DC bias circuit effects in CV measurements
A.Chilingarov, D.Campbell
Lancaster University, UK
9
thRD50 Workshop
Outline
1.Introduction
2.Theoretical considerations
3.Simulation
1. Introduction
A DC bias circuit is a necessary part of every CV
measurement set-up. We will show that in some
situations the effects of such a circuit cannot be
taken into account by the usual “Open Correction”
procedure.
The analysis presented here is applicable to the DC
biasing
external
to the LCR meter and with
The circuit elements have the following values: C
H=10
F, R
H=R
G=10k
,
C
L=0.1
F, R
L=220k
, C
F=1
F, R
F=100k
.
It is also possible to use
R
L=10k
.
1. Introduction (continued)
2. Theoretical considerations
The equivalent diagram for a measurement with a 4-terminal LCR meter without biasing is shown to the left. The measured
impedance
Z
m=V
AC/I
AC,
where allparameters are complex numbers. Typically a stray impedance
Z
s is measured without any DUT (Device Under Test) and subtracted from the measured results. This is called “Open Corrections”.Also shown is an example of a measurement with a simple external DC bias circuit.
A V
Hp Hc
Lc Lp
AC
Zs
DUT
VAC IAC
A V
Hp Hc
Lc Lp
AC
Zs
DUT
VAC IAC
General equivalent diagram for the 4-terminal LCR meter measuring a biased DUT.
Z
a is the total actual impedance includingZ
s.Ya=Gpa+jCpa. If Gpa/Cpa= = const Ya=Cpa ( + j) and as follows from eq.(1) Ym is about scaled with Cpa. Also eq.(1) means that the conversion of Ya into Ym is approximately linear:
Ym(Ya1+Ya2)Ym(Ya1)+Ym(Ya2).
and similarly for admittance
Y=1/Z
Solving Kirchhoff’s equations one finds
H CL L
CH H
L a
m
Z
F
F
Z
F
Z
F
Z
where
Typically
H CH H
L CL L
Z
Z
F
Z
Z
F
1
;
1
Therefore
CL a
CH
a
Z
Z
Z
Z
;
H L a
m
Z
F
F
Z
H L
a m
F
F
Y
Y
(1)
A V
Hp Hc
Lc Lp
AC
Za
ZCH
VAC IAC
ZL ZH
This parameter usually controls the major frequency dependence of the measured impedance (admittance). In practice it is often dominated by a minimum RC.
Consider a simple case, when
Z
CL,Z
CH are pure capacitors andZ
L,Z
H are pure resistors. Thenwhere
aver H
H L L H
L H
H H
L L L
RC
j
R
C
R
C
F
F
R
C
j
F
R
C
j
F
)
(
1
1
;
1
;
1
2
H H L
L
aver
C
R
C
R
RC
1
1
)
(
1
It is easy to show that for the measured Cpm Cpa (actual Cp value) while
Gpm Gpa – Cpa/(RC)aver , i.e. the asymptotic value of the measured conductivity is shifted down
relative to its actual value and this shift is proportional to Cpa.
It is also clear that shorting of a decoupling capacitor makes the corresponding resistor irrelevant. Shorting of both capacitors nullify all DC circuit effects (for ideal generator,
voltmeter, ammeter in the diagram!). Disconnecting the resistors can also practically eliminate the circuit effects when the decoupling capacitors are large enough.
3. Simulation
All above conclusions are confirmed by simulation though the simulated circuit is slightly more complicated than the simple case analysed above. Presented here are Cp and Gp measured for a pure capacitor. Scaling of both parameters with Cpa and the offset in the asymptotic value of Gpm are clearly seen. The latter agrees with expectations. The circuit effects saturate for
(CR) >10.
101 102 103 104 105 106 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 101 102 103 104 105 C p (m e a s) /C p (a ct u a l) Frequency, Hz 0.1 pF 1.0 pF 10. pF 100 pF
Measured Cp normalised by actual Cp for actual Gp=0
(CR)aver
101 102 103 104 105 106
-0.059 -0.058 -0.057 -0.056 -0.055 -0.054 -0.053 -0.052 -0.051 -0.050 -0.049 -0.048 101 102 103 104 105 G p (m e a s) /C p (a ct u al ), n S /p F Frequency, Hz 0.1 pF 1.0 pF 10. pF 100 pF
Measured Gp normalised by actual Cp for actual Gp=0
1/(RC)aver=1/RLCL+1/RHCH
The same Cpa set with Gpa=1nS. Note the similarity in the Gpm shift relative to the case Gpa=0 and the variety of shapes for Cpm. The value of (CR)aver
>30 is needed for Cpm to become close to Cpa=1pF.
