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

2. A.Chilingarov, CV distortion, 17.3.20142 Contents 1.Introduction 2.Two models 3.Example with un-irradiated sensor 4.Discussion 5.Conclusions

3. A.Chilingarov, CV distortion, 17.3.201433 The CV measurements with the strip detectors are normally performed between the backside and the bias rail in C s -R s mode. C s represents the capacitance in the depleted volume and R s all bias resistors, R bias, 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. 1. Introduction.

4. A.Chilingarov, CV distortion, 17.3.20144 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 R b represent the actual capacitance and resistance while R g reflects the effective conductivity due to the current generated in the depleted bulk. The C s and R s measured with this circuit at frequency f can be expressed by the following equations, where Q p =  CR g,  =2  f. Obviously C s > C and R s > R b. When R g → ∞, then C s → C and R s → R b. When R g → 0, C s → ∞.

5. A.Chilingarov, CV distortion, 17.3.20145 If the current is mostly due to leakage over the sensor edge the additional resistor, R l, appears in parallel to the C and R b chain as shown in the diagram. The C s and R s measured with this circuit at frequency f can be expressed by the following equations, where D s =  C(R l + R b ) and  = R l /(R l + R b ). Obviously  C. When R l → ∞, then  → 1, C s → C and R s → R b. When R l → 0, then  → 0 and C s → ∞. Note that in both models an additional resistor makes C s larger than the actual capacitance C.

6. A.Chilingarov, CV distortion, 17.3.201466 Above 200V the sensor is fully depleted with C s and R s reaching a plateau. Above 500V the current grows steeply and both C s and R s increase with bias. 3. An example. Un-irradiated sensor w01-bz4-p4 The plot shows the C s in pF, R s in k  and the current in  A. The bias resistor, R bias, is ~2 M  and 100 of them in parallel give R s of ~ 20 k .

7. A.Chilingarov, CV distortion, 17.3.201477 It was assumed that for any model an additional resistance can be estimated as the dynamic resistance following from the IV curve: R dyn = dU/dI. It is presented in the above plot in M . Note that even at its lowest level R dyn >> R s at the plateau.

8. A.Chilingarov, CV distortion, 17.3.201488 The average C s and R s values between 200 and 260 V were used as C and R b. Then C s and R s were calculated for both models using R dyn as R g or R l respectively. The plot shows the experimental C s values and those calculated from the two models. Both models agree well with the data.

9. A.Chilingarov, CV distortion, 17.3.201499 Similar plot for the R s values. Again both models agree well with the experimental data.

10. A.Chilingarov, CV distortion, 17.3.201410 4. Discussion It is not surprising that both models give very similar results. R dyn is always more than 1 M  while R b is ~ 20 k . Therefore the parameter  = R l /(R l +R b ) with R l = R dyn 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 R l in place of R g. 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 R g and R l. The C s and R s can in this case be calculated combining the equations on slides 4 and 5. For both models C s > C. It is easy to show that the same is true when both R g and R l resistors are present.

11. A.Chilingarov, CV distortion, 17.3.201411 5. Conclusions 1.The distortion of the experimentally measured parameters C s and R s 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 R g and R l resistors may be required to be included in the equivalent circuit diagram. However in all cases C s > C i.e. a high leakage current should always lead to an increase in the measured capacitance.

12. A.Chilingarov, CV distortion, 17.3.201412 Backup slides

13. A.Chilingarov, CV distortion, 17.3.201413 Use equation on the slide 4; C sg > C C s calculation in the case when both R g and R l are present Use equation on the slide 5; C s > C sg > C