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Room-Temperature Photoconductivity Far Below the Semiconductor Bandgap Zhiming Huang,* Jinchao Tong, Jingguo Huang, Wei Zhou, Jing Wu, Yanqing Gao, Jinxing Lu, Tie Lin, Yanfeng Wei, and Junhao Chu Today most information is transformed from light into electrical signals using photon detectors.[1] When light is absorbed by a material such as a semiconductor, the number of free electrons and/or holes increases and raises its electrical conductivity. Photon detectors exhibit both good signal-to-noise performance[2] and a very fast response.[3] Many attractive applications have been already demonstrated in optical communications,[4,5] imaging sensing,[6,7] astronomy,[8] biology,[9] medicine[10] and non-destructive material characterization.[11,12] However, photon detectors show a selective wavelength dependence of response. To cause excitation, the light that strikes the semiconductor must have enough energy to raise electrons across the bandgap and subbands, or to excite the impurities within the bandgap. The detection efficiency decreases significantly for long wavelength photons with the energy lower than the bandgap of a semiconductor, because thermal transitions compete with the optical ones, making noncooled devices very noisy and requiring cryogenic cooling. Usually, liquid-nitrogen cooling (ca. 77 K) is needed in the mid-infrared for intrinsic semiconductors;[6] and liquid helium cooling (4.2 K) or even dilution refrigeration (ca. 100–300 mK) is required for extrinsic detection in order to suppress noise due to thermally induced transitions between close-lying energy levels in the far infrared and terahertz range.[13–15] Up to now, room-temperature photoconductivity has been considered to be impossible in semiconductors excited by photons with quantum energy far below the bandgap due to the strong thermal noise disturbance. Here, we propose a way to generate electrons at room temperature by photons in a semiconductor well below its bandgap, achieved in a metal– semiconductor–metal (MSM) structure with sub-wavelength spacing between two metallic contacts. When an external
Prof. Z. M. Huang, Dr. J. C. Tong, Dr. J. G. Huang, Dr. W. Zhou, Dr. J. Wu, Dr. Y. Q. Gao, Dr. J. X. Lu, Dr. T. Lin, Prof. Y. F. Wei, Prof. J. H. Chu National Laboratory for Infrared Physics Shanghai Institute of Technical Physics Chinese Academy of Sciences 500 Yu Tian Road, Shanghai 200083, PR China E-mail: [email protected] Prof. Z. M. Huang Key laboratory of Space Active Opto-Electronics Technology Shanghai Institute of Technical Physics Chinese Academy of Sciences 500 Yu Tian Road, Shanghai 200083, PR China
DOI: 10.1002/adma.201402352
Adv. Mater. 2014, DOI: 10.1002/adma.201402352
electromagnetic radiation (photons) is impinged onto the structure, potential wells will be induced to trap carriers originating from the metallic contacts because of the great difference in the electron concentration between the metal and the semiconductor. Thus, the resistivity of the semiconductor is changed by the extra generated carriers. This concept is a breakthrough to photoconductivity and has important applications in the bandgap tailoring of semiconductors,[16] plasmonics,[17,18] metamaterials,[19,20] long-wavelength infrared detection,[21] as well as far-infrared and terahertz photonics.[22] Considering an MSM structure as shown in Figure 1a with the thickness of semiconductor d, spacing length a and width W, we propose that the anti-symmetric electric field of the timedependent electromagnetic transverse magnetic (TM) wave in the x direction of the MSM structure has the form:[23]
E x = E 1 sin(π x /a ) exp ( − z ε r (π /a )2 − k 02 − iω t )
(1)
where E1 is the amplitude of the enhanced electric field, εr is the relative permittivity of the semiconductor, k0 = ω/c0 is the free space wave vector, ω is the angular frequency of light, and c0 is the light velocity in the free space. It will produce a corresponding symmetric potential (Figure 1b) according to the relationship of E x = −∇ xϕ :
ϕ = ϕ 1cos(π x /a ) exp ( − z ε r
(π /a )2 − k02 − iω t ) + C
(2)
where ϕ1 is the amplitude of the potential. According to Equation 2, the potential varies as the ac factor exp(–iωt). That is, in one half period an induced potential well is formed by the anti-symmetric electric field of external electromagnetic radiation, the electrons from the two metallic contacts are accelerated toward the semiconductor by the force of the electric field and accumulated in the well. But in the other half period of the external electromagnetic radiation, an induced potential barrier is generated. Fortunately, the electrons are slowed down from the finial velocity in the first period by the following reversed force of the electric field. Hence, the barrier is to block the electrons to drift from one side to the other side of the two metallic contacts, and helpful to remain the electrons in the potential well. Finally, the electrons coming from the metallic contacts are trapped in electromagnetic induced wells. Then the electron concentration in the semiconductor is changed, leading to the variation of the resistance. It should be noted here that if a potential barrier is firstly formed in one half period, the same result will be realized in the MSM structure. Because the electron concentration in the metals (ca. 5.89 × 1022 cm–3) is close to seven orders greater than that in the semiconductor
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Figure 1. Photon-induced carrier generation in the MSM structure. a) Schematic diagram of the MSM structure. b) Plots of the anti-symmetrical electric field E (dark grey) and the generated potential well −eϕ (green) by E = −∇ϕ . c) Distribution of extra electrons (blue dots) in the semiconductor trapped in the induced wells (green lines) at different cross sections (yellow panels) along the direction of z axis. Red dots: intrinsic carriers in the semiconductor.
