Study on the quantum efficiency of resonant cavity enhanced GaAs far-infrared detectors

Transcription

1 JOURNAL OF APPLIED PHYSICS VOLUME 91, NUMBER 9 1 MAY 2002 Study on the quantum efficiency of resonant cavity enhanced GaAs far-infrared detectors Y. H. Zhang, H. T. Luo, and W. Z. Shen a) Laboratory of Condensed Matter Spectroscopy and Opto-Electronic Physics, Department of Physics, Shanghai Jiao Tong University, 1954 Hua Shan Road, Shanghai , People s Republic of China Received 27 November 2001; accepted for publication 6 February 2002 We present a detailed theoretical analysis on the quantum efficiency of a resonant cavity enhanced RCE GaAs homojunction work function internal photoemission far-infrared FIR detector. The quantum efficiency under both resonant and nonresonant conditions has been calculated. All the detector parameters are optimized under the realistically nonresonant condition. The further investigation of the standing wave effect SWE shows that the SWE is important and cannot be neglected for the FIR detector. The resulting quantum efficiency is about two times higher than that in the normal GaAs homojunction FIR detector measured by experiment, showing a promising effect. In contrast to the case in the near-infrared region, the wavelength selectivity is not obvious in the FIR region. The theoretical analysis can be applied to other RCE homojunction FIR detectors American Institute of Physics. DOI: / I. INTRODUCTION a Author to whom correspondence should be addressed; electronic mail: wenzshen@sina.com High performance far-infrared FIR semiconductor detectors have attracted much attention in past years because of their potential application for space astronomy, such as NASA s space infrared telescope facility program. 1 Up to now, several types of semiconductor detectors have been proposed and demonstrated in the FIR radiation range. Among them, extrinsic Ge photoconductors unstressed or stressed 2 and Ge block-impurity-band detectors 3 are commonly studied. Although stressed Ge:Ga detectors respond up to 220 m, 4 there are many technological challenges for fabricating large format arrays in germanium. Recently, FIR detection concept has been proposed based on the internal photoemission in homojunction structures. The corresponding GaAs 5 and Si 6 homojunction work function internal photoemission HIWIP FIR detectors have been fabricated and demonstrated successfully in these two mature materials. The unique feature of these HIWIP detectors is that the cutoff wavelength is tailorable, i.e., any cutoff wavelength, in principle, can be obtained as needed. This opens new options for developing semiconductor FIR detectors because the HIWIP detectors could have performance 5 comparable to that of conventional Ge FIR photoconductors and blocked-impurity-band FIR detectors, with unique material advantage. Quantum efficiency is a key parameter to characterize the performance of detectors. However, the highest quantum efficiency of GaAs HIWIP FIR detectors that even measured is only 12.5%, 5 which is far from satisfactory. Furthermore, the quantum efficiency decreases rapidly when the photon energy is close to the cutoff wavelength, limiting the performance of these FIR detectors. Therefore, it is critical to improve the quantum efficiency of HIWIP detectors significantly. Researchers show that applying a resonant cavity in semiconductor detectors can increase the quantum efficiency efficiently in many cases. Such a resonant cavity enhanced RCE structure offers the possibility of overcoming the low quantum efficiency limitation of conventional photodetectors. 