Dark current mechanisms in stabilized amorphous selenium based detectors for x-ray imaging applications Cite as: J. Vac. Sci. Technol. A 29, 031603 (2011); https://doi.org/10.1116/1.3580902 Submitted: 06 January 2011 • Accepted: 20 March 2011 • Published Online: 14 April 2011 S. A. Mahmood and M. Z. Kabir ARTICLES YOU MAY BE INTERESTED IN Dark current in multilayer stabilized amorphous selenium based photoconductive x-ray detectors Journal of Applied Physics 112, 014502 (2012); https://doi.org/10.1063/1.4730135 Dark current in multilayer amorphous selenium x-ray imaging detectors Applied Physics Letters 92, 223506 (2008); https://doi.org/10.1063/1.2938888 Columnar recombination for X-ray generated electron-holes in amorphous selenium and its significance in a-Se x-ray detectors Journal of Applied Physics 119, 124511 (2016); https://doi.org/10.1063/1.4944880 J. Vac. Sci. Technol. A 29, 031603 (2011); https://doi.org/10.1116/1.3580902 © 2011 American Vacuum Society. 29, 031603 Dark current mechanisms in stabilized amorphous selenium based n-i detectors for x-ray imaging applications S. A. Mahmooda兲 and M. Z. Kabir Department of Electrical and Computer Engineering, Concordia University, 1455 De Maisonneuve Blvd. West, Montréal, Québec H3G 1M8, Canada 共Received 6 January 2011; accepted 20 March 2011; published 14 April 2011兲 The dark current behavior under operating bias is one of the important selection criteria for an x-ray photoconductor to be usable in a practical x-ray image detector. The authors have developed an analytical model for describing the transient and steady-state behavior of dark current in n-i-type amorphous selenium 共a-Se兲 detectors by considering carrier injections from the metal contacts and thermally generated carriers. It has been found that the thermal generation current is almost two orders of magnitude smaller than the total steady-state dark current in n-i-type a-Se detectors. The main source of dark current is the injection of holes from the metal/n-layer interface which is described by the diffusion theory. The hole injection from the metal depends on the blocking layer 共n-layer兲 thickness, the concentration of trap centers in the blocking layer, the characteristic carrier release time, and the effective barrier height. The fitting of the first principles model with the experimental results estimates the concentration of deep hole trap center in the n-layer, the trap depth from the valence band edge, and the effective barrier heights for the injecting carriers. The electron injection varies with the work function of the contact metal. © 2011 American Vacuum Society. 关DOI: 10.1116/1.3580902兴 I. INTRODUCTION Amorphous selenium 共a-Se兲 in stabilized form 共a-Se alloyed with 0.2%–0.5% As and doped with 10–40 ppm Cl兲 is one of the best candidates for direct conversion flat panel x-ray imager 共FPXI兲.1–3 The stabilized a-Se based x-ray detectors with an active matrix array 共AMA兲 can provide excellent x-ray images, have been commercialized for mammography and general radiography, and have potentials for use in fluoroscopy and portal imaging.4 In flat panel detectors, a stabilized a-Se structure is sandwiched between two parallel electrodes on top of an AMA. A FPXI has to be operated under a large applied electric field 共⬃5 – 10 V / m兲 to get a reasonably good quality image.5,6 The current that flows due to the applied bias through the detector in the absence of radiation or light is called dark current. It is important to consider the dark current magnitude of a photoconductive detector for its use in x-ray imaging applications. The dark current has many unwanted effects in FPXIs. The dark current is a source of noise that is added to the signal. It limits the dynamic range due to the accumulation of undesirable charge on the pixel capacitor.1,7 The charge carriers can be trapped in