(ca. 1.0 × 1016 cm–3), electrons are still generated in the wells after the balance adjustment of one or several periods of the external electromagnetic radiation. Therefore, only one-half period of the time-dependent factor exp(–iωt) in Equation 2 needs to be considered to accumulate electrons in the induced potential wells. In addition, as shown in Figure 1c the depth of the well decreases along the direction of the z axis. According to D’Alembert’s equation[24] ∇2ϕ − ε 0 μ 0 2ϕ/2t = –ρe/ε0 (ε0 and μ0 are the permittivity and permeability, respectively, and ρe is the generated electric density), and integrating ρe over the above mentioned half phase period in the direction of the x and z axes, we can then get the averaged electric density ρe. Finally, in terms of ρe = Δn ⋅ ( − q) , the variation of electron concentration can be obtained in the semiconductor as follows: Δn =
4 ε 0 aE 1 π 3qd ε r
(
(π /a )2 − k02 [1 − exp − d ε r
)
(π /a )2 − k02 ]
(3)
Furthermore, for a bundle of photons with flux density of radiation ϕs received in the structure, the amplitude of the electric field E0 and the power P can be expressed as E 0 = φshc 0 /(qλ 2 ) and P = φshc 02 /λ 2 , respectively, where h is the Planck constant and λ is the wavelength of the incident radiaε (ω ) ε 0 μ 0 k0 − (π /a ) 2
tion. In addition, as E 1 = ηE 0 , where
η=
ε (ω )ε 0 μ 0 k0 − (π /a ) 2
2
2
(ε(ω) is the relative permittivity of the metal) is the electric field enhancement factor in the spacing and is determined by boundary conditions (for example, a value of ca. 42 000 at the frequency of 0.0375 THz for a = 30 μm), the variation of the electron concentration can be further written as: Δn =
2
4 ε 0 aηP ( π /a )2 − k02 [1 − exp( − d ε r (π / a ) 2 − k 02 )] (4) π 3q 2c 0 d ε r
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Equation 4 shows clearly that extra carriers will be induced by external photons when the wavelength λ of the incident radiation is greater than two times of the spacing a in MSM structure (λ > 60 μm at the spacing of a = 30 μm). To verify that carriers can be truly generated and trapped in electromagnetic induced wells, we use mercury cadmium telluride Hg1−xCdxTe (MCT) to fabricate MSM structures (Figure 1a). MCT is a narrow-bandgap semiconductor with high electron mobility, and the resistance is dominated by electrons at room temperature. The value of composition x is 0.225 in our case and the corresponding bandgap energy is about 202.5 meV (48.91 THz) at room temperature. Band-to-band transitions are fully excited by the strong background radiation at room temperature, so it is very clear to confirm the concept that the carriers come from the two metal sides. Specifically, the MCT epitaxial layers were grown on semi-insulating (SI) substrate cadmium zinc telluride (CZT) by the liquid-phase epitaxial (LPE) method with In dopant. The In-doping concentration of the as-grown samples was ca. 5 × 1014 cm–3. After growth, the samples were annealed in Hg-rich ambient conditions at 240 °C for 24 hours to annihilate the Hg vacancies. The annealed samples were n-type single crystalline semiconductors (Figure S1, Supporting Information) with the electron concentration of ca. 1.0 × 1016 cm–3 at room temperature. After mesa etching and UV photolithography, a series with nominal central spacing of 10–110 μm in the length direction were formed between two thin gold metals. Each metallic contact of the structures on the MCT material had a nominal length of 30 μm. The thickness of the central mesa d was 8 μm and the width of the spacing W was 50 μm (see scanning electron microspcopy (SEM) image shown in Figure S2, Supporting Information). Excellent Ohmic contacts were confirmed between the MCT and Au by current– voltage measurements (as shown in Figure S3, Supporting Information). To measure the variation of electrons in the MCT material, the structure is biased with a direct current of 3 mA. When modulated radiation impinges onto it, a variation of electron concentration leads to the variation of the resistance (i.e., resistivity); therefore, an ac voltage rises between the two metallic contacts. For a semiconductor with fixed mobility of carriers, the variation of the resistance can be described as:[25] ΔR =
−( μe Δn + μ h Δh ) a ⋅ q( μe n + μ h h )2 Wd
(5)
where n is the concentration of electrons, h is the concentration of holes, µe is the mobility of electrons, µh is the mobility of holes, and Δh is the variation of hole concentration. Meanwhile, as Vout = IΔR, where I is the direct bias current, and considering that µe > µh, n > h, then Δn can be finally expressed as: Δn = − n 2 qμeWdVout /(Ia )
(6)
To demonstrate the photoconductivity far below the bandgap of semiconductor in experiments, three light sources were used with the frequencies of 0.0375 THz (0.155 meV), 0.075 THz (0.310 meV), and 0.15 THz (0.620 meV). The actual microwave power output from the Gunn diode source at 0.0375 THz was ca. 50 mW, that from the sextupler of the microwave source at
