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TCAD Studies on the Determination of Diffusion Length for the Planar-Collector EBIC Configuration With Any Size of the Schottky Contact Chee Chin Tan, Vincent K. S. Ong, and K. Radhakrishnan, Member, IEEE
Abstract— In this brief, the transient single-contact electron-beam-induced current (SC-EBIC) and the conventional steady-state EBIC modes of the planar-collector configuration that were studied using a Technology Computer Aided Design device simulator are presented. The feasibility of these EBIC data in the extraction of the diffusion length of the planarcollector configuration with any values of surface recombination velocities and any size of the Schottky contact is also presented. The effect of the size of the Schottky contact on steady state and transient EBIC signals as well as the extracted diffusion length and linearization coefficient is discussed in this brief. The EBIC information obtained from the SC-EBIC and the conventional EBIC is found to be able to evaluate the diffusion length accurately regardless of the size of the Schottky contact. Index Terms— Electron microscopy, semiconductor device measurement, semiconductor materials, simulation.
I. I NTRODUCTION
T
HE beam-induced current technique, either in steady-state mode [1]–[3] or in transient mode [4]–[6], is one of the most popular and reliable methods for the characterization of the minority carrier transport properties, i.e., the diffusion length and carrier lifetime, which play a vital role in the functionality and performance of semiconductor devices [7]. Fig. 1(a) shows the planar-collector configuration for the conventional electron-beam-induced current (EBIC) technique, while Fig. 1(b) shows that it is equivalent for the single-contact EBIC (SC-EBIC) technique. The notable differences between the two techniques are the completeness of the electrical loop across the charge-collecting junction and the nature of the generated signal. In the conventional EBIC, both the Schottky contact and the bulk semiconductor are shorted to ground, causing a constant potential difference at the charge-collecting junction. This gives rise to the steady-state EBIC signal. On the other hand, one of the terminals in the SC-EBIC is floated. This causes the majority carriers to accumulate at the floated region when the semiconductor is subjected to the electron beam and to discharge when the collecting junction
Manuscript received July 16, 2014; revised June 27, 2015; accepted July 18, 2015. Date of publication August 5, 2015; date of current version August 19, 2015. The review of this brief was arranged by Editor Z. Celik-Butler. The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail:
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2015.2458988
Fig. 1. Planar-collector configuration for (a) conventional EBIC and (b) SC-EBIC.
is forward biased. This changes the potential difference at the charge-collecting junction accordingly and gives rise to the transient EBIC signal for the SC-EBIC technique. The theory is discussed for the conventional EBIC in [8]–[10] and SC-EBIC in [11]–[13]. With the increasing complexity in today’s semiconductor devices, the double-contact requirement in the conventional EBIC technique may be difficult to fulfill. The SC-EBIC technique overcomes this limitation, making it a convenient and highly flexible technique in the characterization of today’s semiconductor devices. The most commonly used equation, where the EBIC data IEBIC are fitted to, to determine the diffusion length L, to date is proposed in [14]–[16] and is given as [17] IEBIC x ln (1) = − + ln(k1 ). α x L where x is the beam distance, k1 is a constant, and α is the linearization coefficient [18]. The role of α is to
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TABLE I S IMULATION PARAMETERS
Fig. 2. Transient ISC-EBIC signals for different widths of the Schottky contact. The simulation parameters are x = 15 μm, L = 3 μm, vs = 0 cms−1 , tON = 3 ms, and tOFF = 53 ms.
