Charge Transport Mechanisms in a Pb2P2Se6 Semiconductor - ACS

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Charge Transport Mechanisms in PbPSe Semiconductor Svetlana S Kostina, Micah Hanson, Peng L. Wang, John A. Peters, David A. ValverdeChavez, Pice Chen, David G Cooke, Mercouri G. Kanatzidis, and Bruce W. Wessels ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00396 • Publication Date (Web): 29 Aug 2016 Downloaded from http://pubs.acs.org on September 5, 2016

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Charge Transport Mechanisms in Pb2P2Se6 Semiconductor Svetlana S. Kostina1, Micah P. Hanson1, Peng L. Wang2, John A. Peters1,3, David A. ValverdeChávez4, Pice Chen1, David G. Cooke4, Mercouri G. Kanatzidis1,2, and Bruce W. Wessels1 1

Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA

2

Department of Chemistry, Northwestern University, Evanston, IL, USA

3

Department of Chemistry and Physics, Chicago State University, Chicago, IL, USA

4

Department of Physics, McGill University, Montreal, QC, Canada

Abstract Charge transport in semi-insulating Pb2P2Se6 single crystals was investigated. The dark current was dominated by the ionization of deep level defects within the gap of the material, with activation energies between 0.6 eV and 0.8 eV. A model for charge transport was developed where a continuum of these mid-gap defect levels determined the conductivity of Pb2P2Se6. Current-voltage characteristics in Pb2P2Se6 single crystals showed non-linear behavior at high voltages. The non-linear characteristics are attributed to competing Poole-Frenkel emission and phonon-assisted tunneling processes, such that at lower fields the former effect dominates, while at higher electric fields the latter mechanism emerges. Calculated tunneling times in the 250-500 fs range indicate that the deep traps promote weak electron-phonon coupling, and that the tunneling involves deep defect levels. Transient multi-THz spectroscopy and temperature dependent photoconductivity measurements reveal signatures of dispersive transport and low mobility on the order of 10 cm2/Vs consistent with a disordered potential energy landscape in Pb2P2Se6. Photoresponse in these crystals is therefore limited by a distribution of trapping and recombination sites within the bandgap. Keywords: charge transport, deep levels, conductivity, transient spectroscopy, terahertz spectroscopy

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For Table of Contents Use Only Charge Transport Mechanisms in Pb2P2Se6 Semiconductor Svetlana S. Kostina1, Micah P. Hanson1, Peng L. Wang2, John A. Peters1,3, David A. ValverdeChávez4, Pice Chen1, David G. Cooke4, Mercouri G. Kanatzidis1,2, and Bruce W. Wessels1 1

Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA

2

Department of Chemistry, Northwestern University, Evanston, IL, USA

3

Department of Chemistry and Physics, Chicago State University, Chicago, IL, USA

4

Department of Physics, McGill University, Montreal, QC, Canada


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Recently, there has been considerable interest in identifying new low-cost, heavy element, chemical compounds as detector materials for room-temperature hard radiation detection.1-6 Although cadmium zinc telluride (CZT) is undeniably the leading candidate material, its widespread deployment is impeded by high cost as well as structural imperfections.7 Our group has recently been investigating suitable cost-effective alternatives by expanding the pool of potential detector materials to comprise heavy element semiconducting compounds incorporating light p-block elements, such as Cl, S, and P.8-10 Of particular interest is the heavy metal selenophosphate, Pb2P2Se6.11 This stoichiometric ternary compound is a highly resistive (ρ ~1011 Ω-cm) semiconducting material with an indirect band gap of 1.88 eV at 295 K. Pb2P2Se6 has an average atomic number (Z) of 39.8 and a high mass density of 6.14 g·cm-3, which result in a high attenuation coefficient for high energy radiation.12 In addition to its desirable bulk physical properties, Pb2P2Se6 is attractive as a detector material due to its potential for low cost. The three primary elements of Pb2P2Se6 are abundant and widely available, while their robust chemical and physical properties allow them to be easily extracted, isolated, and purified. As a single phase compound,11 Pb2P2Se6 promises less technological and engineering challenges in terms of crystal growth and scale-up development in comparison to the benchmark material CZT, a solid solution of CdTe and ZnTe.13 We have previously reported on its spectroscopic response to gamma radiation at room temperature.11,

