Model 4200A-SCS Prober and External Instrument Control Section 6: Using a Model 82 C-V System
4200A-913-01 Rev. A December 2020 6-21
The values for constants used in the formulas are in the Constants area in the Formulator. The
constants include:
• Area, with a value of 0.012 mm
2
• eOX, with a value of 3.4e-013 F/cm
• eS, with a value of 1.04e-012 F/cm
Refer to Simultaneous C-V analysis (on page 6-45) for details on simultaneous C-V theory and the
formulas.
Formulas for system82-cvsweep test (simcv project)
Gate voltage:
VGS = −VSub
Serial resistance calculated by high frequency CV:
RS = (AT(MAVG(G_OR_R,5)/(WF*MAVG(CHF,5)),MAXPOS(MAVG(CHF,5))))^2/
((1+(AT(MAVG(G_OR_R,5)/(WF*MAVG(CHF,5)),MAXPOS(MAVG(CHF,5))))^2)
*(AT(MAVG(G_OR_R,5),MAXPOS(MAVG(CHF,5)))))
Intermediate parameter for calculation of CC:
AR = G_OR_R-(G_OR_R^2+(WF*CHF)^2)*RS
Corrected high frequency capacitance by compensating serial resistance:
CC = ((G_OR_R^2+(WF*CHF)^2))*CHF/(AR^2+(WF*CHF)^2)
Offset for high frequency capacitance (entered by user):
HOFFSET = 0
Gain for quasistatic capacitance (entered by user):
QGAIN = 1
Offset for quasistatic capacitance (entered by user):
QOFFSET = 0
Adjusted quasistatic capacitance by using QGAIN and QOFFSET:
CQADJ = QGAIN*CQS+QOFFSET
Gain for calculated high frequency capacitance that is calculated:
HGAIN = AT(MAVG(CQS,5)/MAVG(CC,5),MAXPOS(MAVG(CC,5)))
Adjusted high frequency capacitance by using HGAIN and HOFFSET:
CHADJ = HGAIN*CC+HOFFSET
Oxide capacitance:
COX = MAX(MAVG(CHADJ,5))+1E-15
Minimum capacitance from high frequency:
CMIN = MIN(MAVG(CHADJ,5))+1E-15
Calculated thickness of oxide (in nanometers):
TOXNM = 1E7*AREA*EOX/COX
Inversed square of high frequency capacitance:
INVCSQR = 1/(MAVG(CHADJ,5))^2
Stretch out factor due to interfacial states:
STRETCHOUT = MAVG((1-CQADJ/COX)/(1-CHADJ/COX),5)
Doping density:
NDOPING = ABS(-2*STRETCHOUT/(AREA^2*Q*ES)/(DELTA(INVCSQR)/DELTA(VGS)))
Depletion depth (in meters):
DEPTHM = 1E-2*AREA*ES*(1/CHADJ-1/COX)
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