A novel model of photo-carrier screening effect on the GaN-based p-i-n ultraviolet detector

049 SCIENCE CHINA Physics, Mechanics & Astronomy May 2010 Vol.53 No.5: 793 801 doi: 10.1007/s11433-010-0177-z A novel model of photo-carrier screening effect on the GaN-based p-i-n ultraviolet detector GAO Bo *, LIU HongXia, KUANG QianWei, ZHOU Wen & CAO Lei School of Microelectronics, Xidian University, Key Laboratory of Wide Band-Gap Semiconductor Materials and Devices, Xi an 710071, China Received October 21, 2009; accepted February 5, 2010 The photo-carrier density in the depletion region of the GaN-based p-i-n ultraviolet (UV) detector is calculated by solving the photo-carrier continuity equation, and the photo-carrier screening electric field is calculated according to Poisson s equation. Using the numerical calculation method, a novel model of photo-carrier screening effect is presented. Then the influence of photo-carrier screening effect on the distribution of photo-carrier density in the depletion region of p-i-n detector is discussed. The influence of incident power, bias voltage and carrier life time on the photo-carrier screening effect is also analyzed. It is concluded that the influence of photo-carrier screening effect on the performance of GaN-based p-i-n UV detector is non-monotone, the maximum of carrier drift velocity and the minimum of response time can be realized by adjusting the applied voltage. Besides, the incident light duration has strong impact on the photo-carrier screening effect. GaN, p-i-n, ultraviolet detector, photo-carrier screening effect PACS: 78.66.Fd, 85.60.Bt, 85.60.Gz 1 Introduction As one of typical wide band-gap semiconductor, GaN material has the characteristics of large energy gap, high electron saturation velocity and small dielectric constant. It has wide application in the area of power device, microwave device and optoelectronic device. The large energy gap of GaN and its binary alloys AlGaN make it a good material for manufacturing the photo detector in the 200 365 nm wavelength range, i.e. in the UV light spectrum. So, GaN-based detector is a natural solar-blind UV detector used for body detecting and tracing, space UV communication and ozone monitoring. Compared with other structure detector, the performance of GaN-based detectors with p-i-n [1,2] and MSM [3,4] structures is impressive, such as low dark current and high spectral responsivity. Unfortunately, most research work in this area mainly focuses on decreasing the dark *Corresponding author (email: bobbygoff@foxmail.com) current [5,6] and enhancing the spectral responsivity [7,8] by improving and optimizing the fabrication process of devices, and only a few studies investigate the physical mechanism of the device performance improvement. The influence of p-gan layer depth on the performance of GaN-based p-i-n UV detector has been discussed in the ref. [9], which indicates the performance of GaN-based p-i-n UV detector can be improved by optimizing its working conditions. In the application of photo detecting, the photocarrier screening effect affects the performance of GaNbased p-i-n UV detector, which has not been found in the published papers. This paper investigates the influence of photo-carrier screening effect on the performance of GaN-based p-i-n UV detector by solving the photo-carrier continuity equation in the depletion region and adopting the numerical calculation method. A novel model of photo-carrier screening effect is presented. Furthermore, the influence of photo-carrier screening effect on the distribution of photo-carrier density

