Method for measuring interface traps in thin gate oxide MOSFETs

Abstract

A method for measuring interface traps in a MOSFET, comprising measuring charge pumping current of a pulse wave form for various frequencies over a predetermined frequency range, creating plotted points of the measured charge pumping current versus the predetermined frequency range, determining the total number of interface traps participating in the charge pumping current by calculating the slope of a best fit line through the plotted points.

1 . A method for measuring interface traps in a MOSFET, comprising:
 measuring substrate or source/drain current of a pulse wave form for various frequencies over a predetermined frequency range;   creating plotted points of the measured substrate or source/drain current versus the predetermined frequency range;   I sub =I tunneling     —     avg .+I cp ; Slope of I sub  vs. frequency=Q cp ; Intercept of I sub  vs. frequency=I tunneling     —     avg ; N it =Q cp /Ag.   determining the total number of interface traps (N it ) participating in the charge pumping current by calculating the slope of a best fit line through the plotted points;   
   
   
       2 . The method of  claim 1 , wherein tunneling current from a gate to a substrate for a prearranged duty cycle is determined by calculating y-intercept of the best fit line through the plotted points. 
   
   
       3 . The method of  claim 1 , wherein an R 2  value is calculated to determine a correlation between the best fit line and the plotted points. 
   
   
       4 . The method of  claim 1 , wherein the range of energy of the interface traps that contributes to the charge pumping current comprises:
   Δ E =−2  kT Ln [(σ p  σ n    t   r    t   f ) 1/2    v   th    n   i    |V   t   −V   fb   |/V   a ]   ,wherein k comprises the Boltzmann's constant, T comprises the absolute temperature in Kelvin, σ p  comprises the hole-capture cross-section, σ n  comprises the electron-capture cross-section, t r  comprises the pulse rise time, t f  comprises the pulse fall time, v th  comprises the thermal velocity, n i  comprises the intrinsic carrier concentration at the temperature of measurement, V t  comprises the threshold voltage, V fb  comprises the flat-band voltage, and V a  comprises the amplitude (V hi −V lo ) of the gate pulse, V hi  comprises the high voltage and V low  comprises the low voltage.   
   
   
       5 . The method of  claim 4 , wherein a density of the interface traps comprises:
     D   it   ˜N   it   /ΔE      ,wherein N it  comprises the number of interface traps, and ΔE comprises the range of energy within the semiconductor band-gap that contributes to the charge-pumping current.   
   
   
       6 . The method of  claim 5 , wherein the charge pumping current total charge comprises:
   Q CP   =D   it (2)( q )( k )( T ) Ag Ln[ (σ p  σ n    t   r    t   f ) 1/2    v   th    n   i    |V   t   −V   fb |/V a ]   ,wherein D it  comprises the density of the interface traps in the contributing energy range, k comprises the Boltzmann's constant, T comprises the absolute temperature in Kelvin, Ag comprises area of the MOSFET gate, σ n  comprises the electron-capture cross-section, σ p  comprises the hole-capture cross-section, t r  comprises the pulse rise time, and t f  comprises pulse fall time, v th  comprises the thermal velocity, n i  comprises the intrinsic carrier concentration at the temperature of measurement, V t  comprises the threshold voltage, V fb  comprises the flat-band voltage, and V a  comprises the amplitude, (V hi −V lo ), of the gate pulse.   
   
   
       7 . The method of  claim 1 , wherein the average tunneling current into the substrate comprises:
   I tunnel, avg =(1 /T   period ) (1 /K   f +1 /K   r )∫ I ( V ) dV +{(1 −DC ) ( t   r   +t   f )/2  T   period   }I ( V   lo )   ,wherein K f  comprises a constant equal to [t f /(V hi −V lo )], t r  comprises the pulse rise time, t f  comprises the pulse fall time, K r  comprises a constant equal to [t r /(V hi −V lo )], T period  comprises the time-period of the pulse, I(V) is the substrate current (I SUB ) with the gate voltage at V and source/drain grounded to 0 volts, ∫I(V) dV comprises the integral of I with gate voltage ranging from V=V hi  to V=V lo , dV comprises an incremental change in the gate voltage, DC comprises the duty cycle, and V lo  comprises the lower level of the pulse.   
   
   
       8 . The method of  claim 1 , wherein the errors in Q CP  measurements are estimated comprising:
 utilizing the two T period  dependent tunneling current terms, the rise and fall times, V hi , V lo  and N it ; and   the measured DC I sub  vs. V gate  data was used to compute ∫ I(V) dV.   
   
   
       9 . The method of  claim 1 , wherein the frequency range is from about 1 KHz-10 MHz. 
   
   
       10 . The method of  claim 1 , wherein the charge pumping current is from about zero to 10 nA. 
   
   
       11 . The method of  claim 1 , wherein the gate thickness of the MOSFET is less than or equal to 20 Angstroms. 
   
   
       12 . The method of  claim 1 , wherein the pulse wave is trapezoidal or square or both. 
   