14

The electron carrier mobility-lifetime

product of the Pb2P2Se6 was calculated to be 3.5x10-5 cm2 V-1.11 Despite the numerous advantages of using Pb2P2Se6 as a potential alternative to CZT,11, 14 its effectiveness as a room-temperature radiation detector depends on development of high purity material with good crystalline quality and minimal electronic defects. The crystalline quality was previously reflected in the photoluminescent (PL) properties, where high quality crystals of 3 ACS Paragon Plus Environment

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Pb2P2Se6 with good radiation response exhibit strong PL emission intensities centered at 1.52 eV, 1.62 eV, and 1.75 eV.14 Further improvements in its optoelectronic properties require detection and elimination of electrically active defects. One such defect is oxygen. First-principles density functional theory (DFT) calculations indicate that both interstitial and substitutional oxygen defects influence the electronic properties of Pb2P2Se6.14 Oxygen atoms can occupy four unique interstitial sites in the Pb2P2Se6 unit cell and lead to the formation of mid-gap defect states, as well as shallow acceptor states near the valence band maximum. The presence of electrically active native defects and impurities in Pb2P2Se6 single crystals are particularly important for detector applications because they influence conductivity and carrier mobility. Furthermore, they act as scattering and recombination centers as well as charge trapping centers,15 becoming a limiting factor with regard to radiation detection efficiency. The presence of mid-gap states impacts the electrical properties of semi-insulating crystals.16-18 Pb2P2Se6 crystals with secondary phase inclusions exhibited non-linear dark currentvoltage (I-V) characteristics,14 consistent with an electrical breakdown behavior under an applied bias. In contrast, crystals without secondary precipitates exhibited a higher breakdown voltage. Conduction mechanisms resulting in non-linear I-V characteristics could either be contactlimited or bulk-limited.19-23 Contact-limited conduction mechanisms include Schottky emission, Fowler-Nordheim tunneling, and direct tunneling.19-23 Bulk-limited conduction mechanisms include Poole-Frenkel emission (P-F), hopping conduction, space-charge limited conduction (SCLC), and phonon-assisted tunneling (PAT).19-23 In semiconductors that have a high concentration of deep level defects, the two leading mechanisms determining conduction are P-F and PAT.24-26 Band bending occurs as a result of an applied electric field, which in turn results in a reduction in the defect barrier height.27-28 The reduction in the barrier height is associated 4 ACS Paragon Plus Environment

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with an increased ionization rate of charge carriers.27 Emission of deep level defects over this potential barrier is due to the P-F mechanism and it occurs at intermediate electric fields.29-30 At higher applied fields a phonon assisted tunneling mechanism occurs due to a further increase in band bending, leading to additional barrier thinning such that carriers can tunnel through the potential barrier.31 P-F effect occurs for charged defects only, while the tunneling mechanism is possible for defects in all charge states. The aim of this work is to identify and characterize the charge transport mechanism in semi-insulating Pb2P2Se6 single crystals. We report on the nature of charge transport in these crystals using electrical and photoconductivity measurements and photo-induced current transient spectroscopy (PICTS). In addition, THz photoconductivity spectroscopy was carried out to provide additional insight into the nature of carrier dynamics in Pb2P2Se6 due to its sensitivity to the conductivity of the crystal. Transport measurements indicate that charge transport in Pb2P2Se6 is determined by the ionization of deep traps. Temperature dependent dark conductivity measurements revealed defect states with activation energies in the 0.6 - 0.8 eV range. From analysis of the I-V characteristics, the conduction mechanism was attributed to competing P-F effect and PAT. At lower fields P-F effect dominates, while at higher electric fields a competing PAT mechanism emerges. PICTS measurements identified two electrically active defect levels with ionization energies of 0.17 eV and 0.6 eV from the valence band, with capture cross sections of 1 × 10-21 cm2 and 3.5 × 10-12 cm2, respectively. Analysis of the THz spectroscopy measurements revealed a carrier mobility of ~10 cm2 V-1 s-1 that is attributed to dispersive transport, indicating that the photoresponse in Pb2P2Se6 is being limited by a distribution of trapping and recombination sites within the crystal.


