Study of radiation damage in silicon detectors for high ... - F9
Study of radiation damage in silicon detectors for high ... - F9
Study of radiation damage in silicon detectors for high ... - F9
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3. Ir<strong>radiation</strong> Facility 49width <strong>of</strong> depleted region w and consequently to p V , i.e. I = A p V . The magnitude <strong>of</strong>the parameter A can be estimated from the conditions at full depletion A = p I FDVFD. Thenthe resistance <strong>of</strong> the depleted bulk at given depletion voltage is given byR d = V I =VpVA p V = A= V FDI FDpV0(3.13)Us<strong>in</strong>g reverse current <strong>of</strong> I FD 25 A at full depletion voltage 25 <strong>of</strong> V FD 250 V oneobta<strong>in</strong>sR d =10M p V 0 : (3.14)One can see that <strong>in</strong> the described case R d =Z d 20 and Z u =R u 15. Thus thedepleted region can be approximated by a capacitor and the undepleted by a resistor.The signicance <strong>of</strong> the resistance <strong>of</strong> the undepleted region is however decreas<strong>in</strong>g with<strong>in</strong>creas<strong>in</strong>g depletion depth. Thus at half <strong>of</strong> full depletion depth (V = V FD =4), one alreadyobta<strong>in</strong>s Z d =R u > 15. Thus <strong>for</strong> large depletion depths the bulk can be described well bya s<strong>in</strong>gle capacitor and both serial and parallel model should give the same result. Theparallel model however has the advantage that it can take <strong>in</strong>to account changes <strong>in</strong> thesurface current, presented by the surface resistor. They are hard to predict but can getvery important close to the breakdown where the dierential resistance is small. S<strong>in</strong>ce <strong>for</strong>determ<strong>in</strong>ation <strong>of</strong> full depletion voltage from the C/V characteristic, we are <strong>in</strong>terested <strong>in</strong>its shape close to full depletion, the parallel model suits better and was used throughoutthis work.The situation however changes dramatically when the measur<strong>in</strong>g frequency is <strong>in</strong>creased.This is reected <strong>in</strong> a decrease <strong>of</strong> impedance <strong>of</strong> both capacitors and at 1 MHz,Z u has the lead<strong>in</strong>g role also <strong>in</strong> the undepleted region. Then the equivalent circuit can beapproximated by two serial capacitors with a constant sum <strong>of</strong> capacitances. Thus at 1MHz the measured capacitance is almost <strong>in</strong>dependent <strong>of</strong> applied voltage, as seen <strong>in</strong> gure3.12. Similar eect is obta<strong>in</strong>ed by <strong>in</strong>creas<strong>in</strong>g the temperature. S<strong>in</strong>ce resistance <strong>of</strong> both depletedand undepleted region is approximately proportional 26 to e ;Eg=2k BT , <strong>in</strong>creas<strong>in</strong>g thetemperature by a few 10 C has the same relative eect as the above mentioned <strong>in</strong>crease<strong>in</strong> frequency.Static resistivities, used <strong>in</strong> the above estimation, do not describe the system veryaccurately. And although dynamic resistivities are somewhat dierent 27 , the qualitativeconclusions rema<strong>in</strong> the same.25Values <strong>of</strong> reverse current and full depletion voltage at the m<strong>in</strong>imum after benecial anneal<strong>in</strong>g wereused.26For depleted region see eq. 2.38 and <strong>for</strong> undepleted regions equations 2.11 and 2.1.27A dierence <strong>of</strong> up to about factor <strong>of</strong> two was estimated.