[Paper Review] Role of carbon and hydrogen in limiting $n$-type doping of monoclinic (Al$_x$Ga$_{1-x}$)$_2$O$_3$

Sai Mu, Mengen Wang+4 more|arXiv (Cornell University)|Nov 13, 2021

Semiconductor materials and devices1 references4 citations

TL;DR

This study uses hybrid density functional theory to investigate n-type doping limitations in monoclinic (AlₓGa₁₋ₓ)₂O₃, identifying silicon as a viable shallow donor up to 70% Al content. However, unintentional carbon and hydrogen impurities—common in MOCVD growth—form compensating acceptors, especially Cₐ–H and Cₒ–H complexes, severely limiting free carrier concentrations even at low Al compositions.

ABSTRACT

We use hybrid density functional calculations to assess n-type doping in monoclinic (Al$_x$Ga$_{1-x}$)$_2$O$_3$ alloys. We focus on Si, the most promising donor dopant, and study the structural properties, formation energies and charge-state transition levels of its various configurations. We also explore the impact of C and H, which are common impurities in metal-organic chemical vapor deposition (MOCVD). In Ga$_2$O$_3$, Si$_{Ga}$ is an effective shallow donor, but in Al$_2O_3$ Si$_{Al}$ acts as a DX center with a (+/-) transition level in the band gap. Interstitial H acts as a shallow donor in Ga$_2$O$_3$, but behaves as a compensating acceptor in n-type Al$_2O_3$. Interpolation indicates that Si is an effective donor in (Al$_x$Ga$_{1-x}$)$_2$O$_3$ up to 70% Al, but it can be compensated by H already at 1% Al. We also assess the diffusivity of H and study complex formation. Si$_{cation}$-H complexes have relatively low binding energies. Substitutional C on a cation site acts as a shallow donor in Ga$_2$O$_3$, but can be stable in a negative charge state in (Al$_x$Ga$_{1-x}$)$_2$O$_3$ when x>5%. Substitutional C on an O site (C$_O$) always acts as an acceptor in n-type (Al$_x$Ga$_{1-x}$)$_2$O$_3$, but will incorporate only under relatively O-poor conditions. C$_O$-H complexes can actually incorporate more easily, explaining observations of C-related compensation in Ga$_2$O$_3$ grown by MOCVD. We also investigate C$_{cation}$-H complexes, finding they have high binding energies and act as compensating acceptors when x>56%; otherwise the H just passivates the unintentional C donors. C-H complex formation explains why MOCVD grown Ga$_2$O$_3$ can exhibit record-low free-carrier concentrations, in spite of the unavoidable incorporation of C. Our study highlights that, while Si is a suitable shallow donor in ALGO alloys, control of unintentional impurities is essential to avoid compensation.

Motivation & Objective

• To determine the viability of silicon as a shallow n-type dopant in monoclinic (AlₓGa₁₋ₓ)₂O₃ across varying Al compositions.
• To investigate the role of common impurities—carbon and hydrogen—in compensating n-type doping during metal-organic chemical vapor deposition (MOCVD) growth.
• To assess the formation energies, charge-state transition levels, and complex formation of Si, C, and H defects in (AlₓGa₁₋ₓ)₂O₃.
• To explain experimental observations of low free-carrier concentrations in MOCVD-grown Ga₂O₃ despite Si doping.
• To provide a theoretical basis for optimizing growth and processing conditions to suppress compensation by carbon and hydrogen.

Proposed method

• Hybrid density functional theory (DFT) calculations were used to compute formation energies and charge-state transition levels of Si, C, and H defects in monoclinic (AlₓGa₁₋ₓ)₂O₃.
• Interpolation of transition levels between β-Ga₂O₃ and θ-Al₂O₃ was performed to estimate Si donor behavior across the alloy composition range.
• Formation energies of C and H defects were calculated under varying chemical potential conditions, including O-rich and O-poor environments.
• Binding energies of Si–H, C–H, and C–O–H complexes were evaluated to assess their stability and electronic impact.
• Diffusivity of hydrogen was studied to assess its role in defect migration and complex formation during growth and annealing.
• The electronic structure of key defect configurations was analyzed to determine their donor or acceptor character in n-type (AlₓGa₁₋ₓ)₂O₃.

Experimental results

Research questions

• RQ1 Can silicon remain a shallow donor in monoclinic (AlₓGa₁₋ₓ)₂O₃ up to high aluminum compositions, and what is its effective doping range?
• RQ2 How do carbon and hydrogen impurities, prevalent in MOCVD-grown (AlₓGa₁₋ₓ)₂O₃, affect n-type doping efficiency?
• RQ3 What is the role of C–H and Cₒ–H complexes in compensating shallow donors like Si and C_Ga in (AlₓGa₁₋ₓ)₂O₃?
• RQ4 At what Al composition do hydrogen and carbon begin to act as compensating acceptors in n-type (AlₓGa₁₋ₓ)₂O₃?
• RQ5 How do defect complexes such as C_cation–H and C_oxygen–H influence carrier concentration and doping control?

Key findings

• Silicon remains an effective shallow donor in (AlₓGa₁₋ₓ)₂O₃ up to 70% Al composition, based on interpolated ( + / 0 ) transition levels.
• Hydrogen acts as a shallow donor in Ga₂O₃ but becomes a compensating acceptor in n-type Al₂O₃, with compensation onset at just 1% Al composition.
• C_Ga (carbon on gallium site) acts as a shallow donor in Ga₂O₃ but becomes a stable negative charge state donor in (AlₓGa₁₋ₓ)₂O₃ only when x > 5%.
• C_O (carbon on oxygen site) always acts as an acceptor in n-type (AlₓGa₁₋ₓ)₂O₃ and forms C_O–H complexes that are energetically favorable under O-poor conditions.
• C_cation–H complexes form high-binding-energy acceptors that compensate n-type doping when x > 56%, while C_O–H complexes act as acceptors across the entire composition range.
• C_O–H complex formation explains experimental observations of carbon-related compensation in MOCVD-grown Ga₂O₃, despite unavoidable carbon incorporation.