Sheet conductance of laser-doped layers using a Gaussian laser beam: an effective depth approximation

Abstract Laser doping of silicon with pulsed and scanned laser beams is now well-established to obtain defect-free, doping profile tailored, and locally selectively doped regions with a high spatial resolution. Picking the correct laser parameters (pulse power, pulse shape, and scanning speed) impacts the depth and uniformity of the melted region geometry. This work performs laser doping on the surface of single crystalline silicon, using a pulsed and scanned laser profile with a Gaussian intensity distribution. A deposited boron oxide precursor layer serves as a doping source. Increasing the local inter-pulse distance $$x_\text {irr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>x</mml:mi> <mml:mtext>irr</mml:mtext> </mml:msub> </mml:math> between subsequent pulses causes a quadratic decrease of the sheet conductance $$G_\text {sh}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mtext>sh</mml:mtext> </mml:msub> </mml:math> of the doped surface layer. Here, we present a simple geometric model that explains all experimental findings. The quadratic dependence stems from the approximately parabolic shape of the individual melted regions directly after the laser beam has hit the Si surface. The sheet resistance depends critically on the intersection depth $$d_\text {ch}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mtext>ch</mml:mtext> </mml:msub> </mml:math> and the distance $$x_\text {irr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>x</mml:mi> <mml:mtext>irr</mml:mtext> </mml:msub> </mml:math> of overlap between two subsequent, neighboring pulses. The intersection depth $$d_\text {ch}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mtext>ch</mml:mtext> </mml:msub> </mml:math> quadratically depends on the pulse distance $$x_\text {irr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>x</mml:mi> <mml:mtext>irr</mml:mtext> </mml:msub> </mml:math> and therefore also on the scanning speed $$v_\text {scan}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mtext>scan</mml:mtext> </mml:msub> </mml:math> of the laser. Finally, we present a simple model that reduces the complicated three dimensional, laterally inhomogeneous doping profile to an effective two-dimensional, homogeneously doped layer which varies its thickness with the scanning speed.