ = 1 is

The magnitude of the photocurrent depends on both temperature and excitation intensity while the temperature dependence of the photoconductivity depends on defect capture cross sections for charge carriers in the crystal.17 The photocurrent was measured under varying laser power of 5−20 mW (corresponding intensity range: 1000−4000 mW/cm2) over the temperature range 120−330 K. The electric field was fixed at 100 or 250 V/cm for both negative and positive applied biases. The photocurrent (Iph) depends on light intensity (F) 1540

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by a laser with an intensity of 2000 mW/cm2 for 60 s and the dark current was measured at different time intervals after the laser was turned off (Figure 4b). The current remained at a level of 100 nA for more than 2 h exhibiting a large persistent photoconductivity (PPC). The decay behavior of the persistent current after the cessation of laser illumination followed a stretched exponential decay kinetics given by, IPPC(t) = IPPC(0)exp[−(t/τ)β], where IPPC(0) is the persistent current immediately after the illumination is turned off, τ is the PPC decay time constant, and β is the decay exponent.26,27 The fit of the above equation with the data shown in Figure 4c yielded τ and β values of 7.5 ± 2.4 min and 0.39 ± 0.07, respectively. The PPC (Figure 4d) showed a quenching temperature of ∼160 K, similar to that of photoconductivity (Figure 4a). The observed PPC can be described by the energy band diagram and the configuration coordinate model shown in Figure 5, where D+,

an indication of the free carrier lifetime being constant with illumination intensity. For γ < 1, the lifetime decreases with increasing illumination intensity. Thus, Figure 3 indicates the changes in carrier lifetime with temperature. Figure 4a shows the measured photocurrent as a function of temperature for a Tl6SeI4 single crystal. A large photocurrent of

Figure 4. (a) Photocurrent versus temperature in Tl6SeI4 single crystal under 1000 mW/cm2 of laser intensity. (b) Dark current behavior after prior excitation as a function of time at 104 K. (c) Decay of the persistent photocurrent at 104 K after cessation of illumination (blue circles), which was fitted (blue solid curve) using a stretched exponential decay function. (d) Measured persistent current as a function of temperature; laser illumination was turned on and off at 104 K, then the sample was warmed up at a heating rate of 0.13 K/s.

1 μA was observed at temperatures below 160 K. The photocurrent was strongly thermally quenched with increasing temperature between 150 and 170 K, where the photoconductivity decreased by a factor of 104. In contrast, in the temperature region between 170 and 250 K the photocurrent remained nearly constant followed by a small increase in the temperature range 250−330 K. A similar trend was observed at all applied light intensities for all samples measured (Figure S3). At each temperature, the photocurrent increased with increasing illumination intensity (Figure S3). As can be seen from Figure 4a, the photocurrent increased with increasing temperature in the range 250−330 K. In the regions where γ approaches 0.5, as shown in Figure 3, the values of the activation energy under laser illumination (Ea3 and Ea4) were calculated from the Arrhenius plots of ln(Iph) versus 1/T. The measured activation energies in the temperature regions of 300−330 K and 270−300 K, as shown in Figure S4, are (0.77 ± 0.02) eV and (0.11 ± 0.02) eV for the sample WW2002S and (0.76 ± 0.04) eV and (0.12 ± 0.01) eV for WW2002L, respectively. The activation energies measured from both dark conductivity and photoconductivity, as listed in Table 1, indicate that there are multiple defect states within the bandgap of Tl6SeI4 single crystals. Another interesting charge transport characteristic exhibited by Tl6SeI4 is that there is higher dark current at low temperatures after the cessation of laser illumination compared to the dark current without any prior laser excitation. To further elucidate this behavior, a sample was cooled down and maintained at 104 K, and its dark current was measured to be 6.1 pA (Figure 4b). Subsequently, the sample was illuminated

Figure 5. (a) Energy band diagram of Tl6SeI4 showing valence and conduction bands, Fermi level, and an ionized deep-donor level. (b) Configuration coordinate diagram showing the conduction and valence bands of Tl6SeI4, and the deep donor level which has undergone lattice relaxation.