7 The RCE detectors are based on the enhancement of the optical field within a Fabry-Pérot resonator. The increased field allows the use of a thin absorbing layer, which minimizes the transit time of the photogenerated carriers without hampering the quantum efficiency. Some efforts have been made on p-i-n photodiodes, 8 avalanche photodiodes 9 and Schottky photodetectors, 10 where quantum efficiency even up to 90% can be achieved, showing the excellent effect and structure popularity. Previous reports on the application of resonant cavities concentrate mainly on the near- or mid-infrared semiconductor detectors and have not made any discussion on the application of RCE structures for FIR detectors. In this article, we apply a resonant cavity to the GaAs HIWIP FIR detector and present a general method to optimize the cavity design, so that the RCE FIR detectors can provide the highest quantum efficiency. The analysis starts with expressing the quantum efficiency as a function of photodetectors optical and physical parameters. We first present a theoretical model for quantum efficiency in HIWIP detectors in Sec. II, which allows us to calculate the quantum efficiency of the multi-period structure. Then in Sec. III, we focus on the theoretical design and optimization of RCE HIWIP structures by neglecting the effect of standing wave, where the quantum efficiency under both the resonant and nonresonant conditions has been discussed separately, and all the optimized parameters are presented. Furthermore, in Sec. IV, we take into account the effect of standing wave on quantum efficiency, and compare the optimized quantum efficiency with that of the normal GaAs HIWIP detector demonstrated by experiment. And finally, some concluding remarks and discussions are presented in Sec. V /2002/91(9)/5538/7/$ American Institute of Physics

2 J. Appl. Phys., Vol. 91, No. 9, 1 May 2002 Zhang, Luo, and Shen 5539 FIG. 1. a Schematic of a p-gaas multilayer HIWIP detector after device processing, p, p and i are the contact layer, emitter layer and intrinsic layer, respectively. b Analysis model of a RCE HIWIP detector. The thickness of the emitter layer and the intrinsic layer is d and h, respectively. The top and bottom mirrors M t and M b are distributed Bragg reflectors DBR. II. THEORETICAL MODEL The schematic of a p-gaas HIWIP detector after device processing is illustrated in Fig. 1 a. It is clear that the basic structure of the HIWIP detector consists of N periods of heavily doped emitter layers and undoped intrinsic layers across which most of the voltage is dropped. Figure 1 b illustrates the schematic of the theoretical model for the RCE HIWIP detector, which is obtained by sandwiching the HI- WIP detector between a top mirror and a bottom mirror. Generally, the end mirrors are made of quarter-wave stacks of semiconductor or insulator materials that are capable of providing the desired reflection in the expected radiation range. In a simplified design, the top mirror can be a native semiconductor and air interface, which provides a reflectivity of approximately 30% for GaAs. The infrared absorption mainly occurs in the heavily doped emitter layers. Unlike the interband transition where both electrons and holes can be created when the photon energy is larger than the energy gap, in HIWIP detectors, the absorption mechanism involved is the free carrier absorption. 11 The quantum efficiency of a detector is defined as the probability that a single photon incident on the device generates a carrier that contributes to the detector current. For the HIWIP detectors, the detection mechanism involves absorption in the emitter layers followed by the internal photoemission of photoexcited carriers across the junction barrier and then collection. Therefore, the total quantum efficiency is the product of photon absorption probability a, internal quantum efficiency b and barrier collection efficiency c, 5 i.e., total a b c. In the present article, we will not discuss the effect of c, since it does not involve any parameters relating to our study. As a result, we just focus on a b, which corresponds to the maximum quantum efficiency ( c 1) of the HIWIP FIR detectors. 5 We first derive the formulation of photon absorption probability a. a is the ratio of the absorbed optical field power to the incident optical power. The electrical field inside the RCE structures can be divided into the forward traveling field E f and the backward traveling field E b, as shown in Fig. 1 b. Under the general consideration, the reflection at the interfaces between the emitter and intrinsic layers is ignored, 7 and the standing wave effect is temporarily neglected here we will consider it in Sec. IV. Through a selfconsistent consideration, the E f at the front and E b at the back interface of the mth emitter layer are given by f E me m 1 e i h/2 j i 1 R h 1 1 n e 1 E in, 1a

