In this paper, the properties of point defects in Cd1−xZnxTe1−ySey (CZTS) radiation detectors are characterized using deep-level transient spectroscopy and compared between materials grown using two different methods, the Bridgman method and the traveling heater method. The nature of the traps was analyzed in terms of their capture cross-sections and trap concentrations, as well as their effects on the measured charge-carrier trapping and de-trapping times, and then compared for the two growth techniques. The results revealed that Se addition to CdZnTe can reduce the VCd− concentration. In Travelling Heater Method (THM) and Bridgman Method (BM) grown CZTS detectors, besides a few similarities in the shallow and medium energy traps, there were major differences in the deep traps. It was observed that the excess-Te and lower growth-temperature conditions in THM-grown CZTS led to a complete compensation of VCd− and two additional traps (attributed to Tei− and TeCd++ appearing at around Ev + 0.26 eV and Ec − 0.78 eV, respectively). The 1.1-eV deep trap related to large Te secondary phases was a dominant trap in the BM-grown CZTS crystals. In addition to i-DLTS data, the effects of point defects induced due to different processing techniques on the detector's resistivity, spectral response to gammas, and μτ product were determined.
I. INTRODUCTION
For decades, researchers have investigated means to improve the crystal quality of CdTe and its alloys for use in room-temperature (RT) radiation detectors for applications in nonproliferation, national security, medical imaging, and space imaging, in addition to interest in semiconductor and optoelectronic technologies.1–3 CdTe and its alloys with Zn (CdZnTe or CZT) have been effectively used for detectors, sensors, and substrates for infrared imaging applications, but there are still some drawbacks of the material that have been difficult to fully overcome.4 Most of the issues arise from the melt-growth techniques used for the synthesis of large, nearly single crystals. For CdTe-based alloys incorporating Zn, which are advantageous for increasing the band-gap of room-temperature detectors, obtaining desirable crystal uniformity is complicated by a significant variation in the Zn concentration along the ingot growth direction due to the segregation coefficient of Zn in the CdTe matrix being greater than 1. In addition, CZT growth by melt solidification causes various types of extended defects to form, such as stacking faults, twins, dislocations, and sub-grain boundaries and their networks.5 To achieve the required high resistivity for room-temperature detector applications, crystals are grown under a Te-rich atmosphere, which can cause the generation of Te-rich secondary phases (TeSP), especially Te inclusions, during the crystal growth. These secondary phases affect the quality, uniformity, and performance of the detectors to various degrees, depending on their concentration and size.6 Furthermore, point defects at the microscopic level control the resistivity of the material and the performance of the detectors by inducing deep traps, which play an important role as trapping and recombination centers for the charge carriers.7
To obtain a high yield of a high-quality material, the control of defects in CdTe and its alloys must be addressed. One common approach is to employ new or modified crystal-growth and purification techniques. Another option is to modify the chemical composition of CdTe and its alloys, particularly by adding new dopants and/or additional alloy constituents. Due to the widespread drive for detector improvements, crystal growers, researchers, and vendors have searched for alternative materials having fewer microscopic and macroscopic defects compared to CZT, in addition to taking steps to improve the processes used to grow and purify CZT. Several related alternative materials have been investigated, including CdMnTe,8 CdTeSe,9,10 and CdMgTe.11 Recently, Se was added to CZT to achieve improved crystallinity of CdZnTeSe crystals and comparable electron lifetimes compared to CZT. In this research, the focus is on the point defects induced in the CdZnTeSe crystalline material grown by two different techniques, the Bridgman Method (BM) and the Travelling Heater Method (THM).
II. EXPERIMENTAL DETAILS
In this research, we investigated two sets of detectors: In-doped high resistivity Cd1−xZnxTe1−ySey (CZTS) grown by the BM and by the THM. The BM-grown detector (CZTS:BM) contains 2% Se with a composition of Cd0.9Zn0.1Te0.98Se0.02, while the THM-grown sample (CZTS:THM) contains 7% Se with a composition of Cd0.9Zn0.1Te0.93Se0.07. The growth temperature for the THM method was about 850 °C, while, for BM growth, the temperature was raised about 20 °C above the melting point of CZT (∼1120 °C), and then the ampoule was lowered for solidification. One of the main differences in the growth of these two types of crystals was the additional Te-rich conditions and lower growth temperature in the case of CZTS:THM. The CZTS crystals used for this research were grown at the Brookhaven National Laboratory. The crystallinity of the CZTS was better than that of CZT crystals, and there were less detrimental defects due to a reduction of sub-grain boundaries and their networks and a reduced concentration of Te-rich secondary phases. In addition, the compositional homogeneity of Zn was better than that of for CZT, and the Se composition of the CZTS was highly uniform. The details of the crystal growth process will be published later.
