Modeling of the Substrate Current and Characterization of Traps in MOSFETs under Sub-Bandgap Photonic Excitation

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1 Journal of the Korean Physical Society, Vol. 45, No. 5, November 2004, pp Modeling of the Substrate Current and Characterization of Traps in MOSFETs under Sub-Bandgap Photonic Excitation I. C. Nam, H. T. Kim, H. S. Park, K. S. Kim, K. H. Kim, J. B. Choi, J. U. Lee, S. W. Kim, G. C. Kang, D. J. Kim, K. S. Min and D. M. Kim School of Electrical Engineering, Kookmin University, Seoul (Received 7 July 2004) The substrate current is a good indicator for the hot-carrier and electrostatic discharge reliability of MOSFETs. However, the observation of the substrate current induced by generated holes from hot-carrier or impact ionization in dark condition does not objectively offer information on the interface states. By using a sub-bandgap optical source (E ph = 0.95 ev, P opt = 5 dbm, λ = 1310 nm), electrons on the traps below the Fermi level (E t < E F and E C E ph E t E C) can be excited to the conduction band and contribute to the substrate current. We modeled and characterized the substrate current under photonic characterization. We used the conventional substrate current model for universality of this analysis and found that it agreed well with experimental results obtained under sub-bandgap optical excitation. PACS numbers: w Keywords: Substrate current, Trap, Interface state, Optical, Photonic I. INTRODUCTION Recently, MOS (metal-oxide-semiconductor) device size has been extremely scaled down to deep submicron without a comparable reduction of supply voltage, which leads to higher electric field near the drain region to generate energetic hot carriers. As a result, the oxide trapping and interface state generation cause degradation of long-term performance and reliability of devices and their integrated circuits [1]. It is well known that the substrate current plays an important role in determining the robustness and hot-carrier reliability of MOSFETs (MOS field effect transistors). So, we investigated the substrate current with and without sub-bandgap (E ph < E g ) optical source which confines excess carriers only from traps (trap-to-band generation), excluding the band-to-band carrier generation. We expect that changes in the substrate current under sub-bandgap optical illumination can be used to characterize the density and distribution of the traps in the MOS systems. where I D is the drain current, l d is the characteristic length of the velocity saturation region, α n is the impact ionization rate, A and B are the ionization constants, and E(y) is the electric field in the channel of MOS- FETs under test. Based on the quasi-two-dimensional approximation, the channel electric field, E(y), is expressed as E(y) = E SAT cosh(y/l d ), where E SAT is the channel electric field at which the carriers reach velocity saturation. E SAT is known to be V/cm for electrons. From Eq. (1), I SUB can be derived as [3] (1) I SUB = I D C(V D ηv Dsat ) ( ) B exp l d, (2) V D ηv Dsat l d = l o + l 1 (V DS V geff ) + l 2 (V DS V geff ) 2, (3) II. SUBSTRATE CURRENT MODEL It is well known that the substrate current (I SUB ) can be obtained from [2] ld ld ( I SUB = I D α n dy = A I D exp B ) dy, 0 dmkim@kookmin.ac.kr; Tel: ; Fax: E(y) V geff = V gs V T o. (4) Characteristic model parameters including C, B, η, l o, l 1 and l 2 are empirical fitting parameters and can be extracted from the experimentally obtained substrate current I SUB. nmos test transistors were fabricated at ISRC (Interuniversity Semiconductor Research Center) by using a 1.5-µm CMOS process. The gate oxide was grown to a thickness of 25 nm. Boron ( 11 B +, 1.5 times cm 2,

2 Journal of the Korean Physical Society, Vol. 45, No. 5, November 2004 Fig. 1. Substrate current (I SUB) versus gate to source voltage (V GS) under dark condition in N-MOSFET 20/2 [µm/µm] ( : experimental substrate current; : calculated substrate current; Table: extracted parameters). Fig. 3. I SUB/I D versus V GS under dark condition ( : experimental I SUB/I D; : generalized I SUB/I D; : calculated I SUB/I D) where a fitting error occurs between calculated I SUB/I D and experimental I SUB/I D. Fig. 2. Substrate current (I SUB) versus gate to source voltage (V GS) under sub-bandgap optical illumination in N- MOSFET 20/2 [µm/µm] ( : experimental substrate current; : generalized substrate current; : calculated substrate current; Table: extracted parameters under dark condition). Fig. 4. I SUB/I D versus V GS under sub-bandgap optical illumination ( : experimental I SUB/I D; : generalized I SUB/I D; : calculated I SUB/I D) where a fitting error occurs between calculated I SUB/I D and experimental I SUB/I D. 40 kev) was implanted for the threshold voltage adjustment, and arsenic ( 75 As +, cm 2, 80 kev) was implanted to form the highly doped n + source and drain. Based on Eq. (2), I SUB is calculated and the parameters are extracted under dark condition as shown in figure 1. The measured substrate current under sub-bandgap optical illumination appears as circles in figure 2. As a result of applying the extracted parameters under dark condition and the measured drain current under subbandgap optical illumination to Eq. (2), the calculated substrate current under sub-bandgap optical illumination appears as triangles in figure 2. Experimental data and calculated data show significant errors, as shown in figure 2. These errors are caused by the exclusion of the average drain-to-substrate leakage current component in the model. Therefore, we should consider the average drain-to-substrate leakage current to adopt a change in the bell-shaped substrate current Fig. 5. I SUB/I D versus V GS with and without subbandgap optical illumination ( : without sub-bandgap optical illumination; : with sub-bandgap optical illumination). under sub-bandgap optical illumination. The modeling result is shown as a solid line in figure 2, and the conventional model including the photonic effect