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Equation 4 are also shown, and they present excellent agreement with our experimental results of Δn. According to Equation 4, the variation of carrier concentration is dependent on the spacing distance. To verify this, Figure 2b depicts the photoconductivity response to the different nominal spacing distances of 10–110 μm at the frequency of 0.0375 THz. The results show that the photoconductivity changes following the spacing distance of the devices, which is well consistent with the spacing-dependent prediction in the theory. Moreover, Figure 2c shows the experimental photoconductivity of the device to the radiated sources at different frequencies. The measured results clearly show that the photoconductivity response is really reduced at high frequency, which is in good agreement with the frequency-dependent prediction in Equation 4. The influence of temperature must be eliminated in the experiments. To fully verify the variation of the resistance resulted from the trapped electrons, rather than from the absorption of the radiation, firstly, we need to know the temperature elevation of the material under the electromagnetic radiation. While neglecting the thermal conductance of the material, the temperature rise can be calculated by: ΔT =
ΔQ PΔt = mC p mC p
(7)
Figure 2. a) Variation of electron concentration as a function of the received power at the frequency of 0.0375 THz for the spacing distance of a = 30 µm. Inset: Typical response signal of voltage radiated by 0.0375 THz at a modulation frequency of 2900 Hz. b) Variation of photoconductivity as a function of the spacing distance at the frequency of 0.0375 THz with P = 1.456 × 10 −5 mW . c) Variation of photoconductivity as a function of radiation frequency for the spacing distance of a = 30 µm with P = 1.456 × 10 −5 mW . Experimental data represented by the dots; theoretical prediction: solid line. d) Response signal of the MSM structure under the impulse of 10 GHz radiation frequency with 52 kHz repetition rate. e) Expansion of the response signal in (d) to show the response time. Gray background strip: 90% of the full amplitude. f) Intrinsic carrier concentration (filled circles) and its differentiation (open squares). g,h) Electric mobility (filled circles) and its differentiation (open squares) (g), and resistivity (filled circles) and its differentiation (open squares) (h) for Hall measurements of the MCT material at the temperature of 250–300 K.
0.075 THz was ca. 10 mW, that from the narrow-band IMPATT at 0.15 THz was ca. 8 mW. The radiation energy of photons is 2–3 orders smaller than the MCT bandgap energy. An adjustable aperture was employed to change the power and the power received by the structure was calibrated by a Golay cell, combined with the frequency-dependent effective area of the structure (Figure S4, Supporting Information). Figure 2a shows the variation of electron concentration Δn for a = 30 μm at a frequency of 0.0375 THz, retrieved from Equation 6 using the photovoltage response of the radiation Vout as shown in the inset of Figure 2a. It increases with the increase of the received power P. The data of theoretical calculation Δn obtained from
Adv. Mater. 2014, DOI: 10.1002/adma.201402352
where m is the mass and Cp is the specific heat of the material, and Δt is the response time of our MSM structure to the incident radiation. To obtain Δt, a microwave source (Agilent E8257D) was set to radiate the structure in free space. It is exciting to see that our structures are also very sensitive to a low microwave frequency, far below the bandgap of semiconductor, and the pulse shape is still well preserved (Figure 2d). By expanding the oscilloscope trace of the response signal (Figure 2e), we estimate that the response time of the MSM structures to be better than 1 μs. Thus the temperature rise under the received power of 1.456 × 10–5 mW (the maximal power in Figure 2a) can be calculated as 9.2 × 10–7 K (C p = 175.6 J kg –1 K –1, ρMCT = 7533 kg m −3 )[26] for the structure with a = 30 μm. Then, Hall measurement was adopted to obtain the variation of intrinsic electron concentration and electron mobility at the temperature from 250 K to 300 K. The results and their differentiations to temperature are shown in Figure 2f and 2g. The measured intrinsic electron concentration increases as the temperature rising but the mobility of electron has the opposite variation trend. Now a detailed estimation is given for
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rising distribution in the MSM structure, which is non-uniform in the MCT material. The temperature rise is lower than 2.82 × 10–6 K (the maximal value at the points in the structure) at P = 1.456 × 10 −5 mW , which is consistent with the evaluation by Equation 7. The simulation in Figure 3b predicts that the temperature rise increases with the increase of the received power. Figure 3c clearly shows that the variation of resistivity in our experiments is the order of ca. 10–5 Ω cm. However, the variation of the resistivity is only about the order of ca. 10–10 Ω cm due to thermal effects of the incident radiation. Figure 3d plots the distribution of the electric field pattern at 0.0375 THz in the x–z cross section. It Figure 3. Simulation of the temperature contribution and electromagnetic fields at the fre- shows an obvious anti-symmetric field disquency of 0.0375 THz by COMSOL for the spacing distance of a = 30 µm. a) Distribution of tribution inside the MCT. A strong electric the relative temperature rise in the structure under the received power P = 1.456 × 10 −5 mW . field intensity is achieved at the metal-semb) Maximal temperature rise versus the received power. c) Experimental variation of the resisiconductor interfaces, leading