the a-Se layer during the flow of dark current, which modifies the internal field and therefore changes the photogeneration efficiency across the thickness of the photoconductor layer.1 Therefore, the dark current should be as small as possible 共preferably smaller than 100 pA/ cm2兲 for diagnostic x-ray imaging applications.1,2,8 Under normal operating bias 共that creates an applied electric field of ⬃10 V / m兲 the dark current in a simple a兲 Electronic mail: sh_mahmo@encs.concordia.ca 031603-1 J. Vac. Sci. Technol. A 29„3…, May/Jun 2011 metal/a-Se/metal structure is particularly high 共⬃1 – 100 nA/ cm2兲, which is unacceptable for x-ray imaging applications.2,9 It is believed that the main source of this high dark current is the injection of carriers from the metal contacts since the bulk thermal generation current is negligible due to the large mobility gap of a-Se.1,10 Recent experiments on a-Se detectors have shown that low dark current can be achieved in a multilayer detector where thin blocking layers are used between the intrinsic layer 共i-layer兲 of a-Se and the metal contacts.11–13 The blocking layers are p- and n-type layers which are appropriately doped to serve as unipolar conducting layers that can easily trap electrons and holes, respectively, but allow the transport of oppositely charged carriers.14 This signifies that the p and n layers have a very high concentration of deep trap centers for electrons and holes, respectively.10 The intrinsic a-Se is slightly p-type and thus the Fermi level EF at zero bias is ⬃0.045 eV below the midgap.15 The p- and n-type a-Se are defined by the relative magnitude of mobility-lifetime product . In case of n-type a-Se hh Ⰶ ee, although the exact position of the Fermi level is not known. The subscripts e and h represent electrons and holes, respectively. The p-layer is usually As2Se3 and the n-layer is alkaline doped a-Se.11 The dark current in the a-Se based detector has been measured by Kasap et al. for different structures: a single intrinsic layer, i-n and p-i double layers, and p-i-n triple layers.1,9,11 The dark current in a-Se detectors may have two origins: 共i兲 carrier injections from the metal contacts to the selenium layers and 共ii兲 thermally generated carriers in the bulk. After applying the bias voltage across the detector, the high dark current decays with time and, most of the cases, reaches a plateau within the time range of 100–1000 s.16 In our previous publication,10 we have explained the transient 0734-2101/2011/29„3…/031603/6/$30.00 ©2011 American Vacuum Society 031603-1 031603-2 S. A. Mahmood and M. Z. Kabir: Dark current mechanisms behavior of dark current in a-Se based p-i-n detectors by considering carrier injections from the metal contacts using diffusion theory and trapping in the blocking layers.17 The carrier injection mechanism in low-mobility semiconductors 共typically ⬍ 1 cm2 / V s兲 is described by the diffusion theory.17 However, at a very high field the carrier injection modeled by the thermionic-emission-diffusion theory is more applicable. In this article, we have extended our previous model by incorporating the thermal generation current and the injection current following the thermionic-emissiondiffusion theory. We have developed an analytical expression for the steady-state thermal generation current by solving the continuity equations for both electrons and holes. The time and voltage dependent total dark current is obtained by adding the thermal generation current with the injection current. The model is applied to n-i and metal/a-Se 共n-type兲/metal structures. We calculate the level of thermal generation current in n-i structures and compare it with the total dark current. We analyze the transient and steady-state dark current behavior in n-i structures as a function of the applied electric field, n-layer thickness, and