3 5540 J. Appl. Phys., Vol. 91, No. 9, 1 May 2002 Zhang, Luo, and Shen with E b me 2N m R 2 e 2 1 R j 1 1 n e 1 E in, s 2 n s 0 s i,e, 1b 2N R 1 R 2 e j 1 2, where E in is the optical field of the incident light, the superscripts f and b indicate forward and backward, respectively, the subscript me mi indicates the mth emitter layer intrinsic layer, 0 is the wavelength in the air, d, e, n e and h, i, n i are the thickness, absorption coefficient and refractive index in emitter and intrinsic layers, respectively. R 1 and R 2 are the reflectivity of the top and bottom mirrors, respectively. The optical power inside the resonant cavity is given by e i h e d /2 j i h e d, P s n s 2y 0 E s 2 s i,e,in, 2 where y 0 is the vacuum characteristic impedance of electromagnetic waves. In this case, the light power absorbed in the emitter layer is P a n e 2y 0 N m 1 f E me 2 E b me 2 1 e e d e i h e N i h e d R 2 1 e e d 1 2 R 1 R 2 e N i h e d cos 2N i h e d 1 2 R 1 R 2 e 2N i h e d 1 e i h e d 1 R 1 1 e N i h e d P in, 3 where N is the number of the periods. a is the ratio of the absorbed power P a to the incident optical power P in, i.e., a P a /P in, and gives e i h e N i h e d R 2 1 e e d a 1 2 R 1 R 2 e N i h e d cos 2N i h e d 1 2 R 1 R 2 e 2N i h e d 1 e i h e d 1 R 1 1 e N i h e d. 4 The first term at the right of Eq. 4 represents the cavity enhancement effect. When R 2 0, Eq. 4 yields a for a conventional detector. The internal quantum efficiency b is given by 5 b exp d/l z, 5 where L z denotes the inelastic scattering mean free path with a typical value of Å. Therefore, the maximum quantum efficiency is given by a b e i h e N i h e d R 2 1 e e d 1 2 R 1 R 2 e N i h e d cos 2N i h e d 1 2 R 1 R 2 e 2N i h e d 1 e i h e d 1 R 1 1 e N i h e d exp d/l z. 6 To compare the calculated results with the experiment, all the basic parameters used in the process of calculation are first taken from a typical p-gaas HIWIP FIR detector 5 with a doping concentration of cm 3 in the emitter layers. The detector has been shown with a cutoff wavelength of 100 m at a bias of 192 mv and a maximum quantum efficiency of 12.5%. III. OPTIMIZING STRUCTURE A. Resonant condition According to Eq. 6, it is easy to find out that changes periodically with the wavelength. The resonant wavelengths are satisfied: 2N( i h e d) 1 2 2k (k 0, 1, 2...).Proper selection of the device parameters allows us to obtain a high. In the resonant condition, Eq. 6 can be reduced to e i h e N i h e d R 2 1 e e d 1 R 1 R 2 e N i h e d 2 1 e i h e d 1 R 1 1 e N i h e d exp d/l z.

4 J. Appl. Phys., Vol. 91, No. 9, 1 May 2002 Zhang, Luo, and Shen 5541 FIG. 2. Comparison of the absorption coefficient in the emitter cm 3 and the intrinsic around cm 3 layers, which is calculated from the complex permittivity of each layer by matching the electric and magnetic fields at the interfaces. The absorption peak at 37.3 m is due to the transverse optical TO phonons of GaAs. Furthermore, the absorption in intrinsic layers can be neglected. It is known that photon is mostly absorbed in the heavily doped emitter layers and i is negligibly small compared to e in the entire infrared radiation range. Taking the p-gaas detector with the doping concentration of cm 3 as an example, the comparison of e with i is displayed in Fig. 2. The FIR absorption coefficients are calculated from the complex permittivity of each layer by matching the electric and magnetic fields at the interfaces. 