dc bias circuit effects in cv measurements a.chilingarov , d.campbell lancaster university, uk

DC bias circuit effects in CV measurements

A.Chilingarov, D.Campbell Lancaster University, UK

9th RD50 Workshop

CERN, 16-18.10.06

A.Chilingarov, DC bias circuit effects in CV measurements2

Outline

1. Introduction

2.Theoretical considerations

3.Simulation

4.Experimental results

5.Conclusions


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

capacitors decoupling the DC potential from the

LCR meter inputs.


The circuit elements have the following values: CH=10F, RH=RG=10k,

CL=0.1F, RL=220k, CF=1F, RF=100k. It is also possible to use

RL=10k.

1. Introduction (continued)

In the simulation and tests reported here we used our standard bias

circuit described in NIM A492 (2002) 402.


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 Zm=VAC/IAC , where all

parameters are complex numbers. Typically a

stray impedance Zs 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 HcLc Lp

AC

Zs

DUT

VACIAC

A V

Hp HcLc Lp

AC

Zs

DUT

VACIAC

RL RH


General equivalent diagram for the 4-terminal LCR

meter measuring a biased DUT. Za is the total actual

impedance including Zs.

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

HCLLCHHLam FZFZFFZZ where

TypicallyH

CHH

L

CLL Z

ZF

Z

ZF 1;1

Therefore

CLaCHa ZZZZ ;

HLam FFZZ

HL

am FF

YY (1)

A V

Hp HcLc Lp

AC

Za

ZCH

VACIAC

ZL ZH

ZCL


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 ZCL, ZCH are pure capacitors and ZL, ZH are pure resistors. Then

where

averHHLLHL

HHH

LLL RC

j

RCRCFF

RC

jF

RC

jF

)(

11;1;1

2

HHLLaver RCRCRC

11

)(

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)aver >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

Cp(m

ea

s)/C

p(act

ua

l)

Frequency, Hz

0.1 pF 1.0 pF 10. pF 100 pF

Measured Cp normalised by actual C

p for actual G

p=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

Gp(m

ea

s)/C

p(a

ctu

al)

, nS

/pF

Frequency, Hz

0.1 pF 1.0 pF 10. pF 100 pF

Measured Gp normalised by actual C

p for actual G

p=0

1/(RC)aver

=1/RLC

L+1/R

HC

H

(CR)aver


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

G

p(m

ea

s), n

S

Frequency, Hz

Measured Gp for actual G

p=0 or 1 nS and different C

p

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

Me

as.

Gp(1

nS

)-G

p(0

), n

S

Frequency, Hz

0.1 pF 1.0 pF 10. pF 100 pF

Difference in measured Gp for actual G

p=1 and 0 nS and different C

p 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

Cp(m

eas)

/Cp(a

ctua

l)

Frequency, Hz

1.0 pF 10. pF 100 pF


p for actual G

p=1 nS


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

Cp(m

eas)

/Cp(a

ctu

al)

Frequency, Hz

0.1 pF 1.0 pF 10. pF 100 pF


p for actual G

p/C

p=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 G

p for actual G

p/C

p=0.1 nS/pF

Gp(m

ea

s)/G

p(a

ctu

al)

Frequency, Hz

.01 nS 0.1 nS 1.0 nS 10. nS


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

0.81

2

4

6

810

20

40 101 102 103 104 105

(CR)aver

Cp(m

ea

s)/C

p(a

ctu

al)

Frequency, Hz

0.1 nS 1.0 nS 10. nS 100 nS


p=10 pF for different actual G

p

101 102 103 104 105 106

-5

-4

-3

-2

-1

0

1

Measured Gp normalised by actual G

p for actual C

p=10 pF

Gp(m

ea

s)/G

p(act

ua

l)

Frequency, Hz

Actual Gp

.01 nS 0.1 nS 1.0 nS 10. nS


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

Cp(m

ea

s)/C

p(a

ctu

al)

Frequency, Hz

0.1 pF 1.0 pF 10. pF 100 pF


p for actual G

p=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

0.110-1 100 101 102 103

RL=10 k

Gp(m

ea

s)/C

p(a

ctu

al)

, nS

/pF

Frequency, Hz

0.1 pF 1.0 pF 10. pF 100 pF

Measured Gp normalised by actual C

p for actual G

p=0

1/(RC)aver

=1/RLC

L+1/R

HC

H

(CR)aver


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

Cp(m

ea

s), p

F

(CR)aver

RL=220 k

RL= 10 k

Measured Cp for actual C

p=10 pF,G

p=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

Gp(m

ea

s)/G

p(a

sym

pto

tic)

(CR)aver

Normalised measured Gp for actual G

p=0, C

p=10 pF vs average CR

Frequency range 20Hz-1MHz


Similarly one can restore the admittance Y=1/Z .