various metal contacts. We compare our model with the published experimental results for several n-i structures. The comparisons of the dark current model with the experimental results evaluate few important parameters of the n-layer such as trap center concentrations and barrier heights. II. ANALYTICAL MODEL In a-Se based n-i structures, the contacts are generally blocking in nature and the carrier injection is mainly controlled by the Schottky emission. After injection, carriers drift in the a-Se layer through shallow-trap controlled transport.18 The carrier injection from the metal to the semiconductor depends on the internal electric field at the metal/a-Se interface. It is believed that the electric field right after applying bias is uniform but quickly becomes nonuniform due to high initial current and high carrier trapping in the blocking layer.1 The steady-state electric field profile before applying any radiation in the a-Se based n-i structure is shown in Fig. 1. It is assumed that the carrier trapping, over a long time, is effectively uniform in the n-layer and the trapping in the intrinsic layer is negligible as compared to trapping in the n-layer. This is a reasonable assumption since the density of deep trap centers for holes in the n-layer is much higher than that in the intrinsic layer.14 In a-Se the carrier mobility is independent of electric field under normal operating bias. As a result the drift velocity of the carrier would be proportional to the instantaneous electric field at the metal/semiconductor interface. Therefore, the injected current densities due to hole and electron injections can be written as Jh共t兲 = eNVvdh共t兲 冉 冊 再 冎 h − s冑F1共t兲 vR exp − , kT vdh共t兲 + vR 共1兲 J. Vac. Sci. Technol. A, Vol. 29, No. 3, May/Jun 2011 031603-2 F(x) F2 F0=V/L L F1 Ln x Bottom electrode i-layer n-layer Top electrode Trapped holes V FIG. 1. Simplified schematic diagram of the a-Se based n-i structure showing the time-dependent electric field profile. The dashed line represents the initial uniform electric field and the solid line represents the field distribution sometime after the application of field. Je共t兲 = eNCvde共t兲 冉 再 冊 冎 e − s冑F2共t兲 vR exp − , kT vde共t兲 + vR 共2兲 where e is the elementary charge, F1共t兲 is the instantaneous electric field at the metal/n-layer interface, F2共t兲 is the instantaneous electric field at the metal/i-layer interface, s = 冑共e3 / 4s兲 is the Schottky coefficient, s 共=0r兲 is the permittivity of the photoconductor, T is the absolute temperature, k is the Boltzmann constant, vR = AⴱT2 / eNC is the thermal velocity, Aⴱ is the effective Richardson constant, NV共C兲 is the effective density of states in the valence 共conduction兲 band, vd共t兲 ⬇ 0F共t兲 is the instantaneous drift velocity of the injected carriers, 0 is the band mobility of carriers, and is the effective barrier height for injecting carriers from metal into the a-Se layer considering the effect of surface states. The total injection current density Jinj共t兲 = Je共t兲 + Jh共t兲. Once the carriers are injected into the a-Se layer, they move by drift mechanism 共diffusion component of current is negligible compared to its drift component because of very high applied field as described in the Appendix兲. Therefore, Jh共t兲 ⬇ eh p共t兲F1共t兲 in the a-Se layer, where h is the effective drift mobility of holes considering shallow trapping.19 Therefore, the drifting hole and electron concentrations near the interfaces are 冉 冉 冊 冊 再 再 冎 冎 p共t兲 = NV h − s冑F1共t兲 0h vR exp − , h vdh共t兲 + vR kT 共3兲 n共t兲 = NC e − s冑F2共t兲 0e vR exp − . e vde共t兲 + vR kT 共4兲 The instantaneous electric fields F1共t兲 and F2共t兲 are determined by solving Poisson’s equation in a-Se layers and are given by 031603-3 S. A. Mahmood and M. Z. Kabir: Dark current mechanisms F1共t兲 = F0 − 冉 冊 L2 e Ln − n pt共t兲, 2L 共5兲 冋 冉 p共x兲 = ghh 1 − exp − x h hF 0 冊册 共11兲 . The hole