D0, C, and V are the ionized and neutral states of the deep donor, conduction band and valence band of Tl6SeI4, respectively.27−29 Upon photoexcitation, electrons are promoted from the valence band to the conduction band leading to photoconductivity (Process 1, Figure 5a). After the cessation of illumination at low temperature, the carriers remain in the 1541

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ature dependent. Temperature-dependent dark current and PICTS measurements revealed the presence of multiple deep level defect states with activation energies in the range 0.10− 0.90 eV. The temperature dependence of both dark conductivity and photoconductivity indicated that the charge transport in Tl6SeI4 is dominated by recombination through midgap deep level defect states (∼0.70−0.90 eV) at room temperature (∼296 K), presumably through Shockley-ReadHall recombination. At low temperatures (105−170 K), the current is limited by transport involving defect levels in the range 0.10−0.40 eV. These defects were attributed to native point defects as well as other extrinsic impurities. The semiconductor exhibited large persistent photoconductivity at temperatures below 160 K that was well-described by a configuration coordinate diagram with a deep level donor that undergoes lattice relaxation. The observed defect donor level is tentatively assigned to the presence of point defects due to either iodine vacancies or Si interstitial impurities based on DFT calculations. Reduction of these defects should lead to highly sensitive X-ray and γ-ray detectors that operate at room temperature.

conduction band as they do not have sufficient thermal energy to overcome the capture barrier, Eb. At ∼160 K, the carriers have sufficient thermal energy to overcome the barrier, resulting in the quenching of the observed PPC (Process 2). The ionized donor defect level (D+) transforms into a neutral state (D0), undergoing lattice relaxation.30 To calculate the capture barrier Eb, the decay of PPC was measured at four different temperatures in the range 100−150 K (Figure S5a), and each decay curve was fitted with the stretched exponential decay function to calculate τ and β values. From the slope of the Arrhenius plot of ln(τ) versus 1/T (Figure S5b), Eb was estimated to be ∼0.10 eV (within the margin of error). Tl6SeI4 samples did not exhibit any sign of PPC above 160 K (see Figure S6). The apparent increase in conductivity at temperatures above 220 K is presumably due to an increase in carrier density as indicated and discussed in Figure 1a. As to the identity of the defects obtained from the dark- and photoconductivity measurements, previously reported firstprinciples density functional theory (DFT) calculations indicate that disorder in Tl6SeI4 arises from native defects. These include iodine, selenium and thallium vacancies (VI, VSe, and VTl), antisite disorder (ISe, and SeI) and iodine interstitials (Iint).12,13 The calculated ionization energies of these native defects indicate that the antisite defect SeI and the thallium vacancy VTl act as shallow acceptors with energy levels of ∼0.04 eV above the valence band maximum (VBM). On the other hand, the antisite defect ISe is a shallow donor at ∼0.04 eV below the conduction band minimum (CBM). Furthermore, calculations of defect formation energy indicate that the iodine vacancy VI and the selenium vacancy VSe are deep donors with defect levels at 0.10 and 0.47 eV below CBM, respectively, whereas Iint has a deep level at 0.57 eV above VBM. The measured activation energies under dark (Ea1 and Ea2) and illumination (Ea3 and Ea4) listed in Table 1 indicate that ionization energies of defects in Tl6SeI4 range from ∼0.10 eV to ∼0.90 eV. Thus, by comparing the activation energies listed in Table 1 to those from DFT calculations, the defect levels Ea2 and Ea4 (∼0.10−0.19 eV) for all the measured samples are likely due to the iodine vacancy VI. The energies Ea3 (∼0.49 eV and ∼0.45 eV) are likely due to the deep donors VSe, and Iint. Finally, the activation energies Ea1, i.e., those with energies of ∼0.68 and 0.83 eV, as well as the midgap states at ∼0.90 eV, may be attributed to other extrinsic impurities that were not considered in the DFT calculations. As to the identity of the deep donor level causing the PPC at low temperatures, recent glow discharge mass spectroscopy experiments on this compound showed the presence of various substitutional and interstitial impurities including Si, Pb, Sn, and Al (unpublished results). Preliminary theoretical calculations revealed Si interstitials to be deep donor levels, whereas Al as Tlsubstitutional impurities act as deep acceptor levels, and Pb and Sn are shallow Tl-substitutional impurities (unpublished results). Upon correlating our charge transport measurements to these results and previously published DFT calculations, we attribute the PPC in the Tl6SeI4 compound to iodine vacancies (intrinsic point defects) and/or Si interstitial impurities (extrinsic defects). In summary, we have investigated the detailed charge transport characteristics of semi-insulating Tl6SeI4 single crystals. Resistivity values of the measured samples were in the 1011−1012 Ω-cm range at room temperature. All samples were highly photoconductive with photoresponse as high as 2 orders of magnitude. Charge transport was strongly temper-

