Noise Modeling and Calibration of a Two-Stage Cryogenic Charge Amplifier for the SPLENDOR Experiment

TL;DR

This work addresses enabling $\mathcal{O}(\text{meV})$ energy sensitivity for sub-MeV dark matter by developing a substrate-agnostic, split-stage CryoHEMT charge amplifier with a base-temperature buffer and a 4 K gain stage to minimize input capacitance. Gain is extracted from frequency-response measurements, and an input-referred noise model identifies Johnson noise, 1/f voltage noise, white noise, and current noise as key contributors, with a measured broadband gain of $A_{V2} \approx 34$. Absolute charge sensitivity is established via LED shot-noise calibration, yielding a charge-resolution of $19 \pm 4\,e^-$, in agreement with a noise-integration prediction of about $17\,e^-$, confirming thermally limited operation. The results demonstrate a viable, low-capacitance readout platform for sub-eV depositions in narrow-gap semiconductors, and outline clear paths toward single-electron sensitivity through thermalization improvements and room-temperature electronics.

Abstract

The SPLENDOR Collaboration studies novel narrow-gap semiconductors and engineered a substrate agnostic detector platform to achieve $\mathcal{O}$(meV) energy sensitivity designed for low mass dark matter searches. This was achieved using low-capacitance and low-noise commercial CryoHEMTs in a split-stage topology integrated throughout a dilution refrigerator. Designed with a source-follower HEMT at the base temperature stage and a voltage amplifier at 4\,K, this amplifier has input-limited voltage noise of 10 $\text{nV}/\sqrt{\text{Hz}}$ and current noise of 100 $\text{aA}/\sqrt{\text{Hz}}$ at 1kHz. In agreement with this noise level and a photon calibration, this amplifier has a $\text{19} \pm \text{4} $ electron resolution.

Figures (4)

• Figure 1: Schematic of the full experimental setup for characterization and pulse detection. Cryogenic stages are shown in dark teal (25 mK) and light teal (4 K); at 4 K the voltage-gain stage includes a filter bank. At room temperature, an injection board (yellow) provides selectable filtering to signal ground or fridge ground. Signal and fridge grounds are connected at the chassis of the power supply. The output signal is amplified by a Stanford Research Systems SR560 to overcome the MokuPro’s noise floor. The MokuPro is a multi-instrument DAQ with input/output control; its output is used either to inject a signal at Q1’s gate for gain and frequency-response measurements or to drive LED pulses which inject light down optical fibers connecting to the base temperature housing. The LED pulses are used for shot-noise calibration. A battery can be connected or disconnected to bias the detector at base temperature.
• Figure 2: (Left) Frequency response data used to estimate broadband gain ($A_{V2}$) of the cryogenic amplifier shown in Figure \ref{['fig: Schematic Offical']}. Eq. \ref{['eq:transferequation']} is fit to the data with parameters shown in Table \ref{['tab:gain fit']}. (Right) Simplified circuit used to derive Eq. \ref{['eq:transferequation']} and estimated gain.
• Figure 3: (Top) shows the input noise for Q1 and Q2 with each stage at 25 mK and 4 K respectively. The dominate noise sources are Johnson noise $v_\text{J}$ (eq. \ref{['eq: johnson noise']}) and 1/f voltage noise $v_\text{pink}$ (eq. \ref{['eq: pink noise']}) for Q1. Both components vary by $\sqrt{T}$. (Bottom Left) By normalizing the noise and plotting vs $\sqrt{T}$, you can see a divergence from the linear trend at 400 mK. The green dashed line shows this expected linear trend. (Bottom Right) The flattest part of the spectrum, from 1 kHz-10 kHz, was normalized to the 10 K noise.
• Figure 4: (Left) 300 filtered averaged pulses for 14 different LED intensities. (Bottom Right) Histogram of pulse heights for each LED intensity fitted to a gaussian. The color indicates the LED intensity. Black corresponds to zero point amplitude and variance. These data include 300 LED pulses of 625nm light, each with a 50 $\mu$s pulse width. 5 $\sigma$ quality cuts were done on both $\chi^2$ fits and pulse amplitudes. The pulse template used along with the optimal filter formalism was a 3 pole pulse with a one rise time and two fall times. (Top Right) Linear relationship between mean pulse amplitude and variance based on equation \ref{['eq:linfit']}. From fit parameters and equation \ref{['eq: charge resolution']}, a $19\,\pm 4 e^-$ resolution is measured.