101 102 103 104 105 106
-6 -5 -4 -3 -2 -1 0 1 2
Gp=0
Gp=0 Gp=1nS
Cp=100 pF
Gp (m e a s) , n S Frequency, Hz
Measured Gp for actual Gp=0 or 1 nS and different Cp Gp=1nS
Cp=1 pF
101 102 103 104 105 106
0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 M ea s. G p (1 n S )-G p (0 ), n S 0.1 pF 1.0 pF 10. pF 100 pF
Difference in measured Gp for actual Gp=1 and 0 nS and different Cp 101
102 103 104 105 106 1.0 1.5 2.0 2.5 3.0 3.5
4.0 101
102
103
104
105
(CR)aver
C p (m ea s) /C p (a ct u al ) Frequency, Hz 1.0 pF 10. pF 100 pF
The same set of Cpa with proportional Gpa. Note the change of the Cpm curve shape compared to the case of Gpa =0 and ~60% shift in the asymptotic value of Gpm.
101
102
103
104
105
106
0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16
C p
(m
ea
s)
/C p
(a
ct
u
al
)
Frequency, Hz
0.1 pF 1.0 pF 10. pF 100 pF
Measured Cp normalised by actual Cp for actual Gp/Cp=0.1 nS/pF
101
102
103
104
105
106
0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44
Measured Gp normalised by actual Gp for actual Gp/Cp=0.1 nS/pF
G p
(m
e
a
s)
/G
p
(a
ct
u
a
l)
Frequency, Hz
The data for Cpa =10 pF with different Gpa. Note that for Gpa= 100 nS the Cpm at low
frequency is ~ 40 times higher than Cpa. The value of (CR)aver >100 is needed for Cpm to become close to Cpa.
101
102
103
104
105
106
0.8 1 2 4 6 8 10 20
40 101
102 103 104 105
(CR)aver
C p
(m
e
a
s)
/C p
(a
ct
u
a
l)
Frequency, Hz
0.1 nS 1.0 nS 10. nS 100 nS Measured Cp normalised by actual Cp=10 pF for different actual Gp
101 102 103 104 105 106
-5 -4 -3 -2 -1 0 1
Measured Gp normalised by actual Gp for actual Cp=10 pF
G p
(m
e
a
s)
/G
p
(a
ct
u
a
l)
Frequency, Hz
Measured Cp and Gp for a pure capacitive Ya with RL=10k instead of standard 220 k. For the same range of frequency the range of (CR)aver extends to much lower values, which increases the Cp and Gp deviations from their asymptotic values. Note also that Gpm saturates at the expected level, which is much lower than for RL=220 k.
101 102 103 104 105 106 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
10-1 100 101 102 103
C p (m e as )/ C p (a ct ua l) Frequency, Hz 0.1 pF 1.0 pF 10. pF 100 pF
Measured Cp normalised by actual Cp for actual Gp=0
(CR)aver
RL=10 k
101 102 103 104 105 106 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
10-1 100 101 102 103
RL=10 k
G p (m e as )/ C p (a ct ua l), n S /p F Frequency, Hz 0.1 pF 1.0 pF 10. pF 100 pF
Measured Gp normalised by actual Cp for actual Gp=0
1/(RC)aver=1/RLCL+1/RHCH
To a good approximation Cp measured with different RL can be regarded as a universal
function of (CR)aver that is illustrated above for a pure 10 pF capacitor. To a lesser extent the same is also true for Gpm .
10-1 100 101 102 103 104 105 0 1 2 3 4 5 6 7 8 9 10 11 C p (m e a s) , p F
(CR)aver
RL=220 k
RL= 10 k
Measured Cp for actual Cp=10 pF,Gp=0 vs average CR
Frequency range 20Hz-1MHz
10-1 100 101 102 103 104 105 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
RL=220 k
RL= 10 k
G p (m ea s) /G p (a sy m p to tic )
(CR)aver
Normalised measured Gp for actual Gp=0, Cp=10 pF vs average CR
Similarly one can restore the admittance
Y=1/Z
.From the mentioned before equation for the measured impedance
Z
mH CL L
CH H
L a
m
Z
F
F
Z
F
Z
F
Z
one can easily obtain the actual impedance
Z
aHowever this reconstruction relies on an accurate description of the real biasing circuit especially if the corrections are large compared to the final parameter value.
Reconstruction of the actual impedance
H L H
CL L
CH m
a
Z
Z
F
Z
F
F
F
As an example the reconstructed values for Cpa=10 pF and two values of Gpa are shown for the values of decoupling capacitor CL used in reconstruction differing by ±1% from its value in the simulation. Note that the deviations in reconstructed Cp and Gp are sometimes >> 1%.
