J. C. Tinoco and J.-P. Raskin Université catholique de Louvain Microwave Laboratory B-1348 Louvain-la-Neuve, Belgium

1. RF Extraction Techniques for Series Resistances of MOSFETs J. C. Tinoco and J.-P. Raskin Université catholique de Louvain Microwave Laboratory B-1348 Louvain-la-Neuve, Belgium

2. OUTLINE • Introduction • Bracale´s Method • Bracale´s Modified Method • Results • Conclusions

3. INTRODUCTION Different methods have been developed to determine the extrinsic series resistances. They can be divided in two groups:DC and RF methods. DC Methods RF Methods • It is possible to extract independently the drain, source and gate resistances. • Device biased under different conditions. • Requires the equivalent circuit analysis. • It is not possible to extract independently the drain and source resistances: • RT = Rd + Rs • It is not possible to determine the gate resistance.

4. INTRODUCTION The main RF methods are: Lovelace, Torres-Torres, Raskin and Bracale. • Lovelace and Torres-Torres´ methods are quite sensitive to noise. • Signal pre-treatments do not improve the extraction. Torres-Torres Lovelace

5. INTRODUCTION • Raskin´s method also is quite sensitive to noise. • Signal pre-treatments seem to improve the extraction. • For deep-submicron devices its application seems limited. • Bracale´s method is less sensitive to noise. • Fails to determine the correct resistance values. Raskin Bracale • Deep analysis is necessary for the Bracale´s method

6. Bracale´s Method Bias: VDS = 0 V & VGS>VT Gmi → 0 • Assumptions: • Perfectly symmetric Device: Cgsi = Cgdi = C • Constant mobility

7. INTRODUCTION Bracale´s Method Impedance Relationships: 

8. Bracale´s Method Linear regression of the impedance relationship respect to the inverse of the gate overdrive. The intercept gives the corresponding series resistance.

9. Bracale´s Method • The extracted values differ from the values used in the simulations. • It is necessary to review the assumptions made: • Perfectly symmetric Device: Cgsi = Cgdi = C • Constant mobility

10. Bracale´s Modified Method Mobility degradation coefficient: The inverse of the output conductance is a linear function of the inverse of the gate overdrive: The slope “s” and the intercept “b” are: And thus:

11. Bracale´s Modified Method The impedance relationships will be expressed as:  They follow linear function respect to the inverse of the gate overdrive, the slope “x” will be:

12. Bracale´s Modified Method • The mobility degradation strongly affects the extraction accuracy. • Considering non-perfectly symmetry, the impedance relationships will be expressed as: Where k = Cgs/Cgd is called the asymmetry coefficient.

13. Bracale´s Modified Method Thus, the extracted series resistances will be obtained as: • Overcome the limitations of the classical method. • Non-perfectly symmetry is considered. • Mobility degradation coefficient is included (θ).

14. Bracale´s Modified Method Asymmetry coefficient: The imaginary part of the impedance parameters follow the next relationships: Thus, we can obtain k as:

15. Results ELDO software was used to simulate the S-Parameters of Partially-Depleted 0.13 µm SOI n-MOSFETs. The BSIM3SOI model from ST-Microelectronics was used. Rse = Rde = 3 W & Rge = 5 W

16. Results q = 0.6 Rse = 3 W

17. Results Rge = 4.85 W Rde = 3.2 W

18. Conclusions • Original Bracale´s method does not allow accurate extraction of the series resistances. • The main limitations of this method are: the carrier mobility degradation and transistor asymmetry. • A new procedure was established, where the both effects are included. • q is obtained from DC output conductance measurements. • k is obtained as the ratio of the imaginary part of Z-parameters. • The new procedure allows to determine the correct resistance values.