794 GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 in the depletion region of p-i-n detector is discussed, and the influence of incident power, bias voltage and carrier life time on the photo-carrier screening effect is analyzed. 2 A physical model of device 2.1 Device structure The device structure of GaN-based p-i-n UV detector is shown in Figure 1(a). In the structure, the carrier concentration in the p-gan and n-gan region is 8.0 10 18 and 5.0 10 18 cm 3 respectively. The electron concentration in the i-gan region is 1.61 10 16 cm 3, and the width of the i-layer is 0.3 μm. Charges distribution in the depletion region is shown in Figure 1(b). Based on the Poisson s equation, the distribution of electric field in the depletion region of ideal abrupt p-i-n junction is calculated for the applied voltage of 5 V, which is shown in Figure 2. It shows the depletion region is mainly concentrated in the intrinsic layer, and the electric field is not a constant, which is very important in the calculation. 2.2 Distribution of photo-carrier density The incident light is used to irradiate the photo detector. If the photon energy of incident light is higher than the energy gap of GaN, the electron-hole pairs will be generated in the detector. These electron-hole pairs drift to the two sides of the depletion region immediately because of the high electric field. This means there is some distribution for the photo-generated electron near the n-gan region and photo-generated hole near the p-gan region in the depletion region, which can be obtained by solving the photo-carrier continuity equation in the depletion region. In one dimension, the photo-generated hole and photogenerated electron continuity equation are presented in eqs. (1) and (2), respectively. px ( ) 1 Jp( x) = Gx ( ) Up( x), t q x nx ( ) 1 J ( x) = Gx U x+ t q x n ( ) n ( ), where p(x) and n(x) are the photo-generated holes density and photo-generated electrons density respectively. G(x) and U(x) are the generation rate and recombination rate for photo-carriers in the depletion region respectively. J p (x) and J n (x) are the current density of photo-generated holes and the photo-generated electrons respectively. Based on the drift-diffusion transport model in one dimension, the current density of photo-generated holes and the photo-generated electrons are shown in eqs. (3) and (4). (1) (2) d p( x) J p( x) = qp( x) μpe qdp, (3) dx d nx ( ) Jn( x) = qn( x) μne+ qdn, (4) dx Figure 1 (a) A schematic diagram of device structure of the GaN-based p-i-n UV detector; (b) charges distribution in the depletion region. where μ p and μ n are the hole mobility and electron mobility respectively. D p and D n are the diffusion coefficient of hole and electron respectively. E is the electric field in the depletion region. And the generation rate G(x) and recombination rate U(x) of photo-carriers in the depletion region are shown in eqs. (5) (7). P (1 ) opt R Gx ( ) = αexp( αx), Ah ν (5) p( x) Up ( x) =, (6) τ p nx ( ) Un ( x) =, (7) τ n Figure 2 Distribution of the electric field in the depletion region. where P opt is the incident optical power, R is the reflectivity of device surface, A is the active area, hν is the photon energy, α is the optical absorption coefficient of GaN material, and τ p and τ n is the lifetime of photo-generated hole and photo-generated electron, respectively. The value of these parameters in calculation is shown in Table 1.

GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 795 Table 1 The parameter values in calculation Parameter Value Unit Parameter Value Unit P opt 10 W A 0.01 cm 2 α 1.0 10 5 cm 1 hv 4.4308 ev τ p =τ n 0.2 ns R 0.2 2.3 Mobility modeling As a photovoltaic device, GaN-based p-i-n UV detector usually works with reverse bias voltage. Because of the high electric field stress, the photo-carriers in the depletion region always drift with the saturation velocity. Indeed, the model of carrier mobility for GaN material is very complicated especially for high electric field. With Monte Carlo calculation [10], fitting the data gotten from the experimental test, the model can be obtained. In the paper, the mobility model presented by Kabra et al. [11] and Bhapkar et al. [12] is adopted, as shown in eq. (8). μ0, 0 < E < EL, 1 + E / EC μ( E) = α1e + α2 + α3 / E, EL < E < ET, β1e + β2 + β3 / E, ET < E < EH, [ γ1exp( γ2e) + γ 3 / E, E > EH, where E H represents the high electric field, μ 0 represents the mobility of low electric field which is equal to 650 cm 2 /V, E C represents the critical electric field, E L represents the low electric field, and E T represents the threshold