1. Development of an analytical mobility model for the simulation of ultra thin SOI MOSFETs. M.Alessandrini, *D.Esseni, C.Fiegna Department of Engineering - University of Ferrara, Italy *DEGM, University of Udine, Italy

2. Introduction The scaling of the conventional bulk CMOS technology requires high doping concentration to counteract short channel effects (SCE). Problem Problem: the increase of doping concentration leads to a significant degradation of the low field mobility (black curves in figure): SOI devices with almost undoped ultra- thin silicon layer represent a possible solution for mobility degradation

3. Dependence of effective mobility on Tsi  Recent works reported a dependence of effective mobility in SOI MOSFETs on the thickness of the silicon layer (T SI ) which is particularly evident at low inversion densities Conventional mobility models overestimate experimental mobility and are not able to qualitatively reproduce the dependence of mobility on Tsi

4. This work In this work we developed analytical models for electron mobility limited by two scattering processes that lead to the mobility modulation by T SI in SOI MOSFETs: Surface optical phonos scattering ● Surface optical phonos scattering ● Coulomb scattering with interface states

5. Scattering with surface optical phonons The model for mobility limited by surface optical phonons has been developed starting from the general formulation of M. Fischetti and S.Laux (''Monte Carlo study of electron transport in silicon inversion layers'' Phys.Rev. B Vol 48, 1993) * under the following approximations: ● single parabolic umprimed subband, ● one constant effective value for the exchanged wave vector with no angular dependence (q e ). Under these approximations we obtained the following scattering rate: * This formulation has been used in D. Esseni et al. ''Study of low field electron transport in ultra-thin single and double gate SOI MOSFETs'' IEDM 2002

6. Scattering with surface optical phonons ● The wave function is approximated as follow*: ● We empirically relate the parameter b to the effective field Eeff as follows: * According to F.Stern and W. Howard ''Properties of Semiconductor Sueface Inversion Layer in the Electric Quantum Limit'' Phis.Rev. Vol.163 1997 Fitting parameter Normalized concentration: n(z)/Ninv

7. Determination of the parameter . Determination of the parameter . We determined the value of the parameter  by comparing the calculated g(z) with the normalized charge density obtained from Schroedinger-Poisson calculations: Bulk MOSFET SOI MOSFET (TSI=5.2 nm) Schroedinger Poisson simulations g(z) approximation Schroedinger Poisson simulations g(z) approximation

8. Scattering rate for the case of two Si-SiO2 interfaces: Scattering with surface optical phonons Mobility in the relaxation-time approximation:

9. Scattering with surface optical phonons Parameter values used in this model: The effective exchanged wave vector is obtained by fitting the results of rigorous numerical calculation : D.Esseni et al. ''Study of low field electron transport in ultra-thin single and double gate SOI MOSFETs'' IEDM 2002

10. Simulation Results : fitting of rigorous numerical calculation Numerical model Analytical model applied to electric field obtained by Schrodinger/Poisson calculation Scattering with surface optical phonons

11. Calculation of total effective mobility ● We performed a drift diffusion simulation of long MOSFETs using a mobility model for bulk MOSFETs and accounting for quantization by the density gradient model. ● We evaluated the mobility limited by SO phonons scattering by post- processing the electric-field distribution with equation: We calculated the total electron mobility composing, by the Mathiessen rule, the mobility evaluated at discretization points within the inversion layer with mobility limited by SO phonons scattering. The effective mobility in the inversion layer is then obtained as an average weigthed by carrier concentration according to:

12. Effective mobility in ultra-thin SOI SG MOSFETs including surface optical phonons scattering (symbols) and experimental data for low- doped Bulk MOSFETs (line) (qualitative agreement with Koga et al. IEEE TED June 2002). Scattering with surface optical phonons

13. Simulation Results: effective mobility versus E eff for bulk structures Scattering with surface optical phonons Simulations including the effects of SO phonons Experimental data

14. Coulomb scattering with interface states Following the same procedure we described for SO phonons scattering, we obtained the following scattering rate with unscreened interface charge: Where Mf and Mb are the same used for SO phonons scattering and Areal density of interface states

15. Coulomb scattering with interface states Screening The screening by inversion carrier is accounted for by a modified : Where is the Debye length.

16. Coulomb scattering with interface states Left: experimental mobility versus Ninv Right: simulations including SO phonons scattering and interface states scattering.

17. Conclusions ● In this work, analytical models for the mobility limited by surface optical phonons and by interface states has been developed and applied to the calculation of electron effective mobility in MOSFETs. ● The proposed models can be adopted in conjunction with conventional mobility models developed for bulk devices, and allow to reproduce the main feature of recently-reported mobility data for ultra-thin SOI MOSFETs. ● The model for SO-phonons-limited mobility has been recently implemented in DESSIS using the physical-model software interface.