Solid-State Electronics

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1 Solid-State Electronics 68 (01) Contents lists available at SciVerse ScienceDirect Solid-State Electronics journal homepage: Point defect determination by eliminating frequency dispersion in C V measurement for AlGaN/GaN heterostructure Liang Li, Lin-An Yang, Jin-Cheng Zhang, Lin-Xia Zhang, Li-Sha Dang, Qian-Wei Kuang, Yue Hao State Key Discipline Laboratory of Wide Band Gap Semiconductor Technology, School of Microelectronics, Xidian University, Xi an , China article info abstract Article history: Received 3 June 011 Received in revised form 1 October 011 Accepted 4 November 011 Available online 30 November 011 The review of this paper was arranged by E. Calleja In this paper, an improved small-signal equivalent model is introduced to eliminate frequency dispersion phenomenon in capacitance voltage (C V) measurement, and a new mathematic method is proposed to calculate the amount of bulk defect existing in the GaN buffer layer. Compared with photoluminescence (PL) and high resolution X-ray diffraction (HRXRD) data, it is identified that the main component of the bulk defect concentration is made up of the point defect concentration, rather than the edge dislocation concentration. All these results prove the accuracy of the improved C V model and feasibility of the mathematic model. Ó 011 Elsevier Ltd. All rights reserved. Keywords: Bulk defect AlGaN/GaN Frequency dispersion Capacitance voltage characteristic 1. Introduction The Hg probe capacitance voltage (C V) measurement is widely used to characterize AlGaN/GaN heterostructure epitaxial materials, such as the two-dimensional electron gas (DEG) spatial profile, the buried buffer charge, the pinch-off voltage, and the barrier thickness [1,]. In fact, the C V characteristics are commonly affected by the measuring frequency since the electron trapping behavior would vary with the frequency. This phenomenon is called frequency dispersion, and the frequency-dependent C V measurement has been used for identifying the shallow-traps adjacent to heterojunction AlGaN/GaN and the deep-traps in GaN buffer layer to reveal in-depth information of C V data [3 5]. Clearly, the effect of measurement conditions such as bias and frequency on C V data acquisition are identified, which should be chosen properly to eliminate significant errors in measurement. The hysteresis in C V characteristics is commonly used to represent the total density of interface state, surface state and deeply trapped charge. Especially, the bulk defect in GaN buffer layer acting as the deeply trapped charge could lead to current collapse, which is caused by the hot carriers transferring from the DEG channel to GaN buffer layer when a high drain source voltage was applied to the device. So a further work should be done by taking these Corresponding author. Tel.: ; fax: x616. address: layang@xidian.edu.cn (L.-A. Yang). conditions into account for an identification of the bulk defect in buffer layer. In this paper, we propose an improved equivalent circuit model for nitride material C V measurement to eliminate the frequency dispersion and other impact factors by extracting the accurate capacitance parameter from the data measured at 100 khz and 1 MHz, by which one can reveal precise capacitance characteristics of nitride material, and then estimate the amount of surface state, interface state and bulk defect in buffer layer. Furthermore, a mathematic model is taken into account to rule out the effect of surface state and interface state, which provides a direct insight into bulk defect in buffer layer. To identify the accuracy of the new model and the feasibility of the mathematic model, the results have a further comparison with the photoluminescence (PL) and the high resolution X-ray diffraction (HRXRD) data.. Equivalent circuit model The traditional equivalent circuit model in C V measurement consists of two parallel elements: capacitance (C) and conductance (G). In fact, there are many other impact factors existing in the measurement. For instance, there are surface states at the metal/ semiconductor interface [6 8], which act as trapping centers, where the electron capture or release directly affect the accurate capacitance value in C V measurement [9 11]. In addition, the delay and phase change of AC signals through the cable also affect the measured results. We introduce the improved model, which aims /$ - see front matter Ó 011 Elsevier Ltd. All rights reserved. doi: /j.sse