current density is given by e L2n pt共t兲, F2共t兲 = F0 + 2L 共6兲 where F0 共=V / L兲 is the applied field, V is the bias voltage, L is the total photoconductor thickness, Ln is the n-layer thickness, and pt共t兲 is the instantaneous trapped hole concentration in the n-layer. The time-dependent trapped hole concentration can be determined by solving the trapping rate equation in the n-layer. If we consider trap filling and carrier detrapping from a single discrete state, the trapping rate equation for holes is 冉 031603-3 冊 h pt共t兲 pt共t兲 dpt共t兲 = C tN t 1− p共t兲 − , 0h dt Nt r 共7兲 where Ct is the deep trapping capture coefficient, Nt is the concentration of the deep trap centers in the n-layer, and r is the release time constant for the trapped holes. The release time r is related to the trap depth Et by −1 0 exp共Et / kT兲, where 0 is the attempt-to-escape frequency. The relation between 0 and Ct can be determined by the principle of detailed balance, which gives 0 = NVCt.20,21 The steady-state thermal generation current in a-Se arises from the carriers excited from the deep states near Fermi level to the band edges of the intrinsic layer. The n-layer is much thinner compared to the intrinsic layer and there is negligible trapped charge in the intrinsic layer. Therefore, the electric field is constant throughout the i-layer and nearly close to the applied field 共F0兲. Considering uniform thermal emission of trapped carriers throughout the i-layer, the continuity equation for holes can be written as 1 p共x,t兲 p共x,t兲 + hF 0 = − p共x,t兲 + gh , t x h 共8兲 where h and p are the effective charge carrier lifetime and the concentration of holes, respectively. The lifetime h is related to trap center concentration in the intrinsic layer by 共h / 0hCtNt兲. The lifetime in a-Se is easily measured by interrupted field time-of-flight experiments.22 In a-Se the trap levels are likely to be charged defect 共positive or negative兲 and thus field enhanced thermal generation occurs.15 The thermal generation rate is dominated by the emission from traps within kT of the Fermi level. The generation rate for holes and electrons can be expressed as23 gh = N共EF兲kT0 exp关− 共EF − EV −  pf 冑F0兲/kT兴, 共9兲 ge = N共EF兲kT0 exp关− 共EC − EF −  pf 冑F0兲/kT兴, 共10兲 where N共EF兲 is the density of states of a-Se at energy EF near the midgap, EV共C兲 is the valence 共conduction兲 band edge, and  pf = 冑共e3 / s兲 is the Poole–Frenkel coefficient. In Eqs. 共9兲 and 共10兲 it is assumed that N共EF兲 is constant over kT near EF. At steady state, the solution of Eq. 共8兲 is JVST A - Vacuum, Surfaces, and Films Jsh = e hF 0 L 冕 L 共12兲 p共x兲dx. 0 Therefore, the steady-state thermal generation current is 冋 冊冎册 Jse共h兲 = ee共h兲e共h兲F0ge共h兲 1 − − L e共h兲e共h兲F0 e共h兲e共h兲F0 L . 再 冉 1 − exp 共13兲 After adding the transient and the steady-state current, the time and voltage dependent total dark current in the a-Se based n-i detector is J共t兲 = Jinj共t兲 + Jse + Jsh . 共14兲 III. RESULTS AND DISCUSSION The developed dark current model is verified with the published experimental data. The band mobilities of electrons and holes are 0e = 0.1 cm2 / V s and 0h = 0.3 cm2 / V s, whereas their effective mobilities are e = 0.003 cm2 / V s and h = 0.12 cm2 / V s.24,25 The parameters 0 = 1012 / s, r = 6.7, e = 7.3⫻ 10−4 s, h = 7.1⫻ 10−5 s, EC − EF = 1.155 eV, and EF − EV = 1.065 eV are taken in the calculations.15,24 The effective density of states is assumed to be NC = NV = 1019 / cm3 in all layers and the density of states near midgap in the i-layer is N共EF兲 = 1014 cm3 / eV.15,26 Unless otherwise specified all the parameters mentioned above are fixed for all the theoretical calculations in this article. Other parameters such as effective barrier height 共兲, trap center concentration 共Nt兲, and trap depth in the n-layer depend on the fabrication processes and, therefore, these are considered as fitting parameters in the model. Assuming Aⴱ = 120 A / cm2 K2 and T = 295 K, the thermal velocity vR ⬃ 6.5⫻ 106 cm/ s. At a very high field of 100 V / m vdh ⬃ 3 ⫻ 105 cm/ s. Even at a very high field vdh in a-Se is approximately one order of magnitude smaller than the thermal velocity. Since vR Ⰷ vdh, the hole injection current is dominated by vdh 关Eq. 