electric field. α 1, α 2, α 3, β 1, β 2, β 3, γ 1, γ 2 and γ 3 are different fitting parameters respectively. According to the refs. [13 16], let μ p =μ n /25. Table 2 shows the parameters value in eq. (8). Figure 3 shows the variation of electron drift velocity with the applied electric field. The whole region is divided into four parts. For the low electric field region, the electric field is below E L, and V s increases quickly when the applied electric field increases. For the medium electric field region, the electric field is between E L and E T. V s increases slowly. V s reaches the maximum when the electric field is equal to the threshold field (E T ). For the high electric field region, the electric field is greater than E T and less than E H, and V s decreases with increasing electric field, which causes the negative differential mobility. For the very high electric (8) field region, the electric field is greater than E H. V s decreases slowly and settles down to a constant saturation velocity in this region. 2.4 Photo-carrier screening effect When the incident light irradiates the device, the distribution of photo-generated holes density p(x) and photo-generated electrons density n(x) can be obtained by solving the photo-carrier continuity Equation (1) and Equation (2), respectively. Based on the Poisson s equation, the photo-carrier can generate an additional electric field impeding the photo-carriers drift. This paper uses the photo-generated screening electric field to show the impediment action, which is shown in eq. (9). x V q Esc ( x) = = ( p( x) n( x))d x, x (9) εε 0 0 where E sc is the photo-generated screening electric field generated by the photo-carriers in the depletion region, and ε 0 and ε r is the absolute and relative dielectric constant respectively. Figure 3 Electrons drift velocity versus the electric field. r Table 2 The parameter values in eq. (8) Parameter Value Unit Parameter Value Unit μ 0 650 cm 2 /V α 3 9.54 10 6 cm/s E c 4.349 10 4 V/cm β 1 2.301 10 4 cm 3 /V 2.s E L 9 10 4 V/cm β 2 9.674 cm 2 /V.s E T 2.3 10 5 V/cm β 3 1.604 10 7 cm/s E H 3.3 10 5 V/cm γ 1 2.096 10 8 cm/s α 1 2.501 10 4 cm 3 /V 2.s γ 2 1.204 10 5 cm/s α 2 130 cm 2 /V.s γ 3 1.909 10 7 cm/s

796 GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 So, when the incident light irradiates, the total electric field in the depletion region is the sum of build-in electric field E in, the applied electric field E a and the photo-generated screening electric field E sc, as shown as follows: 3 Numerical calculation E = E + E + E. (10) in a sc When the GaN-based p-i-n UV detector works with bias voltage of 5 V and incident optical power of 10 W, the distribution of photo-carrier density in the depletion region can be calculated according to eqs. (1) and (2), and then the photo-generated screening electric field can be calculated according to eq. (9). And now the total electric field that acts on the photo-carriers is the sum of the build-in electric field, the applied electric field and the photo-generated screening electric field. However, the total electric field also affects the distribution of photo-carriers in reverse. Therefore, a new distribution of photo-carriers will form, and a new total electric field will be obtained. By repeating it again and again, a steady distribution of photo-carriers and a constant photo-generated screening electric field will form finally in the depletion region of GaN-based p-i-n UV detector, and this process is expressed by the numerical method in calculation, as shown in Figure 4. 4 Results and discussion The photo-carrier screening effect taken into consideration, the total electric field E, the photo-generated screening electric field E sc and the photo-carrier density in the depletion region are calculated according to the numerical calculation method in Figure 4. The results are shown in Figures 5 7, respectively. Figure 4 A flow chart of the numerical calculation method with photo-carrier screening effect. Figure 5 (a) Distribution of total electric field E; (b) average total electric field E varied with time.

GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 797 From Figure 5(a), the total electric field in the depletion region of detector with incident light has not changed considerably compared with that without incident light, and it changes slightly with the incident duration, shown clearly in Figure 5(b). To be more specific, the average total electric field in the depletion region decreases with the incident duration influenced by the photo-carrier screening effect, and it reaches the saturation value of 410.325 kv/cm after the incident duration of 50 ps. According to eq. (9), the photo-generated screening electric field is calculated, which is shown in Figure 6. Figure 6 shows the photo-generated screening electric field changes with the incident duration. The photo-generated screening electric field increases quickly with the incident duration at the beginning, it increases slightly after 25 ps, and finally reaches saturation. The photo-generated screening electric field in the depletion region is not a constant. It increases quickly from 0 to 50 nm in Figure 6, and then slowly reaches the maximum in some location. It decreases slightly when the location gets to the boundary of the depletion region. The location in the depletion region corresponding to the maximum of photo-generated screening electric field shifts to the right with the incident duration until the photo-generated screening electric field reaches the saturation. And this phenomenon results from the change of photo-carrier density in the depletion region with the incident duration, which is shown in Figure 7. Figure 7(a) shows the photo-generated holes are accumulated near the p-gan layer in the depletion region, the photo-generated electrons are accumulated near the n-gan layer in the depletion region, and the holes accumulation is greater than that of the electrons, because the hole mobility is much smaller than that of electron mobility. Therefore, a screening electric field with an opposite direction of the original electric field takes shape because of the accumulation of photo-carriers, which impedes the photo-carriers drift and diffusion. With the irradiation continuing, the photo-carriers accumulation becomes stronger and stronger, until the photo-generated holes density saturates after the Figure 7 (a) Distribution of photo-carrier density; (b) distribution of net photo-carrier density. incident duration of 8 ps, while the photo-generated electron density saturates after 50 ps. With the incident duration, the location where the photo-generated holes density equal to the photo-generated electrons density in the depletion region, shifts to the right gradually until the photo-generated holes density saturates, as shown in Figure 7(b). Therefore, the photo-carrier screening effect has a more profound impact on the photo-generated holes than photo-generated electrons. Furthermore, the influence of photo-carrier screening effect on the performance of GaN-based p-i-n UV detector is discussed. It is well known that the response time is an important parameter for the detector used in the high speed application. For p-i-n UV detector, the response time mainly depends on the transit time τ drift, the diffusion time τ diff for photo-carriers outside the depletion region diffusing to the depletion region and the RC time constant τ RC. Because the diffusion time is very short, the response time of GaN-based p-i-n UV detector is defined as follows: 2 2 w 2 τ = τdrift + τrc = + ( RC), Vs 2 (11) Figure 6 The photo-generated screening electric field E sc. where w is the width of depletion region, V s is the carrier drift velocity, R is the total resistance of 50 Ω in circuit, and C is the capacitance of 4 ff in circuit. From the above discussion, the total electric field in the depletion region is not a constant, rather a function of the location. So, the carrier drift velocity in the depletion region is also a function of the location. The average carrier drift velocity is used to calcu-

798 GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 late the response time of detector, which is shown in eq. (12). V s = w+ xn xp μ( xex ) ( )dx x + w+ x p n. (12) Based on eqs. (11) and (12), the average drift velocity Vs and the response time τ of GaN-based p-i-n UV detector are calculated after the consideration of the photo-carrier screening effect, shown in Figures 8(a) and (b) respectively. Figure 8(s) shows, under the above working condition, the average electron drift velocity increases nonlinearly with the incident duration because of the photo-carrier screening effect, and reaches the saturation of 2.0695 10 7 cm/s after the incident duration of 50 ps. Figure 8(b) shows, influenced by the photo-carrier screening effect, the response time decreases from 1.4897 to 1.4882 ps after the incident duration of 50 ps. So, there is a fine tuning effect for photo-carrier