Distortion of the CV characteristics by a high current

1. Vidyo meeting 17.3.2014 Distortion of the CV characteristics by a high current A.Chilingarov, Lancaster University, UK

2. Contents • Introduction • Two models • Example with un-irradiated sensor • Discussion • Conclusions A.Chilingarov, CV distortion, 17.3.2014

3. 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

4. 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 → ∞. A.Chilingarov, CV distortion, 17.3.2014

5. 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. A.Chilingarov, CV distortion, 17.3.2014

6. 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

7. 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

8. 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

9. Similar plot for the Rs values. Again both models agree well with the experimental data. 9 A.Chilingarov, CV distortion, 17.3.2014

10. 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. A.Chilingarov, CV distortion, 17.3.2014

11. 5. Conclusions • 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. • 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. • 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. A.Chilingarov, CV distortion, 17.3.2014

12. Backup slides 12 A.Chilingarov, CV distortion, 17.3.2014

13. 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 A.Chilingarov, CV distortion, 17.3.2014