3 Modeling of the Substrate Current and Characterization of Traps I. C. Nam et al in figure 6. III. DENSITY AND DISTRIBUTION OF THE INTERFACE TRAPS Fig. 6. Substrate current (I SUB) versus gate to source voltage (V GS) under sub-bandgap optical illumination in N- MOSFET 20/2 [µm/µm] ( : experimental substrate current; : calculated substrate current; : generalized substrate current; : ζ-adopted substrate current). can be rewritten as I SUB.gen = I SUB.conv + I AV G.leak, (5) where the average leakage current (I AV G.leak ) is the substrate current before V DS is increased up to the saturation voltage V Dsat. Based on Eq. (5), I SUB /I D is shown in figure 3 (without sub-bandgap optical illumination) and figure 4 (with sub-bandgap optical illumination). However, we note that the correct quantity is not fully considered in the substrate current with sub-bandgap optical illumination, as shown in figure 2. Therefore, we propose a model parameter ζ that is a physics-based empirical fitting parameter. The subbandgap optical energy contributes to an increase of the substrate current and this can be implemented as ηv Dsat under dark condition and ζηv Dsat when the optical effect is included. Based on the physical point of view in the definition of ζ, we may understand that the drain saturation voltage is reduced (ζv Dsat < V Dsat ) under sub-bandgap optical illumination. This also means that the change of the substrate current caused by the gate voltage is also changed by the sub-bandgap illumination, as shown in figure 5. This is because the optical source supplies extra energy to the carriers. The other observation in figure 5 is a change caused by the excitation and contribution of electrons residing on the trap levels below the Fermi level (E t < E F ). Electrons created by sub-bandgap optical illumination [4,5] cause additional impact ionization by higher electric field near the drain region. Thereby, electron-hole pairs are created, and these electron-hole pairs change the peak substrate current and the gate to source voltage at which the peak substrate current appears, as well as the shape of the substrate current on the gate voltage. This implies that the quantitative extraction of interface states is possible with substrate current monitoring under sub-bandgap photonic excitation. The optical substrate current that is denoted as ζ is shown Based on the increased substrate current caused by the excitation of the trap charges, we may regard the MOS- FET (metal-oxide-semiconductor field effect transistor) as a system responding to any given input signal. This system operates as an amplifier within the measurement range, and the multiplication factor (M) of this system depends on the gate and drain biases (V GS and V DS ). First, if we assume that the increase in the substrate current is proportional to the increase in the carrier concentration (any current density can be simply described as J = qnv), the substrate current (I SUB ) as a function of the gate bias (V GS ) under dark condition can be written as I SUB1 (V GS1, V DS1 ) n 1 (V GS1, V DS1 ) M(V GS1, V DS1 ), I SUB2 (V GS2, V DS1 ) n 2 (V GS2, V DS1 ) M(V GS2, V DS1 ), I SUBn (V GSn, V DS1 ) n n (V GSn, V DS1 ) M(V GSn, V DS1 ), (6) and the system response to the increased carriers ( n) can be described as I SUB (V GS, V DS ) (n(v GS, V DS ) + n(v GS, V DS )) M(V GS, V DS ). (7) Based on Eqs. (6) and (7), the substrate currents both with (I SUB.op ) and without (I SUB.dk ) sub-bandgap optical illumination can be modeled by I SUB.dk = I SUB.dk0 M dk (V GS, V DS ), (8) I SUB.op = I SUB.op0 M op (V GS, V DS ), (9) and I SUB.dk0 = A q n dk0 v dk, (10) I SUB.op0 = A q n op0 v op, (11) where A is the area, v dk and v op are the velocity of carriers, and n dk0 and n op0 are the channel carrier concentration under dark condition and sub-bandgap optical illumination, respectively. If the traps are only responsive to photons with subbandgap energy and directly result in the increase of the

