1. Accumulation Gate Capacitance of MOS Devices with Ultra-thin High-K Gate Dielectrics: Modeling and Characterization Ahmad Ehteshamul Islam and Anisul Haque Dept. of EEE, BUET

2. Outline Importance of Accumulation region modeling Modeling CV and Verification Snapshot of the proposed characterization technique (EOT Extraction) Origin of the proposed technique Wave-function penetration (WP) effect Comparison with other QMCV Future work Summary

3. Importance of Accumulation region modeling We can model both MOSCAP and MOSFET Poly-Si effect on Capacitance is small s(acc) < s(inv) for a particular carrier density QM effect on CV is lower in accumulation (for same carrier) As poly doping is high, this effect is further reduced So, C G = C ox || C Sem There is no depletion capacitance Helps in EOT extraction CGCG C ox C acc CGCG C ox C inv C dep C poly

4. Modeling CV and Verification Self-consistent Schrödinger-Poisson Solution Schrödinger Equation: Greens function formalism with Transmission line analogy T di = 42 Å (TEM Image) ε di = 14

5. Snapshot of the EOT Extraction Technique Previous Techniques Semi-classical technique (Sheet charge model) McNutt and C. T. Sah, JAP 46, pp. 3909, 1975 J. Maserjian et. al., SSE 17, pp. 335, 1974 S. Kar, TED 50(10), pp. 2112, Oct. 2003 QM Simulation With or without (EOT underestimation) wave function penetration (WP) Proposed Technique Simple as Semi-classical techniques Takes QM (including WP)

6. Origin of Proposed Technique Device Information: Wilk, Wallace, JAP 89(10), pp. 5243

7. Origin of Proposed Technique Region 2 and 3 (QM) Region 1: Semi-classical Ref.: R.F. Pierret Y. Tsividis Region 1 Corrupted by Interface charge Pretty small region Region 3 Varies from device to device

8. Origin of Proposed Technique Processing in Region 2 Equation to be used X-axis Intercept gives, C ox Region 1 Region 3

9. Wave Function Penetration Effect 1.The technique is almost independent of barrier height S. Mudanai et. al., EDL 22(3), pp. 145, Mar. 2001. 1~2 A shift for 1nm Device

10. Wave Function Penetration Effect 2.Takes into account WP Effect for electron is less than that for hole A. Haque et. al., TED 49(9), pp. 1580, Sep. 2002. Effective mass: Electron: 0.98, 0.19 Hole: 0.5, 0.16 [Sze] 0.29, 0.2 [Takagi, TED 46(7)] WP Effect lower Compared our results with QM simlulator results: J. J. Chambers et. al., JAP, 90(2), pp. 918 Our extracted EOT Matches with PMOS device (electron in accumulation) Greater than referred value for NMOS (as EOT underestimated in reference, neglecting WP effect)

11. Using C di, we can extract C acc a Extracted C acc vs. Φ s

12. Comparison with QUASI (A. Ghetti) and UTQUANT QUASI UTQUANT (Compact Model) F. Li, et. al., TED 52(6), pp. 1148, June 2005. Considers WP in High-K same as that in SiO 2. Neglects increased penetration in High-K So this papers extraction of EOT (for High-K) < Our extraction Whereas, extraction for SiO 2 is almost identical

13. Summary A new EOT extraction technique proposed Simpler as the semi-classical techniques Takes into account QM effects Technique compared with different QMCV Extracted C acc - Φ s shows expected behavior Physical Origin of C acc -Φ s relationship (To be published)