2 L. Li et al. / Solid-State Electronics 68 (01) at considering these impact factors and extracting a real capacitance to present accurate characteristics of AlGaN/GaN heterostructure. A sketch of the improved equivalent circuit model including four components is shown in Fig. 1, where C 0 is the accurate capacitance of AlGaN/GaN heterostructure, D t is the surface state factor, R s is the series resistance caused by a series interconnecting resistance between inner contact and outer contact of Hg probe, and C s is the parallel capacitance induced by the connecting wire and probe system. Evidently, a precise capacitance value can be deduced at two different measured frequencies by using the improved equivalent circuit model. Impedance Z of the traditional two elements parallel circuit can be given as follows: D j ZðxÞ ¼ xcð1 þ D Þ ; where D = G/xC is a dissipation factor with G and C as measured values, x is the angular frequency. In the four components parallel circuit, the impedance Z is given as ZðxÞ ¼ R sð1 jxc s R s Þ 1 þðxc s R s Þ þ D t j xc 0 ð1 þ D t Þ : Mathematically, there are the equal real and imaginary components between (1) and (), which can result in D xcð1 þ D Þ ¼ and R s 1 þðxc s R s Þ þ D t xc 0 ð1 þ D t Þ ; 1 xcð1 þ D Þ ¼ xc s Rs 1 þðxc s R s Þ þ 1 xc 0 ð1 þ D t Þ : Simultaneously solving (3) and (4) can yield the parameter C 0, D t, C s and R s, as shown as follows: " D C 0 ¼ðx 1 x t x 1 D 1 Þ 1 þ D t C 1 ð1 þ D 1 Þ x # D C ð1 þ D Þ ; ð5þ h i C 1 C 1þD 1 1þD D t ¼ h ih i; ð6þ x 1 C 1þD x C 1 1þD 1 x1 D 1 C 1þD x D C 1 1þD 1 C s ¼ x DC 0ð1 þ D t Þ D tð1 þ D Þ C 0 ð1 þ D t Þ Cð1 þ D Þ ; CC 0 ð1 þ D Þð1 þ D t R s ¼ h ih Þ i; C s DC 0 1 þ D t D t Cð1 þ D Þ C 0 1 þ D t Cð1 þ D Þ ð8þ Fig. 1. Schematic diagram of equivalent circuit of new model consisting of four elements. ð1þ ðþ ð3þ ð4þ ð7þ where C 1, G 1 and D 1 correspond to measure condition x 1, C, G and D correspond to measure condition x. These parameters can be used to accurately describe characteristics of an AlGaN/GaN heterostructure. 3. Measurement and discussion The AlGaN/GaN heterostructure samples were grown on (0001) sapphire by metalorganic chemical vapor deposition (MOCVD) system. H was used as the carrier gas and triethylgallium, trimethylaluminium and ammonia (NH 3 ) were used as source compounds. The heterostructures were grown on high-temperature AlN nuclear layers. The growth condition of AlGaN/GaN layers was as follows: a growth temperature of 1060 C, a chamber pressure of 40 Torr, and a growth rate of 14 nm/min. Three samples that were grown with the same AlGaN layer structure but different growth conditions in GaN buffer layers are used for this work. The ratio of V/III growth of GaN buffer layer for samples A, B and C is from high to low, and other growth conditions are the same. In detail, sample A consists of a single Al 0.7 Ga 0.73 N ( nm)/gan (1.5 lm) heterostructure with high V/III growth ratio of buffer layer growth, sample B has medium V/III growth ratio, and sample C has low V/III growth ratio. The ratio of V/III growth of all three samples are lower than 400. The measuring system used in this work is Keithley 590 C V Analytical Instrumentation. Sweeping range from 0 to 8 V, sweeping rate of 0.1 V/s, and the AC small signal amplitude of 50 mv are used to investigate C V characteristics of AlGaN/GaN heterostructure at high frequency. It is noted that the frequency dispersion occurred primarily for measurement frequencies ranging from 50 khz to 1 MHz [1,13]. The de-trapping time of several microseconds [11 13] is obtained, and the carrier generation rate (the reciprocal of the de-trapping time) may be within the frequency range. In this work, two different frequencies 100 khz and 1 MHz were chosen to build the model. The C V curves at 100 khz and 1 MHz are obtained at first, from which we deduce a corrected curve in order to eliminate the frequency dispersion by using the improved four-element equivalent circuit. The results are shown in Fig. for samples A, B and C, respectively. It is observed from the 100 khz, 1 MHz and corrected C V curves that there exists a significant effect of frequency dispersion on C V curves at high frequency. It has been reported that large frequency dispersion of the capacitance in accumulation is due to not only the series resistance but also the electrical response of the metal/semiconductor interface of unknown composition (moisture, organic compounds, or mercury oxide) [14]. With the increase of the frequency, the effects of these phenomenons on capacitance grow up and cause significant measurement errors. Thus, we employ the C V curve at 100 khz, rather than that of 1 MHz, to compare with the corrected C V curve in order to assure the accuracy of analyzing the AlGaN/GaN heterostructure. Some authors proposed that the traps are responsible for the hysteresis in C V characteristics of the HEMT structures. Actually, the traps include not only the bulk defect in the GaN buffer layer but also the surface state and the interface state. In this paper, we put an emphasis on the bulk defect of the GaN buffer layer region beneath the AlGaN/GaN heterointerface by a mathematic model. The band bending (induced by the work function difference and interface state of the heterostructure [13]) could form a potential well in GaN buffer layer. Therefore, the DEG is confined to this potential well, and the width of the DEG is considered as 3 nm approximately [15,16]. This 3-nm thick GaN does involve the DEG, moreover, involve the effect of the interface state in the interfacial layer. By this mean, the position that is 3 nm below the interface is defined as the boundary in this work. Fig. 3a and b give the sketches to interpret the mathematic model with the introduction of boundary. The region above the

