In this paper, we present a new ultra fast detector called Low Gain Avalanche Detector (LGAD) with low internal gain. The LGAD is fabricated with conventional APD technology with a modified doping profile, in the multiplication region, which affects the device performance such as: breakdown, multiplication gain and noise factor. For this reason, a numerical method based on Newton-Raphson calculation is proposed to estimate the electrostatic potential and electric field models of low gain avalanche detectors (LGADs) in order to investigate their performances. These models have been validated by their agreement with TCAD numerical simulation results. The effect of Boron doping profile, with different doses in the multiplication region, on the LGAD electrical performance is studied for various device structures in order to extend the device capability to its limit. In addition, LGAD devices are simulated for different temperature considering the effect of the temperature on the multiplication gain.

In this paper, we present a new ultra fast detector called Low Gain Avalanche Detector (LGAD) with low internal gain. The LGAD is fabricated with conventional APD technology with a modified doping profile, in the multiplication region, which affects the device performance such as: breakdown, multiplication gain and noise factor. For this reason, a numerical method based on Newton-Raphson calculation is proposed to estimate the electrostatic potential and electric field models of low gain avalanche detectors (LGADs) in order to investigate their performances. These models have been validated by their agreement with TCAD numerical simulation results. The effect of Boron doping profile, with different doses in the multiplication region, on the LGAD electrical performance is studied for various device structures in order to extend the device capability to its limit. In addition, LGAD devices are simulated for different temperature considering the effect of the temperature on the multiplication gain.

In this paper, we present a new ultra fast detector called Low Gain Avalanche Detector (LGAD) with low internal gain. The LGAD is fabricated with conventional APD technology with a modified doping profile, in the multiplication region, which affects the device performance such as: breakdown, multiplication gain and noise factor. For this reason, a numerical method based on Newton-Raphson calculation is proposed to estimate the electrostatic potential and electric field models of low gain avalanche detectors (LGADs) in order to investigate their performances. These models have been validated by their agreement with TCAD numerical simulation results. The effect of Boron doping profile, with different doses in the multiplication region, on the LGAD electrical performance is studied for various device structures in order to extend the device capability to its limit. In addition, LGAD devices are simulated for different temperature considering the effect of the temperature on the multiplication gain.

In this paper, we present a new ultra fast detector called Low Gain Avalanche Detector (LGAD) with low internal gain. The LGAD is fabricated with conventional APD technology with a modified doping profile, in the multiplication region, which affects the device performance such as: breakdown, multiplication gain and noise factor. For this reason, a numerical method based on Newton-Raphson calculation is proposed to estimate the electrostatic potential and electric field models of low gain avalanche detectors (LGADs) in order to investigate their performances. These models have been validated by their agreement with TCAD numerical simulation results. The effect of Boron doping profile, with different doses in the multiplication region, on the LGAD electrical performance is studied for various device structures in order to extend the device capability to its limit. In addition, LGAD devices are simulated for different temperature considering the effect of the temperature on the multiplication gain.

In this paper, we present a new ultra fast detector called Low Gain Avalanche Detector (LGAD) with low internal gain. The LGAD is fabricated with conventional APD technology with a modified doping profile, in the multiplication region, which affects the device performance such as: breakdown, multiplication gain and noise factor. For this reason, a numerical method based on Newton-Raphson calculation is proposed to estimate the electrostatic potential and electric field models of low gain avalanche detectors (LGADs) in order to investigate their performances. These models have been validated by their agreement with TCAD numerical simulation results. The effect of Boron doping profile, with different doses in the multiplication region, on the LGAD electrical performance is studied for various device structures in order to extend the device capability to its limit. In addition, LGAD devices are simulated for different temperature considering the effect of the temperature on the multiplication gain.

Let E,F,G,D be infinite complex Banach spaces and B(F,E) the Banach space of all bounded linear operators from F into E. Consider A1,A2∈B(F,E), B1,B2∈B(D,G)B1,B2∈B(D,G). Let MA1,B1:X→A1XB1 be the multiplication operator on B(G,F) induced by A1,B1. In particular, LA1=MA1,I and RB1=MI,B1, where I is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on B(G,F)B(G,F) is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations MA1,B1(X)=C1 and MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation MA,B(X)=C. As a consequence, we obtain well-known results of Dajic´ and Koliha.

Let E,F,G,D be infinite complex Banach spaces and B(F,E) the Banach space of all bounded linear operators from F into E. Consider A1,A2∈B(F,E), B1,B2∈B(D,G)B1,B2∈B(D,G). Let MA1,B1:X→A1XB1 be the multiplication operator on B(G,F) induced by A1,B1. In particular, LA1=MA1,I and RB1=MI,B1, where I is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on B(G,F)B(G,F) is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations MA1,B1(X)=C1 and MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation MA,B(X)=C. As a consequence, we obtain well-known results of Dajic´ and Koliha.