共1兲兴. Figure 2 shows the dark current density as a function of time for the n-i structure. The symbol represents the experimental data and the solid line represents the theoretical fit to the experimental data. The experimental result has been extracted from Fig. 5 of Ref. 1. The total photoconductor thickness is 130 m and the n-layer thickness is 20 m. The proposed model has a good agreement with the experimental result. We consider two discrete deep trapping states for holes in the n-layer to fit the experimental data. The depths of these two trapping states are 0.78 eV 共r1 = 13 s兲 and 0.83 eV 共r2 = 87 s兲 from the mobility edge of the valence band. This result is equivalent to a broadened state of width ⬃0.05 eV. The fitted parameters are Nt1 = 1.9⫻ 1015 / cm3, Nt2 = 4 ⫻ 1014 / cm3, h = 0.85 eV, and 031603-4 S. A. Mahmood and M. Z. Kabir: Dark current mechanisms 031603-4 0 1 10 10 Experimental results Experimental results 10 Theoretical hole injection current n−i structure n−layer thickness 20 µm Total thickness 130 µm Field, F = 10 V/µm −1 10 0 −2 10 −3 10 Theoretical electron injection current Theoretical thermal generation current −2 10 n−i structure −3 10 −4 10 −5 1 2 10 10 Time after applying bias (s) FIG. 2. Dark current density in the n-i structure as a function of time at 10 V / m applied field. The symbol represents experimental data and the solid line represents the theoretical fit to the experimental data 共Ref. 1兲. e = 0.99 eV. The concentration of deep hole trap center in the n-layer is found to be ⬃1014 – 1015 / cm3. 共Note that the concentration of deep trap centers in the i-layer is in the range of 1012 – 1013 / cm3.兲15 The trapped hole concentration pt increases with time and its saturation value is ⬃1.96 ⫻ 1014 / cm3. It has been found that the thermal generation current is ⬃6.6⫻ 10−5 nA/ cm2, whereas the carrier injection current is ⬃5.9⫻ 10−3 nA/ cm2. It is evident from Fig. 2 that the electron injection current is almost three times smaller than the hole injection current because of high effective barrier for the injecting electron. However, the electron current increases slightly with time since the sample does not have electron blocking layer 共e.g., p-layer兲. Therefore, the dark current in a-Se based n-i detector is mainly controlled by hole injection which has also been suggested in our previous study.10 Figure 3 shows the steady-state dark current density as a function of applied electric field for the same a-Se based n-i structure shown in Fig. 2. The square symbol represents experimental data and the star symbol with solid line represents the theoretical fit to the experimental data. The experimental result has been extracted from Fig. 6 of Ref. 1. The dasheddotted line represents the electron injection current and the dotted line represents the bulk thermal generation current. The proposed model shows a very good match with the experimental result. The dark current reaches a plateau within 1000 s after the application of field as shown in Fig. 2. Therefore, we have solved the trapping rate equation up to 1000 s to get the steady-state dark current. The fitted value of effective barrier for injecting holes varies from 0.89 to 0.85 eV with varying the applied field from 2.5 to 10 V / m. The other parameters are the same as in Fig. 2. From Fig. 3 we find that, at steady state, the thermal generation current is ⬃0.1 pA/ cm2 at 10 V / m applied field which is about two orders of magnitude smaller than the injection current beJ. Vac. Sci. Technol. A, Vol. 