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Results 1. I-V characteristics Radiation detection requires the device to operate at high bias with minimal dark current and demonstrate high sensitivity to hard radiation. In order to assess the sample quality of Pb2P2Se6, its I-V behavior was examined at room temperature. Typical I-V plots for a lower quality and a higher quality Pb2P2Se6 single crystal as determined by transparency of the sample, response to gamma radiation, and PL properties14 are shown in Fig. 1a and Fig. 1b, respectively. The samples are highly resistive (1010-1012 Ω⋅cm). At low fields the current is linearly dependent on voltage but at high fields the I-V plots were non-linear. The onset of non-linear behavior varied among samples, such that the non-linear region for a lower quality sample occurs at lower fields than that for a higher quality sample. The resistivity measured in the linear region of the plots is 1.5×1012 and 3×1010 Ω⋅cm for samples 5 and 6, respectively. The differences in quality of samples is also reflected in their differences in photo-response, such that the measured difference between photo and dark conductivity is ∆σph = 1.7×10-9 and 1.8×10-10 S⋅cm-1 for samples 5 and 6, respectively, under positive bias. The plot of photocurrent vs voltage under 50 mW, 405 nm laser radiation for 6, shows nonlinear behavior similar to the dark current measurement (Fig. 1a). Since the high voltage is applied to the top contact (Fig. 1), the photocurrent is limited by the transport of holes under positive applied bias and electrons under negative bias. A summary of resistivity and photo-response for Pb2P2Se6 samples used in this work is given in Table 1.


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Figure 1. (a) I-V curve for Pb2P2Se6 sample 6, measured at room temperature in the dark (●) and under 50 mW, 405 nm laser irradiation (○). (b) I-V curve for sample 5, measured at room temperature in the dark (●) and under 50 mW, 405 nm laser irradiation (○). (c) Energy diagram depicting mechanisms of emission of charge from a trapping center in an electric field (only donor level is considered for simplicity). The Poole-Frenkel (PF) emission and phonon-assisted tunneling (PAT) are shown, where ΦB is the ionization energy.

The non-linearity of the dark I-V plots for Pb2P2Se6 indicates that at higher electric fields the ionization of carriers from traps is increased. The two main processes that enhance the rate of carrier emission from trapping centers in semiconductors are Poole-Frenkel (PF) effect and phonon-assisted tunneling (PAT) (Fig. 1c).24,

28-29, 32-33

The main requirement for these

mechanisms to occur is the presence of electrically active donors or acceptors in the band gap. The PF effect is dominant at intermediate electric fields where carrier tunneling does not play a significant role and carrier ionization is controlled by thermal emission over the barrier. The PF mechanism is characterized by an increase in conductivity (σ) due to barrier lowering as a result of the applied field (E) according to19

 − q(Φ B − qE /(πε ) )  ,  k T B  

σ = qµN C exp

(1)


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where ΦB is the barrier height, ε is the dielectric constant, q is the elementary charge of electron, µ is the carrier mobility, and NC is the density of states in the conduction (valence) band. The physical basis of the classical, one-dimensional Poole-Frenkel model given by Eq. 1 is very simplified, and is typically used as an order-of-magnitude approximation for barrier heights.24, 29, 34

In addition to the enhancement of the emission due to PF mechanism, the applied field induces tilting of the bands leading to an increase in tunneling probability of charge through the thin tunneling barrier (PAT). The PAT mechanism results in a conductivity that depends exponentially on E2 according to24, 30

 (qE ) 2 τ T 3  ,  3 m * h  

σ ∝ exp

(2)

where ћ is the reduced Planck constant, and the tunneling time τT is given by

τT =

h ±τT 2 . 2 k BT

(3)

The value of the tunneling time in Eq. 3 is increased or decreased from ћ/2kBT by τT2 depending on the nature of traps in the material i.e. substitutional impurities or autolocalized centers such as self-trapped DX- centers, respectively.35-37 PF and PAT are two competing mechanisms of emission from charged impurities (Fig. 1), therefore the electric-field dependence of conductivity generally cannot be fitted using only one of these processes. Eqs. 1 and 2 indicate that to differentiate between the two mechanisms the dependence of ln(σ) on E1/2 and E2 should be compared.24 Since Schottky emission over a contact is also expected to show a linear dependence of ln(σ) on E1/2, care must be taken in ascribing the appropriate mechanism for the observed I-V behavior to only PF or PAT.22-23 8 ACS Paragon Plus Environment