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EXPERIMENTAL METHODS Crystal Growth. Tl6SeI4 single crystals were grown using the Bridgman technique. The Tl6SeI4 raw material was prepared from direct combination of Tl metal (99.999 wt %, Alfa Aesar), Se (pellets, 99.999 wt %, Alfa Aesar), and TlI (beads 99.999 wt %, Alfa Aesar) with the appropriate stoichiometry. Since Tl is sensitive to air, Tl precursor was used after removing the oxidation layer using a blade. To further eliminate the oxygen impurities in these precursors, a small amount of fine graphite powder was added into the ampule (0.1 wt %, purity of 99.9995%, 200 mesh, Alfa Aesar). The graphite reacts with adventitious oxygen to form CO and CO2 gases which liberate from the melt. These precursors were sealed under vacuum in a fused silica ampule (inner diameter 11 mm) to minimize oxygen contamination. The synthesis was performed in a rocking furnace at 500 °C for 24 h to ensure complete reaction of precursors. After synthesis, the tail section with accumulated impurities and unreacted graphite was discarded. A conical-tip and carbon coated silica tube with an inner diameter of 9 mm was used for crystal growth. The raw material was melted in the vertical two-zone Bridgman furnace prior to crystal growth. Crystal growth was performed at a translation speed of 0.5 mm/h at a temperature gradient of around 30 °C/cm. The temperature for hot zone and cold zone were set to 600 and 200 °C, respectively. After the growth, boule was cut by using a waferizing saw with a diamond-impregnated blade. Subsequently, the wafers were polished with sand papers and alumina slurries with an average particle size of 0.05−1 μm. Electrical and Optical Characterizations. For electrical characterizations, devices were fabricated by depositing 50 nm thick Au electrodes using electron beam evaporation (Auto 500, BOC Edwards) on both sides of the polished Tl6SeI4 single crystals. The thickness of the samples was in the range 0.6−1 mm. Samples of this type were also used for gamma-ray detection studies.10 The samples were mounted on a holder where carbon paint was used to connect the gold electrodes to copper leads through colloidal silver paint. High voltage I−V characteristics were measured by applying a voltage that was swept from 0 to ±200/300 V in increments of 25 V with a dwell time of 10s. For temperature-dependent dark conductivity measurements, a constant voltage of ±10 V or ±25 V 1542

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The Journal of Physical Chemistry Letters was applied to the sample, and the temperature was increased from 130 to 360 K using a temperature controller (Model 330, Lake Shore Cryotronics, Inc.). Photoconductivity was measured by using a continuous-wave (CW) 405 nm semiconductor laser source (OBIS laser, Coherent Inc.) for excitation. The photoresponse (σph) was defined as σph = (σL − σD)/σD, where σD and σL are the dark and photoconductivities, respectively. For temperature-dependent photoconductivity measurements, the laser intensity was increased from 1000 to 4000 mW/cm2 in 1000 mW/cm2 increments, with 4 s dwell time between measurements to allow the current to stabilize. For PICTS measurement, the sample was mounted analogous to that used for temperature-dependent conductivity measurements using a setup reported elsewhere.12,31 A CW semiconductor diode laser (OBIS 405 nm) was pulsed using a pulse generator, such that the laser was on for 10 ms and off for 90 ms. The laser intensity was 4000 mW/cm2. The transient current signal was passed through a 50-Ω resistor and amplified using a current amplifier (Keithley 428) with a gain of 105. The signal was then fed into an oscilloscope, and its output was recorded by a computer. Transient signal was measured every 2 K over the temperature range 102−200 K, with 30 s interval between each step. Thermal activation energies and the capture cross sections were extracted by analyzing the data using two-gate technique,32 where the normalized PICTS signal S(T) is given by

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*E-mail: [email protected]. ORCID

Sanjib Das: 0000-0002-5281-4458 Mercouri G. Kanatzidis: 0000-0003-2037-4168 Bruce W. Wessels: 0000-0002-8957-7097 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Department of Homeland Security with grant DN-077-ARI086-01 and RMD Inc. through a contract from the Department of Homeland Security. This work made use of the Materials Processing and Microfabrication Facility supported by the MRSEC program of the National Science Foundation (DMR-1121262) at the Materials Research Center of Northwestern University. The authors would like to thank Dr. Zhifu Liu and Dr. Oleg Kontsevoi for technical discussions.

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where t1 and t2 are the two times at which the readings are taken, I(t) is the transient current at time t, ei is the thermal emission rate (s−1) from trap i, and K is a material-specific prefactor. The thermal emission rate is related to the trap activation energy (Ea) and the capture cross section (σi) by (2)

where kB is the Boltzmann constant and the constant C is given by33 (3)

where g is the band degeneracy factor, m* is the effective mass for hole (or electron) carriers, and h is the Planck’s constant. The effective masses for electrons and holes in Tl6SeI4 were calculated to be 0.27m0 and 0.39m0, respectively, using the formula, m* = 3/(1/mxx + 1/myy + 1/mzz), where the mxx, myy, and mzz values were previously reported.10 Assuming the degeneracy factor to be 2, the values of σi and Ea were calculated from the slope and intercept of a plot of ln(ei/T2) versus 1/T, respectively. The temperature T corresponds to the temperature at which the maximum PICTS signal S(T) is obtained.