29, No. 3, May/Jun 2011 10 3 10 2 3 4 5 6 7 8 Applied electric field (V/µm) 9 10 11 FIG. 3. Dark current density in the n-i structure vs applied electric field. The square symbol represents experimental data and the star symbol with solid line represents the theoretical fit to the experimental data 共Ref. 1兲. cause of large energy band gap in a-Se. The thermal generation current increases almost exponentially with increasing the applied field. Figure 4 shows the steady-state dark current density versus blocking layer 共n-layer兲 thickness of n-i structure for two applied electric fields. The square and diamond symbols represent experimental data and the star symbols with solid lines represent the theoretical fit to the experimental data. The experimental results have been extracted from Fig. 4 of Ref. 9. The proposed model shows a very good validity with the experimental results. The i-layer thickness is 130 m for all the samples. We have solved the trapping rate equation up to 1000 s to get the steady-state dark current. For both the applied fields we have considered two discrete deep trapping states for holes in the n-layer and the fitted values are Nt1 5 10 Experimental data at 8 V/µm Experimental data at 4 V/µm 4 2 0 10 Dark current density (pA/cm ) 10 Theoretical fit −1 Theoretical electron injection current 0 Dark current density (nA/cm2) 2 Dark current density (nA/cm ) Theoretical fit 10 Theoretical fit n−i structure i−layer thickness 130 µm 3 10 2 10 1 10 0 10 0 10 20 30 40 Blocking layer thickness (µm) 50 FIG. 4. Dark current density in the n-i structure vs blocking layer 共n-layer兲 thickness at two applied electric fields. The square and diamond symbols represent experimental data and the star symbols with solid lines represent the theoretical fit to the experimental data 共Ref. 9兲. 031603-5 S. A. Mahmood and M. Z. Kabir: Dark current mechanisms 5 10 Experimental data at 10 V/µm Experimental data at 5 V/µm Dark current density (pA/cm2) 4 Theoretical fit 10 Theoretical electron injection current 3 10 Al metal/a−Se(n−type)/metal structure Au Pt 2 10 1 10 0 10 4.5 5 5.5 Work function (eV) 6 FIG. 5. Dark current density in the metal/a-Se 共n-type兲/metal structure vs work function of the negative electrode material at two applied electric fields. The square and diamond symbols represent experimental data and the star symbols with solid lines represent the theoretical fit to the experimental data 共Ref. 9兲. = 4 ⫻ 1014 / cm3 and Nt2 = 1.5⫻ 1014 / cm3. The depths of these trapping states are 0.77 eV 共r1 = 8 s兲 and 0.79 eV 共r2 = 18 s兲 from the mobility edge of the valence band. This result is equivalent to a broadened state of width ⬃0.02 eV. The fitted value of effective barrier for injecting electrons is 0.99 eV for both the applied fields. The fitted value of the effective barrier for injecting holes varies from 0.78 to 0.83 eV with varying the blocking layer 共n-layer兲 thickness from 5 to 50 m. The total trap charge in the n-layer increases with the n-layer thickness Ln and thus reduces the interface electric field F1共t兲 as well as the dark current. Moreover, the thicker n-layer ensures more uniformity between metal and a-Se interface and thus provides less interface states.27–29 As a result the effective barrier for the injecting holes increases with the blocking layer 共n-layer兲 thickness which eventually reduces the dark current in n-i structures. However, the x-ray generated carrier in the large blocking layer 共n-layer兲 will move slowly under lower electric field which will reduce the overall charge collection efficiency of the detector. Therefore, a tradeoff between the lower dark current 共wider n-layer兲 and the higher sensitivity 共thinner n-layer兲 is necessary to find an optimum n-layer thickness in n-i structures for x-ray imaging applications. Although hole injection mainly controls the dark