12 In the entire infrared region, e is several orders larger than i, and it is reasonable to neglect i. The absorption peak at 37.3 m in Fig. 2 is due to the transverse optical TO phonons of GaAs. The wavelength range interested below is m, which falls outside of the TO phonon peak. Figure 3 presents the calculation of the dependence of on R 1 and R 2 under the resonant condition. It is easy to see that increases with R 2 at any R 1, indicating that R 2 should FIG. 3. The dependence of quantum efficiency on the R 1 and R 2 under the resonant condition when N 20, d 150 Å and h 800 Å. FIG. 4. The effect of N and d on under the resonant condition when R and R and h 800 Å. be as high as possible in the process of device design. Nevertheless, at a given R 2, the peak of occurs at a certain R 1, which satisfies R 1 R 2 e 2N e d 7 and the maximum is 51.8% when R and R The effects of N and d on are shown in Fig. 4. Evidently, N and d should match each other to obtain the highest. Excess periods of layers and too thick emitter layers are not only unnecessary, but also may decrease. However, even if the parameters of RCE detectors vary in a large scope, the resonant condition is usually unsatisfied for FIR detectors under the assumption that 1, 2 0, 13 due to the long wavelength which may span much longer than the thickness of the detector. This is in contrast to the cases of near-infrared or mid-infrared detectors. Therefore, in the following, we will concentrate the analysis on the realistically nonresonant condition. B. Nonresonant condition In the design of RCE detectors, the material and the structure parameters, such as the reflectivity of the end mirrors (R 1,R 2 ), the thickness of the emitter and intrinsic layers (d,h), and the number of periods N, should be selected properly to obtain as high as possible. In the following, these parameters will be optimized step by step. Again, we take the p-gaas detector with doping concentration of cm 3 as an example. To compare with the experiment result, all the following results are calculated at 0 60 m, since the measured quantum efficiency does not change within m. 5 Figure 5 demonstrates the dependence of on R 1 and R 2 under the nonresonant condition when N 20, d 150 Å, h 800 Å, which are the same as the detector parameters given in Ref. 5. These curves show that the highest quantum efficiency is 26.6%, when R and R As stated above, the mirrors are generally made of quarter-wave stacks of semiconductor or insulator, which means that the thickness of a single layer of the mirror material is scaled as 0 /4n n is the refractive index of the mirror material. In FIR region, the wavelength is larger than

5 5542 J. Appl. Phys., Vol. 91, No. 9, 1 May 2002 Zhang, Luo, and Shen FIG. 5. The dependence of on R 1 and R 2 under the nonresonant condition when N 20, d 150 Å, h 800 Å which are the same as the structure parameters of the detector in Ref. 5. FIG. 6. The calculated as a function of d and N under the nonresonant condition with h 800 Å, R and R tens of micrometer. The bottom mirror with reflectivity larger than 90% usually needs multiperiod, which may be confronted with some technical difficulties. Nevertheless, according to a simple estimation made by the transfer matrix method, 14 a mirror with a reflectivity of 80% is possible as long as the refractive index contrast between the mirror materials is proper. For the top mirror, unless the anti-reflection film is used, the semiconductor and air interface naturally provides a reflectivity of approximately 30% as stated above. Therefore, R and R are reasonable parameters for the p-gaas FIR detectors. In such a case, the quantum efficiency is 16.4%, which is higher than 12.5% measured by experiment 5 in the normal p-gaas HIWIP FIR detector. However, the improvement of the quantum efficiency given by the calculation for RCE detectors seems to be not very obvious, which results from the fact that the detector itself gives rise to a simple cavity architecture formed by the bottom contact layer and the semiconductor/air interface. Therefore, other parameters should be further optimized. Having determined material parameters R and R 2 0.8, we