3 100 L. Li et al. / Solid-State Electronics 68 (01) defect in GaN buffer layer is maintained. By this mean, a direct sight into the bulk defect in GaN buffer layer is achieved. The capacitance value corresponding to the boundary is defined as C b, and the depth of the boundary is defined as Z b. The relation between the capacitance of the AlGaN/GaN structure and the depth away from the surface is simply given as C b ¼ e AlGaNA Z b ; ð9þ Fig.. Measured and corrected C V curves of sample A, sample B, and sample C. Fig. 3. (a) Sketch of the mathematic model to the AlGaN/GaN heterostructure, and (b) sketch of the mathematic model to the C V data. boundary including the interface state and the surface state is neglected, while the region below the boundary including the bulk where e AlGaN is the permittivity of the AlGaN (e AlGaN = 9.3e 0 ), and A is the Schottky contact area between Hg probe and material surface. According to Eq. (9), the capacitance value decreases with the increased depth. So the capacitance is less than C b when the depth is deeper than Z b. According to the previous definition of the position of the boundary, we have determined its location in Fig. a c, and marked it with a straight line crossing the 100 khz and the corrected C V curves, respectively. During the high frequency (100 khz) measurement, electrons are captured by the bulk defect, in which case the electrons cannot keep up with the change rate of high frequency, therefore, are confined to the bulk defect [10,11,17]. While in the corrected model condition, the effect of frequency dispersion is less. So the electrons can overcome the confinement of bulk defect, so as to be depleted with the increase of the bias voltage simultaneously. In that case, an integration of the part below C b of the area difference between the 100 khz and the corrected C V curves accurately indicates the amount of bulk defect in the buffer layer, by means of which, the effect of interface state and the surface state is excluded. The bulk defect concentration N bulkdefect is therefore given as R VdC N bulkdefect ¼ e A Z ; ð10þ where R VdC is the integration of the part below C b of the area difference between the 100 khz and the corrected C V curves, e is the electron charge, and Z is the thickness of the material. According to Eq. (10), the amounts of bulk defect of three samples are calculated as cm 3 (sample A), cm 3 (sample B), cm 3 (sample C), respectively. In addition, as shown in Fig. a c, the abrupt region slope of the 100 khz measurement curve is larger than that of the corrected curve. It is due to that the slope is determined by the doping concentration of GaN buffer layer [18]. The slope of capacitance variation increases with increased GaN doping concentration. Because electrons are confined by the bulk defect in buffer layer at 100 khz, the equivalent doping concentration in the buffer layer at 100 khz measurement is lower than that of correction, which leads to this phenomenon. However, the origin of the bulk defect in buffer layer is still not identified, which could come from point defect such as the gallium vacancies (V Ga )-involved defect, or the edge dislocation. Both of the V Ga -involved defect and the edge dislocation could hold or trap electrons as a potential well. So the frequency dispersion in the region beneath the boundary may result from the buffer layer concerned with bulk defect. To obtain a further investigation of bulk defect in the buffer layer, PL and HRXRD measurements are employed for these samples. Fig. 4 shows the PL spectra at 300 K for samples A, B, and C. It is found that these samples show different yellow luminescence (YL) intensities centered at..3 ev in the luminescence spectra. The ratio of YL intensity to band-edge emission intensity (I YL /I BE ) is corresponding to the effect of the deep acceptors [19], which is 10.0, 7.1 and 4.6, respectively, for samples A, B and C. The defect-related YL emission is an important deep-level phenomenon in GaN. It is reported that the point defect such as the gallium vacancies (V Ga )-involved defects [0,1] is regarded as the candidate of the deep acceptors to enhance the YL band. Fig. 5 shows that the full width at half maximum (FWHM) of the (10) plane of samples A, B and C is 714 arcsec, 831 arcsec and 904 arcsec, respectively.