screening effect to electron drift velocity and response time of detector, which is influenced by the bias voltage and incident power, as shown in Figures 9 and 10. Figure 9 shows, with the bias voltage of 0 and 2 V, the average electron drift velocity decreases and the response time increases because of the photo-carrier screening effect, and the influence is stronger with the bias voltage of 0 V than 2 V. For the bias voltage of 4 and 6 V, the average electron drift velocity increases and the response time decreases influenced by the photo-carrier screening effect, and the influence increases for the bias voltage of 4 V. Therefore, the influence of photo-carrier screening effect on the electron drift velocity and response time is non-monotonic for the GaN-based p-i-n UV detector, which results from the non-monotonic influence of electric field on the electron saturation velocity for the GaN material. According to the Figure 8 (a) Average electrons drift velocity varied with the incident duration; (b) response time of the detector varied with the incident duration. electron mobility model for the GaN material, the electron saturation velocity increases when the total electric field in the depletion region is close to 230 kv/cm. The electron drift velocity decreases and the response time increases because of the photo-carrier screening effect when the bias voltage is in the range of 0 to 2.3 V. The influence is opposite when the bias voltage is in the range of 2.3 V to the reverse breakdown voltage. When the bias voltage is equal to 2.3 V, the average electron drift velocity in the depletion region reaches the maximum, while the response time reaches the minimum. From Figure 10, the influence of photo-carrier screening effect on the electron drift velocity and response time is not obvious when the incident power is 0.1 W. The influence seems obvious when the incident power is 1 W, and the influence is very obvious when the incident power is 10 W. The photo-carrier density in the depletion region increases with the incident power increasing, which leads to the photo-generated screening electric field increasing and the influence of photo-carrier screening effect on the electron drift velocity and response time increasing. In the actual design, the quantum efficiency can be increased by improving the device structure [17], and the incident power can be increased by setting the anti-reflective layer in surface [18]. Both can increase the influence of photo-carrier screening effect on the response time of detector. The GaN material is known for its high defect concentration because of lattice mismatch and thermal mismatch [19,20] in the hetero-epitaxial growth, so the minority carrier life time is very short, which seriously affects the device performance. According to the model presented in this paper, the influence of photo-carrier screening effect on the response time with different carrier life time is discussed, which is shown in Figure 11. Under the same working condition, the shorter the minority carrier life time, the weaker the influence of the photo-carrier screening effect on the response time of detector. The decrease of the minority life time results in a quick recombination of photo-carriers, so the photo-carrier density decreases, the photo-generated screening electric field decreases, and the photo-carrier screening effect is not obvious. When the minority carrier life time is short enough, the photo-carriers recombine immediately when they are generated, and the photo-carrier screening effect disappears completely. When the minority carrier life time is large enough, the photo-carrier screening effect is very obvious. With the development of technology of hetero-epitaxial growth for the GaN material, the defect concentration in the GaN material is less, and the carrier life time is enlarged. So, the photo-carrier screening effect can meet the requirement of high speed application in GaN-based p-i-n UV detector. From the above calculation results, the influence of photo-carrier screening effect on the response time of detector becomes steady after the incident duration of 50 ps. However, in actual applications, the incident light generally

GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 799 Figure 9 The influence of bias voltage on the photo-carrier screening effect. (a) Electron drift velocity; (b) response time of the detector. is transient light or frequency-modulated pulse light, so the influence of photo-carrier screening effect on the response time is discussed, which is shown in Figure 12. Figure 12 shows, with the transient light duration down