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To determine whether either the PF or PAT mechanism is responsible for the curved I-V plot observed for sample 6, the plots of ln(σ) vs E1/2 and ln(σ) vs E2 were examined. The PF plot of Fig. 2a indicates that at lower electric field ln(σ) depends linearly on E1/2 indicating that the PF mechanism is dominant. Higher electric field results in sufficient band bending for PAT mechanism to become dominant. In this case, ln (σ) depends linearly on E2 (Fig. 2b). The same analysis was done for several Pb2P2Se6 samples (Fig. 2c and d). All samples indicated the presence of the PF effect, indicated by the linear dependence of ln (σ) on E1/2. A few samples deviated from the PF dependence at higher electric fields. In these cases, at higher fields the ln(σ) depends linearly on E2 indicating that PAT mechanism becomes dominant. Both plots show a notable spread of the data, which could be caused by the slight differences in the growth procedures in different batches of crystal growth. Assuming the effective mass of majority carriers in the 0.3 mo - 0.8 mo range,38 the barrier heights were calculated using the P-F expression of Eq. 1 (Table 1). The errors in these values reflect the uncertainty in the effective mass, indicating that a 0.5m variation in the m* value does not change the energy level significantly. The results are separated into two groups, where the majority of samples give ΦB barrier heights in the 0.7-0.8 eV range, while in some others it is ~0.18 eV. The differences may be due to the fact that the crystals were cut from different regions along the ingot, which could result in variation in the quality of samples and in defects with different origins and densities. Although the P-F mechanism fits the I-V data for Pb2P2Se6 reasonably well, the required dielectric constants are unphysical in most cases. Analysis of the data using Schottky emission equation also suffers from the same issue. Linear fitting of the data in Fig. 2d according to Eq. 2 gives the tunneling times in the 0.25-0.45 ps range. These longer tunneling times indicate weak electron-phonon coupling facilitated by substitutional impurities.30, 39 9 ACS Paragon Plus Environment

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Figure 2. (a) a plot of ln(σ) vs E1/2 and (b) a plot of ln(σ) vs E2 for sample 6. (b) A plot of ln(σ) vs E1/2 for Pb2P2Se6 samples at lower voltages where the I-V curves deviate from linearity; (c) A plot of ln(σ) vs E2 for Pb2P2Se6 samples at higher voltages where the plot of ln(σ) vs E1/2 becomes superlinear. Solid lines indicate linear fitting of the data. Only negative bias regions where electrons dominate transport are shown for clarity (see SI for forward bias regions). Table 1. Resistivity, photoconductivity response, the P-F barrier heights, and sample thickness for the Pb2P2Se6 samples measured under positive and negative bias sample #

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

ρ (+) 1010 Ω⋅cm

ρ (-) 1010 Ω⋅cm

∆σph (+) 10-10 S cm-1

∆σph (-) 10-10 S cm-1

ΦB (+) eV

ΦB (-) eV

410 8.7 4.1 2.1 150 3.1 0.05 20 280 23 44 28 270 0.32 0.92 2.8

510 20 3.4 7.0 43 2.0 0.27 12 35 22 49 21 450 0.81 0.75 3.8

0.021 0.067 0.82 1.4 17 1.8 79 0.26 0.81 0.090 0.046 0.038 0.79 5.0 1.4 1.4

0.020 0.15 0.33 0.68 8.2 1.8 38 0.32 1.0 0.073 0.030 0.018 2.2 5.1 0.68 1.6

0.18 ± 0.02 0.74 ± 0.02 0.88 ± 0.02 0.69 ± 0.02 0.83 ± 0.02 0.73 ± 0.02 0.66 ± 0.02 0.76 ± 0.02 0.82 ± 0.02 0.18 ± 0.02 0.18 ± 0.02 0.83 ± 0.02 0.18 ± 0.02 0.64 ± 0.02 0.69 ± 0.02 0.73 ± 0.02

0.18 ± 0.01 0.79 ± 0.02 0.87 ± 0.02 0.73 ± 0.02 0.88 ± 0.02 0.72 ± 0.02 0.75 ± 0.02 0.76 ± 0.02 0.76 ± 0.02 0.18 ± 0.02 0.18 ± 0.02 0.86 ± 0.02 0.85 ± 0.02 0.68 ± 0.02 0.68 ± 0.02 0.73 ± 0.02

Sample thickness (mm) 1 1 1 0.6 0.4 0.43 0.32 0.32 0.4 0.71 0.67 0.76 0.22 0.71 0.71 0.71


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2. Temperature dependence of dark conductivity (ID-T) Given that a high density of deep traps is required to support P-F and PAT mechanisms, we examined the temperature dependence on dark conductivity in Pb2P2Se6. Temperature dependent conductivity measurements were performed on four Pb2P2Se6 samples in order to further probe the charge transport properties and its dependence on defects indicated by the I-V characteristics. A plot of dark conductivity (σD) vs T indicates that σD increases exponentially with increasing temperature above 275 K (Fig. 3a), while below 275 K it is relatively unchanged and near the measurement limit. Dark conductivity σD is described by an Arrhenius equation40