examine the thickness of the emitter layer d and the number of periods N next. The effect of d and N on under the nonresonant condition with R 1 0.3, R and h 800 Å is calculated in Fig. 6. It is seen that is high when d varies between 50 and 300 Å and N falls in the range of 8 12, the highest ( 18.3%) is obtained at d 150 Å and N 10. More numbers of layers are unnecessary and may even hamper the increase of. Therefore, it is meaningless to increase the number of layers indefinitely. The remnant structure parameter is h. Figure 7 shows the dependence of on h and N when R 1 0.3, R and d 150 Å. When N 10, the highest occurs at h 100 Å. However, h cannot be too thin due to the space charge effect and is usually 3 5 times larger than d, 15 so h 500 Å is preferred. Therefore, all the detector parameters have been optimized: d 150 Å, h 500 Å, N 10, R 1 0.3, R 2 0.8, which are close to the previous design of d 150 Å, h 800 Å, N 20 for p-gaas HIWIP detectors. 5 The detailed analysis to design the mirrors will be discussed elsewhere. IV. STANDING WAVE EFFECT In the above analysis, the spatial distribution of the optical field inside the cavity has been neglected. The spatial distribution arises from the standing wave formed by the two counter propagating waves. When the detectors with thick emitter layers that span several periods of the standing wave are considered, the standing wave effect SWE can be neglected. For very thin emitter layers, the SWE must be considered. In the case of the FIR region, the thickness of the emitter layer is much smaller than the wavelength and the SWE should be included in the analysis of. By conveniently calculating the optical field inside a lossless and uniformity cavity, the SWE is included in the formulation of as an effective absorption coefficient, i.e., eff SWE, which is either enhanced SWE 1 or decreased SWE 1 by the placement of the emitter layers. 7 The optical field E and intensity E 2 are f E z E 1i e j i z E b Ne e j i L z 8 FIG. 7. The dependence of on h and N under the nonresonant condition for R 1 0.3, R and d 150 Å.

6 J. Appl. Phys., Vol. 91, No. 9, 1 May 2002 Zhang, Luo, and Shen 5543 FIG. 8. The SWE as a function of the emitter layer thickness d for various intrinsic layer thickness h, where d is normalized by h. FIG. 9. The wavelength dependence of the SWE and including the standing wave effect for R 1 0.3, R 2 0.8, d 150 Å, h 500 Å and N 10. E z 2 1 R 2 2 R 2 cos 2 i L z 2 1 R 1 1 R 1 R 2 2 R 1 R 2 cos 2 i L 1 2 E in 2, 9 where L N(h d) is total length of the cavity and all the other parameters are defined in Sec. II. The effective absorption coefficient can be expressed as 16 eff 1/d 0 d z E 2 z, dz, 10 2/ /2 0 E 2 z, dz where 0 /n e and the denominator is the average of the standing wave. Taking (z) to be negligible outside the emitter layer and constant within the emitter layer, we have SWE eff N m 1 L 1/d m d Lm E 2 z, dz 2/ 0 /2 E 2 z, dz, 11 where L m (m 1)(h d) h. For an ideal bottom (R 2 1), the SWE reduces to a simple form SWE 1 sin id, 12 i d where and correspond to the cases when the emitter layers are at the standing wave maximum and minimum, respectively. It is seen from Eq. 12 that SWE may change between 0 and 2. Figure 8 shows the dependence of SWE calculated from Eq. 11 on the emitter layer thickness d for various intrinsic layer thickness h when R and R Considering the case that 0 60 m, when h ranges between 0 /800 and 0 /2000 which corresponds to h of Å, the SWE is much larger than 1 at any consideration of d shown in the present article. Such a high SWE indicates that the emitter layers for the detector with such structure parameters (d,h) are just centered around the maximum optical field position and the RCE FIR detector can fully utilize the SWE to increase the quantum efficiency. Figure 9 shows the dependence of the SWE dashed curve on the wavelength for the detector with the optimized parameters given in Sec. III. In the entire wavelength range where the HIWIP detector may work, the SWE changes with the wavelength