800 GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 to 10 from 60 ps, the influence of photo-carrier screening effect on the response time weakens gradually, and the influence disappears gradually after a period of time. When the transient light duration is shorter than 50 ps, the photo-carrier screening effect is not obvious. When the transient light duration is larger than 50 ps, the photo-carrier screening effect becomes very obvious. 5 Conclusions Figure 10 The influence of incident power on the photo-carrier screening effect. (a) Electron drift velocity; (b) response time of the detector. By solving the photo-carrier continuity equation in the depletion region and adopting numerical calculation method, a novel model of photo-carrier screening effect is presented. Based on this model, the influence of photo-carrier screening effect on the response time of GaN-based p-i-n UV detector is discussed in different working conditions. The calculation results show the influence of photo-carrier screening effect on the performance of GaN-based p-i-n UV detector is non-monotonic, and the maximum of carrier drift velocity and the minimum of response time can be realized by adjusting the bias voltage. Furthermore, the influence of photo-carrier screening effect on the performance of detector is very obvious for great incident power or long carrier life time, and the duration of transient light has a major impact on the photo-carrier screening effect. This work was supported by the National Natural Science Foundation of China (Grant Nos. 60976068 and 60936005), the Cultivation Fund of the Key Scientific and Technical Innovation Project, and the Ministry of Education of China Program (Grant No. 708083). Figure 11 The influence of carrier life time on the photo-carrier screening effect. Figure 12 Influence of transient light on the photo-carrier screening effect. 1 Smith G M, Boutros K S, Phanse V M. Visible-blind GaN photodiodes. IEEE Lasers and Electro-Optics Society Annual Meeting. 1998, 1: 366 367 2 Chang P C, Yu C L, Chang S J, et al. Low-noise and high-detectivity GaN-based UV photodiode with a semi-insulating Mg-doped GaN cap layer. IEEE Sensors J, 2007, 7(9): 1270 1273 3 Chen C H, Chang S J, Su Y K, et al. GaN metal-semiconductor-metal UV photodetectors with transparent Indium-Tin-Oxide schottky contacts. IEEE Photonics Technol Lett, 2001, 13(8): 848 850 4 Li J L, Donaldson E R, Hsiang T Y. Very fast metal-semiconductor-metal UV photodetectors on GaN with submicron finger width. IEEE Photonics Technol Lett, 2003, 15(8): 1141 1143 5 Carrano J C, Li T, Brown D L, et al. Low dark current pin UV photodetectors fabricated on GaN grown by metal organic chemical vapour deposition. Electron Lett, 1998, 34(7): 692 694 6 Dobrzański L, Strupinski W. On charge transport and low-frequency noise in the GaN p-i-n diode. IEEE J Quantum Electron, 2007, 43(2): 188 195 7 Chang P C, Yu C L, Chang S J. Low-noise and high-detectivity GaN-based UV photodiode with a semi-insulating Mg-doped GaN cap layer. IEEE Sens J, 2007, 7(9): 1270 1273 8 Shen S C, Zhang Y, Dongwon Y, et al. Performance of deep UV GaN avalanche photodiodes grown by MOCVD. IEEE Photonics Technol Lett, 2007, 19(21): 1744 1746 9 Zhou M, Zhao D G. Effect of p-gan layer thickness on the performance of p-i-n sructure GaN UV photodetectors. Acta Phys Sin, 2008, 57(7): 4570 4574 10 Farahmand M, Garetto C, Bellotti E, et al. Monte carlo simulation of electron transport in the III-nitride wurtzite phase materials system:

GAO Bo, et al. Sci China Phys Mech Astron May (2010) Vol. 53 No. 5 801 Binaries and terniaries. IEEE Trans Electron Devices, 2001, 48(3): 535 542 11 Kabra S, Kaur H, Haldar S, et al. An analytical model for GaN MESFET s using new velocity-field dependence. Phys Stat Sol C, 2006, 3(6): 2350 2355 12 Bhapkar U V, Shur M S. Monte Carlo calculation of velocity-field characteristics of wurtzite GaN. J Appl Phys, 1997, 82(4): 1649 1655 13 Bhatttacharyya A, Li W, Cahalu J, et al. Efficient p-type doping of GaN films by plasma-assisted molecular beam epitaxy. Appl Phys Lett, 2004, 85(21): 4956 4958 14 Kumakura K, Makimoto T. Carrier transport mechanisms of Pnp Al- GaN/GaN heterojunction bipolar transistors. Appl Phys Lett, 2008, 92: 093504-1 3 15 Rodrigues C G, Femandez J T L, Leite J R, et al. Hole mobility in zincblend c-gan. J Appl Phys, 2004, 95(9): 4914 4917 16 Kim K S, Cheong M G, Hong C H, et al. Hole transport in Mg-doped GaN epiayers grown by metalorganic chemical vapor deposition. Appl Phys Lett, 2000, 76(9): 1149 1151 17 Ting L, Carrano J C, Campbell J C, et al. Analysis of external quantum efficiencie of GaN homojunction p-i-n UV photodetectors. IEEE J Quantum Electron, 1999, 35(8): 1203 1206 18 Chang S J, Lee M L, Sheu J K, et al. GaN metal-semiconductor-metal photodetectors with low-temperature-gan cap layers and ITO metal contacts. IEEE Electron Device Lett, 2003, 24(4): 212 214 19 Tuomisto F, Paskova T, Kröger R, et al. Defect distribution in a-phane GaN on Al 2 O 3. Appl Phys Lett, 2007, 90: 121915-1 3 20 Lin J C, Su Y K, Chang S J, et al. GaN p-i-n photodetectors with an LT-GaN inter layer. IET Optoelectron, 2008, 2(2): 59 62