Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling

We analyze the interaction-induced renormalization of single-particle excitations in the two-dimensional Hubbard model at weak coupling using the Wick-ordered version of the functional renormalization group. The self energy is computed for real frequencies by integrating a flow equation with renormalized two-particle interactions. In the vicinity of hot spots, that is points where the Fermi surface intersects the umklapp surface, self energy effects beyond the usual quasi-particle renormalizations and damping occur near instabilities of the normal, metallic phase. Strongly enhanced renormalized interactions between particles at different hot spots generate a pronounced low-energy peak in the imaginary part of the self energy, leading to a pseudogap-like double-peak structure in the spectral function for single-particle excitations.Comment: 14 pages, 7 figure

Fluence Dependence of Charge Collection of irradiated Pixel Sensors

The barrel region of the CMS pixel detector will be equipped with ``n-in-n'' type silicon sensors. They are processed on DOFZ material, use the moderated p-spray technique and feature a bias grid. The latter leads to a small fraction of the pixel area to be less sensitive to particles. In order to quantify this inefficiency prototype pixel sensors irradiated to particle fluences between $4.7\times 10^{13}$ and 2.6\times 10^{15} \Neq have been bump bonded to un-irradiated readout chips and tested using high energy pions at the H2 beam line of the CERN SPS. The readout chip allows a non zero suppressed analogue readout and is therefore well suited to measure the charge collection properties of the sensors. In this paper we discuss the fluence dependence of the collected signal and the particle detection efficiency. Further the position dependence of the efficiency is investigated.Comment: 11 Pages, Presented at the 5th Int. Conf. on Radiation Effects on Semiconductor Materials Detectors and Devices, October 10-13, 2004 in Florence, Italy, v3: more typos corrected, minor changes required by the refere

Tests of silicon sensors for the CMS pixel detector

The tracking system of the CMS experiment, currently under construction at the Large Hadron Collider (LHC) at CERN (Geneva, Switzerland), will include a silicon pixel detector providing three spacial measurements in its final configuration for tracks produced in high energy pp collisions. In this paper we present the results of test beam measurements performed at CERN on irradiated silicon pixel sensors. Lorentz angle and charge collection efficiency were measured for two sensor designs and at various bias voltages.Comment: Talk presented at 6th International Conference on Large Scale Applications and Radiation Hardness of Semiconductor Detectors, September 29-October 1, 2003, Firenze, Italy. Proceedings will be published in Nuclear Instr. & Methods in Phys. Research, Section

Radiation hardness of CMS pixel barrel modules

Pixel detectors are used in the innermost part of the multi purpose experiments at LHC and are therefore exposed to the highest fluences of ionising radiation, which in this part of the detectors consists mainly of charged pions. The radiation hardness of all detector components has thoroughly been tested up to the fluences expected at the LHC. In case of an LHC upgrade, the fluence will be much higher and it is not yet clear how long the present pixel modules will stay operative in such a harsh environment. The aim of this study was to establish such a limit as a benchmark for other possible detector concepts considered for the upgrade. As the sensors and the readout chip are the parts most sensitive to radiation damage, samples consisting of a small pixel sensor bump-bonded to a CMS-readout chip (PSI46V2.1) have been irradiated with positive 200 MeV pions at PSI up to 6E14 Neq and with 21 GeV protons at CERN up to 5E15 Neq. After irradiation the response of the system to beta particles from a Sr-90 source was measured to characterise the charge collection efficiency of the sensor. Radiation induced changes in the readout chip were also measured. The results show that the present pixel modules can be expected to be still operational after a fluence of 2.8E15 Neq. Samples irradiated up to 5E15 Neq still see the beta particles. However, further tests are needed to confirm whether a stable operation with high particle detection efficiency is possible after such a high fluence.Comment: Contribution to the 11th European Symposium on Semiconductor Detectors June 7-11, 2009 Wildbad Kreuth, German

Position Dependence of Charge Collection in Prototype Sensors for the CMS Pixel Detector