to the large tivity by generated carriers (black) and estimated variation of the resistivity resulted from the enhancement of the external electromaginuence of the temperature rise (blue). d) Distribution of the anti-symmetric electric fields in MSM structure. e) Plots of the electric field (red) at the section position of z = 1 µm and its netic electric field. However, the intensity corresponding potential well distribution (green) along the x axis. f) Three-dimensional distri- attenuates quickly when the position is far away from the interfaces. This is in conbution of the induced potential wells. sistent with our theory in Equation 1. The enhanced anti-symmetric field can induce an electric potential well inside the semiconductor material the structure with a = 30 μm as an example. The variation of the (Figure 3e). Therefore we describe it as an electromagneticelectron mobility with temperature rise of 9.2 × 10–7 K is about induced well. Figure 3f shows the distribution of the induced – 6.5 × 10–9 m2 V−1 s−1), which is so small that we can almost potential wells in the MSM structure. It shows that the depth of neglect it. The retrieved variation of the intrinsic electron conthe induced wells decreases with an increase in the value of z. centration is ca. 1.5 × 1014 m–3, at least 4 orders less than that Free electrons coming from the metallic contacts are accuobtained in the measurement of ca. 7.0 × 1018 m–3 (see Figure 2a). mulated in the wells, like a puddle holding water in the level Furthermore, Figure 2h shows the measured variation of resisground. The concentration of free carriers is changed in the tivity of the material obtained from Figure 2f and Figure 2g. material between two metal contacts. Therefore, the resistThe rate of variation is about −5.0 × 10 −4 Ω cm K –1 at 293 K, ance of the devices is varied. and the corresponding variation of the resistance is about –3.46 × 10–7 Ω in the MSM, which is also much less than that Finally, results using other semiconductors further supports we obtained in the above measurements, i.e., –3.33 × 10–2 Ω that the free carriers come from the two metal contacts in the MSM structures (see Figure S6 and Figure S7, Supporting (Vout = 100.02 μV, I = 3 mA). These results have strongly demInformation). onstrated that the variation of the resistance does not come In conclusion, we have experimentally and theoretically from the variation of the temperature-dependent resistivity. The demonstrated a way to generate photoconductive carriers at polarization-dependent photoconductivity of the MSM structure a photon energy 2–3 orders below the bandgap energy of a in Figure S5 further exculded the influence of the temperature semiconductor at room temperature in MSM structures. This enhancement. discovery has jumped out of the typical methods of intrinsic Next, for better understanding of the principle to generate absorption, extrinsic absorption, and free-carrier absorption carriers in the MSM structures, the anti-symmetric mode was to realize photoconductivity, and solved the puzzle to generate calculated for our experimental geometry using finite element photon carriers irradiated by energy quanta much lower than simulation COMSOL. By doing this, the relative permittivity the bandgap of semiconductor. It is a great breakthrough in of the MCT material was set as 25 + 0.4i[27] and the dielectric photonics science and technology. We believe it will have huge parameter of metal Au was calculated by the Drude model:[28] effects on the development of semiconductors, metamaterials, plasmonics and low-quanta photon detection, such as the curω p2 ε (ω ) = ε ∞ − (8) rently immature terahertz detection. ω (ω + iω τ ) 16 where ε ∞ = 1 , the plasma frequency ω p = 1.37 × 10 Hz , and 13 ω τ = 4.07 × 10 Hz . The specific results are shown in Figure 3 for the structure with a = 30 μm. Figure 3a shows the typical temperature
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Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2014, DOI: 10.1002/adma.201402352
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This work was supported by the Foundations of China (No. 61274138, 2013CB922301 and No. 61290302). Received: May 26, 2014 Revised: July 4, 2014 Published online:
[1] M. Pospischil, M. Humer, M. Furchi, D. Bachmann, R. Guider, T. Fromherz, T. Mueller, Nat. Photonics 2013, 7, 892. [2] R. H. Hadeld, Nat. Photonics 2009, 3, 696. [3] T. Y. Zhai, M. F. Ye, L. Li, X. S. Fang, M. Y. Liao, Y. F. Li, Y. Koide, Y. Bando, D. Golberg, Adv. Mater. 2010, 22, 453. [4] L. Tang, S. E. Kocabas, S. Latif, A. Okyay, D. Ly-Gagnon, K. C. Saraswatand, D. A. B. Miller, Nat. Photonics 2008, 2, 226. [5] M. W. Geis, J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, S. Deneault, F. Gan, F. X. Kaertner, T. M. Lyszczarz, IEEE Photonics Technol. Lett. 2007, 19, 152. [6] A. Rogalski, J. Antoszewski, L. Faraone, J. Appl. Phys. 2009, 105, 091101. [7] M. Razeghi, Technology of Quantum Devices, Springer, New York, 2010. [8] J. Wei, D. Olaya, B. S. Karasik, S. V. Pereverzev, A. V. Sergeev, M. E. Gershenson, Nat. Nanotechnol. 2008, 3, 496. [9] M. Boberl, M. V. Kovalenko, S. Gamerith, E. J. W. List, W. Heiss, Adv. Mater. 2007, 19, 3574. [10] X. Gao, Y. Cui, R. M. Levenson, L. W. Chung, S. Nie, Nat. Biotechnol. 2004, 22, 969. [11] M. Ettenberg, Adv. Imaging 2005, 20, 29. [12] E. H. Sargent, Adv. Mater. 2005, 17, 515.