Planar detectors were made by fabricating Au contacts on two opposing planar sides using an electroless technique. The dimensions of the detectors are reported in Table I. The resistivity of the detectors was determined from I-V measurements, which helped to define the electrical parameters and the temperature range for the photo-induced current deep-level transient spectroscopy (iDLTS) experiments used to characterize the point defects. The spectral response was tested using an 241Am standard source. The mobility-lifetime (μτ) products were measured from the charge-collection data at different applied biases for the two detectors followed by fitting to the Hecht equation.
Detector specifications, structural, and electrical transport properties.
Detector . | Dimensions l × w × t (mm3) . | Average concentration of TeSP (cm−3) . | Size of dominant TeSP (μm) . | Resistivity (Ω cm) . | γ-ray response . | μτe cm2/V s . |
---|---|---|---|---|---|---|
Cd0.9Zn0.1Te0.98Se0.02 (BM) | 5.5 × 5.1 × 3.7 | 8 × 104 | 0–30 | 1 × 1010 | No | … |
Cd0.9Zn0.1Te0.93Se0.07 (THM) | 5.0 × 4.2 × 2.3 | 3 × 105 | 0–10 | 2 × 109 | Yes | 1–2 × 10−3 |
Cd0.9Zn0.1Te (BM) | 3.6 × 3.3 × 1.1 | … | … | 9 × 109 | Yes | 0.4 × 10−3 |
Cd0.9Zn0.1Te (THM) | 9.5 × 9.6 × 1.8 | … | … | 1 × 1010 | Yes | 1 × 10−3 |
Detector . | Dimensions l × w × t (mm3) . | Average concentration of TeSP (cm−3) . | Size of dominant TeSP (μm) . | Resistivity (Ω cm) . | γ-ray response . | μτe cm2/V s . |
---|---|---|---|---|---|---|
Cd0.9Zn0.1Te0.98Se0.02 (BM) | 5.5 × 5.1 × 3.7 | 8 × 104 | 0–30 | 1 × 1010 | No | … |
Cd0.9Zn0.1Te0.93Se0.07 (THM) | 5.0 × 4.2 × 2.3 | 3 × 105 | 0–10 | 2 × 109 | Yes | 1–2 × 10−3 |
Cd0.9Zn0.1Te (BM) | 3.6 × 3.3 × 1.1 | … | … | 9 × 109 | Yes | 0.4 × 10−3 |
Cd0.9Zn0.1Te (THM) | 9.5 × 9.6 × 1.8 | … | … | 1 × 1010 | Yes | 1 × 10−3 |
The details of the iDLTS system and the experimental and analytical procedures are described elsewhere by Gul et al.12 An improved illumination set-up using an 850-nm diode laser with the optimized power and better alignment with a laser spot of about 1 mm was used for the filling of traps. The laser pulse parameters were 2-mm width and 1-s period with a 10-ns pulse rise time. The use of a 1-s period is beneficial for collecting more of the long tail of the transient current due to slow de-trapping from some of the deep traps.
To obtain good statistical data, iDLTS experiments were run four times for each sample, including a first run from 10 to 300 K (RT-run) and then three runs from 10 to 400 K (above RT-run). The first two runs helped in evaluating the changes due to the above-RT heating (up to 400 K) on the shallow traps (<100 K). The values for energy levels and capture cross-sections for the traps were calculated based on average values obtained from all the four runs.
This research focuses on the differences and similarities in the nature of the traps induced in CZTS crystals due to the two different growth techniques and the corresponding concentrations of these traps. Point defects and their effects on the charge carrier lifetimes were evaluated by measuring the trapping and de-trapping times. In addition, the effects of point defects induced by the two growth techniques on the resistivity, spectral response to gammas, and μτ product were investigated.
