J. C. Tinoco and J.-P. Raskin MOS-AK – 2008 J. C. Tinoco and J.-P. Raskin Université catholique de Louvain Microwave Laboratory B-1348 Louvain-la-Neuve, Belgium RF Extraction Techniques for Series Resistances of MOSFETs

J. C. Tinoco and J.-P. Raskin MOS-AK – OUTLINE Introduction Bracale´s Method Bracale´s Modified Method Results Conclusions

J. C. Tinoco and J.-P. Raskin MOS-AK – INTRODUCTION Different methods have been developed to determine the extrinsic series resistances. They can be divided in two groups: DC and RF methods. DC MethodsRF Methods  It is not possible to extract independently the drain and source resistances: R T = R d + R s  It is not possible to determine the gate resistance. It is possible to extract independently the drain, source and gate resistances. Device biased under different conditions. Requires the equivalent circuit analysis.

J. C. Tinoco and J.-P. Raskin MOS-AK – 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. Lovelace Torres-Torres

J. C. Tinoco and J.-P. Raskin MOS-AK – INTRODUCTION Bracale Raskin  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.  Deep analysis is necessary for the Bracale´s method

J. C. Tinoco and J.-P. Raskin MOS-AK – Bracale´s Method Bias:V DS = 0 V & V GS >V T G mi → 0 Assumptions:  Perfectly symmetric Device:C gsi = C gdi = C  Constant mobility

J. C. Tinoco and J.-P. Raskin MOS-AK – INTRODUCTIONBracale´s Method Impedance Relationships: 

J. C. Tinoco and J.-P. Raskin MOS-AK – Bracale´s Method Linear regression of the impedance relationship respect to the inverse of the gate overdrive. The intercept gives the corresponding series resistance.

J. C. Tinoco and J.-P. Raskin MOS-AK – Bracale´s Method Extraction MethodsR se R de R ge Classical Bracale Used in Simulations335 The extracted values differ from the values used in the simulations. It is necessary to review the assumptions made:  Perfectly symmetric Device:C gsi = C gdi = C  Constant mobility

J. C. Tinoco and J.-P. Raskin MOS-AK – 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:

J. C. Tinoco and J.-P. Raskin MOS-AK – 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:  Extraction MethodsR se R de R ge Classical Bracale Mobility degradation included Used in Simulations335

J. C. Tinoco and J.-P. Raskin MOS-AK – 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 = C gs /C gd is called the asymmetry coefficient.

J. C. Tinoco and J.-P. Raskin MOS-AK – Bracale´s Modified Method Overcome the limitations of the classical method.  Non-perfectly symmetry is considered.  Mobility degradation coefficient is included (θ). Thus, the extracted series resistances will be obtained as: Extraction MethodsR se R de R ge Classical Bracale Mobility and asymmetry included Used in Simulations335

J. C. Tinoco and J.-P. Raskin MOS-AK – Bracale´s Modified Method Asymmetry coefficient: The imaginary part of the impedance parameters follow the next relationships: Thus, we can obtain k as:

J. C. Tinoco and J.-P. Raskin MOS-AK – 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. R se = R de = 3  & R ge = 5 

J. C. Tinoco and J.-P. Raskin MOS-AK – Results  = 0.6 R se = 3 

J. C. Tinoco and J.-P. Raskin MOS-AK – Results R de = 3.2  R ge = 4.85  Extraction MethodsR se R de R ge Classical Bracale Mobility degradation included Mobility and asymmetry included Used in Simulations335

J. C. Tinoco and J.-P. Raskin MOS-AK – 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.   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.