slowly. We can simply take the SWE at 60 m 1.87 as the SWE of the entire interesting range. Thus the effective absorption coefficient eff Substituting eff into Eq. 6, we can calculate the quantum efficiency including the standing wave effect. Figure 9 also illustrates the wavelength dependence of solid curve with the optimized parameters. At 60 m, 33.1% which is about two times higher than 12.5% measured by experiment in the normal p-gaas FIR detector, indicating that the RCE structure can obviously improve the quantum efficiency of HIWIP FIR detectors. The decrease of with the wavelength results from the wavelength selectivity of the quantum efficiency, however, due to the long wavelength, the wavelength selectivity is not obvious in the entire FIR radiation range, in contrast to the case in near-infrared radiation range. 7 On the other hand, the increase in quantum efficiency with the wavelength overcomes the problem of rapid decrease of quantum efficiency near the cutoff wavelength in HIWIP FIR detectors. V. CONCLUSIONS A proposal to increase the quantum efficiency for p-gaas HIWIP FIR detectors has been presented by employing RCE structures. The quantum efficiency under resonant and nonresonant conditions has been calculated. It has been shown that the material (R 1,R 2 ) and structure parameters (d,h,n) may affect the quantum efficiency significantly. Considering the possibility of growth technique, all the detector parameters optimized under the nonresonant condition are: R 1 0.3, R 2 0.8, d 150 Å, h 500 Å and N 10. The analysis of the standing wave effect shows that the SWE is important and cannot be neglected for the FIR detector with such optimized parameters. The resulting quantum efficiency of 33.1% is about two times higher than that in the normal HIWIP detectors measured by experiment, indicating a promising effect. The wavelength selectivity of the quantum efficiency is not obvious in the entire FIR radiation range, in contrast to the case in near-infrared radiation range. The theoretical analysis can be applied to other RCE HIWIP FIR detectors. Further work is to investigate the detailed design

7 5544 J. Appl. Phys., Vol. 91, No. 9, 1 May 2002 Zhang, Luo, and Shen of the mirrors including the selection of the mirror materials and the effect of 1 and 2 and the effect of interface reflection on the quantum efficiency. ACKNOWLEDGMENTS This work is supported in part by the Natural Science Foundation of China under Contract Nos and and Shanghai QMX Project No. 00QA The authors would like to acknowledge G. Yu for his technical help. 1 M. W. Werner, Infrared Phys. Technol. 35, J. W. Berman and E. E. Haller, Infrared Phys. Technol. 35, D. M. Watson, M. T. Guptill, J. E. Huffman, T. N. Krabach, S. N. Raines, and S. Satyapal, J. Appl. Phys. 74, N. M. Haegel, Nucl. Instrum. Methods Phys. Res. A 377, W. Z. Shen, A. G. U. Perera, H. C. Liu, M. Buchanan, and W. J. Schaff, Appl. Phys. Lett. 71, A. G. U. Perera, W. Z. Shen, H. C. Liu, M. Buchanan, M. O. Tanner, and K. L. Wang, Appl. Phys. Lett. 72, M. S. Unlu and S. Strite, J. Appl. Phys. 78, H. Nie, K. A. Anselm, V. Hu, S. S. Murtaza, B. G. Streetman, and J. C. Campbell, Appl. Phys. Lett. 70, C. Lennox, H. Nie, P. Yuan, G. Kinsley, A. L. Holmes, Jr., B. G. Streetman, and J. C. Campbell, IEEE Photonics Technol. Lett. 11, M. S. Unlu, M. Gokkavas, B. M. Onat, E. Ata, E. Ozbay, T. P. Mirin, K. J. Knopp, K. A. Bartness, and D. H. Christensen, Appl. Phys. Lett. 72, A. L. Korotkov, A. G. U. Perera, W. Z. Shen, J. Herfort, K. H. Ploog, W. J. Schaff, and H. C. Liu, J. Appl. Phys. 89, G. Yu, L. F. Jiang, W. Z. Shen, and H. Z. Wu, J. Phys. D 35, D. S. Golubović, P. S. Matavulj, and J. B. Radunović, Semicond. Sci. Technol. 15, J. L. Shen, C. Y. Chang, W. C. Chou, M. C. Wu, and Y. F. Chen, Opt. Express 9, W. Z. Shen, A. G. Perera, M. H. Francombe, H. C. Liu, M. Buchanan, and W. J. Schaff, IEEE Trans. Electron Devices 45, , and references therein. 16 S. C. Corzine, R. S. Geels, J. W. Scott, R. H. Yan, and L. Coldren, IEEE J. Quantum Electron. 25,