IEE5328 Nanodevice Transport Theory and Computational Tools

1. IEE5328 Nanodevice Transport Theory and Computational Tools (Advanced Device Physics with emphasis on hands-on calculations) Lecture 3A: A Self-Consistent Solver of Poisson-Schrodinger Equations in a MOS System Prof. Ming-Jer Chen Dept. Electronics Engineering National Chiao-Tung University March 18, 2013 IEE5328 Prof. MJ Chen NCTU

2. Double-gate MOSFET Simulator:MOS Electrostatics Student:Ting-HsienYeh葉婷銜 Advisor:Dr. Ming-Jer Chen

3. Structure Vg • Schematic double-gate n-MOSFET and its MOS band diagram. • In this work, we set up a simulator called DG-NEP to deal with a symmetrical double-gate n-MOSFET structure. Gate tox Oxide S N+ Body(p-type) N+ D tbody tox Oxide Gate

4. Flowchart for DG-NEP simulator Without Penetration Effect Start Setting the environment and physics parameters. Calculate Ef at equilibrium,and set Ev=0. Use Poisson’s equation to solve potential(V0). Calculate charge density,voltage…. Use V0 to solve Schrodinger equation to obtain wave function and subband occupancy. Yes Use updated concentration to get new potential by using Poisson’s equation. If |Vn+1-Vn|<1.0 × 10-12eV No

5. Schrödinger and Poisson Self-consistent of DG-NEP • The three-dimensional carriers (both electrons and holes) density: • Poisson Equation:

6. Physical Model in DG-NEP • The two-dimensional electron density • The oxide voltage • The total inversion layer charge density • The flat band voltage • The average inversion layer thickness • The gate voltage • The transverse effective field: Nano Electronics Physics Lab @ NCTU

7. Subband Energy and Wave-function • For Tsi=30nm: We can find that our DG-NEP simulation results without penetration effect match Schred'sones.

8. Subband Energy and Wave-function • For Tsi=10nm:

9. Subband Energy and Wave-function • For Tsi=1.5nm:

10. The Comparison of Potentials and Electron Density Distributions with Those of Shoji, et al. • (a) Tsi=30nm: (b) Tsi=5nm • In this paper , ml=0.98m0 , mt=0.19m0 , mox=0.5m0 , Nsub=1x1015cm-3 [10] M. Shoji and S. Horiguchi, “Electronic structures and phonon limited electron mobility of double-gate silicon-on-insulator Si inversion layers,” J. Appl. Phys., vol. 85, no. 5, pp. 2722–2731, Mar. 1999.

11. The Comparison ofSubband Energies with Those of Shoji, et al. • (a) Eeff=1 × 105 V/cm (b) Eeff=5 × 105 V/cm • For thick tSi, two of each subbands have almost the same energy due to the upper and lower inversion layers sufficiently separated as a distinct bulk inversion layer. As tSidecreases, the barrier between two inversion regions becomes lower and making the subband energies split.

12. Comparison with Gamiz, et al. • (a) Non-primed subbands(b) Primed subbands [11] F. Gamiz and M. V. Fischetti, “Monte Carlo simulation of double-gate silicon-on-insulator inversion layers: The role of volume inversion, ” J. Appl. Phys., vol. 89, no. 10, pp. 5478–5487, May 2001.

13. Comparison with Gamiz, et al. • Energy separation for two different body thicknesses

14. The Comparison of C-V with Alam, et al.and Schred. • (a) Different substrate thickness (b) Different oxide thickness • [14] M. K. Alam, A. Alam, S. Ahmed, M. G. Rabbani and Q. D. M. Khosru, “Wavefunction penetration effect on C-V characteristic of double gate MOSFET, ” ISDRS 2007, December 12-14, 2007, College Park, MD, USA.

15. The Comparison of C-V with Alam, et al.and Schred. • (a) Different substrate thickness (b) Different oxide thickness • [14] M. K. Alam, A. Alam, S. Ahmed, M. G. Rabbani and Q. D. M. Khosru, “Wavefunction penetration effect on C-V characteristic of double gate MOSFET, ” ISDRS 2007, December 12-14, 2007, College Park, MD, USA.