1 Introduction 2 The Haynes-Shockley Experiment

By monitoring the absorption coefficient as a function of wavelength one can not only determine the
value of the band gap energy, but also whether or not the material is a direct, indirect or amorphous
semiconductor.
3.2 A note on the equipment...
Of particular importance in this experiment is the determination of the band gap of some specific
solids. The spectrophotometer used in this prac has a wavelength range between 190 nm and 900 nm.
Germanium has its absorption edge outside this range, so its band gap cannot be investigated with
this instrument. The same is true of other important materials like silicon and diamond.
(c) What spectrophotometer range would be required to enable the band gap of these materials to
be analysed? You may need to consult your references to answer this question...
Instead, in this prac we will use ZnSe, single crystal MgO and soda-lime glass, which have their absorption
edges in the visible-UV part of the spectrum (i.e. the part covered by our spectrophotometer).
You will also find a range of other materials available (e.g. quartz, sapphire (crystalline Al 2 O 3 ) and
glassy (i.e. diamond-like) carbon).
Note: Details of the optical path of the spectrophotometer and its operation are described in the
appendices.
3.3 Determination of Absorption Coefficient and Band Gap - Background
The absorption coefficient, α, can be determined from a simple transmission experiment. The measurement
will turn out to be very simple, but we’ll consider the background in some detail.
Consider the case where we have two different samples of the same material but of differing thicknesses,
d 1 and d 2 . Then, from equation (36) above, the ratio of the transmission coefficients for each sample
will be
T 1
T 2
= e −α(d 1−d 2 )
(41)
where, from equation (29), T 1 = I 1
I 0
, T 2 = I 2
I 0
, and I 1 and I 2 are the intensities transmitted through
sample 1 and sample 2 respectively. By placing sample 1 in the reference cell and sample 2 in the
sample cell, one can measure the absorbance
( ) I1
A = log . (42)
I 2
However, the reference and sample beams are of different intensity, so the spectrophotometer reading
is
( ) T1 I 01
A = log
T 2 I 02
(43)
where I 01 and I 02 are the intensities of the beams incident on samples 1 and 2 respectively. To find
one needs to take the spectrophotometer reading without the samples, which is
I 01
I 02
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