In addition to CZTS detectors, two In-doped CZT BM and THM detectors were characterized for point defects. The additional data helped to understand growth-related point defects for the two methods and the effects associated with the addition of Se to BM- and THM-grown CZT detectors.
III. RESULTS AND DISCUSSION
A. Properties and detector response
The data for resistivity, spectral response to incident 241Am gamma-rays, and the μτ product for two detectors are listed in Table I. The CZTS:BM detector shows one order of magnitude higher resistivity (1 × 1010 Ω cm) than the CZTS:THM (∼2 × 109 Ω cm) detector, but despite the higher resistivity, the CZTS:BM detector showed no photocurrent response to white light or to gammas. On the other hand, the CZTS:THM detectors, even with their lower resistivity, showed a gamma response from which it was possible to extract a μτ-product value of ∼1–2 × 10−3 cm2/V s. Infrared microscopy was used to examine the Te secondary phases in the two detectors. The concentration of large Te secondary-phase particles (diameters between 10 and 25 μm) in CZTS:THM was between 102 and 103 cm−3, while in CZTS:BM, it was an order of magnitude larger (i.e., 103–104 cm−3). The density of Te secondary phase particles sized below 10 μm in CZTS:THM detectors (∼105 cm−3) was ∼1 order of magnitude higher than in the CZTS:BM. The comparison of structural, defect, and electrical transport properties shown in Table I suggests that the electron μτ product and the lifetime are mainly correlated with the larger Te secondary-phase particles with size >10 μm.
B. Point defects in detectors
iDLTS data for the two CZTS detectors are plotted in Figures 1–5. There were a few similarities as well as some differences in the types and nature of the point defects. The identified traps in the two detectors are listed in Table II. The details of the defect levels (Et, shown in Figs. 1 and 2), their densities (Nt, shown in Fig. 3), and their capture cross-sections (σ, shown in Fig. 4) in the two differently grown CZTS detectors are described in Secs. III B 1 and III B 2:
iDLTS plots showing point defects for two different time windows with a 2-ms pulse width at 1-V applied bias for: (a) CZTS:BM and (b) CZTS:THM. Arrhenius plots are shown in the insets.
iDLTS plots showing point defects for two different time windows with a 2-ms pulse width at 1-V applied bias for: (a) CZTS:BM and (b) CZTS:THM. Arrhenius plots are shown in the insets.
iDLTS plots showing point defects for two different time windows with a 2-ms pulse width at 1-V applied bias for: (a) CZT:BM and (b) CZT:THM.
iDLTS plots showing point defects for two different time windows with a 2-ms pulse width at 1-V applied bias for: (a) CZT:BM and (b) CZT:THM.
Comparison of the densities of point defects in: (a) CZTS:BM and (b) CZTS:THM.
Capture cross-sections for the charge carriers for traps identified in: (a) CZTS:BM and (b) CZTS:THM.
Capture cross-sections for the charge carriers for traps identified in: (a) CZTS:BM and (b) CZTS:THM.
Proposed model for the role of the Te secondary phase (gettering centers), Cd vacancies, interstitial Te, and impurities in the point-defect formation in CZTS.
Proposed model for the role of the Te secondary phase (gettering centers), Cd vacancies, interstitial Te, and impurities in the point-defect formation in CZTS.
Traps identified in CZTS and CZT detectors, their expected origins and capture cross-sections (σ).
