Download ACh_CV_distortion - Indico

Vidyo meeting
17.3.2014
Distortion of the CV characteristics
by a high current
A.Chilingarov,
Lancaster University, UK
Contents
1. Introduction
2. Two models
3. Example with un-irradiated sensor
4. Discussion
5. Conclusions
2
A.Chilingarov, CV distortion, 17.3.2014
1. Introduction.
The CV measurements with the strip detectors are normally performed
between the backside and the bias rail in Cs-Rs mode. Cs represents the
capacitance in the depleted volume and Rs all bias resistors, Rbias, connected
in parallel plus the resistance of the un-depleted bulk.
It was observed experimentally that the results may be distorted by a high
sensor current. The aim of this talk is to investigate possible reasons for this
distortion.
The talk is based on a Technical Note: A.Chilingarov, “Distortion of the CV
characteristics by a high current”, which can be found at the RD50 website:
http://rd50.web.cern.ch/rd50/doc/recommendations.html
Please refer to it for the details.
3
A.Chilingarov, CV distortion, 17.3.2014
2. Two models
High current may be interpreted as the presence in the equivalent circuit diagram
of an additional resistance with a relatively low value. If the current is mostly
generated inside the depleted volume the modified diagram looks like follows.
Here C and Rb represent the actual capacitance and
resistance while Rg reflects the effective conductivity
due to the current generated in the depleted bulk.
The Cs and Rs measured with this circuit at frequency f
can be expressed by the following equations, where
Qp=wCRg, w=2pf.
Obviously Cs > C and Rs > Rb. When Rg → ∞, then
Cs → C and Rs → Rb. When Rg → 0, Cs → ∞.
4
A.Chilingarov, CV distortion, 17.3.2014
If the current is mostly due to leakage over the sensor
edge the additional resistor, Rl, appears in parallel to
the C and Rb chain as shown in the diagram.
The Cs and Rs measured with this circuit at frequency f
can be expressed by the following equations, where
Ds=wC(Rl + Rb) and r = Rl/(Rl + Rb).
Obviously r <1 and Cs > C. When Rl → ∞, then r → 1,
Cs → C and Rs → Rb. When Rl → 0, then r → 0 and
Cs → ∞.
Note that in both models an additional resistor makes
Cs larger than the actual capacitance C.
5
A.Chilingarov, CV distortion, 17.3.2014
3. An example. Un-irradiated sensor w01-bz4-p4
The plot shows
the Cs in pF, Rs
in kW and the
current in mA.
The bias
resistor, Rbias,
is ~2 MW and
100 of them in
parallel give Rs
of ~ 20 kW.
Above 200V the sensor is fully depleted with Cs and Rs reaching a plateau. Above
500V the current grows steeply and both Cs and Rs increase with bias.
6
A.Chilingarov, CV distortion, 17.3.2014
It was assumed that for any model an additional resistance can be estimated as
the dynamic resistance following from the IV curve: Rdyn = dU/dI. It is presented
in the above plot in MW. Note that even at its lowest level Rdyn >> Rs at the
plateau.
7
A.Chilingarov, CV distortion, 17.3.2014
The average Cs and Rs values between 200 and 260 V were used as C and Rb.
Then Cs and Rs were calculated for both models using Rdyn as Rg or Rl respectively.
The plot shows the experimental Cs values and those calculated from the two
models. Both models agree well with the data.
8
A.Chilingarov, CV distortion, 17.3.2014
Similar plot for the Rs values. Again both models agree well with the experimental
data.
9
A.Chilingarov, CV distortion, 17.3.2014
4. Discussion
It is not surprising that both models give very similar results. Rdyn is always more
than 1 MW while Rb is ~ 20 kW. Therefore the parameter r = Rl/(Rl+Rb) with Rl =
Rdyn is very close to 1. In this situation the equations for the leakage current model
(slide 5) revert to the equations for the generation current model (slide 4) with Rl
in place of Rg.
In the above example the additional resistor value set to dU/dI explains the
experimental data quite well. However this is not always the case. Moreover the
high current may have both generation and leakage components and the
equivalent circuit diagram should include both Rg and Rl. The Cs and Rs can in this
case be calculated combining the equations on slides 4 and 5.
For both models Cs > C. It is easy to show that the same is true when both Rg and
Rl resistors are present.
10
A.Chilingarov, CV distortion, 17.3.2014
5. Conclusions
1. The distortion of the experimentally measured parameters
Cs and Rs can be explained by an additional resistance
with a relatively low value, which appears because of a
high current.
2. In the example given in this talk the assumption of the
additional resistor to be equal to dU/dI explains the data
quite well by both models.
3. In the general case both Rg and Rl resistors may be
required to be included in the equivalent circuit diagram.
However in all cases Cs > C i.e. a high leakage current
should always lead to an increase in the measured
capacitance.
11
A.Chilingarov, CV distortion, 17.3.2014
Backup slides
12
A.Chilingarov, CV distortion, 17.3.2014
Cs calculation in the case when both Rg and Rl are present
Use equation on the slide 4; Csg > C
Use equation on the slide 5; Cs > Csg > C
13
A.Chilingarov, CV distortion, 17.3.2014