= ,

(4)

where σ0 is a prefactor and Ea is an activation energy for conduction. The activation energy can be extracted from the slope of the plot of ln(σD) vs 1/kT. This first order approximation assumes that an exponential temperature dependence of carrier density dominates the power-law dependence of the mobility and density of states in the term over the measured temperature range.40 Plots of ln(σD) vs 1/kT for the four Pb2P2Se6 samples were linear in each case (Fig. 3b). Analysis of the conductivity data yielded activation energies from 0.6 to 0.8 eV (Table 2). These activation energies are in good agreement with those extracted from the P-F analysis in Table 1 in each case. The I-V plot for sample 13 was asymmetrical, resulting in different resistivity and photo-response values under positive and negative applied bias. Consequently, the P-F ionization energies are different at each bias, such that levels at 0.18 eV and 0.85 eV were observed under positive and negative bias, respectively. The temperature dependence on conductivity for this sample was measured and the ionization energy of Ea = 0.84 eV was calculated under negative bias, in excellent agreement with the value of 0.85 eV measured from I-V characteristics. 11 ACS Paragon Plus Environment

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Figure 3. (a) Plot of dark conductivity σ vs T for four Pb2P2Se6 devices. The applied voltage is listed in Table 2 for each sample. (b) Plot of ln(σ) vs 1/kT. Table 2. Calculated parameters from ID-T Arrhenius plots for Pb2P2Se6 samples Sample # EA(eV) Applied bias (V) a -150 5 0.67 ± 0.03 b (0.6 ± 0.1) -200 13 0.83 ± 0.05c -50 12 0.70 ± 0.04 -50 16 0.64 ± 0.03 a

average of two independent measurements; b energy level from PICTS experiment; c average of four independent measurements

Considering the results obtained from I-V and ID-T analysis, the dispersion in activation energies among samples implies that there is a band of defect levels in the 0.64 to 0.88 eV range contributing to the conduction. This suggests the position of the Fermi level determines which level is involved in charge transport.40 The Fermi level is determined by the degree of compensation between donor and acceptor states.


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3. Photo-induced current transient spectroscopy (PICTS) Deep level spectroscopy was carried out in order to further probe the properties of deep level defects in Pb2P2Se6. PICTS spectra of sample 5 was collected in the 80 - 324 K temperature range under positive and negative bias applied to the top contact. While no peaks were observed in the PICTS signal under negative bias, several peaks were obtained under positive bias where hole conduction prevails. The spectrum revealed the existence of at least two deep levels in the 140 - 320 K range labeled A and B, while no signals were observed in the 80 - 140 K range (Fig. 4a). The spectrum also shows that peak B closely overlaps with another higher temperature peak, indicating the presence of a least one more level. However, the temperature limitations of our cryostat (max. 325 K) precludes detailed analysis of the peak at higher temperature. The Arrhenius plots reveal that the two levels have activation energies of 0.6 ± 0.1 (trap A) and 0.17 ± 0.02 eV (trap B) above the valence band, with capture cross sections (σi) of (3.5 ± 0.8) × 10-12 and (1 ± 4) × 10-21 cm2, respectively (Fig. 4b). These activation energies are in excellent agreement with energies obtained from the PF effect analysis as well as temperature dependence on conductivity. The large capture cross section σi of trap A indicates a strong coulombic attraction between the trap and the carrier, while the small value for σi for trap B is indicative of coulombic repulsion.40 Therefore, the carrier lifetime in Pb2P2Se6 is likely determined by trap A due to its large σi value. For trap B, the strong temperature dependence and the low value of σi (Fig. 4b) suggest that thermal excitation of carriers over the repulsive barrier is required, as opposed to thermally assisted tunneling through a repulsive barrier where a larger σi and smaller temperature dependence are expected.40


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Figure 4. (a) PICTS spectra for Pb2P2Se6 sample 1 between 140 and 320 K, under +225 V applied bias to the illuminated contact (shifted waterfall plot). Time t1 was chosen at (-●-) 2.5 ms, (-○-) 5.5 ms, (-●-) 7 ms, and (-○-) 10 ms, and t2/t1 = 2. The inset shows photo-induced current transient profiles recorded at different temperatures. (b) Arrhenius plots of ln(ei/T2) vs 1000/T for the observed defects; solid lines are the linear analysis of the data.