Et . | Expected origin of the trap . | σ (cm2) . | Detectors . | |||
---|---|---|---|---|---|---|
CZTS (BM) . | CZTS (THM) . | CZT (BM) . | CZT (THM) . | |||
Ec − 22 meV | Donor impurities | 9 × 10−21 | √ | √ | x | 20 meV |
Ec − 58 meV | Se-related donor | 5 × 10−17 | √ | √ | 50 meV | 45 meV |
Ev + 0.18 eV | A-center | 1 × 10−16 | √ | √ | x | √ |
Ev + 0.26 eV | Tei- | 1 × 10−14 | √ | √ | x | x |
Ev + 0.37 eV | VCd− | 1 × 10−15 | √ | x | √ | √ |
Ec − 0.78 eV | TeCd++ | 5 × 10−11 | x | √ | √ | x |
Ev + 1.1 eV | TeSP | 1 × 10−10 | √ | x | √ | √ |
Et . | Expected origin of the trap . | σ (cm2) . | Detectors . | |||
---|---|---|---|---|---|---|
CZTS (BM) . | CZTS (THM) . | CZT (BM) . | CZT (THM) . | |||
Ec − 22 meV | Donor impurities | 9 × 10−21 | √ | √ | x | 20 meV |
Ec − 58 meV | Se-related donor | 5 × 10−17 | √ | √ | 50 meV | 45 meV |
Ev + 0.18 eV | A-center | 1 × 10−16 | √ | √ | x | √ |
Ev + 0.26 eV | Tei- | 1 × 10−14 | √ | √ | x | x |
Ev + 0.37 eV | VCd− | 1 × 10−15 | √ | x | √ | √ |
Ec − 0.78 eV | TeCd++ | 5 × 10−11 | x | √ | √ | x |
Ev + 1.1 eV | TeSP | 1 × 10−10 | √ | x | √ | √ |
1. CZTS:BM
The iDLTS plots for CZTS:BM detectors are shown in Fig. 1(a), where the inset shows the Arrhenius plot for 1000/KT vs. log(T2t1); herein, t1 is the starting time for the time-current window for the transient collected at temperature T. The first four traps, as shown in Figs. 1(a) and 1(b), are identified as the same traps in both THM- and BM-grown CZTS detectors. The difference can be seen only in the amplitudes of the signals, which is one of the key parameters affecting the densities of traps (Fig. 3).
Two shallow traps in the temperature scan below 100 K were identified at 23 and 57 meV with an occupational density of 6 × 1011 and 5 × 1011 cm−3, respectively. The value for the capture cross-section σ shown in Fig. 4 for the first shallow trap is very small (i.e., less than 10−19 cm2). The second shallow trap at 57 meV has a considerably higher σ of ∼10−17 cm2. This trap is found in both CZTS detectors but was not identified in CZT detectors in our previous reported research.13,14 Thus, there is a high probability that the 57-meV trap is related in some manner to a shallow donor induced by the addition of Se into CZT. In the temperature range of 100–300 K, two medium level traps with energies at 0.18 eV (A-center) and 0.26 eV (most probably related to Te interstitials (Tei−)) are observed. It was observed that the shallow traps in BM-grown CZTS detectors were present with slightly lower densities compared to THM-grown detectors. The densities of A-centers (0.18 eV) for both growth methods were very similar ∼1 × 1011 cm−3, while Cd vacancies (VCd−) for BM-grown CZTS were present with a lower density (∼4 × 1010 cm−3) than for the THM-grown material. For the deep traps, in BM-grown CZTS, the 1.1-eV trap (labeled as TeSP) was present with a higher density (∼4 × 1011 cm−3) for large-size (∼30 μm) secondary phases but the method was observed to correlate with much lower densities of Tei (2 × 1010 cm−3) and TeCd++ (below detection). These observations suggest a connection between the large (20–30 μm diameter) Te-rich phases and the 1.1-eV trap. The inability to quantify the electron charge collection prevented the measurement of the electron μτ product from that sample. These results indicate that an excess of the TeSP deep trap (and hence large Te-rich phases of ∼30-μm size) generates more detrimental electron trapping centers in the BM-grown as compared to the THM-grown CZTS crystal. Such an explanation does not hold for CZT. Additional growth runs and further studies are being carried out to improve the CZTS quality and provide additional data to strengthen the analysis of our observations.
2. CZTS:THM
Point defects in these detectors are shown in Fig. 1(b). Arrhenius plots are shown in the inset. Five different traps were identified, although some data above 350 K were probably masked due to the higher leakage current. This higher noise level makes it hard to distinguish the TeSP trap (expected in the 350–400 K temperature range where the dark current begins to increase rapidly with temperature), particularly when it has a relatively low density.
Regarding shallow traps, two were clearly identified around 23 and 57 meV with densities of 3 × 1011 and 4 × 1011 cm−3, respectively, as shown in Fig. 3(b). The four traps identified below 300 K were similar to the traps identified in CZTS:BM but with different occupied densities. For the levels below 300 K in CZTS:THM, the concentrations were about an order of magnitude higher density (∼1011 cm−3) compared to CZTS:BM (∼1010 cm−3), except for the A-center. Above room temperature, one deep trap at ∼0.78 eV was identified, which is due to the occupancy of Te on a Cd lattice point, which causes the TeCd++ energy trap. The density for TeCd++ in THM-grown CZTS was almost the same as VCd− in BM-grown CZTS. This indicates that nearly all VCd− in THM-grown CZTS was replaced by Te, forming a Te anti-site (TeCd++). In addition, the density of the Tei-related trap at around 0.26 eV increased by a factor of ten in CZTS:THM.