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Acknowledgements
[13] G. H. Rieke, M. W. Werner, R. I. Thompson, E. E. Becklin, W. F. Hoffmann, J. R. Houck, F. J. Low, W. A. Stein, F. C. Witteborn, Science 1986, 231, 807. [14] A. D. Turner, J. J. Bock, J. W. Beeman, J. Glenn, P. C. Hargrave, V. V. Hristov, H. T. Nguyen, F. Rahman, S. Sethuraman, A. L. Woodcraft, Appl. Opt. 2001, 40, 4921. [15] T. Ueda, Z. An, S. Komiyama, J. Infrared Millimeter, Terahertz Waves 2011, 32, 673. [16] L. Y. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, Nat. Mater. 2009, 8, 643. [17] J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, M. L. Brongersma, Nat. Mater. 2010, 9, 193. [18] G. C. Dyer, G. R. Aizin, S. Preu, N. Q. Vinh, S. J. Allen, J. L. Reno, E. A. Shaner, Phys. Rev. Lett. 2012, 109, 126803. [19] K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, R. D. Averitt, Phys. Rev. Lett. 2013, 110, 217404. [20] H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, R. D. Averitt, Phys. Rev. Lett. 2009, 103, 147401. [21] S. Keuleyan, E. Lhuillier, V. Brajuskovic, P. G. Sionnest, Nat. Photonics 2011, 5, 489. [22] P. Tassin, T. Koschmy, C. M. Soukoulis, Science 2013, 341, 620. [23] J. A. Kong, Electronmagnetic Wave Theory, 2nd ed., Wiley, New York, 1990. [24] R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, California Institute of Technology, Pasadena, CA, USA 1964. [25] Donald A. Neamen, Semiconductor Physics and Devices: Basic Principles, 3rd ed., McGraw–Hill Higher Education, New York, 2002. [26] P. Capper, J. W. Garland, Mercury Cadmium Telluride Growth, Properties and Applications, John Wiley & Sons Ltd, Chichester, UK, 2011. [27] E. D. Palik, Handbook of Optical Constants of Solids II, Academic Press, New York, 1991. [28] M. A. Ordal, Appl. Opt. 1983, 22, 1099.
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Room-Temperature Photoconductivity Far Below the Semiconductor Bandgap Zhiming Huang,* Jinchao Tong, Jingguo Huang, Wei Zhou, Jing Wu, Yanqing Gao, Jinxing Lu, Tie Lin, Yanfeng Wei, and Junhao Chu Today most information is transformed from light into electrical signals using photon detectors.[1] When light is absorbed by a material such as a semiconductor, the number of free electrons and/or holes increases and raises its electrical conductivity. Photon detectors exhibit both good signal-to-noise performance[2] and a very fast response.[3] Many attractive applications have been already demonstrated in optical communications,[4,5] imaging sensing,[6,7] astronomy,[8] biology,[9] medicine[10] and non-destructive material characterization.[11,12] However, photon detectors show a selective wavelength dependence of response. To cause excitation, the light that strikes the semiconductor must have enough energy to raise electrons across the bandgap and subbands, or to excite the impurities within the bandgap. The detection efficiency decreases significantly for long wavelength photons with the energy lower than the bandgap of a semiconductor, because thermal transitions compete with the optical ones, making noncooled devices very noisy and requiring cryogenic cooling. Usually, liquid-nitrogen cooling (ca. 77 K) is needed in the mid-infrared for intrinsic semiconductors;[6] and liquid helium cooling (4.2 K) or even dilution refrigeration (ca. 100–300 mK) is required for extrinsic detection in order to suppress noise due to thermally induced transitions between close-lying energy levels in the far infrared and terahertz range.[13–15] Up to now, room-temperature photoconductivity has been considered to be impossible in semiconductors excited by photons with quantum energy far below the bandgap due to the strong thermal noise disturbance. Here, we propose a way to generate electrons at room temperature by photons in a semiconductor well below its bandgap, achieved in a metal– semiconductor–metal (MSM) structure with sub-wavelength spacing between two metallic contacts. When an external
Prof. Z. M. Huang, Dr. J. C. Tong, Dr. J. G. Huang, Dr. W. Zhou, Dr. J. Wu, Dr. Y. Q. Gao, Dr. J. X. Lu, Dr. T. Lin, Prof. Y. F. Wei, Prof. J. H. Chu National Laboratory for Infrared Physics Shanghai Institute of Technical Physics Chinese Academy of Sciences 500 Yu Tian Road, Shanghai 200083, PR China E-mail: [email protected] Prof. Z. M. Huang Key laboratory of Space Active Opto-Electronics Technology Shanghai Institute of Technical Physics Chinese Academy of Sciences 500 Yu Tian Road, Shanghai 200083, PR China
DOI: 10.1002/adma.201402352
Adv. Mater. 2014, DOI: 10.1002/adma.201402352
electromagnetic radiation (photons) is impinged onto the structure, potential wells will be induced to trap carriers originating from the metallic contacts because of the great difference in the electron concentration between the metal and the semiconductor. Thus, the resistivity of the semiconductor is changed by the extra generated carriers. This concept is a breakthrough to photoconductivity and has important applications in the bandgap tailoring of semiconductors,[16] plasmonics,[17,18] metamaterials,[19,20] long-wavelength infrared detection,[21] as well as far-infrared and terahertz photonics.[22] Considering an MSM structure as shown in Figure 1a with the thickness of semiconductor d, spacing length a and width W, we propose that the anti-symmetric electric field of the timedependent electromagnetic transverse magnetic (TM) wave in the x direction of the MSM structure has the form:[23]