current in a-Se based n-i structures, the electron injection can also have a significant effect if the barrier for the electron injection is small. The barrier for the electron injection depends on the work function of the metal contact. Belev et al. compared the dark current in the metal/a-Se 共n-type兲/metal structure by using aluminum 共Al兲, gold 共Au兲, and platinum 共Pt兲 as the negatively biased top contacts.9 They have found that the dark current depends on the work function of the metal electrode. Figure 5 shows the steady-state dark current density versus work function of the negative electrode material in the metal/a-Se 共n-type兲/metal structure for two applied electric JVST A - Vacuum, Surfaces, and Films 031603-5 fields. The square and diamond symbols represent experimental data and the star symbols with solid lines represent the theoretical fit to the experimental data. The experimental results have been extracted from Fig. 5 of Ref. 9. The dotted lines represent the electron injection current from the top electrode. The bottom electrode is Al for all the samples. We have solved the trapping rate equation up to 1000 s to get the steady-state dark current. For both the applied fields we have considered two discrete deep trapping states for holes in the n-layer and the fitted values are Nt1 = 4 ⫻ 1014 / cm3 and Nt2 = 1.5⫻ 1014 / cm3. The depths of these trapping states are 0.77 eV 共r1 = 8 s兲 and 0.8 eV 共r2 = 30 s兲 from the mobility edge of the valence band. This result is equivalent to a broadened state of width ⬃0.03 eV. The fitted value of the effective barrier for the injecting hole is ⬃0.82 eV for both the applied fields. The fitted value of the effective barrier for the injecting electrons increases from 0.89 to 0.98 eV with changing the top electrode from Al to Pt. It is evident form Fig. 5 that the electron injection current is significant in the metal/a-Se 共n-type兲/metal structure, whereas it is less significant in the n-i structure. In the metal/a-Se 共n-type兲/metal structure, the interface electric fields are F1共t兲 = F0 − 0.5eLpt共t兲 / s and F2共t兲 = F0 + 0.5eLpt共t兲 / s. Therefore, the electric field at the negative electrode increases, whereas it decreases at the positive electrode with increasing pt. Thus, carrier trapping in the metal/a-Se 共n-type兲/metal structure enhances the electron injection and reduces the hole injection. We also find that the effective barrier for injecting electron increases with the metal work function which eventually reduces the dark current in the metal/a-Se 共n-type兲/metal structure. Therefore, metals with high work function used as a negative electrode can reduce the dark current. IV. CONCLUSION An analytical model for describing the transient and steady-state behavior of dark current in a-Se based n-i detectors for x-ray imaging applications has been developed. The proposed theoretical model shows a very good agreement with the experimental results. The dark current in the a-Se based n-i detector is mainly governed by the injection of holes from the metal electrode. The thermal generation current is much smaller compared to the injection current due to the large band gap in a-Se. The carrier injection from the metal/n-layer interface depends on the concentration of trap centers in the blocking layer 共n-layer兲, the average depth of the trap center from the valence band edge, and the effective barrier height. The concentration of deep hole trap center in the n-layer is in the range of 1014 – 1015 / cm3. The bulk thermal generation current is ⬃0.1 pA/ cm2 at 10 V / m applied field, which is negligible compared to the injection current. The electron injection from the negative electrode increases due to the reduced effective barrier height resulting from the smaller metal work function. ACKNOWLEDGMENT The authors thank Safa Kasap for many useful discussions. 