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IV measurement

IV measurement:

There are several parameters could extraxted from IV measurement such as threshould voltage and resistance :

  • Threshould voltage:

The threshold voltage is a significant parameter for MOSFET. It is defined as a voltage when
the device turns on, where the surface potential is equal to twice the Fermi potential 

Φs= 2Φf 
Vt= Vfb+2Φf + (2qksϵ0NA2Φf /Cox)0.5


                                        
 There are  several methods  to extract Vt,  such as extrapolation  in the linear region method,
transconductance extrapolation method in the linear  region,  second-derivative method,  ratio
method,  transition method,  second derivative logarithmic  method;  non-linear optimization
method and integral method .All of these methods give slightly different values of Vt.  the transconductance extrapolation method, which  uses  a
transconductance (gm) versus gate voltage curve. Vt is the gate voltage maximum slope at the point as shown in following figure

Vt

 

  •   Subthreshold slope (S.S):

       This parameter determines how fast the device switches off and it is extracted from the slope of log Id versus Vg curve .The theoretical value is given by the following equation:

 
S.S= [ d(logId)/dVG]-1
=2.3 kBT (1+Cdm/Cox)/q  

                      
Cdm depletion layer capacitance. The theoretical minimum value for a MOSFET is 60mV/dec. next figure illustrate the curve between drain current and gate voltage whereit could determine subthershold slope .  

 

ss

 

  • Resistance:

 

Series resistance becomes more important with the down  scaling of MOS devices, since in long channel devices the channel resistance is much larger than the contact resistance. From equation 2-3 the channel resistance could be define by

 
Rch = Leff / µeff CoxWeff (Vg-Vt)                                              


Leff= L-ΔL                                                                         
The total resistance is channel resistance and source –drain resistance

Rm= Vds/Ids= Rsd +Rch                                                     
Rm = Rsd +A (L- ΔL)                                

Where A= (µeff CoxWeff (Vg-Vt))-1

By drawing  the relation between channel length and resistance for different gate voltage the channel resistance is the y value where the lines are intersecting and the x value is ΔL.This

method is not accurate .Therefore, another method have been used to get more accurate value.

resistance

 

Terada and Muta  pointed out another method to extract channel resistance which define 

Rch=ƍ Leff/W             ƍ channel sheet resistance 

 
Rm = Rsd + ƍ /W (L- ΔL)                               Rm= A + (ƍ/W) L                                          

By drawing this equation for different gate voltages A  is  the  intercept point, and  the slop is ƍ/W. The slope of the relation between ƍ/W and A is ΔL and the intercept is the source drain
resistance.

resistance1

 

 

  •   Kazuo Terada and Hiroki Muta ,A new method to determine effective MOSFET channel length ,  Japaness Journal of applied physics Vol.18,No,5,May1979.
  •  K. Terada and H. Muta. "A New Method to Determine Effective MOSFET Channel Length". Jap. J. of Appl. Phys., 18:953{959, 1979.
  • A. Ortiz-Condea , F.J. Garc ,S a ancheza, J.J. Liou b,1, A. Cerdeira c,M. Estrada c, Y.Yue d ,A review of recent MOSFET threshold voltage extraction methods,
    Microelectronics eliability 42 (2002) 583–596.