4. Temperature dependence of the photocurrent (IPh-T) Temperature dependent photoconductivity (PC) of four Pb2P2Se6 samples was measured using a 50 mW, 405 nm laser as the excitation source to determine the mechanisms by which defects may be limiting the photoconductive transport in Pb2P2Se6. Measurements were carried out over the 80 - 324 K range under a -150 V bias applied to the top contact, such that electrons are collected. The photoconductivity was highly temperature dependent, varying as much as two to three orders of magnitude over the given temperature range. Upon increasing the temperature from 80 to 324 K, the photocurrent initially decreases reaching a minimum around 150 K, then increases with a further increase in temperature for all samples (Fig. 5). Sample 5 had the highest photo-response and showed a strong temperature dependence of photoconductivity from 80 K to 130 K. In contrast, sample 12 with the lowest photoresponse showed minimal increase in σph at low temperature (Fig. 5). 14 ACS Paragon Plus Environment

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Figure

5.

Photoconductivity

vs

temperature at -150V for 4 samples of Pb2P2Se6 only one of which (5) showed an increase in conductivity at 80K larger than its room temperature conductivity.

The PC in Pb2P2Se6 was measured under negative bias conditions such that the photocurrent is limited by the electron transport. The sample thickness (>300 µm) is much greater than the expected optical absorption length at 405 nm. As a result, most of the electronhole pairs are generated in a region nearest the top contact. When the top contact is under -150 V, holes are drawn to the nearby top contact and the photocurrent is limited by the transport of the electrons across the thickness of the sample to the positive contact (see Fig. 1). The resulting change in conductivity under laser illumination (∆ is given by: ∆ = ∆

(5)

where is the electron charge, is the electron mobility. The change in electron density, ∆ , is given by ∆ =

(6)

where is the generation rate of electron-hole pairs and is the electron lifetime. Therefore, the change in photoconductivity as a function of temperature is: ∆ =

(7) 15

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In order to determine which term in Eq. 7 is most temperature dependent we examined the temperature dependence of each term. The generation rate of electron-hole pairs for a given power density and incident photon energy is dependent on the / temperature dependence of the density of states (DOS).27 However, since above-gap light is used for excitation at all temperatures, and our sample thickness is much greater than the expected penetration depth, all of the incident photons not reflected are absorbed in the sample. The generation rate for the full thickness of the sample can be assumed to be constant over the temperature range measured. The lifetime term, , in Eq. 7 is limited by the various recombination processes within the semiconductor: intrinsic recombination, Shockley-Read-Hall (SRH) recombination, and Auger recombination.41 The effective lifetime can be approximated using Matthiessen's Rule to give:

!"#

= +

+

(8)

$%&

where is the intrinsic lifetime, '() is the lifetime limited by SRH, and *+, is the Auger recombination lifetime. Since the Pb2P2Se6 samples are highly resistive and contain a large concentration of midgap states, the lifetime is likely dominated by the SRH recombination. SRH recombination is particularly effective for traps with energy of Eg/2. In this case the temperature dependence of lifetime increases with increasing temperature according to41-43 - = - + .'() /0 1

3 0

2

(9)

where .'() is the SRH coefficient, /0 is the trap concentration, and the exponent α is a positive number. 16 ACS Paragon Plus Environment

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The effective lifetime in Eq. 8 is determined by the term with the shortest lifetime. The Auger term is inversely proportional to temperature. If the effective lifetime is limited by the Auger recombination, a similar trend is expected in the and ∆ terms. However, the trend of photoconductivity vs temperature for Pb2P2Se6 samples is reversed, where an increase in temperature results in an enhancement of ∆ (Fig. 5). In addition, the Auger process dominates only under high doping concentrations and temperatures. Therefore, our results indicate that Auger recombination is not the dominating mechanism over the measured temperature range for our samples.

Figure 6. Simulated plots showing the qualitative

temperature

dependence

of

different scattering processes limiting the mobility in equation 11. (a) Mobility limited by acoustic phonon scattering; (b) mobility limited by ionized impurity concentration.