E x = E 1 sin(π x /a ) exp ( − z ε r (π /a )2 − k 02 − iω t )
(1)
where E1 is the amplitude of the enhanced electric field, εr is the relative permittivity of the semiconductor, k0 = ω/c0 is the free space wave vector, ω is the angular frequency of light, and c0 is the light velocity in the free space. It will produce a corresponding symmetric potential (Figure 1b) according to the relationship of E x = −∇ xϕ :
ϕ = ϕ 1cos(π x /a ) exp ( − z ε r
(π /a )2 − k02 − iω t ) + C
(2)
where ϕ1 is the amplitude of the potential. According to Equation 2, the potential varies as the ac factor exp(–iωt). That is, in one half period an induced potential well is formed by the anti-symmetric electric field of external electromagnetic radiation, the electrons from the two metallic contacts are accelerated toward the semiconductor by the force of the electric field and accumulated in the well. But in the other half period of the external electromagnetic radiation, an induced potential barrier is generated. Fortunately, the electrons are slowed down from the finial velocity in the first period by the following reversed force of the electric field. Hence, the barrier is to block the electrons to drift from one side to the other side of the two metallic contacts, and helpful to remain the electrons in the potential well. Finally, the electrons coming from the metallic contacts are trapped in electromagnetic induced wells. Then the electron concentration in the semiconductor is changed, leading to the variation of the resistance. It should be noted here that if a potential barrier is firstly formed in one half period, the same result will be realized in the MSM structure. Because the electron concentration in the metals (ca. 5.89 × 1022 cm–3) is close to seven orders greater than that in the semiconductor
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Figure 1. Photon-induced carrier generation in the MSM structure. a) Schematic diagram of the MSM structure. b) Plots of the anti-symmetrical electric field E (dark grey) and the generated potential well −eϕ (green) by E = −∇ϕ . c) Distribution of extra electrons (blue dots) in the semiconductor trapped in the induced wells (green lines) at different cross sections (yellow panels) along the direction of z axis. Red dots: intrinsic carriers in the semiconductor.
(ca. 1.0 × 1016 cm–3), electrons are still generated in the wells after the balance adjustment of one or several periods of the external electromagnetic radiation. Therefore, only one-half period of the time-dependent factor exp(–iωt) in Equation 2 needs to be considered to accumulate electrons in the induced potential wells. In addition, as shown in Figure 1c the depth of the well decreases along the direction of the z axis. According to D’Alembert’s equation[24] ∇2ϕ − ε 0 μ 0 2ϕ/2t = –ρe/ε0 (ε0 and μ0 are the permittivity and permeability, respectively, and ρe is the generated electric density), and integrating ρe over the above mentioned half phase period in the direction of the x and z axes, we can then get the averaged electric density ρe. Finally, in terms of ρe = Δn ⋅ ( − q) , the variation of electron concentration can be obtained in the semiconductor as follows: Δn =
4 ε 0 aE 1 π 3qd ε r
(
(π /a )2 − k02 [1 − exp − d ε r
)
(π /a )2 − k02 ]
(3)
Furthermore, for a bundle of photons with flux density of radiation ϕs received in the structure, the amplitude of the electric field E0 and the power P can be expressed as E 0 = φshc 0 /(qλ 2 ) and P = φshc 02 /λ 2 , respectively, where h is the Planck constant and λ is the wavelength of the incident radiaε (ω ) ε 0 μ 0 k0 − (π /a ) 2
tion. In addition, as E 1 = ηE 0 , where
η=
ε (ω )ε 0 μ 0 k0 − (π /a ) 2
2
2
(ε(ω) is the relative permittivity of the metal) is the electric field enhancement factor in the spacing and is determined by boundary conditions (for example, a value of ca. 42 000 at the frequency of 0.0375 THz for a = 30 μm), the variation of the electron concentration can be further written as: Δn =
2
4 ε 0 aηP ( π /a )2 − k02 [1 − exp( − d ε r (π / a ) 2 − k 02 )] (4) π 3q 2c 0 d ε r