straighten the plot of ln(IEBIC ) against x that would normally be concave upward. The diffusion lengths extracted using (1) were found to be accurate for any values of the surface recombination velocity with the extracted α ranging from −0.5 to −1.5 [3], [17], [19]. Equation (1), which was generalized based on the analytical EBIC model for semi-infinite planar-collector configuration, is for the case where the Schottky contact is infinite in size, i.e., wc = ∞. However, the size of the Schottky contact is found to have a significant impact on the EBIC data, especially when the size of the Schottky contact is less than the size of the diffusion length [20], [21]. This makes the applicability of Chan et al.’s [17] method for the determination of diffusion length on a finite-sized Schottky contact a topic of great interest. In this brief, the determination of diffusion length L with the use of the EBIC data for the planar-collector configuration with finite-sized Schottky contact is presented. The EBIC data of the conventional EBIC and SC-EBIC techniques were obtained using MEDICI, a 2-D device simulator. The advantages of simulation studies over experimental studies are discussed in [17] and [22]. The EBIC information, such as the steady-state IEBIC signal for the conventional EBIC technique and ISC-EBICo , and the SC-EBIC signal at the instance when the electron beam was turned ON, were fitted into (1) using the method of linear regression [17], [23] to extract the diffusion length L and the linearization coefficient α. II. S IMULATION D ETAILS In this MEDICI simulation, the 2-D simulation structures for the planar-collector configurations, as shown in Fig. 1(a) and (b), for the conventional EBIC and SC-EBIC techniques, respectively, were created. A fine simulation mesh grid of 0.1 μm was defined at the region near the Schottky contact and the beam entry surface. This will ensure a high degree of accuracy in the results. In this MEDICI simulation, the Shockley–Read–Hall recombination model is used. The parameters used in this simulation are tabulated in Table. I. In this brief, the beam condition is chosen to fulfill the criteria for accurate extraction of diffusion length, as discussed in [24]. The generation volume was modeled based on the pear-shaped Gaussian model as proposed in [25], where the
depth distribution follows that proposed in [26]. The details of the implementation of the generation volume model in MEDICI are discussed in [27]. Since the ISC-EBIC signal is transient in nature, the simulation of the SC-EBIC technique was performed in the transient mode with a time step of 0.5 ms. Beam modulation was used in the SC-EBIC technique, where the electron beam was modeled to turn ON at t = 3 ms and turned OFF after 50 ms. III. R ESULTS AND D ISCUSSION Fig. 2 shows the transient ISC-EBIC signals for different widths of the Schottky contact. The shape of the transient ISC-EBIC signals is similar to those discussed in [11], [12], and [28], except for a change in the polarity. This change in polarity is due to the fact that of region subjected to electron beam in this brief is a p-doped region while those in [11], [12], and [28] were n-doped regions. The mechanism behind the shape of the transient ISC-EBIC signals is well explained in [11] and [28]. It is observed in Fig. 2 that the time taken for the positive ISC-EBIC , detected after the beam is turned ON, to decay to zero, is longer when the Schottky contact is smaller. This is because a smaller Schottky contact will reduce the rate, at which charge carriers are collected at the junction. This, in turn, reduces the rate that charges accumulate at the floating p-type bulk semiconductor region, which in turn causes it to take a longer time for charges to accumulate to provide sufficient bias to turn the diode ON. The rate that the charge carriers are collected at the junction is also reduced, if the beam distance x is further away from the junction. Therefore, the time for the current to decay to zero will be longer for larger beam distance x. The comparisons between the ISC-EBICo , the value of ISC-EBIC at the instance that the electron beam is turned ON, and the IEBIC , the conventional steady-state EBIC current, for the planar-collector configuration are shown in Fig. 3. It is shown in [11] and [28] that Cs ig . ISC-EBICo = (2) (Cs + C j ) Given that i g is rate of the charge carriers collection at the junction, which is equivalent to the conventional IEBIC signal,
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Fig. 5. Plots of α versus vs for different widths of the Schottky contact. Lines: data from IEBIC . Points: data from ISC-EBICo . The actual diffusion length is 3 μm.
Fig. 3. Plots of ISC-EBICo (ISC-EBIC measured when the beam is just turned OFF) and IEBIC versus x for different widths of the Schottky contact. Lines: IEBIC in the conventional steady-state EBIC mode. Points: ISC-EBICo in SC-EBIC mode. The simulation parameters are L = 3 μm. (a) vs = 0 cms−1 . (b) vs = 108 cms−1 .
