Efficient Monte Carlo Simulation of Tunnel Currents in MOS Structures

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1 Efficient Monte Carlo Simulation of Tunnel Currents in MOS Structures D. Grgec, M.I. Vexler, C. Jungemann, B. Meinerhagen Grg-P/02-1

2 Presentation Outline Introduction: quantum effects in MOS structures Improed modified local density apprimation MC-Tunneling rate model Fullband Monte Carlo (FBMC) simulations Results and comparison with experiment Conclusions Grg-P/02-2

3 Introduction : Quantum Effects in MOS Structures Important effects at the MOS interface: Quantum correction of carrier densities Tunneling through thin dielectric layer Goals for implementation in the FBMC deice simulator: Physics based semiempirical models Reproducing experimental results Predictie simulation for normal operating conditions Insignificant simulation time oerhead Grg-P/02-3

4 nmos Energy Band Diagram for Typical OP Grg-P/02-4

5 Improed Modified Local Density Apprimation * Quantum potential calculated from structure parameters Fitted to measurements of macroscopic quantities Small influence on stability and simulation time * C. Jungemann et al: Improed Modified Local Density Apprimation for Modeling of Sie Quantiation in NMOSFETs, MSM 2001 Grg-P/02-5

6 S tunn T τ = tunn MC-Tunneling Rate Model T tunn particle tunneling probability through the potential barrier τ aller-retour time for a particle in a quantum well Introduced in analogy to scattering rates in MC simulations Any suitable method can be used to calculate tunneling probability Tunneling rate is ealuated for all particles and not only for those at the surface (nonlocal tunneling) model is compatible with quantum correction for carrier density Grg-P/02-6

7 Tunneling Probability Θ WKB = exp ( 2 d) r k WKB-apprimation h 2 k r 2 2 mf E = γ = + E 1 Eg Fran-type dispersion relation T T corr tunn = 4 S 2 S + S S = min FR 2 4 G 2 G + G G ( Θ T,1) WKB corr 2 elocity correction factor Grg-P/02-7

8 Aller-retour Time τ = 2 min( b, L) a d ς ( ς) exactly τ = min( b, L) a 2 υ ( ) appr. Grg-P/02-8

9 FBMC Simulations Tunneling eent is represented by the calculation of the tunneling rate Space and time aerage of carrier tunneling contributions (q i S tunn ) tunnel current density Non self-consistent tunnel current model Control of simulation accuracy achieed through ealuation of stochastic error Grg-P/02-9

10 Results nmos Technology d = 3.5nm N Apeak = cm -3 N Dgate = cm -3 Electron eff. mass m F = 0.51m Operating point U B =U S =U D =0V 0 Grg-P/02-10

11 Conclusions New efficient model for the ealuation of MOS tunnel currents in a MC deice simulator Compatible with quantum correction of carrier density Different methods for tunneling probability applicable Good agreement with measurements Prediction of tunnel currents possible if the deice operation is not strongly influenced by tunneling Grg-P/02-11

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