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-Hsien Yeh 葉婷銜
Advisor: Dr. Ming-Jer Chen

3. Structure 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.
tox
Body(p-type) N+
Oxide D S
Gate
tbody Vg

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).
Use V0 to solve Schrodinger equation to obtain wave function and subband occupancy.
Use updated concentration to get new potential by using Poisson’s equation.
If |Vn+1-Vn|<1.0 × eV
Calculate charge density,voltage….
Yes 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 NCTU

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

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

11. The Comparison of Subband 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 tSi decreases, 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.