Simulation method for semiconductor device

Claim 1

A method for simulating operation of a semiconductor device by analyzing two-dimensional current and light distributions of a semiconductor laser including an active layer, a cladding layer, and a light absorbing layer with a higher refractive index than the cladding layer, the simulation method comprising: obtaining initial values of light distribution and carrier distribution; setting a bias condition; and analyzing current and light distributions, wherein calculation of the initial value of the two-dimensional light distribution includes: calculating a provisional absorption coefficient α m of the light absorbing layer from a refractive index n 1 of the cladding layer, a refractive index n 2 of the light absorbing layer, and a light wavelength λ from ##EQU7## obtaining a solution in which a real part of the propagation constant β of the wave equation has a maximum, the equation being ∇.sup.2 E(x, y)+ {n(x, y)k.sub.0 }.sup.2 -β.sup.2 !E(x, y)=0 where E is the light distribution, k 0 is the wave number 2π/λ of light with a wavelength λ 0 in vacuum, and ∇ is the operator represented by ∇.sup.2 =∂.sup.2 /∂x.sup.2 +∂.sup.2 /∂y.sup.2, n is the complex refractive index depending on material constants and carrier concentration, and β is the complex propagation constant: β=k.sub.0 {n.sub.r +i(α.sub.z /2k.sub.0)}, wherein n r is the real part of a refractive index, i is the complex number, and α 2 is the absorption coefficient in the light traveling direction, using the provisional absorption coefficient α m ; and repeating the calculation to obtain a solution of the wave equation utilizing a sequential approximation, with the solution obtained using the provisional absorption coefficient α m as the initial value, until the value of the absorption coefficient α 2 in the propagation constant β becomes the value in the original light absorbing layer.

Claim 2

A method for simulating operation of a semiconductor device by analyzing two-dimensional current and light distributions of a semiconductor laser including an active layer, a cladding layer, and a light absorbing layer with a higher refractive index than the cladding layer, the simulation method comprising: obtaining initial values of light distribution and carrier distribution; setting a bias condition; and analyzing current and light distributions, wherein calculation of the initial value of the two-dimensional light distribution includes: calculating a provisional absorption coefficient α m of the light absorbing layer from a refractive index n 1 of the cladding layer, a refractive index n 2 of the light absorbing layer, and a light wavelength λ from ##EQU7## obtaining a solution in which a real part of the propagation constant β of the wave equation has a maximum, the equation being ∇.sup.2 E(x, y)+ {n(x, y)k.sub.0 }.sup.2 -β.sup.2 !E(x, y)=0 where E is the light distribution, k 0 is the wave number 2π/λ of light with a wavelength λ 0 in vacuum, and ∇ is the operator represented by ∇.sup.2 =∂.sup.2 /∂x.sup.2 +∂.sup.2 /∂y.sup.2, n is the complex refractive index depending on material constants and carrier concentration, and β is the complex propagation constant: β=k.sub.0 {n.sub.r +i(α.sub.z /2k.sub.0)}, wherein n r is the real part of a refractive index, i is the complex number, and α 2 is the absorption coefficient in the light traveling direction, using the provisional absorption coefficient α m ; and repeating the calculation to obtain a solution of the wave equation utilizing a sequential approximation, with the solution obtained using the provisional absorption coefficient α m as the initial value, until the value of the absorption coefficient α 2 in the propagation constant β becomes the value in the original light absorbing layer.

Claim 4

A method for simulating operation of a semiconductor device by analyzing two-dimensional current and light distributions of a semiconductor device comprising a light waveguide including a core layer, and a cladding layer with a higher refractive index than the core layer, the simulation method comprising: obtaining initial values of light distribution and carrier distribution; setting a bias condition; and analyzing current and light distributions, wherein calculation of the initial value of the two-dimensional light distribution includes: calculating a provisional absorption coefficient α m of the cladding layer from a refractive index n 1 of the core layer, the refractive index n 2 of the cladding layer, and a light wavelength λ from ##EQU8## obtaining a solution in which a real part of the propagation constant β of the wave equation has a maximum, the equation being ∇.sup.2 E(x, y)+ {n(x, y)k.sub.0 }.sup.2 -β.sup.2 !E(x, y)=0 where E is the light distribution, k 0 is the wave number 2π/λ of light with a wavelength λ in vacuum and ∇ is the operator represented by ∇.sup.2 =∂.sup.2 /∂x.sup.2 +∂.sup.2 /∂y.sup.2, n is the complex refractive index depending on material constants and carrier concentration, and β is the complex propagation constant: β=k.sub.0 {n.sub.r +i(α.sub.z /2k.sub.0)}, wherein n r is the real part of a refractive index, i is the complex number, and α z is the absorption coefficient in the light traveling direction, using the provisional absorption coefficient α m ; and repeating the calculation to obtain a solution of the wave equation utilizing a sequential approximation with the solution obtained using the provisional absorption coefficient α m as the initial value, until the value of the absorption coefficient α z in the propagation constant β becomes the value in the original cladding layer.

Claim 5

A method for simulating operation of a semiconductor device by analyzing two-dimensional current and light distributions of a semiconductor device comprising a light waveguide including a core layer, and a cladding layer with a higher refractive index than the core layer, the simulation method comprising: obtaining initial values of light distribution and carrier distribution; setting a bias condition; and analyzing current and light distributions, wherein calculation of the initial value of the two-dimensional light distribution includes: calculating a provisional absorption coefficient α m of the cladding layer from a refractive index n 1 of the core layer, the refractive index n 2 of the cladding layer, and a light wavelength λ from ##EQU8## obtaining a solution in which a real part of the propagation constant β of the wave equation has a maximum, the equation being ∇.sup.2 E(x, y)+ {n(x, y)k.sub.0 }.sup.2 -β.sup.2 !E(x, y)=0 where E is the light distribution, k 0 is the wave number 2π/λ of light with a wavelength λ in vacuum and ∇ is the operator represented by ∇.sup.2 =∂.sup.2 /∂x.sup.2 +∂.sup.2 /∂y.sup.2, n is the complex refractive index depending on material constants and carrier concentration, and β is the complex propagation constant: β=k.sub.0 {n.sub.r +i(α.sub.z /2k.sub.0)}, wherein n r is the real part of a refractive index, i is the complex number, and α z is the absorption coefficient in the light traveling direction, using the provisional absorption coefficient α m ; and repeating the calculation to obtain a solution of the wave equation utilizing a sequential approximation with the solution obtained using the provisional absorption coefficient α m as the initial value, until the value of the absorption coefficient α z in the propagation constant β becomes the value in the original cladding layer.