Evolution of high-energy positron ionization loss spectra in a silicon crystal with the change of its orientation from axial to planar

Abstract On the basis of computer simulation, the ionization energy loss distributions (spectra) of high-energy positrons impinging on a silicon crystal at various angles $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> with respect to the axis $$\langle 100\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:mn>100</mml:mn> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> are considered. The method of simulation of high-energy particle ionization loss in oriented crystals is presented in detail. It is demonstrated that along with the probability of particle close collisions with atoms, the probability of distant collisions can be also sensitive to the particle position in the crystal lattice. Evolution of the ionization loss spectra with the change of crystal orientation relative to the incident particle momentum from the axial $$\langle 100\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:mn>100</mml:mn> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> to the planar (100) and (110) with the increase of $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> is investigated. It is shown that in the transition $$\langle 100\rangle \rightarrow (100)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:mn>100</mml:mn> <mml:mo>⟩</mml:mo> <mml:mo>→</mml:mo> <mml:mo>(</mml:mo> <mml:mn>100</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> the most probable energy loss $$E_\mathrm{{MP}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>MP</mml:mi> </mml:msub> </mml:math> experiences a sharp maximum and discontinuity, while in the transition $$\langle 100\rangle \rightarrow (110)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:mn>100</mml:mn> <mml:mo>⟩</mml:mo> <mml:mo>→</mml:mo> <mml:mo>(</mml:mo> <mml:mn>110</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> the amplitude of its variation is much smaller. Behavior of the average restricted energy loss $$E_\mathrm{{AV}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>AV</mml:mi> </mml:msub> </mml:math> in these transitions is investigated as well. Correlation of the dependences of $$E_\mathrm{{MP}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>MP</mml:mi> </mml:msub> </mml:math> and $$E_\mathrm{{AV}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>AV</mml:mi> </mml:msub> </mml:math> on $$\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ψ</mml:mi> </mml:math> with the change of the particle motion regime is discussed.