indDG: A New Model for Independent Double-Gate MOSFET

1. indDG: A New Model for Independent Double-Gate MOSFET Santanu Mahapatra Nano-Scale Device Research Lab Indian Institute of Science Bangalore Email: santanu@cedt.iisc.ernet.in Web: http://www.cedt.iisc.ernet.in/nanolab/

2. Common versus Independent double gate • Development of indDG Core • Single Implicit Equation based IVE • Solution Technique for IVE • Charge Model • Extension to Tri-Gate • SPICE Implementation • Future Works Outline

3. Common vs Independent DG MOSFET (1) Courtesy: Endo et al. IEEE EDL 2009

4. With IDG MOSFET the design space gets extended from 2D to 3D, which leads to novel circuit design possibilities e.g., High density reduced stack logic, IEEE T-ED 2006 Compact sequential circuit, IEEE T-ED 2006 Mixer, IEEE T-ED 2005 SRAM, IEEE EDL 2009 Common vs Independent DG MOSFET (2) Vds Dynamic Threshold Voltage Control: Use one gate to drive, other gate to Vth control Vg1 Vg2

5. Single Implicit Equation Based IVE (1) Previous solution (Taur, and then Gildenblat) Development of indDG Core SDG device has symmetric BC, that leads to additional implied BC (electric field =0 at y=0), which results in very simple trigonometric IVE A Very Complex Problem Requires Solution of COUPLED implicit equations which has DISCONTINUITY!!

6. Single Implicit Equation Based IVE (2) By indigenous handling of BC, we introduced single implicit equation based IVE that is 5x faster than coupled IVE. Development of indDG Core Sahooet al., IEEE T-ED, V 57, N 3, 2010

7. Solution technique for IVE (1) Development of indDG Core Singularity @ γ = π for Trig IVE Conventional NR method doesn’t GUARANTEE convergence!! Discontinuity @ G = 0 for both Trig and Hyp IVE

8. Solution technique for IVE (1) • We use RBM (Root Bracketing Method) instead of NR-based method to achieve guaranteed convergence. • We did a rigorous study of all RBMs available in the literatures (~20). And finally choose LZ4 technique (D. Le, ACM T-MS 1985) to solve the IVEs. Development of indDG Core But RBM requires solution space…. So we need to solve ONE more implicit equation, to find the solution space for Trig/Hyp IVE. We do some smart optimization of solution space to improve overall computational efficiency. And so we need to solve THREE implicit equations SEQUENCIALLY (one to choose mode, one to find solution space and finally the main IVE) to calculate the surface potential. Srivatsava et al., IEEE T-ED, V 58, N 6, 2011 Abraham et al., IEEE T-ED, April, 2012

9. The Charge Model : Issues with existing Model Development of indDG Core TT Why this mismatch? THREE MODES OF OPERATION HH TH Line: Model (G. Dessai, IEEE T-ED 2010) Symbol : Numerical

10. The Charge Model: Charge linearization Concept Development of indDG Core As the exact solution of the integrals are not available ‘charge linearization’ techniques are introduced over the years to approximate F as quadratic function of surface potentials (or charge densities) so that closed form expressions for terminal charges are obtained.

11. The Charge Model : The NLF Factor Development of indDG Core To approximate F as quadratic function of ψ1 or ψ2 (Qi1 or Qi2 ), they should hold linear-relationship along the channel for a given bias condition.

12. The Charge Model: Piecewise Linearization Technique Development of indDG Core We segment the channel, so that for each segment ψ1holds linear relationship with ψ2 so that conventional charge linearization technique could be applied to formulate the Terminal Charges. Srivatsava et al., Appearing in IEEE T-ED, 2012

13. The Charge Model: Comparison of linearization Development of indDG Core • indDG charge model is based on the relationship of the surface potentials • It is derivative free and thus numerically robust

14. There will always be some amount of asymmetry between the gate oxide thicknesses due to process variation and uncertainties • indDG-c handles the asymmetry as it is based on the relationship between surface potential (which is linear for this case) • We use an accurate analytical approximation of surface potential by novel perturbation technique SDG with small Tox asymmetry (indDG-c) Simple closed form function of Bias and device parameters, derived from the IDG IVEs Srivatsava et al., IEEE T-ED, April, 2012

15. Including Body Doping Tox1=1nm Tox2=1.5nm Tsi = 10nm Tox1=Tox2=1nm; Tsi = 20nm

16. Tri Gate MOSFET cannot be model like Bulk or DG as the 3D Poisson Equation cannot be approximated as 1D Poisson for long channel cases. • Models for Tri Gate are developed on top of the planner DG Models Tri Gate Extension

17. Model is implemented in SilvacoSmartSpice through Verilog-A interface Model Implementation S/D Symmetry of Terminal Charge 101 Stage Ring Oscillator Also successfully simulated 8-bit Ripple carry adder, Jhonson Counter

18. To include Small geometry effects, NQS, Noise, extrinsic elements to make it applicable for practical devices… Future Plans

19. My Masters and Ph.D. students • Department of Science and Technology (DST), Government of India • Dr. Ivan Pesic and his team @ Silvaco International Acknowledgement