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The Absorption Coefficient
Appendix A
The Absorption Coefficient A few of the terms used in photovoltaics can have more than one definition. One such situation, and a very important one, is the definition of “absorption coefficient”; one definition uses the natural log, while another uses log to the base 10. If illumination of wavelength and intensity I() (photons per cm2 per second) impinges on a material of thickness d, some of the light is reflected R() and some T() emerges from the other side of the material at d. The fluxes I, R, and T are related by the simple expression
I( ) T( ) R( ) A( )
(A.1)
where A() is the absorption taking place for this wavelength. When the Beer-Lambert law is applicable,1 then the relationship between T and I-R can be expressed as
T( ) [I( ) R( )][exp ( ( )d)]
(A.2)
Where () is the material’s absorption coefficient at the wavelength . This means that
A( ) [I R][1 exp( ( )d]
© 2010 Elsevier Inc. All rights reserved. Doi: 10.1016/B978-0-12-374774-7.00009-1
(A.3)
312 Appendix A
Going back to Eq. A.2, we see that it can be rearranged to read
T ( ) [exp( ( )d)] I( ) R( )
(A.4)
This is a convenient form since minus the natural logarithm (ln) of Eq. A.4 is defined as the absorbance Aabs for the wavelength ; i.e.,
T ( ) Aabs ( ) ln I( ) R( )
(A.5)
As can be seen from Eqs. A.4 and A.5, this last expression is very useful, since the absorption � coefficient () at wavelength can be extracted from it by noting
( )
Aabs ( ) d
(A.6)
The definition of absorption coefficient given by Eq. A.6 is used throughout this text. The complication that arises with the absorption coefficient is that a different definition for absorbance can be found in the literature. This other definition is given by
T ( ) Aabs ( ) log10 I( ) R( )
(A.7)
Equation A.7 is then used to determine () through Eq. A.6. The impact of this is that the absorption coefficient deduced from T, R, and I using Eq. A.7 must be multiplied by ln 10 to convert that data to the absorption coefficient deduced from Eq. A.5 and used in Eq. A.3. Obviously, when looking at absorption coefficient data, one must be careful in determining which () is being presented.
Reference 1. J.D.J. Ingle, S.R. Crouch, Spectrochemical Analysis, Prentice �Hall, New Jersey, 1988.
The Absorption Coefficient A few of the terms used in photovoltaics can have more than one definition. One such situation, and a very important one, is the definition of “absorption coefficient”; one definition uses the natural log, while another uses log to the base 10. If illumination of wavelength and intensity I() (photons per cm2 per second) impinges on a material of thickness d, some of the light is reflected R() and some T() emerges from the other side of the material at d. The fluxes I, R, and T are related by the simple expression
I( ) T( ) R( ) A( )
(A.1)
where A() is the absorption taking place for this wavelength. When the Beer-Lambert law is applicable,1 then the relationship between T and I-R can be expressed as
T( ) [I( ) R( )][exp ( ( )d)]
(A.2)
Where () is the material’s absorption coefficient at the wavelength . This means that
A( ) [I R][1 exp( ( )d]
© 2010 Elsevier Inc. All rights reserved. Doi: 10.1016/B978-0-12-374774-7.00009-1
(A.3)
312 Appendix A
Going back to Eq. A.2, we see that it can be rearranged to read
T ( ) [exp( ( )d)] I( ) R( )
(A.4)
This is a convenient form since minus the natural logarithm (ln) of Eq. A.4 is defined as the absorbance Aabs for the wavelength ; i.e.,
T ( ) Aabs ( ) ln I( ) R( )
(A.5)
As can be seen from Eqs. A.4 and A.5, this last expression is very useful, since the absorption � coefficient () at wavelength can be extracted from it by noting
( )
Aabs ( ) d
(A.6)
The definition of absorption coefficient given by Eq. A.6 is used throughout this text. The complication that arises with the absorption coefficient is that a different definition for absorbance can be found in the literature. This other definition is given by
T ( ) Aabs ( ) log10 I( ) R( )
(A.7)
Equation A.7 is then used to determine () through Eq. A.6. The impact of this is that the absorption coefficient deduced from T, R, and I using Eq. A.7 must be multiplied by ln 10 to convert that data to the absorption coefficient deduced from Eq. A.5 and used in Eq. A.3. Obviously, when looking at absorption coefficient data, one must be careful in determining which () is being presented.
Reference 1. J.D.J. Ingle, S.R. Crouch, Spectrochemical Analysis, Prentice �Hall, New Jersey, 1988.