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Why (and How) LGADs Work: Ionization, Space Charge, and Gain Saturation

N. Cartiglia, A. R. Altamura, R. Arcidiacono, M. Durando, S. Galletto, M. Ferrero, L. Lanteri, A. Losana, L. Massaccesi, L. Menzio, F. Siviero, V. Sola, R. White

Abstract

The temporal resolution of Low-Gain Avalanche Detectors (LGADs), also known as Ultra-Fast Silicon Detectors (UFSDs), is governed by two contributions: jitter, arising from electronic noise and signal slew rate, and the Landau noise term, arising from the non-uniform energy deposition of minimum ionizing particles (MIPs). We show that a correct simulation of the initial ionization alone significantly overestimates the measured Landau noise. Two additional physical mechanisms are necessary to reproduce the data: space charge effects during electron/hole drift, which smooth the granularity of the initial charge distribution, and gain saturation during multiplication, which preferentially suppresses large-amplitude fluctuations. All steps of the model have been implemented in the fast simulation program Weightfield2 (WF2). The model is validated against several independent experimental observations: the evolution of the measured charge distribution with gain, the temporal resolution of events in the Landau tail, and the thickness dependence of timing performance. We also discuss a data-driven gain measurement method based on gain saturation, and implications for gain layer design.

Why (and How) LGADs Work: Ionization, Space Charge, and Gain Saturation

Abstract

The temporal resolution of Low-Gain Avalanche Detectors (LGADs), also known as Ultra-Fast Silicon Detectors (UFSDs), is governed by two contributions: jitter, arising from electronic noise and signal slew rate, and the Landau noise term, arising from the non-uniform energy deposition of minimum ionizing particles (MIPs). We show that a correct simulation of the initial ionization alone significantly overestimates the measured Landau noise. Two additional physical mechanisms are necessary to reproduce the data: space charge effects during electron/hole drift, which smooth the granularity of the initial charge distribution, and gain saturation during multiplication, which preferentially suppresses large-amplitude fluctuations. All steps of the model have been implemented in the fast simulation program Weightfield2 (WF2). The model is validated against several independent experimental observations: the evolution of the measured charge distribution with gain, the temporal resolution of events in the Landau tail, and the thickness dependence of timing performance. We also discuss a data-driven gain measurement method based on gain saturation, and implications for gain layer design.
Paper Structure (19 sections, 9 equations, 12 figures)

This paper contains 19 sections, 9 equations, 12 figures.

Table of Contents

  1. Introduction
  2. MIP Ionization in Silicon Sensors
  3. The Seed Distribution Model
  4. Long-Range Correlations from Delta Rays
  5. Components of the Temporal Resolution
  6. Jitter and Landau Noise
  7. Analytical Derivation of the Landau Noise Term
  8. The Discrepancy Between Simulation and Data
  9. Smoothing Mechanisms
  10. Space Charge Effects During Drift
  11. Gain Saturation
  12. Experimental Evidence for Gain Saturation
  13. Evolution of the Charge Distribution with Gain
  14. Temporal Resolution as a Function of Landau Position
  15. Combined Effect and Agreement with Data
  16. ...and 4 more sections

Figures (12)

  • Figure 1: Measured (red) and WF2-simulated Landau energy distributions (blue). The simulation correctly reproduces both the MPV and the FWHM as a function of sensor thickness.
  • Figure 2: Measured values of the Landau noise as a function of sensor thickness and a line that shows the $\propto\sqrt{d}$ behaviour.
  • Figure 3: Temporal resolution (Landau noise contribution, jitter subtracted) vs. sensor thickness. The WF2 prediction using only the initial Landau ionization significantly overestimates the measured values, especially for thick sensors.
  • Figure 4: The measured Landau noise contribution is compared with the WF2 simulation with and without space charge effects.
  • Figure 5: Simulated gain suppression factor as a function of gain. Gain saturation is stronger for larger charge deposits and higher gains.
  • ...and 7 more figures