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Equation 4 shows clearly that extra carriers will be induced by external photons when the wavelength λ of the incident radiation is greater than two times of the spacing a in MSM structure (λ > 60 μm at the spacing of a = 30 μm). To verify that carriers can be truly generated and trapped in electromagnetic induced wells, we use mercury cadmium telluride Hg1−xCdxTe (MCT) to fabricate MSM structures (Figure 1a). MCT is a narrow-bandgap semiconductor with high electron mobility, and the resistance is dominated by electrons at room temperature. The value of composition x is 0.225 in our case and the corresponding bandgap energy is about 202.5 meV (48.91 THz) at room temperature. Band-to-band transitions are fully excited by the strong background radiation at room temperature, so it is very clear to confirm the concept that the carriers come from the two metal sides. Specifically, the MCT epitaxial layers were grown on semi-insulating (SI) substrate cadmium zinc telluride (CZT) by the liquid-phase epitaxial (LPE) method with In dopant. The In-doping concentration of the as-grown samples was ca. 5 × 1014 cm–3. After growth, the samples were annealed in Hg-rich ambient conditions at 240 °C for 24 hours to annihilate the Hg vacancies. The annealed samples were n-type single crystalline semiconductors (Figure S1, Supporting Information) with the electron concentration of ca. 1.0 × 1016 cm–3 at room temperature. After mesa etching and UV photolithography, a series with nominal central spacing of 10–110 μm in the length direction were formed between two thin gold metals. Each metallic contact of the structures on the MCT material had a nominal length of 30 μm. The thickness of the central mesa d was 8 μm and the width of the spacing W was 50 μm (see scanning electron microspcopy (SEM) image shown in Figure S2, Supporting Information). Excellent Ohmic contacts were confirmed between the MCT and Au by current– voltage measurements (as shown in Figure S3, Supporting Information). To measure the variation of electrons in the MCT material, the structure is biased with a direct current of 3 mA. When modulated radiation impinges onto it, a variation of electron concentration leads to the variation of the resistance (i.e., resistivity); therefore, an ac voltage rises between the two metallic contacts. For a semiconductor with fixed mobility of carriers, the variation of the resistance can be described as:[25] ΔR =
−( μe Δn + μ h Δh ) a ⋅ q( μe n + μ h h )2 Wd
(5)
where n is the concentration of electrons, h is the concentration of holes, µe is the mobility of electrons, µh is the mobility of holes, and Δh is the variation of hole concentration. Meanwhile, as Vout = IΔR, where I is the direct bias current, and considering that µe > µh, n > h, then Δn can be finally expressed as: Δn = − n 2 qμeWdVout /(Ia )
(6)
To demonstrate the photoconductivity far below the bandgap of semiconductor in experiments, three light sources were used with the frequencies of 0.0375 THz (0.155 meV), 0.075 THz (0.310 meV), and 0.15 THz (0.620 meV). The actual microwave power output from the Gunn diode source at 0.0375 THz was ca. 50 mW, that from the sextupler of the microwave source at
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Equation 4 are also shown, and they present excellent agreement with our experimental results of Δn. According to Equation 4, the variation of carrier concentration is dependent on the spacing distance. To verify this, Figure 2b depicts the photoconductivity response to the different nominal spacing distances of 10–110 μm at the frequency of 0.0375 THz. The results show that the photoconductivity changes following the spacing distance of the devices, which is well consistent with the spacing-dependent prediction in the theory. Moreover, Figure 2c shows the experimental photoconductivity of the device to the radiated sources at different frequencies. The measured results clearly show that the photoconductivity response is really reduced at high frequency, which is in good agreement with the frequency-dependent prediction in Equation 4. The influence of temperature must be eliminated in the experiments. To fully verify the variation of the resistance resulted from the trapped electrons, rather than from the absorption of the radiation, firstly, we need to know the temperature elevation of the material under the electromagnetic radiation. While neglecting the thermal conductance of the material, the temperature rise can be calculated by: ΔT =
ΔQ PΔt = mC p mC p
(7)
Figure 2. a) Variation of electron concentration as a function of the received power at the frequency of 0.0375 THz for the spacing distance of a = 30 µm. Inset: Typical response signal of voltage radiated by 0.0375 THz at a modulation frequency of 2900 Hz. b) Variation of photoconductivity as a function of the spacing distance at the frequency of 0.0375 THz with P = 1.456 × 10 −5 mW . c) Variation of photoconductivity as a function of radiation frequency for the spacing distance of a = 30 µm with P = 1.456 × 10 −5 mW . Experimental data represented by the dots; theoretical prediction: solid line. d) Response signal of the MSM structure under the impulse of 10 GHz radiation frequency with 52 kHz repetition rate. e) Expansion of the response signal in (d) to show the response time. Gray background strip: 90% of the full amplitude. f) Intrinsic carrier concentration (filled circles) and its differentiation (open squares). g,h) Electric mobility (filled circles) and its differentiation (open squares) (g), and resistivity (filled circles) and its differentiation (open squares) (h) for Hall measurements of the MCT material at the temperature of 250–300 K.
