Complex implementation

X_mA_n complex is a defect with "n" atoms of B, As, C, F, O or P (called front particles), and "m" I or V (called back particles). DADOS does not take into account the different posible microscopic configurations of X_mA_n and uses effective numbers for each combination.

I and V can be single neutral native defects or associated with the other atoms, for instance, boron in interstitial position.

Back particle emission

Back particles are emitted as follows:

X_mA_n -> X_m-1A_n + X

The emission frequency is calculated by DADOS as follows:

Where:

• B is the back particle.
• λ is the jump distance.

• D0F_ComplexProp is a prefactor in diffusivities units.

• Em is the migration energy.
• Ebarr is an optional energetic barrier.
• Eb is the binding energy of the back particle, calculated as follows:

Eb(m,n) = Etotal(m-1,n) - Etotal(m,n)

• See symbol list.

After emission, if only one particle (or two particles that can form a pair) is remaining, the complex is transformed into a point defect.

The energies associated to this process are plotted below:

Front particle emission

Front particles are emitted:

X_mA_n -> X_mA_n-1 + A

The emission frequency is calculated by DADOS as follows:

Where:

• F is the back particle.
• λ is the jump distance.

• D0F_ComplexProp is a prefactor in diffusivities units.

• Em is the migration energy.
• Ebarr is an optional energetic barrier.
• Eb is the binding energy of the front particle, calculated as follows:

Eb(m,n) = Etotal(m,n-1) - Etotal(m,n)

• See symbols list.

After emission, if only one particle (or two particles that can form a pair) is remaining, the complex is transformed into a point defect.

The energies associated to this process are plotted below:

Immobile single impurity (B, As, C,...)

It is emitted within a mobile pair:

X_mA_n -> X_m-1A_n-1 + XA

The emission frequency is calculated by DADOS as follows:

Where:

• F is the back particle.

• λ is the jump distance.

• D0F_ComplexProp is a prefactor in diffusivities units.

• Em is the migration energy.
• Ebarr is an optional energetic barrier.
• Eb is the binding energy of the front particle, calculated as follows:

Eb(m,n) = Etotal(m-1,n-1) - EbXA-Etotal(m,n)

• See symbols list.

The energies associated to this process are plotted below:

Back particle capture

Complexes can capture single neutral "native defects".

X_mA_n + X -> X_m+1A_n

These captures are not automatic, because of the associated energies. DADOS uses a capture probability defined as follows:

 Where:

• B is the back particle.
• Ebarr is an optional energetic barrier.
• Eb is the binding energy of the back particle, calculated as follows:

Eb(m,n) = Etotal(m,n) - Etotal(m+1,n)

If there is no energy included in the DDP file, DADOS assumes that this configuration is unstable and it gives a value of +5 eV to the potential energy to avoid the creation of this kind of complexes.

• See symbols list.

The energies associated to this process are plotted below:

Front particle capture

Complexes can capture single impurities:

Mobile single impurity (F, O,...)

X_mA_n + A -> X_mA_n+1

These captures are not automatic, because of the associated energies. DADOS uses a capture probability defined as follows:

 Where:

• F is the front particle.
• Ebarr is an optional energetic barrier.
• Eb is the binding energy of the back particle, calculated as follows:

Eb(m,n) = Etotal(m,n) - Etotal(m,n+1)

• See symbols list.

The energies associated to this process are plotted below:

Immobile single impurity (B, As, C,...)

X_mA_n + XA -> X_m+1A_n+1

These captures are not automatic, because of the associated energies. DADOS uses a capture probability defined as follows:

 Where:

• F is the front particle.
• Ebarr is an optional energetic barrier.
• Eb is the binding energy of the back particle, calculated as follows:

Eb(m,n) = Etotal(m,n) - Etotal(m+1,n+1)

• See symbols list.

The energies associated to this process are plotted below:

Shrinkage

Complexes can capture interstitials or vacancies that are recombined with complementary particles. For instance, let's call X' to the complementary particle to X, i. e., interstitials for vacancies and vice versa:

X_mA_n + X' -> X_m-1A_n

The capture probability is calculated as follows:

Where:

• Erec is:

Erec(m,n) = Eform_I + Eform_V - (Etotal(m-1,n) - Etotal(m,n)) = Eform_I + Eform_V - EbB(m,n)
 

• EbB(m,n) is the binding energy for the back particle.
• Eform_I is the formation energy of interstitial.
• Eform_V is the formation energy of vacancy.
• See symbols list.

The energies associated to this process are plotted below:

Complementary emission

Some impurities can diffuse by means of both interstitals and vacancies, for example, arsenic. In this case, complexes can emit not only interstitials and vacancies but also point defects, with complementary particles, i.e., a As_nV_m complex can emit As_i.

X_mA_n -> X_m+1A_n-1 + X'A

The emission frequency is given as follows (the same for AV):

Where:

• λ is the jump distance.

• D0F_ComplexProp is a prefactor in diffusivities units.

• Em is the migration energy.

• Ebarr is an optional energetic barrier.

• Eb is the binding energy, calculated as follows:

  Eb(m,n) = Etotal(m+1,n-1) - Etotal(m,n)

• See symbols list.

Complementary recombination

Some impurities can diffuse by means of both interstitals and vacancies, for example, arsenic. In this case, complexes can recombine not only interstitials and vacancies but also point defects:

X_mA_n + X'A -> X_m-1A_n+1

The capture probability is calculated as follows:

Where:

• Ecapture is the capture energy.
• See symbols list.

And the recombination energy is calculated with the total energies:

Where:

• Ef is the formation energy.
• Em is the migration energy.
• E_Ai->A is an internal, fixed parameter.