Analysis of Energy Resolution vs. Calorimeter Sampling Fraction

(Based on Slide 20 of DRD6 DD4hep Tutorial, April 2025)

1. Objective

This report summarizes the work completed for Hands-on 3 of the DRD6 DD4hep Tutorial. The goal is to study how the energy resolution of a sampling calorimeter varies with changes in the sampling structure, specifically the thickness of the sensitive material layer within each sampling unit.

The code used for this analysis is available at:
👉 https://github.com/lhprojects/DD4hepTutorials

2. Experimental Setup

• The calorimeter is composed of repeating layers, each consisting of:
  • A Silicon sensitive layer (active material)
  • A Brass absorber layer (passive material)
• The total thickness of each sampling unit (1 absorber + 1 sensitive layer) is fixed at 10 cm.
• The sensitive layer thickness is varied from 1 cm to 9 cm, while the absorber thickness is reduced accordingly to maintain the 10 cm total per unit.
• These material configurations (especially thick Silicon) are not realistic for actual detector construction, but are used here for illustrative purposes in simulation.
• All setups use the same number of layers and overall detector depth.
• For each configuration, 400 events are simulated using a particle gun shooting monoenergetic electrons (e⁻) directly into the calorimeter.

Geometry Comparison

• Figure A: Geometry with 1 cm Silicon + 9 cm Brass → mostly absorber
  

• Figure B: Geometry with 5 cm Silicon + 5 cm Brass → more sensitive material
  

3. Analysis Method

• The .root files are processed using a Python script with podio and ROOT.
• For each event, the total energy deposited in the Silicon layers is summed.
• Histograms are created and fitted with a Gaussian to extract:
  • Mean deposited energy (μ)
  • Standard deviation (σ)

• The relative energy resolution is calculated as: σ / μ

• A summary plot is generated to show how resolution changes with sensitive layer thickness.

4. Results

4.1 Energy Distributions

• Figure 1: 1 cm Silicon
  

• Figure 2: 5 cm Silicon
  

• Figure 3: 9 cm Silicon → shows low-energy tail
  

4.2 Resolution Trend

• Figure 4: Relative resolution (σ / μ) vs. sensitive layer thickness
  • Resolution generally improves with increasing sensitive thickness
  • A slight degradation is observed at 9 cm
    

5. Discussion

• Increasing the sensitive layer thickness improves energy resolution due to better sampling of electromagnetic showers.
• However, with 9 cm of Silicon, the remaining 1 cm of Brass absorber is insufficient to fully contain the shower.
• This results in energy leakage, which appears as a low-energy tail in the energy distribution and increases the standard deviation (σ).

6. Conclusion

This simulation study shows that energy resolution in a sampling calorimeter improves with thicker sensitive layers—up to a point. If the absorber becomes too thin, shower containment is compromised, leading to degraded resolution despite increased sensitive material. These results highlight essential trade-offs in calorimeter design and optimization.

Note: This report was initially written by ChatGPT, revised by me, and then refined again with ChatGPT’s assistance.