This paper reports on the sensor R&D activity for the CMS pixel detector. Devices featuring several design and technology options have been irradiated up to a proton fluencec of 1E15 n_eq/cm**2 at the CERN PS. Afterward they were bump bonded to unirradiated readout chips and tested using high energy pions in the H2 beam line of the CERN SPS. The readout chip allows a non zero suppressed full analogue readout and therefore a good characterization of the sensors in terms of noise and charge collection properties. The position dependence of signal is presented and the differences between the two sensor options are discussed.Comment: Contribution to the IEEE-NSS Oct. 2003, Portland, OR, USA, submitted to IEEE-TNS 7 pages, 8 figures, 1 table. Revised, title change

Extraction of electric field in heavily irradiated silicon pixel sensors

A new method for the extraction of the electric field in the bulk of heavily irradiated silicon pixel sensors is presented. It is based on the measurement of the Lorentz deflection and mobility of electrons as a function of depth. The measurements were made at the CERN H2 beam line, with the beam at a shallow angle with respect to the pixel sensor surface. The extracted electric field is used to simulate the charge collection and the Lorentz deflection in the pixel sensor. The simulated charge collection and the Lorentz deflection is in good agreement with the measurements both for non-irradiated and irradiated up to 1E15 neq/cm2 sensors.Comment: 6 pages, 11 figures, presented at the 13th International Workshop on Vertex Detectors for High Energy Physics, September 13-18, 2004, Menaggio-Como, Italy. Submitted to Nucl. Instr. Meth.

Observation, modeling, and temperature dependence of doubly peaked electric fields in irradiated silicon pixel sensors

We show that doubly peaked electric fields are necessary to describe grazing-angle charge collection measurements of irradiated silicon pixel sensors. A model of irradiated silicon based upon two defect levels with opposite charge states and the trapping of charge carriers can be tuned to produce a good description of the measured charge collection profiles in the fluence range from 0.5x10^{14} Neq/cm^2 to 5.9x10^{14} Neq/cm^2. The model correctly predicts the variation in the profiles as the temperature is changed from -10C to -25C. The measured charge collection profiles are inconsistent with the linearly-varying electric fields predicted by the usual description based upon a uniform effective doping density. This observation calls into question the practice of using effective doping densities to characterize irradiated silicon.Comment: 8 pages, LaTeX document, 10 figures. Presented at Pixel 2005 Workshop, Bonn, Sept 2005. Small cosmetic revisions in response to referee comments and to fix broken reference link

A double junction model of irradiated silicon pixel sensors for LHC

In this paper we discuss the measurement of charge collection in irradiated silicon pixel sensors and the comparison with a detailed simulation. The simulation implements a model of radiation damage by including two defect levels with opposite charge states and trapping of charge carriers. The modeling proves that a doubly peaked electric field generated by the two defect levels is necessary to describe the data and excludes a description based on acceptor defects uniformly distributed across the sensor bulk. In addition, the dependence of trap concentrations upon fluence is established by comparing the measured and simulated profiles at several fluences and bias voltages.Comment: Talk presented at the 10th European Symposium on Semiconductor Detectors, June 12-16 2005, Wildbad Kreuth, Germany. 9 pages, 4 figure

Simulation of Heavily Irradiated Silicon Pixel Detectors

We show that doubly peaked electric fields are necessary to describe grazing-angle charge collection measurements of irradiated silicon pixel sensors. A model of irradiated silicon based upon two defect levels with opposite charge states and the trapping of charge carriers can be tuned to produce a good description of the measured charge collection profiles in the fluence range from 0.5x10^{14} Neq/cm^2 to 5.9x10^{14} Neq/cm^2. The model correctly predicts the variation in the profiles as the temperature is changed from -10C to -25C. The measured charge collection profiles are inconsistent with the linearly-varying electric fields predicted by the usual description based upon a uniform effective doping density. This observation calls into question the practice of using effective doping densities to characterize irradiated silicon. The model is now being used to calibrate pixel hit reconstruction algorithms for CMS.Comment: Invited talk at International Symposium on the Development of Detectors for Particle, AstroParticle and Synchrtron Radiation Experiments, Stanford Ca (SNIC06) 8 pages, LaTeX, 11 eps figure