Sequential Quenching to Predict Semiconductor Defect Concentrations from Formation & Migration Energies: The Case of CdTe:As Doping

TL;DR

This paper introduces sequential quenching (SQ), a new defect calculation method that models defect concentrations in semiconductors during finite-rate cooling, improving predictions over traditional equilibrium or instantaneous quenching assumptions.

Contribution

The paper presents SQ as a novel, physically transparent framework for predicting defect concentrations considering diffusion-limited kinetics during cooling in semiconductors.

Findings

Fast-diffusing defects freeze-in at lower temperatures, affecting doping.

Cooling rate influences defect compensation and doping type.

SQ predictions differ significantly from equilibrium or full quenching models.

Abstract

Defect concentrations in semiconductors are strongly influenced by thermal history during growth and cooldown, yet most defect calculations assume either instantaneous quenching from high temperature or that full-equilibrium is maintained - two limiting cases rarely approached in reality. Here, we introduce sequential quenching (SQ) as a 3rd type of defect calculation utilizing defect formation and migration energies to model defect concentrations subject to diffusion-limited kinetics in samples cooled at finite rates. In SQ, the concentration of each defect is frozen at a characteristic temperature determined by its diffusion rate, distance to sources/sinks, and cooling rate. Because different charge-states interact through charge neutrality but freeze at different temperatures, the sequence of freeze-in events is non-commuting. Critically, not all room-temperature SQ solutions can be predicted from full equilibrium (EQ) or full-quenching (FQ) calculations - erroneous predictions are likely without SQ. We illustrate SQ using the example of As-doped CdTe, for which experimental data show differences in doping with cooling rate and between polycrystalline thin-films for photovoltaics and bulk crystals. SQ calculations reveal that fast-diffusing defects such as Cd-interstitials remain mobile to lower temperatures and freeze-in at larger characteristic distances, leading to strong compensation and n-type behavior in rapidly cooled or bulk samples. Slower cooling and reduced characteristic distances suppress donor freeze-in and enhance p-type activation. These results establish SQ as a physically transparent and computationally efficient framework for connecting cooling conditions, sample geometry, and defect kinetics to dopant activation in CdTe and related materials.