Beside the similarities in energy traps identified below RT, there are a few major differences between BM- and THM-grown CZTS, especially in the high-temperature region. In BM-grown crystals, there was no measurable TeCd++ (0.73 eV), and instead there were two additional traps: one labeled as VCd− at around 0.37 eV and another the well-known 1.1-eV Te secondary-phase related trap found in most of the CdTe-based alloyed detectors. The capture cross-section σ as shown in Fig. 4 for the traps at 0.37 eV and 1.1 eV has the value of about 10−15 and 10−10 cm2, respectively. The 1.1-eV trap is the dominant trap at room temperature amongst all the traps identified in BM-grown CZTS detectors.
After making the analysis of the traps and comparing their corresponding occupational densities, as well as the expected origins of traps, it appears that VCd− and TeSP play important roles in generating interstitials or complexes with VCd−. Their conversion and relative variation in densities with the growth process establish a dynamics between the traps, possibly driven more completely during the higher-temperature growth used for BM-grown CZTS. A simple sketch of the trap conversion dynamics is illustrated in Fig. 5, indicating the role of VCd− in complexing with the interstitials/dopants/impurities and combining with the Te secondary phases, causing the relative concentrations of the deep-level point defects to differ substantially for the two growth methods.
The data and description given above indicate that the excess Te in THM-grown CZTS occupies two different levels: Tei− and TeCd++. This might be one of the reasons for little or no VCd− (fully compensated) and a negligibly low density of TeSP although the lower growth temperature for THM may also be important. In addition, the lower resistivity and the negligible concentration of the 1.1-eV trap appear to be correlated. These data provide additional evidence that the 1.1-eV trap is connected to large size (≥25 μm in diameter) Te-rich secondary phases. Based on the iDLTS point defect data evaluated for the two growth methods, a proposed energy band diagram showing the traps within the band-gap in CZTS crystals is shown in Fig. 6.
Proposed band diagram for CZTS crystals based on the energy levels identified by iDLTS.
Proposed band diagram for CZTS crystals based on the energy levels identified by iDLTS.
C. Comparison of traps between CZTS and CZT detectors
To show the effects of the Se addition on point defects in CZT, we include the iDLTS plots for In-doped CZT detectors grown by the BM- and THM-technique, as shown in Fig. 2. To make the comparisons more clear, the results are also presented in Table II. There are similarities and differences in the traps identified by iDLTS in In-doped CZTS and CZT detectors. The shallow traps in CZT and CZTS are almost the same and may be an indication of the presence of In dopants present in both materials. The second shallow level is the A-center, which was identified in all the three detectors, except for CZT:BM, which might be due to CZT:BM growth conditions favoring the generation of Cd vacancies (VCd−) instead of their complex with an In dopant to form an A-center (VCd−-InCd). A major difference in traps was observed in the medium energy traps, see Figs. 1 and 2. The Se addition causes the generation of a new trap at around 0.26 eV in both CZTS BM- and THM-grown detectors. In addition, VCd−, which has a trap level at ∼0.37 eV, is completely compensated in CZTS. The deep trap at ∼1.1 eV was identified in all the three detectors except for CZTS:THM. It seems that the THM growth and the addition of Se (i.e., CZTS crystals) were successful to eliminate the 1.1-eV deep trap. The presence of the 1.1-eV trap helped to achieve high resistivity in CZTS:BM, CZT:BM, and CZT:THM. The good gamma response for CZTS:THM, even with comparably lower resistivity, indicates that the Se addition and the use of the THM growth method are more effective for room-temperature radiation detector applications. There is still a need to improve the quality of crystals by increasing the electrical resistivity and the response towards gamma radiation.
