Evolution of silicon sensors characteristics of the current CMS tracker

Abstract

The CMS silicon strip tracker is the largest detector of its kind. It is expected to operate at the LHC for more than 10 years. In order to quantify aging effects, it is important to keep track of the evolution of fundamental detector properties under radiation and thermal fluctuations. Our aim is to define monitoring procedures to determine the characteristics regularly. In this paper we focus on the silicon sensor's full depletion voltage. We present the first results obtained with two different methods: a standard one with signal from particles and a newly developed approach based on noise. In addition we compare our output with the $C-V$ measurements performed during the construction.

Introduction

Silicon detector properties are changing with irradiation, annealing and aging. The main quantities which are influenced by these effects are the leakage current and the full depletion voltage. The silicon strips tracker of the Compact Muon Solenoid (CMS) includes sensors of many different geometries and a large range of resistivities. This leads to a large spread of full depletion voltage values. Taking also the difference in fluence through the sensors into account, it is important to monitor the detector properties on the granularity of sensor modules. The leakage current for each module is measured at regular intervals by its Detector Control Unit (DCU). A detailed description can be found in Ref. [1]. The full depletion voltage has to be derived out of bias voltage scans. We investigated two different scanning methods, one based on noise measurements (see Section 2.1) the other based on signal of particle tracks (see Section 2.2).

The aim is to collect an integral dataset of the leakage current, the full depletion voltage as well as the fluence and the temperature history for all modules, and compare our data with the current estimations based on the Hamburg model [2].

According to the Hamburg model the leakage current after irradiation evolutes according to:

$$\mathrm{\Delta }{I}_{\mathit{leakage}}=\alpha (T){\Phi }_{\mathit{eq}}V$$

with the temperature dependent current related damage rate $\alpha$ for a given fluence ${\Phi }_{\mathit{eq}}$ and volume V.

The evolution of the effective space charge is given by:

$$\mathrm{\Delta }{N}_{\mathit{eff}}({\Phi }_{\mathit{eq}},T)=N_C({\Phi }_{\mathit{eq}})+N_A({\Phi }_{\mathit{eq}},T)+N_Y({\Phi }_{\mathit{eq}},T)$$

with the stable damage part N_C, the two annealing parts N_A (short term, beneficial) and N_Y (long term, reverse). The number of effective charge carriers is proportional to the full depletion Voltage. The prediction for the evolution of the full depletion voltage based on the current estimations of irradiation within the next 10 years at CMS is shown in Fig. 1.

With the fluence to which the detector was exposed until the end of 2010 (up to $1.8\times {10}^{12}$ fast hadrons), we do not expect a significant change in any of the detector properties, based on the Hamburg model. In order to verify this assumption, and to ensure that no aging effects beyond the Hamburg model occurred, we investigated leakage current measurements from 2009 and from 2010. A comparison showed that, within the accuracy of the DCU readout (about $3\mathrm{\mu }\mathrm{A}$), the leakage currents are very stable and no irradiation damage or aging effects are visible so far (see Fig. 2).