0.075 THz was ca. 10 mW, that from the narrow-band IMPATT at 0.15 THz was ca. 8 mW. The radiation energy of photons is 2–3 orders smaller than the MCT bandgap energy. An adjustable aperture was employed to change the power and the power received by the structure was calibrated by a Golay cell, combined with the frequency-dependent effective area of the structure (Figure S4, Supporting Information). Figure 2a shows the variation of electron concentration Δn for a = 30 μm at a frequency of 0.0375 THz, retrieved from Equation 6 using the photovoltage response of the radiation Vout as shown in the inset of Figure 2a. It increases with the increase of the received power P. The data of theoretical calculation Δn obtained from
Adv. Mater. 2014, DOI: 10.1002/adma.201402352
where m is the mass and Cp is the specific heat of the material, and Δt is the response time of our MSM structure to the incident radiation. To obtain Δt, a microwave source (Agilent E8257D) was set to radiate the structure in free space. It is exciting to see that our structures are also very sensitive to a low microwave frequency, far below the bandgap of semiconductor, and the pulse shape is still well preserved (Figure 2d). By expanding the oscilloscope trace of the response signal (Figure 2e), we estimate that the response time of the MSM structures to be better than 1 μs. Thus the temperature rise under the received power of 1.456 × 10–5 mW (the maximal power in Figure 2a) can be calculated as 9.2 × 10–7 K (C p = 175.6 J kg –1 K –1, ρMCT = 7533 kg m −3 )[26] for the structure with a = 30 μm. Then, Hall measurement was adopted to obtain the variation of intrinsic electron concentration and electron mobility at the temperature from 250 K to 300 K. The results and their differentiations to temperature are shown in Figure 2f and 2g. The measured intrinsic electron concentration increases as the temperature rising but the mobility of electron has the opposite variation trend. Now a detailed estimation is given for
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rising distribution in the MSM structure, which is non-uniform in the MCT material. The temperature rise is lower than 2.82 × 10–6 K (the maximal value at the points in the structure) at P = 1.456 × 10 −5 mW , which is consistent with the evaluation by Equation 7. The simulation in Figure 3b predicts that the temperature rise increases with the increase of the received power. Figure 3c clearly shows that the variation of resistivity in our experiments is the order of ca. 10–5 Ω cm. However, the variation of the resistivity is only about the order of ca. 10–10 Ω cm due to thermal effects of the incident radiation. Figure 3d plots the distribution of the electric field pattern at 0.0375 THz in the x–z cross section. It Figure 3. Simulation of the temperature contribution and electromagnetic fields at the fre- shows an obvious anti-symmetric field disquency of 0.0375 THz by COMSOL for the spacing distance of a = 30 µm. a) Distribution of tribution inside the MCT. A strong electric the relative temperature rise in the structure under the received power P = 1.456 × 10 −5 mW . field intensity is achieved at the metal-semb) Maximal temperature rise versus the received power. c) Experimental variation of the resisiconductor interfaces, leading to the large tivity by generated carriers (black) and estimated variation of the resistivity resulted from the enhancement of the external electromaginuence of the temperature rise (blue). d) Distribution of the anti-symmetric electric fields in MSM structure. e) Plots of the electric field (red) at the section position of z = 1 µm and its netic electric field. However, the intensity corresponding potential well distribution (green) along the x axis. f) Three-dimensional distri- attenuates quickly when the position is far away from the interfaces. This is in conbution of the induced potential wells. sistent with our theory in Equation 1. The enhanced anti-symmetric field can induce an electric potential well inside the semiconductor material the structure with a = 30 μm as an example. The variation of the (Figure 3e). Therefore we describe it as an electromagneticelectron mobility with temperature rise of 9.2 × 10–7 K is about induced well. Figure 3f shows the distribution of the induced – 6.5 × 10–9 m2 V−1 s−1), which is so small that we can almost potential wells in the MSM structure. It shows that the depth of neglect it. The retrieved variation of the intrinsic electron conthe induced wells decreases with an increase in the value of z. centration is ca. 1.5 × 1014 m–3, at least 4 orders less than that Free electrons coming from the metallic contacts are accuobtained in the measurement of ca. 7.0 × 1018 m–3 (see Figure 2a). mulated in the wells, like a puddle holding water in the level Furthermore, Figure 2h shows the measured variation of resisground. The concentration of free carriers is changed in the tivity of the material obtained from Figure 2f and Figure 2g. material between two metal contacts. Therefore, the resistThe rate of variation is about −5.0 × 10 −4 Ω cm K –1 at 293 K, ance of the devices is varied. and the corresponding variation of the resistance is about –3.46 × 10–7 Ω in the MSM, which is also much less than that Finally, results using other semiconductors further supports we obtained in the above measurements, i.e., –3.33 × 10–2 Ω that the free carriers come from the two metal contacts in the MSM structures (see Figure S6 and Figure S7, Supporting (Vout = 100.02 μV, I = 3 mA). These results have strongly demInformation). onstrated that the variation of the resistance does not come In conclusion, we have experimentally and theoretically from the variation of the temperature-dependent resistivity. The demonstrated a way to generate photoconductive carriers at polarization-dependent photoconductivity of the MSM structure a photon energy 2–3 orders below the bandgap energy of a in Figure S5 further exculded the influence of the temperature semiconductor at room temperature in MSM structures. This enhancement. discovery has jumped out of the typical methods of intrinsic Next, for better understanding of the principle to generate absorption, extrinsic absorption, and free-carrier absorption carriers in the MSM structures, the anti-symmetric mode was to realize photoconductivity, and solved the puzzle to generate calculated for our experimental geometry using finite element photon carriers irradiated by energy quanta much lower than simulation COMSOL. By doing this, the relative permittivity the bandgap of semiconductor. It is a great breakthrough in of the MCT material was set as 25 + 0.4i[27] and the dielectric photonics science and technology. We believe it will have huge parameter of metal Au was calculated by the Drude model:[28] effects on the development of semiconductors, metamaterials, plasmonics and low-quanta photon detection, such as the curω p2 ε (ω ) = ε ∞ − (8) rently immature terahertz detection. ω (ω + iω τ ) 16 where ε ∞ = 1 , the plasma frequency ω p = 1.37 × 10 Hz , and 13 ω τ = 4.07 × 10 Hz . The specific results are shown in Figure 3 for the structure with a = 30 μm. Figure 3a shows the typical temperature
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Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
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This work was supported by the Foundations of China (No. 61274138, 2013CB922301 and No. 61290302). Received: May 26, 2014 Revised: July 4, 2014 Published online:
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Acknowledgements
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