D. Charge trapping in defects
We calculated the times for trapping (tt) and de-trapping (tdt) of charge carriers for each trap from the iDLTS data. The values of tt were calculated using the modified Shockley-Read-Hall model, for CdTe-based alloys15
Here, Et is the energy of the point-defect level of the trap, Ei is the intrinsic Fermi level, kB is the Boltzmann constant, T is the temperature (room temperature (RT) used to correspond to detector operation), and Vth is the thermal velocity of the carriers at RT. As the resistivity of the CZTS detectors investigated in this research was between 109 and 1010 Ω cm, the free charge carrier density was estimated at 105 carriers per cm3 in Equation (1), instead of 106 carriers per cm3. The values for tdt are determined from the emission rate (en) of the charge carriers from the laser-filled traps.
The data showing the variation of tt and tdt with the corresponding energies for the different traps are plotted in Fig. 7. The values of tt decrease monotonically with increasing activation energies of the traps, as illustrated by the plots. It can be observed that the deep traps are faster in trapping the charge carriers than the shallow traps. The two regions shown in Fig. 7 can be described as below:
Trapping and de-trapping times of point defects for the charge carriers in (a) CZTS:BM and (b) CZTS:THM detectors.
Trapping and de-trapping times of point defects for the charge carriers in (a) CZTS:BM and (b) CZTS:THM detectors.
RI: The tt and tdt values are almost the same at an energy level of ∼0.45 eV. In the region of shallow and medium energy traps having Et ≤ 0.45 eV, the tt values are longer than the tdt (tt > tdt). This means that in this region, there will be little or no effect on the charge collection (except for Et greater than about 0.40 eV) and hence a negligible effect on the carrier lifetime or the μτ-product.
RII: For deep-level traps having Et > 0.45 eV, tt is shorter than the tdt (tt < tdt), and hence, trapping is faster, while the emission rates from these deep traps are slow and often delayed well beyond the data acquisition time. For most of these deep levels, the difference reaches minutes and the charge carriers are completely lost before the signal can be counted. In this case, the deep traps have a major contribution to charge loss and have a remarkable effect on the carrier lifetimes; hence, they have a major contribution in lowering the μτ-product.
Summarizing the trapping and de-trapping dynamics of the different defects in each detector, the Tei− trap in CZTS:THM has a tt value more than four orders of magnitude higher than tdt (clearly RI, which indicates a negligible role as a trapping center for detectors operating at room temperature), while for CZTS:BM, the trapping and de-trapping times are closer (about 1–2 orders of magnitude different). In CZTS:THM, TeCd++ plays a dominant role in killing charge carriers and ultimately the μτ since the values of tt and tdt are, respectively, less than 0.1 μs and more than 10 ms, respectively; this defect does not appear in CZTS:BM at an appreciable concentration. Instead, in CZTS:BM, TeSP has tt in ns and very high tdt (in minutes), possibly dominating the electron charge loss as the major trapping center and killing the detector response. Also, in CZTS:BM, the VCd− has a value of tt < ms, and tdt is 2 orders shorter, thus having no significant contribution to μτ.
IV. CONCLUSIONS
In this work, we characterized two types of In-doped CZTS detectors (i.e., crystals grown by the Bridgman growth method and by the traveling heater method). Distinct shallow, medium and deep energy traps were identified for each growth method. CZTS crystals, as compared to CZT, have a relatively low concentration of VCd−. It indicates that the Se addition to CZT can be used for the effective compensation of VCd−. Traps with energy levels >0.5 eV mainly limit the lifetime of charge carriers. A deep trap at 1.1 eV due to TeSP (>10–μm diameter in size) helps to achieve high resistivity in CZTS crystals but at the same time, the high density of this deep level generates more trapping/recombination centers that kill the μτ product and cause a degradation of the detector response. For example, the CZTS:BM detector showed a high density of the 1.1-eV trap and a high resistivity of 2 × 1010 Ω cm, but the short trapping time kills the carrier lifetime, and the detector showed no response to gamma rays. The case is opposite for the CZTS:THM detector, where we found no 1.1-eV trap, and the detector showed good response towards gammas. The data on point defects, high electrical resistivity, and high μτ values for electrons in CZTS suggest that it is a promising potential alternative material to CZT for high-performing room-temperature radiation detectors.
ACKNOWLEDGMENTS
This work was supported by the U.S. Department of Energy, Office of Defense Nuclear Nonproliferation Research and Development, DNN R&D. This manuscript was authored by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. Part of this work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.