From the mentioned before equation for the measured impedance Zm

HCLLCHHLam FZFZFFZZ

one can easily obtain the actual impedance Za

However 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

HLHCLLCHma FFFZFZZZ /)(


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 C

p for actual C

p=10 pF and 1% error in C

L

(Cp/1

0p

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

(Gp(r

ec.

)/G

p(a

ctu

al)

-1

), %

Frequency, Hz

Gp=0.1 nS

1.01CL

0.99CL

Gp=100 nS

1.01CL

0.99CL

Relative Gp in reconstructed G

p for actual C

p=10 pF and 1% error in C

L


“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

Cp(m

ea

s), p

F

Frequency, Hz

1.0pF,2.0nS10 pF,0.1nS11 pF,2.1nSSum 1+2

Measured Cp for different actual C

p, G

p

101 102 103 104 105 106

-0.5

0.0

0.5

1.0

1.5

2.0

Gp(m

ea

s), n

S

Frequency, Hz

1.0pF,2.0nS10 pF,0.1nS11 pF,2.1nSSum 1+2

Measured Gp for different actual C

p, G

p


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 ECRun1Run2

No EC

Cp for an empty board with and without external circuit (EC)

Cp (

pF

)

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)

Gp (

nS)

Frequency (Hz)

With ECRun1Run2

No EC


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)

Cp (

pF

)

Frequency (Hz)

101 102 103 104 105

-1

0

1

2

3

4

5



Gp (

nS

)

Frequency (Hz)

Gp for 10pF capacitor with and without external circuit (EC)

Cp and Gp measured for a 10 pF test capacitor with the full DC bias circuit and with disconnected

resistors. The latter gives the actual admittance which is successfully reconstructed from the

measured values. Note the conductance increase at high frequency due to the AC losses in the

capacitor.


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


Measured with full EC no EC


Cp (

pF

)

Frequency (Hz)

101 102 103 104 105

-6

-4

-2

0

2

4

6

8

10

12Measured with

full EC no EC



Gp (

nS

)

Frequency (Hz)


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 (

pF

)

Frequency (Hz)

RL= 10k

101 102 103 104 105

-100

-80

-60

-40

-20

0

20

RL= 10k




Gp (

nS

)

Frequency (Hz)


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 withno EC (no 10M) full EC


Cp for 10pF parallel to 10 M with and without external circuit (EC)

Cp (

pF)

Frequency (Hz)

101 102 103 104 105

80

84

88

92

96

100

104



Gp (

nS

)

Frequency (Hz)

Gp for 100M parallel to 10pF with and without external circuit (EC)


5. Conclusions

1. When biasing of the tested device (DUT) during CV measurement is

provided by an external DC circuit and the capacitors are used to

decouple the input of the LCR meter from the DC potential, the

measured DUT parameters may differ significantly from their actual

values.

2. The effects disappear (apart from the shift in Gpm) when RC>10 for

the minimum RC, but in some situations RC>100 may be needed.

3. The actual DUT parameters can be reconstructed from the measured

values. However for large corrections the reconstruction accuracy

may deteriorate due to insufficient precision of the circuit description.


4. Tests with several known typical impedances (with and without the

external circuit) in the whole range of the frequencies planned to be

used are strongly recommended during commissioning of the CV set-

up.

5. It is better to make “Open Corrections” off-line than to subtract them

at the hardware level. In this way one can see explicitly what the

corrections are and how reproducible are they.

6. In all our results the frequency of 10 kHz is high enough to eliminate

DC bias circuit effects for capacitance.

Conclusions (continued)

dc bias circuit effects in cv measurements a.chilingarov , d.campbell lancaster university, uk

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