101 102 103 104 105 106
-25 -20 -15 -10 -5 0 5 10 15 20 25
Relative Cp in reconstructed Cp for actual Cp=10 pF and 1% error in CL
(C p
/1
0
p
F
1
),
%
Frequency, Hz
Gp=0.1 nS 1.01CL 0.99CL Gp=100 nS
1.01CL 0.99CL
101 102 103 104 105 106
-5 -4 -3 -2 -1 0 1 2 3 4 5
(G
p
(r
ec
.)
/G
p
(a
ct
u
al
)
-1
),
%
Frequency, Hz
Gp=0.1 nS 1.01CL 0.99CL Gp=100 nS
1.01CL 0.99CL
“Open Corrections”
The admittance measured without the DUT consists of the stray impedance ( DUT support etc.) and the LCR meter offset values. Due to the mentioned before linearity of the measured
admittance vs. the real one Ym(Ya) the usual subtraction of YmOC measured without the DUT (“Open Corrections”) from the total Ym eliminates simultaneously both the stray impedance and offsets. The linearity is verified in the plots below for typical admittance values.
101
102
103
104
105
106
0 5 10 15
C p
(m
e
a
s)
, p
F
Frequency, Hz
1.0pF,2.0nS 10 pF,0.1nS 11 pF,2.1nS Sum 1+2
Measured Cp for different actual Cp, Gp
101
102
103
104
105
106
-0.5 0.0 0.5 1.0 1.5 2.0
G p
(m
e
as
),
n
S
Frequency, Hz
1.0pF,2.0nS 10 pF,0.1nS 11 pF,2.1nS Sum 1+2
Cp and Gp measured for an empty support board with the full DC bias circuit (two independent runs) and with disconnected resistors. The similarity between the latter and the former shows that the results are dominated by the LCR meter offsets. Note the very fine y-scale in both plots.
4. Experimental results
101
102
103
104
105
-0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
With EC Run1 Run2 No EC
Cp for an empty board with and without external circuit (EC)
C p
(
p
F
)
Frequency (Hz)
101 102 103 104 105
-0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10
Gp for an empty board with and without external circuit (EC)
G p
(
nS
)
Frequency (Hz)
With EC Run1 Run2
101 102 103 104 105 8.2
8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2
Measured with no EC full EC
Reconstructed from the full EC
Cp for 10pF capacitor with and without external circuit (EC)
C p
(
pF
)
Frequency (Hz)
101
102
103
104
105
-1 0 1 2 3 4 5
Measured with no EC full EC
Reconstructed from the full EC
G p
(
n
S
)
Frequency (Hz)
Gp for 10pF capacitor with and without external circuit (EC)
Very similar results were obtained for a 100 pF test capacitor. Note the large shifts in measured parameters successfully eliminated by the reconstruction procedure.
101 102 103 104 105
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
Cp for 100pF capacitor with and without external circuit (EC)
Measured with full EC no EC
Reconstructed from the full EC C p
(
pF
)
Frequency (Hz)
101 102 103 104 105
-6 -4 -2 0 2 4 6 8 10 12
Measured with full EC no EC
Reconstructed from the full EC
Gp for 100pF capacitor with and without external circuit (EC)
G p
(
nS
)
The same 100 pF test capacitor measured with RL=10 k. The shifts in measured parameters are very large and the reconstruction is less accurate especially at lowest frequencies.
101
102
103
104
105
0 10 20 30 40 50 60 70 80 90 100
Cp for 100pF capacitor with and without external circuit (EC)
Measured with full EC no EC
Reconstructed from the full EC C p
(
p
F
)
Frequency (Hz)
RL= 10k
101 102 103 104 105
-100 -80 -60 -40 -20 0 20
RL= 10k
Measured with full EC no EC
Reconstructed from the full EC
Gp for 100pF capacitor with and without external circuit (EC)
G p
(
n
S
)
The same 10 pF test capacitor as above in parallel with a 10 M resistor. Note very large
deviations in the measured Cp from the actual 10 pF. The reconstruction works reasonably well for both Cp and Gp.
101
102
103
104
105
0 50 100 150 200 250 300 350
Measured with no EC (no 10M) full EC
Reconstructed from the full EC
Cp for 10pF parallel to 10 M with and without external circuit (EC)
C p
(
p
F
)
Frequency (Hz)
101
102
103
104
105
80 84 88 92 96 100 104
Measured with no EC full EC
Reconstructed from the full EC G p
(
n
S
)
Frequency (Hz)