For most semiconductors, the presence of acoustic phonons and ionized impurities greatly influences the temperature dependence of carrier mobility .27 For pure materials, mobility increases with decreasing temperature and effective mass, i.e. µ ~ (m*)-5/2 T-3/2, due to a reduction in acoustic phonon scattering (Fig. 6a). When ionized impurity scattering is present, mobility increases with increasing temperature, i.e. µ ~ (m*)-1/2 Ni-1T3/2 (Figure 7 b). At higher 17 ACS Paragon Plus Environment

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impurity concentrations, impurity scattering suppresses mobility.44 This mechanism counters the mobility gain due to reduced phonon scattering and flattens out the temperature dependence of the mobility in highly doped or imperfect semiconductors.41, 45 As a result, a strong enhancement in photocurrent with decreasing temperature is expected for samples with low defect concentrations where the mobility is primarily limited by phonon scattering (Fig. 6). From the Iph-T dependence for the four samples of Pb2P2Se6, the largest enhancement in photocurrent with decreasing temperature is observed from 120 K to 80 K in sample 5 (Fig. 5). This sample also had the largest photoresponse of more than 8×10-10 S⋅cm-1 at room temperature (Table 1). Considering the effect of defects on mobility at low temperatures (Fig. 6), the results of Fig. 5 suggest a lower concentration of defects in sample 5 in comparison to the other samples.

5. THz Spectroscopy THz spectroscopy measurements were performed to determine the temporal dynamics of the photo-excited carriers in Pb2P2Se6 (17). Sample 1 from the same ingot showed a low photoresponse of ~2×10-8 S-cm (Table 1). We therefore expect the scattering mechanisms that limit the photoresponse of other Pb2P2Se6 samples to be also strongly present in 17. The THz waveform reflected from the surface of 17 was measured in an unexcited sample (45 6) and compared with the waveform reflected after a pump pulse excited the sample. Measurements of these wave forms can be found in the supplemental material. The change in the THz waveform induced by the presence of the pump pulse (74 was found to reach a maximum at ~ 300 fs, indicating that by this time the photoconductivity is fully developed. The complex differential reflectance vs THz frequency (f) is shown in Fig. 7a, recorded at = 300 fs, shows multiple 18 ACS Paragon Plus Environment

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resonant features due to charge carrier induced screening of optically active phonons with frequencies at 3.2, 5.5, 8.8 and 13.8 THz. These features are in fair agreement with previously reported infrared (IR) active Bu phonons (molecular vibrational frequency in a C2h symmetry group) in Pb2P2Se6 located at 4.0, 5.0, 8.6, 13.3 THz.46 In addition, the range of tunneling times determined by the PAT mechanism is on the same order as the strong THz phonons (ωvib) observed in Fig. 7a. The tunneling time is given by

0 = :

; 1010 Ω). Charge transport measurements In a typical measurement of I-V characteristics, the applied voltage was swept from 0 V to 300 V using a high voltage power supply (PS300, Stanford Research Systems) and a current 25 ACS Paragon Plus Environment

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meter (Model 2636A, Keithley) measured the current with a dwell time of 10-15 sec. Photoconductivity (σP) was measured by using a CW 405 nm laser source for excitation (50 mW, 1.2 mm laser spot diameter). The high voltage was applied to the top contact, such that positive bias constitutes hole transport configuration. For temperature dependent conductivity measurements in the dark (ID-T), the sample is placed in a liquid nitrogen cryostat. A schematic diagram of sample is shown in Fig. 9. The sample was mounted on a thermally conductive sapphire substrate using colloidal silver paint, such that the largest possible area of the crystal was in contact with the substrate for best thermal contact. For temperature dependent photoconductivity (IPh-T) measurements, the 405 nm line from a CW semiconductor diode laser (Excelsior One-405, Spectra-Physics) was used with the incident beam diameter of 1.2 mm and power of 50 mW. The applied voltage was constant and the temperature was swept from 80 K to 320 K in increments of 2 K. A dwell time of 30 seconds was used so that the temperature reached the set point before the current was recorded. Figure 9. Schematic of sample mounting for PICTS

and

temperature-dependent

conductivity measurements. The laser passed through an optically transparent cryostat window prior to reaching the sample (not shown).

