Mos Non-Equilibrium And Roper Use Of The Corrected Capacitance Program - Keithley 595 Instruction Manual

APPLICATIONS
53.5 MOS Non-equilibrium and Proper Use of
the Corrected Capacitance Program
The corrected capacitance feature corrects for errors in
capacitance measurements due to stray currents which are
constant during the measurement. It combines capacitance
and Q/t readings based on the assumption that Q/t is due
to DC currents only, and generates a corrected capacitance
reading. If Q/t is not solely due to DC currents,,as when
the device is in non-equilibrium, then the assumption is
false and erroneous corrected capacitance readings will
result.
Figure 3-3 shows the charge waveform of the device under
test and the three charge measurements which are ~made
on that waveform. From the three determinations of charge,
the quantities of capacitance, Q/t, and corrected capacitance
are calculated according the the equations presented in the
figure.
A dramatic example of the magnitude of capacitance error
which can be corrected for is shown in Figure S-12. It shows
the corrected and uncorrected curves of a 98.8pF polysty-
rene capacitor connected in parallel with a lOOGO resistor.
The curve was generated by taking one O.lOV step every
O.lOsec. The slant of the uncorrected curve would affect any
quasistatic CV curve, including those generated by the
ramp or Q-V methods. Without correction, the error
dominates the measured curve. The corrected curve,
however, shows no observable effect of the resistwon the
measured capacitance.
Another example of the proper use of the capacitance cor-
rection program is presented in Figure 5-13 (Equilibrium
curve). This curve was generated from a MO5 capacitor
haying n-type silicon and long lifetime (KLlS~ec). To il-
lustrate the very slow staircase practical with the Model 595,
the curve was measured over a 5% hour period, taking one
0.05V step every lCOsec. The capacitance has been corrected
for leakage, normalized to 195.16pF using UCo, and filtered
using Filter 2.
An example of nonequilibrium is shown in Figures 5X3. The
curves were taken on the same device as used for
equilibrium, but with a much faster staircase. Step V was
O.OSV and delay time was 0.5s~.
The bottom graph illustrates that when staircasing towards
inversion, the device is not in equilibrium. When a voltage
step is applied across the device, C, initially supplies the
charge necessary to satisfy the AQ = C AV relation. Then
C,, which is larger, gradually charges through G,, allow-
ing Co to return to its previous state. If C, never has time
toTharge, then repeated steps drive the capacitor into deep
depletion. Deep depletion is simply the effect of changing
the gate bias so quickly from the depletion region to the
inversion region that the inversion layer cannot appreciably
build up and C, satisfies the majority of charge exchange.
with each step, the space charge region grows wider, C,
grows smaller, and the measured capacitance decreases.
The curve in the bottom graph of Figure S-l3 for a staircase
from inversion back toward depletion shows a response
resembling equilibrium. From the Q/t curves of the top
graph, however, it is apparent that this is not an equilibrium
curve, since current is still flowing. The current flowing is
attempting to charge C,; Since that process is still ongoing
with each voltage step, it is apparent that Co must be pro-
viding the initial charge exchange. During each step toward
depletion in which C, must supply charge thaK, cannot,
the depletion width is reduced. This is observable on the
right-side of graph A as a gradual rise in capacitance to C.,.
When the capacitance has returned to 6, the depletion
width has been reduced to so little that C, in series with
C, is approximately C,. As the voltage bias nears deple-
tion, the conditions that allow inversion to occur (and allow
C, to remain charged) cease to-exist. G,, will increase,
discharging C, and the curve wil1 merge with the normal
depletion curve.
Notice that the value of Q/t is lower for the staircase toward
inversion than for the staircase from inversion toward
depletion. Thii illustrates that G,, is direction dependent.~
The reason is that different processes are responsible for
the charge exchange depending on the staircase direction.
The process involved when changing bias from inversion
toward depletion is faster, so the effective value of G.. in
that~ direction is lower.
The top graph of Figure 5-13 shows the Q/t vs. V curves
for the same staircase. It is clear from these curves that
neither direction of the curve is a true equilibrium measure-
ment-because the level of Q/t rises from the DC leakage
level of the system in inversion. The higher level of Q/t in
the direction from inversion toward depletion agrees with
the hypothesis that G,, is lower in this direction.
Figure 5-14 shows what happens when the corrected
capacitance program is inappropriately used on this curve.
It is improper to use correction in this case because non-
equilibrium currents are being measured by Q/t in inver-
sion. When the Q/t value is used to generate the corrected
capacitance value, not only the error capacitance due to DC
leakage currents, but also the effective capacitance due to
the current flowing through G,, is subtracted from the
capacitance reading. The result is an erroneous and mean-
ingless corrected capacitance curve.
5-13