   
       13 . A method for measuring number of interface traps in a MOSFET, comprising:
 applying a charge pumping waveform at multiple frequencies to the MOSFET to separate charge pumping current from tunneling current.   
   
   
       14 . The method of  claim 13 , wherein a set of plotted points is obtained where the substrate or source/drain current is plotted on a vertical axis and the multiple frequencies are plotted on a horizontal axis. 
   
   
       15 . The method of  claim 14 , wherein the tunneling current is obtained as a y-intercept of a best fit line through the plotted points. 
   
   
       16 . The method of  claim 15 , wherein an R 2  value is calculated to indicate a correlation involving the best fit line and the plotted points. 
   
   
       17 . The method of  claim 13 , wherein a change in energy comprises:
   Δ E =−2 kT Ln [(σ p  σ n    t   r    t   f ) 1/2   v   th    n   i    |V   t   −V   fb   |/V   a ]   ,wherein k comprises the Boltzmann's constant, T comprises the absolute temperature in Kelvin, σ p  comprises the hole-capture cross-section, σ n  comprises the electron-capture cross-section, t r  comprises the pulse rise time, t f  comprises the pulse fall time, v th  comprises the thermal velocity of carriers in the semiconductor, n i  comprises the intrinsic carrier concentration in the semiconductor at the temperature of measurement, V t  comprises the threshold voltage, V fb  comprises the flat-band voltage, and V a  comprises the amplitude (V hi −V lo ) of the gate pulse.   
   
   
       18 . The method of  claim 13 , wherein a density of the interface traps comprises:
     D   it   −N   it   /ΔE      ,wherein N it  comprises the number of interface traps, and ΔE comprises the range of energy within the semiconductor band-gap that contributes to the charge-pumping current.   
   
   
       19 . The method of  claim 13 , wherein the charge pumping current total charge:
     Q   CP   =D   it (2)( q )( k )( T ) Ag Ln [(σ p  σ n    t   r    t   f ) 1/2   v   th    n   i   |V   t   −V   fb   |/V   a ]   ,wherein D it  comprises the density of the interface traps in the contributing energy range, k comprises the Boltzmann's constant, T comprises the absolute temperature in Kelvin, Ag comprises area of the MOSFET gate, σ n  comprises the electron-capture cross-section, σ p  comprises the hole-capture cross-section, t r  comprises the pulse rise time, and t f  comprises pulse fall time, v th  comprises the thermal velocity, n i  comprises the intrinsic carrier concentration at the temperature of measurement, V t  comprises the threshold voltage, V fb  comprises the flat-band voltage, and V a  comprises the amplitude (V hi −V lo ) of the gate pulse.   
   
   
       20 . The method of  claim 13 , wherein the average tunneling current into the substrate comprises:
     I   tunnel, avg =(1 /T   period ) (1 /K   f +1 /K   r )∫ I ( V ) dV +{(1 −DC )−( t   r   +t   f )/2 T   period   }I ( V   lo )   ,wherein K f  comprises a constant equal to [t f /(V hi −V lo )], t r  comprises the pulse rise time, t f  comprises the pulse fall time, K r  comprises a constant equal to [t r /(V hi −V lo )], T period  comprises the time-period of the pulse, I(V) is the substrate current (I SUB ) with the gate voltage at V and source/drain grounded to 0 volts, ∫ I(V) dV comprises the integral of I with gate voltage ranging from V=V hi  to V=V lo , dV comprises an incremental change in the gate voltage, DC comprises the duty cycle, and V lo  comprises the lower level of the pulse.   
   
   
       21 . The method of  claim 13 , wherein the errors in Q CP  measurements are estimated comprising:
 utilizing the two T period  dependent tunneling current terms, the rise and fall times, V hi , V lo  and N it ; and   the measured DC I sub  vs. V gate  data was used to compute ∫ I(V) dV,   wherein, N it  is the total number of interface traps, V hi , is the high voltage, V lo  is the low voltage, T period  is the time for one complete cycle.   
   
   
       22 . The method of  claim 13 , wherein a frequency range is from about 1 kHz-10 MHz. 
   
   
       23 . The method of  claim 13 , wherein the charge pumping current is less than or equal to 10 nA. 
   
   
       24 . The method of  claim 13 , wherein the gate thickness of the MOSFET is less than 20 Angstroms. 
   
   
       25 . The method of  claim 13 , wherein the pulse wave is trapezoidal or square or any linear combination thereof. 
   
   
       26 . A method for measuring tunneling current in a MOSFET, comprising:
 measuring tunneling current of a pulse wave versus duty cycle;   plotting points of the tunneling current versus a duty cycle;   determining the tunneling current flowing into the substrate from the gate by calculating the slope of a best fit line through the plotted points; and   determining the tunnel current by calculating the y-intercept of the best fit line.   
   
   
       27 . The method of  claim 24 , wherein the duty cycle is from about zero to one. 
   
   
       28 . The method of  claim 24 , wherein the tunneling current is from about zero to 100 nA. 
   
   
       29 . The method of  claim 24 , wherein the pulse wave is trapezoidal or square or a combination of both.