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REFERENCES

(1) Stowe, A. C.; Woodward, J.; Tupitsyn, E.; Rowe, E.; Wiggins, B.; Matei, L.; Bhattacharya, P.; Burger, A. Crystal Growth in LiGaSe2 for Semiconductor Radiation Detection Applications. J. Cryst. Growth 2013, 379, 111−114. (2) Roy, U. N.; Camarda, G. S.; Cui, Y.; Gu, G.; Gul, R.; Hossain, A.; Yang, G.; Egarievwe, S. U.; James, R. B. Growth and Characterization of CdMnTe by the Vertical Bridgman Technique. J. Cryst. Growth 2016, 437, 53−58. (3) Szeles, C.; Cameron, S. E.; Ndap, J. O.; Chalmers, W. C. Advances in the Crystal Growth of Semi-Insulating CdZnTe for Radiation Detector Applications. IEEE Trans. Nucl. Sci. 2002, 49, 2535−2540. (4) Milbrath, B. D.; Peurrung, A. J.; Bliss, M.; Weber, W. J. Radiation Detector Materials: An Overview. J. Mater. Res. 2008, 23, 2561−2581. (5) Amman, M.; Lee, J. S.; Luke, P. N. Electron Trapping Nonuniformity in High-Pressure-Bridgman-Grown CdZnTe. J. Appl. Phys. 2002, 92, 3198−3206. (6) Owens, A.; Bavdaz, M.; Brammertz, G.; Krumrey, M.; Martin, D.; Peacock, A.; Tröger, L. The Hard X-ray Response of HgI2. Nucl. Instrum. Methods Phys. Res., Sect. A 2002, 479, 535−547. (7) Zhu, X. H.; Wei, Z. R.; Jin, Y. R.; Xiang, A. P. Growth and Characterization of a PbI2 Single Crystal Used for Gamma Ray Detectors. Cryst. Res. Technol. 2007, 42, 456−459. (8) Saito, T.; Iwasaki, T.; Kurosawa, S.; Yoshikawa, A.; Den, T. BiI3 Single Crystal for Room-Temperature Gamma Ray Detectors. Nucl. Instrum. Methods Phys. Res., Sect. A 2016, 806, 395−400. (9) Owens, A.; Peacock, A. Compound Semiconductor Radiation Detectors. Nucl. Instrum. Methods Phys. Res., Sect. A 2004, 531, 18−37. (10) Johnsen, S.; Liu, Z.; Peters, J. A.; Song, J.-H.; Nguyen, S.; Malliakas, C. D.; Jin, H.; Freeman, A. J.; Wessels, B. W.; Kanatzidis, M. G. Thallium Chalcohalides for X-ray and γ-ray Detection. J. Am. Chem. Soc. 2011, 133, 10030−10033. (11) Kostina, S. S.; Peters, J. A.; Lin, W.; Chen, P.; Liu, Z.; Wang, P. L.; Kanatzidis, M. G.; Wessels, B. W. Photoluminescence Fatigue and Inhomogeneous Line Broadening in Semi-Insulating Tl6SeI4 Single Crystals. Semicond. Sci. Technol. 2016, 31, 065009. (12) Liu, Z.; Peters, J. A.; Sebastian, M.; Kanatzidis, M. G.; Im, J.; Freeman, A. J.; Wessels, B. W. Photo-Induced Current Transient Spectroscopy of Single Crystal Tl6I4Se. Semicond. Sci. Technol. 2014, 29, 115002.

(1)

C = 2 3 g (2π )3/2 kB2m*h−3

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S(T ) = I(t1) − I(t 2) = K ·ei(exp( −eit1) − exp(−eit 2))

⎛ e (T ) ⎞ E ln⎜ i 2 ⎟ = − a + ln(Cσi) ⎝ T ⎠ kBT

dependent conductivity, and persistent conductivity measurements (PDF)

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00336. Current−voltage graphs, temperature-dependent current and conductivity graphs, Arrhenius plots for temperature1543

DOI: 10.1021/acs.jpclett.7b00336 J. Phys. Chem. Lett. 2017, 8, 1538−1544

Letter

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DOI: 10.1021/acs.jpclett.7b00336 J. Phys. Chem. Lett. 2017, 8, 1538−1544