4 L. Li et al. / Solid-State Electronics 68 (01) Normalized luminescence intensity Energy (ev) Fig. 4. Comparison of the PL spectra of the three samples. A B C Table 1 I YL /I BE, SDBD, and EDC of samples A, B and C. Samples I YL /I BE SDBD (cm ) EDC (cm ) A B C the bulk defect concentration in Fig. 6, which means the effect of the point defect concentration on SDBD is significant. Therefore, it reveals that it is the point defect concentration, rather than the edge dislocation, that dominates the bulk defect concentration. 4. Conclusion Fig. 5. Comparison of the XRD rocking-curves of (10) plane of the three samples. It has been reported that the densities of edge dislocation including edge component of mixed dislocation are indirectly represented by the HRXRD FWHM of the (10) planes [ 4]. As shown in Fig. 6, the FWHM in (10) plane of three samples are within the range from 700 to 900 arcsec, which are used to calculate the edge dislocation concentration (EDC) of three samples, the results are listed in Table 1. The results show that the change of EDC is not significant, although the change of FWHM in (10) plane of three samples seems significant. Simultaneously, we calculate the sheet densities of the bulk defect (SDBD) of three samples by the product of the bulk defect concentration and the thickness of the sample (1.5 lm), the results are also listed in Table 1. It reveals that the difference between EDC and SDBD is approximate two orders in magnitude, so the effect of EDC on SDBD can be neglected. Note that the result of EDC being inversely proportional to SDBC in Table 1 is just caused by the epitaxial growth process rather than the defect mechanism. In fact, the relation between EDC and SDBC is very weak. We use PL spectra measurement to obtain the corresponding I YL /I BE values which is induced by the point defect concentration [5]. The results in Table 1 evidently show that I YL /I BE is proportional to SDBD, and there exists a monotonous increase of the I YL /I BE with Fig. 6. The I YL /I BE increase and the FWHM in (10) plane decrease with N bulkdefect. In conclusion, we have proposed an improved four-element model in C V measurement for AlGaN/GaN heterostructure to eliminate the effect of frequency dispersion and other impact factors, by extracting a precise capacitance value from the different high frequency measurement. To further investigate the bulk defect in GaN buffer layer, we have accomplished a comparison between the corrected C V data of the new model and the measured C V data at 100 khz. Particularly, a mathematic model to the comparison has been taken into account to exclude the effect of the surface state and the interface state in order to obtain accurate bulk defect concentration. Meanwhile, the PL spectra and the HRXRD curves of different AlGaN/GaN heterostructures were employed to validate the accuracy of the improved model. By analysis of the results, it reveals that it is the point defect concentration, rather than the edge dislocation, that dominates the bulk defect concentration. Acknowledgements This work was supported by the National Key Science & Technology Special Project (Grant No. 011ZX ), the Major Program and State Key Program of National Natural Science Fund of China (Grant Nos and ), and the National Natural Science Fund of China (Grant No ). References [1] Smart JA, Schremer AT, Weinman NG, Ambacher O, Eastman LF, Shealy JR. Appl Phys Lett 1999;1:388. [] Dimitrov R, Mitchell A, Wittmer L, Ambacher O, Stutzman M, Hilsenbeck J, et al. 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