Photoinduced Current Transient Spectroscopy (PICTS) PICTS spectroscopy is used for detection of deep acceptor and donor levels in highresistivity bulk materials and determination of their parameters.56-62 These defect states are identified by their electronic signatures, i.e. charge state,63 ionization energy,64-65 and capture 26 ACS Paragon Plus Environment

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cross section.65 The measurement involves measuring photocurrent upon filling the traps by photoexcitation of carriers, followed by their thermal ionization. The sample is kept under constant bias, such that a positive bias injects only holes and negative bias injects only electrons. The samples were mounted in a manner similar to that used for dark conductivity (ID-T) and photoconductivity (IPh-T) measurements (Fig. 9). A detailed description of our PICTS setup is given elsewhere.66-67 A semiconductor diode laser (OBIS 405 nm LX 100 mW, rise and fall time ~2 ns) was pulsed using a pulse generator, such that the laser was on for 5 ms and off for 30 ms. The transient current signal passed through a 50-Ω resistor and amplified using a high gain current amplifier (Keithley 428). The amplifier output was then fed into an oscilloscope and its output read by a computer. Transient current signal was measured every 2 degrees over the temperature range 80-320 K, with 30 second interval between each step. Thermal activation energies and the capture cross sections were extracted by analyzing the data using double-gate PICTS method,56 where the normalized PICTS signal S(T) is given by

S(T ) = I (t1) − I (t2 ) = K ⋅ ei (exp(− eit1 ) − exp(− eit2 )) ,

(15)

where t1 and t2 are the 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 E  e (T )  ln  i 2  = − a + ln (Cσ i ) , k BT  T 

(16)

where kB is the Boltzmann constant and the constant C is given by68-69

C = 2 3g (2π ) 3 / 2 k B2 m * h −3 ,

(17)

where g is the band degeneracy factor, m* is the effective mass for hole (or electron) carriers, and h is the Planck’s constant. Assuming the effective masses for holes and electrons in Pb2P2Se6 27 ACS Paragon Plus Environment

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are in the 0.3mo - 0.8mo range,38 and the degeneracy factor is one, the activation energy and capture cross section can be calculated. According to Eq. 16, the values of σi and Ea are obtained from the slope and intercept of a plot of ln(ei/T2) vs 1/T, respectively. The temperature T corresponds to the temperature at which the maximum PICTS signal S(T) is obtained.

Terahertz Spectroscopy Pulses of 40 fs duration from a Ti:sapphire regenerative laser amplifier were used to generate phase stable terahertz (THz) pulses in dry air from a two color laser plasma.70-71 The THz pulse electric field was detected in an air-biased coherent detection (ABCD) scheme with 25 THz bandwidth and 40 fs temporal resolution.48 An ultra-broadband THz pulse was incident on the sample in reflection mode, and the full time-domain profile of the THz pulse was recorded. A second femtosecond pump pulse with wavelength of 560 nm (2.21 eV in energy) colinear with the incident THz field was used to photoexcite the sample at different pump-probe delay times (τp) with respect to the time of arrival of the THz pulse. The pump-induced change in the reflected THz electric field waveform, 74[6, ], at a given pump-probe delay time is given by 74[6, ] = 4 +L [6, ] F 45 6,

(18)

where 4 +L [6, ] is the electric field of the reflected THz pulse in the presence of the pump pulse, and 45 6 is the reference THz waveform in the absence of optical pumping. The complex differential reflectance 7D̃ [C, ]/D̃ is defined in terms of the spectral amplitude and phase of the respective Fourier transformed fields 74^ [C, ] and 4^5 C: _5̃ [:,` ] 5̃

=

_@^ [:,` ] @^a :

(19) 28

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where D̃ = 1 F BC/1 + BC is the reflection coefficient of the unexcited sample with BC being the frequency dependent index of refraction in the dark state. Information on the subpicosecond THz photoconductivity B[C, ] of the sample after excitation at delay can be extracted from the differential reflectance 7D̃ [C, ] spectra by assuming a thin photoconductive film on a semi-insulating substrate:72 _5̃ [:,` ] 5̃

=F

X5̃

c [:,` ] Z Sb

,

c [:,` ] 5̃ XYB:XZ Sb

(20)

where d is the impedance of free space and d is the pump pulse penetration depth. The peak change in conductivity can be estimated from Eq. 20. These measurements were performed at room temperature in a dry air purge gas environment.

Acknowledgements: This work was supported by the Department of Homeland Security ARI program with Grant No. 2014-DN-077-ARI086-01. 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. D.C. gratefully acknowledges financial contributions from NSERC, FRQNT, MDEIE and CFI. Supporting Information Available: Plots of ln(σ) vs E1/2 and ln(σ) vs E2 under positive applied bias, ln(I) vs 1/kT, differential reflection of the peak of the THz pulse as a function of pump-probe delay time, the time evolution of the differential reflected THz signal, and fits to a power law decay as a function of pump fluence. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.XXXXXXX.


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