Hole trapping facilitates the formation of Frenkel pairs in crystalline and amorphous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ga</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">O</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> films

Holes are injected from electrodes or produced by irradiation in many applications of crystalline and amorphous <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Ga</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>3</a:mn> </a:msub> </a:mrow> </a:math> . They are known to trap in polaron states in both phases. We investigate, using density functional theory, how hole trapping in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>Ga</c:mi> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi mathvariant="normal">O</c:mi> <c:mn>3</c:mn> </c:msub> </c:mrow> </c:math> can lead to creation of Frenkel pairs (FPs) of oxygen vacancies in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mo>+</e:mo> <e:mn>2</e:mn> </e:mrow> </e:math> charge state, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msubsup> <f:mi mathvariant="normal">V</f:mi> <f:mi>O</f:mi> <f:mrow> <f:mn>2</f:mn> <f:mo>+</f:mo> </f:mrow> </f:msubsup> </f:math> , and interstitial oxygen atoms. The calculations reveal that hole bipolarons lead to the formation of O–O dimers, distorting adjacent Ga–O bonds and resulting in a significant reduction of the barriers for the nearest-neighbor FP formation with respect to pristine structures. In amorphous <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>Ga</h:mi> <h:mn>2</h:mn> </h:msub> <h:msub> <h:mi mathvariant="normal">O</h:mi> <h:mn>3</h:mn> </h:msub> </h:mrow> </h:math> the barriers are on average 2.05 eV, much lower than in the crystalline phase, where they are 3.47 to 4.80 eV. Furthermore, in the amorphous phase, the migration barriers for oxygen vacancies in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mo>+</j:mo> <j:mn>2</j:mn> </j:mrow> </j:math> charge state, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:msubsup> <k:mi mathvariant="normal">V</k:mi> <k:mi>O</k:mi> <k:mrow> <k:mn>2</k:mn> <k:mo>+</k:mo> </k:mrow> </k:msubsup> </k:math> , are reduced compared to those in the crystalline phase, indicating that <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi mathvariant="normal">V</m:mi> <m:mi>O</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mo>+</m:mo> </m:mrow> </m:msubsup> </m:math> can drift away under the influence of electric fields, creating stable defects. These results show that hole trapping in <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:msub> <o:mi>Ga</o:mi> <o:mn>2</o:mn> </o:msub> <o:msub> <o:mi mathvariant="normal">O</o:mi> <o:mn>3</o:mn> </o:msub> </o:mrow> </o:math> can facilitate the formation of FPs, particularly in amorphous structures. They can be useful in understanding the mechanisms of degradation in <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:msub> <q:mi>Ga</q:mi> <q:mn>2</q:mn> </q:msub> <q:msub> <q:mi mathvariant="normal">O</q:mi> <q:mn>3</q:mn> </q:msub> </q:mrow> </q:math> based devices under negative bias and illumination stress.