using theory of linear regression, for the different sizes of Schottky contact. The shapes of the percentage errors of the extracted diffusion length against the surface recombination velocity are similar to those reported in [24]. The extracted diffusion length is within the accuracy of 2.4%. This means that the extraction of diffusion length using this method and (1) is quite reliable despite the variations in the size of the Schottky contact and the surface recombination velocity. The plots of the extracted alpha values versus surface recombination velocity for different Schottky contact widths are shown in Fig. 5. The value of alpha was found to decrease with the surface recombination velocity. The shape of the alpha versus surface recombination velocity graph is a vertically shifted Gaussian curve, which is similar to those reported in [17]. With a smaller width of the Schottky contact, the alpha versus surface recombination velocity curve shifts downward, as shown in Fig. 5. This is because the plot of ln(ISC-EBICo ) against x or ln(IEBIC ) against x becomes more concave upward when the width of the Schottky contact gets smaller. This effect is more significant when the surface recombination velocity is large. IV. C ONCLUSION
Fig. 4. Plots of percentage error in the extracted diffusion length L ext versus vs for different widths of the Schottky contact. Lines: data from IEBIC . Points: data from ISC-EBICo . The percentage error = (L ext − L actual )/ L actual × 100. The actual diffusion length is 3 μm.
Cs is the stray capacitance, and C j is the junction capacitance, we can conclude that the ISC-EBICo is proportional to IEBIC , where the proportionality constant is always less than unity. The ISC-EBICo signals are smaller than the conventional IEBIC signal even though this is not noticeable in Fig. 3. In this brief, Cs C j , thus, the value of Cs /(Cs + C j ) is close to unity, i.e., ISC-EBICo ≈ IEBIC . This suggests the possibility of applying the EBIC information obtained using the SC-EBIC technique, i.e., ISC-EBICo , in the conventional EBIC applications such as the extraction of diffusion lengths. Fig. 4 shows the percentage error of the extracted diffusion length obtained by fitting the ISE-EBICo and IEBIC data into (1)
The conventional steady-state EBIC and SC-EBIC modes of obtaining the EBIC information in the planar-collector configuration were studied. It was also found that the ISC-EBICo matches IEBIC when Cs C j , indicating that it is feasible to use ISC-EBICo in applications whereby is conventionally used. It was found that the smaller Schottky contacts will have smaller ISC-EBICo and IEBIC values. This effect is more pronounced when the surface recombination velocity values are larger. The time-to-recovery in ISC-EBIC signal was found to increase inversely with the size of the Schottky contact. The ISC-EBICo and IEBIC signals were also used to study the diffusion length extraction method proposed in [17]. It was found that the to method in [17] is able to evaluate the diffusion length accurately regardless of the size of the Schottky contact. R EFERENCES [1] S.-Q. Zhu, E. I. Rau, and F.-H. Yang, “A novel method of determining semiconductor parameters in EBIC and SEBIV modes of SEM,” Semicond. Sci. Technol., vol. 18, no. 4, pp. 361–366, 2003.
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[2] G. Moldovan, P. Kazemian, P. R. Edwards, V. K. S. Ong, O. Kurniawan, and C. J. Humphreys, “Low-voltage cross-sectional EBIC for characterisation of GaN-based light emitting devices,” Ultramicroscopy, vol. 107, nos. 4–5, pp. 382–389, Apr./May 2007. [3] D. E. Joannou and S. M. Davidson, “Diffusion length evaluation of boron-implanted silicon using the SEM-EBIC/Schottky diode technique,” J. Phys. D, Appl. Phys., vol. 12, no. 8, pp. 1339–1344, 1979. [4] D. E. Ioannou, “A SEM-EBIC minority-carrier lifetime-measurement technique,” J. Phys. D, Appl. Phys., vol. 13, no. 4, pp. 611–616, 1980. [5] D. E. Ioannou and R. J. Gledhill, “SEM-EBIC and traveling light spot diffusion length measurements: Normally irradiated charge-collecting