031603-6 S. A. Mahmood and M. Z. Kabir: Dark current mechanisms APPENDIX If the injected hole concentration decays exponentially due to trapping, the carrier concentration can be written as c共x兲 = B exp共− x/F兲, 共A1兲 where is the carrier lifetime and B is the carrier concentration at x = 0. The drift and diffusion current components are Jdrift = eFc 共A2兲 and Jdif f = − eD dc . dx 共A3兲 Taking F ⬇ V / L and using the Einstein relation, the ratio of the diffusion current to the drift current is Jdif f /Jdrift = 共L/F兲共Vt/V兲, 共A4兲 where V is the bias voltage, L is the total photoconductor thickness, and Vt = kT / e is the thermal voltage. The ratio L / F is the inverse of normalized schubweg, which has to be smaller 共preferably smaller than 1兲 for detector applications. The applied voltage is in the range of few hundreds to few thousands of volts. At extreme case, taking L / F = 100 in the i-layer and V = 200 V, the ratio of diffusion current to the drift current at room temperature is ⬃0.01. Therefore, the diffusion current component is negligible compared to its drift component in detector applications. 1 S. Kasap, J. B. Frey, G. Belev, O. Tousignant, H. Mani, L. Laperriere, A. Reznik, and J. A. Rowlands, Phys. Status Solidi B 246, 1794 共2009兲. 2 S. O. Kasap and G. Belev, J. Optoelectron. Adv. Mater. 9, 1 共2007兲. 3 C. Allen, G. Belev, R. Johanson, and S. O. Kasap, J. Non-Cryst. Solids 354, 2711 共2008兲. 4 K. S. Karim, A. Nathan, J. A. Rowlands, and S. O. Kasap, IEE Proc.: Circuits Devices Syst. 150, 267 共2003兲. 5 M. Spahn, Eur. Radiol. 15, 1934 共2005兲. 6 G. Belev and S. O. Kasap, J. Non-Cryst. Solids 352, 1616 共2006兲. J. Vac. Sci. Technol. A, Vol. 29, No. 3, May/Jun 2011 031603-6 7 G. Zentai, L. Partain, R. Pavlyuchkova, C. Proano, M. Schieber, K. Shah, P. Bennett, L. Melekhov, and H. Gilboa, IEEE Trans. Nucl. Sci. 53, 2506 共2006兲. 8 H. Du, L. E. Antonuk, Y. El-Mohri, Q. Zhao, Z. Su, J. Yamamoto, and Y. Wang, Phys. Med. Biol. 53, 1325 共2008兲. 9 George Belev, Safa Kasap, J. A. Rowlands, David Hunter, and Martin Yaffe, Curr. Appl. Phys. 8, 383 共2008兲. 10 S. A. Mahmood, M. Z. Kabir, O. Tousignant, H. Mani, J. Greenspan, and P. Botka, Appl. Phys. Lett. 92, 223506 共2008兲. 11 J. B. Frey, G. Belev, O. Tousignant, H. Mani, and S. O. Kasap, Phys. Status Solidi C 6, S251 共2009兲. 12 J. A. Rowlands and J. Yorkston, in Handbook of Medical Imaging, edited by J. Beutel, H. L. Kundel, and R. L. Van Metter 共SPIE, Washington, 2000兲, Vol. 1, Chap. 4. 13 D. C. Hunt, O. Tousignant, and J. A. Rowlands, Med. Phys. 31, 1166 共2004兲. 14 S. O. Kasap and J. A. Rowlands, IEE Proc.: Circuits Devices Syst. 149, 85 共2002兲. 15 M. Abkowitz, Philos. Mag. Lett. 58, 53 共1988兲. 16 M. F. Stone, W. Zhao, B. V. Jack, P. O’Connor, B. Yu, and P. Rehak, Med. Phys. 29, 319 共2002兲. 17 S. M. Sze and K. K. Ng, Physics of Semiconductor Devices 共Wiley, New Jersey, 2007兲, p. 161. 18 S. O. Kasap and C. Juhasz, Photograph. Sci. Eng. 26, 239 共1982兲. 19 S. O. Kasap, Viswanath Aiyah, B. Polischuk, A. Bhattacharyya, and Z. Liang, Phys. Rev. B 43, 6691 共1991兲. 20 G. J. Rees, H. G. Grimmeiss, E. Janzen, and B. Skarstam, J. Phys. C 13, 6157 共1980兲. 21 G. Micocci, P. Siciliano, and A. Tepore, Sol. Energy Mater. 20, 181 共1990兲. 22 S. O. Kasap, B. Polischuk, and D. Dodds, Rev. Sci. Instrum. 61, 2080 共1990兲. 23 S. A. Mahmood and M. Z. Kabir, Curr. Appl. Phys. 9, 1393 共2009兲. 24 H.-Z. Song, G. J. Adriaenssens, E. V. Emelianova, and V. I. Arkhipov, Phys. Rev. B 59, 10607 共1999兲. 25 Safa O. Kasap and John A. Rowlands, Proc. IEEE 90, 591 共2002兲. 26 G. E. Frank-Kamennetskaya, M. D. Vorontsov, and I. P. Kalinkin, Russ. Phys. J. 33, 952 共1990兲. 27 S. Touihri, G. Safoula, and J. C. Bernéde, Phys. Status Solidi A 159, 569 共1997兲. 28 J. C. Bernède, S. Touihri, and G. Safoula, Solid-State Electron. 42, 1775 共1998兲. 29 S. Kar and W. E. Dahlke, Solid-State Electron. 15, 221 共1972兲.
