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rbert15
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I need to calculate the refractive index of a semiconductor material over a wavelength range (1×10-5m - 1×10-9m) and with different values of electron and hole carrier concentrations (i.e. n/p doped).
I found this equation that relates those parameters:
n+ik = √ [ (εm - [(e2/ω2)*((n0/m*e)+(p0/m*h))]) / ε0 ]
The values ε0 and e are known constants. For each semiconductor material I'm interested in, the values of electron and hole concentrations (n0 and p0) and the effective electron and hole masses (m*e and m*h) have been found, as well as the value of the dielectric constant/relative permittivity (εm), all via literature (http://www.ioffe.ru/SVA/NSM/)
The problem is that whilst the equation is giving me results, the value of the refractive index (n+k) is not varying as much as it should when the wavelength is changed. For example for InAs it should change from about 4 to 1, whereas it is staying almost constant at 3.5 regardless of wavelength.
The frequency (ω) in the equation is calculated by simply ω=c/λ and this value (and the subsequent term) is so small compared to εm and ε0 that it doesn't have much influence. Does εm have a wavelength/frequency dependence I'm not accounting for? I can't see any other variables that would have λ dependence to increase λ effect on n calculation.
I found this equation that relates those parameters:
n+ik = √ [ (εm - [(e2/ω2)*((n0/m*e)+(p0/m*h))]) / ε0 ]
The values ε0 and e are known constants. For each semiconductor material I'm interested in, the values of electron and hole concentrations (n0 and p0) and the effective electron and hole masses (m*e and m*h) have been found, as well as the value of the dielectric constant/relative permittivity (εm), all via literature (http://www.ioffe.ru/SVA/NSM/)
The problem is that whilst the equation is giving me results, the value of the refractive index (n+k) is not varying as much as it should when the wavelength is changed. For example for InAs it should change from about 4 to 1, whereas it is staying almost constant at 3.5 regardless of wavelength.
The frequency (ω) in the equation is calculated by simply ω=c/λ and this value (and the subsequent term) is so small compared to εm and ε0 that it doesn't have much influence. Does εm have a wavelength/frequency dependence I'm not accounting for? I can't see any other variables that would have λ dependence to increase λ effect on n calculation.
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