diode,” IEEE Trans. Electron Devices, vol. 30, no. 6, pp. 577–580, Jun. 1983. [6] D. E. Ioannou, “Analysis of the photocurrent decay (PCD) method for measuring minority-carrier lifetime in solar cells,” IEEE Trans. Electron Devices, vol. 30, no. 12, pp. 1834–1837, Dec. 1983. [7] S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. New York, NY, USA: Wiley, 2007. [8] H. J. Leamy, “Charge collection scanning electron microscopy,” J. Appl. Phys., vol. 53, no. 6, pp. 51–80, 1982. [9] J. W. Orton and P. Blood, The Electrical Characterization of Semiconductors: Measurement of Minority Carrier Properties. London, U.K.: Academic, 1990. [10] A. Cavallini, L. Polenta, and A. Castaldini, “Charge carrier recombination and generation analysis in materials and devices by electron and optical beam microscopy,” Microelectron. Rel., vol. 50, nos. 9–11, pp. 1398–1406, Sep./Nov. 2010. [11] V. K. S. Ong, K. T. Lau, and J. G. Ma, “Theory of the single contact electron beam induced current effect,” IEEE Trans. Electron Devices, vol. 47, no. 4, pp. 897–899, Apr. 2000. [12] L. Meng, A. G. Street, J. C. H. Phang, and C. S. Bhatia, “Application and modeling of single contact electron beam induced current technique on multicrystalline silicon solar cells,” Solar Energy Mater. Solar Cells, vol. 133, pp. 143–147, Feb. 2015. [13] J. C. H. Phang et al., “Single contact beam induced current phenomenon for microelectronic failure analysis,” Microelectron. Rel., vol. 43, nos. 9–11, pp. 1595–1602, Sep./Nov. 2003. [14] Y. Lin et al., “Optical and electron beam studies of carrier transport in quasibulk GaN,” Appl. Phys. Lett., vol. 95, no. 9, pp. 092101–092103, 2009. [15] P. M. Bridger, Z. Z. Bandi´c, E. C. Piquette, and T. C. McGill, “Correlation between the surface defect distribution and minority carrier transport properties in GaN,” Appl. Phys. Lett., vol. 73, no. 23, pp. 3438–3440, 1998. [16] C. Leonid, O. Andrei, T. Henryk, J. W. Yang, Q. Chen, and M. A. Khan, “Electron beam induced current measurements of minority carrier diffusion length in gallium nitride,” Appl. Phys. Lett., vol. 69, no. 17, pp. 2531–2533, 1996. [17] D. S. H. Chan, V. K. S. Ong, and J. C. H. Phang, “A direct method for the extraction of diffusion length and surface recombination velocity from an EBIC line scan: Planar junction configuration,” IEEE Trans. Electron Devices, vol. 42, no. 5, pp. 963–968, May 1995. [18] V. K. S. Ong, “A direct method of extracting surface recombination velocity from an electron beam induced current line scan,” Rev. Sci. Instrum., vol. 69, no. 4, p. 1814, 1998. [19] D. E. Ioannou and C. A. Dimitriadis, “A SEM-EBIC minority-carrier diffusion-length measurement technique,” IEEE Trans. Electron Devices, vol. 29, no. 3, pp. 445–450, Mar. 1982. [20] M. Ledra and N. Tabet, “Monte Carlo simulation of the EBIC collection efficiency of a Schottky nanocontact,” Superlattices Microstructures, vol. 45, nos. 4–5, pp. 444–450, 2009. [21] M. Ledra and N. Tabet, “Electron beam induced current at a Schottky nanocontact,” Int. J. Nano Biomaterials, vol. 2, no. 1, pp. 307–312, 2009. [22] V. K. S. Ong, J. C. H. Phang, and D. S. H. Chan, “A direct and accurate method for the extraction of diffusion length and surface recombination velocity from an EBIC line scan,” Solid-State Electron., vol. 37, no. 1, pp. 1–7, Jan. 1994.
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Chee Chin Tan received the Ph.D. degree in electrical and electronic engineering from Nanyang Technological University, Singapore. He is currently a Senior Product Engineer with Micron Semiconductor Asia Pte. Ltd., Singapore.
Vincent K. S. Ong received the Ph.D. degree in electronics from the National University of Singapore, Singapore. He joined Nanyang Technological University, Singapore, in 1997, where he became an Associate Professor in 1999. He was a Visiting Fellow with the University of Cambridge, Cambridge, U.K., in 2005.
K. Radhakrishnan (M’01) received the Ph.D. degree in physics from the National University of Singapore, Singapore. He is currently an Associate Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.