4 Journal of the Korean Physical Society, Vol. 45, No. 5, November 2004 under sub-bandgap optical illumination is written as n op0 = n dk0 + n. (12) The normalized multiplication factor M(V GS, V DS ) is derived from M dk (V GS, V DS ) = I SUB.dk (V GS, V DS )/I SUB.dk.MAX, (13) M op (V GS, V DS ) = I SUB.op (V GS, V DS )/I SUB.op.MAX, (14) Fig. 7. Difference between M op and M dk versus gate to source voltage (V GS) under sub-bandgap optical illumination in N-MOSFET 20/2 [µm/µm]. and the difference between M op and M dk is shown in figure 7. From Eq. (8) to Eq. (12), the ratio of the substrate currents (I SUB.op /I SUB.dk ) is written as I SUB.op = I SUB.op0 M op (V GS, V DS ) I SUB.dk I SUB.dk0 M dk (V GS, V DS ) = Aqv op n op0 M op (V GS, V DS ) Aqv dk n dk0 M dk (V GS, V DS ), (15) and, assuming v dk v op, the increase in the carrier density ( n) is modeled by Fig. 8. Photo-responsive energy band. E ph is the energy of a photon under sub-bandgap optical illumination, E is the photo-responsive range, qφ s is the potential at the surface, and qφ f is the potential at the bulk. The gray dot-lined box is the range in which the trap is generated (E t < E F and E C E ph E t E C). carrier concentration, the channel carrier concentration Fig. 9. Distribution of the interface trap density versus trap energy from the valence band. E C 1.12 ev; E i 0.56 ev. n = (I SUB.op/I SUB.dk ) n dk0 M dk (V GS, V DS ) n dk0 M op (V GS, V DS ) M op (V GS, V DS ) [cm 3 ]. (16) The sheet charge Q c is numerically solved by the quasi- 2D approximation [6], and n dk0 is expressed as n dk0 = Q c qt inv [cm 3 ], (17) where t inv is the effective channel thickness. If we assume that n is uniformly distributed within t inv, the twodimensional trap density N it [cm 2 ] is obtained from N it = n t inv [cm 2 ]. (18) Figure 8 shows the photo-responsive energy band. In the energy range ( E) in Figure 8, the trap can

5 Modeling of the Substrate Current and Characterization of Traps I. C. Nam et al be excited with the help of the sub-bandgap optical illumination and the contribution of electrons residing on the trap levels below the Fermi level (E t < E F ) is decreased along the x-axis. The two-dimensional average trap density N it extracted from the substrate current change under sub-bandgap optical illumination is found to be [cm 2 ] in the energy region (2qφ f < E t < E C ). By using Eq. (16), Eq. (17), and Eq. (18), D it is derived as D it = 1 q N it φ surf = 1 q and is shown in figure 9. N it V GS [cm 2 ev 1 ], (19) V GS φ surf ACKNOWLEDGMENTS This work was supported by 2004 Kookmin University Research Initiative Program, and simulation software was provided by IC Design Education Center (IDEC). REFERENCES IV. CONCLUSION In this paper, we investigated the modulation in the substrate current under dark condition and optical illumination with a sub-bandgap optical source (E ph = 0.95 ev, P opt = 5 dbm, λ = 1310 nm). The substrate current under sub-bandgap optical illumination is modeled with both the parameters extracted under dark condition and the model parameter ζ. The distribution of the interface trap density (D it ) [cm 2 ev 1 ] is extracted from the change of the substrate current which is due to optically generated electrons on the traps below the Fermi level (E t < E F and E C E ph E t E C ). [1] C. Hu, S. C. Tam, F. C. Hsu, P. K. Ko, T. Y. Chan and K.W. Terrill, Solid-State Circuits 20, 295 (1985). [2] N. D. Arora and M. S. Sharma, IEEE Trans. Electron Dev. 38, 1392 (1991). [3] W. Li, J. S. Yuan, S. Chetlur, J. Zhou and A. S. Oates, Solid-State Electronics 44, 1985 (2000). [4] S. J. Song, H. T. Kim, S. S. Chi, M. S. Kim, W. S. Chang, S. D. Cho, H. T. Shin, T. E. Kim, H. J. Kang, D. J. Kim and D. M. Kim, J. Korean Phys. Soc. 41, 892 (2002). [5] M. S. Kim, H. T. Kim, S. S. Chi, T. E. Kim, H. T. Shin, K. W. Kang, H. S. Park, D. J. Kim, K. S. Min, D. W. Kang and D. M. Kim, J. Korean Phys. Soc. 43, 873 (2003). [6] Z.-H. Liu, C. Hu, J.-H. Huang, T.-Y. Chan, M.-C. Jeng, P. K. Ko and Y. C. Cheng, IEEE Trans. Electron Dev. 40, 86 (1993).