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1 Introduction 2 The Haynes-Shockley Experiment

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1 <strong>Introduction</strong><br />

PART III LABORATORIES – ATOMIC OPTICAL<br />

CHARACTERISATION OF SEMICONDUCTORS<br />

OR ”What this prac is really about”<br />

Imagine a cheery introductory paragraph here!<br />

Things to include - what are minority charge carriers and why are they important? What is it about<br />

things like diffusion etc that make them useful to know? How about band gap energy - notice the<br />

way it relates to optical properties and the fact that being able to understand these makes for better<br />

sunglasses!!<br />

1.1 Some words about third year labs<br />

<strong>The</strong>se notes don’t contain all the information you need - they’re here to define the terms for you, and<br />

to give you an idea of the direction you should be taking. You’ll find that you need to go foraging for<br />

more detailed information in other places - often in the references (Kittel will be your special friend in<br />

this particular lab!), and even more often in the rubble of your demonstrators’ minds. You’re going to<br />

learn a lot while you’re doing that, so don’t waste the effort - share all the work you’re doing with us<br />

in your report! Remember that your report has to be self-contained. It doesn’t have to be beautiful,<br />

but it should be clear and detailed. Perhaps the most important thing to remember is that when you<br />

write your report you’re trying to teach your reader what you did, why you did it, and what you<br />

learned. That way, we get to learn something too! Enjoy!<br />

2 <strong>The</strong> <strong>Haynes</strong>-<strong>Shockley</strong> <strong>Experiment</strong><br />

2.1 <strong>Introduction</strong> and <strong>The</strong>ory<br />

References for this section: ....S. Sze + Serway’s Modern Physics<br />

Minority carriers often play an important role in device operation. <strong>The</strong> dynamics of excess minority<br />

carriers was investigated by J.R. <strong>Haynes</strong> and W. <strong>Shockley</strong> in their experiment (1951) using the creation<br />

of electron-hole pairs in extrinsic semiconductors. <strong>The</strong> basic principles of the experiment, shown<br />

schematically in Figure below, are as follows.<br />

A pulse of minority carriers, for example holes in an n-type bar of semiconductor, is created by a flash<br />

of light incident at some point A near one end of the bar. If the bar has an electric field applied to<br />

it, then the pulse of holes will drift along the bar and eventually reach the contact at point C. <strong>The</strong><br />

presence of these holes will increase the current through the resistance R, and hence the voltage across<br />

it.<br />

If the oscilloscope connected across R is triggered at the instant the flash of light is emitted, then<br />

the time t d take for the pulse of holes to drift from A to C can be measured from the position of the<br />

boltage pulse on the oscilloscope trace. This enables us to calculate the drift velocity of the holes,<br />

which is simply<br />

v d = d t d<br />

(1)<br />

1


where d is the separation of the points A and C. If the electric field is<br />

E = V L<br />

(2)<br />

where L is the length of the bar, then the mobility µ h of the holes will be<br />

µ h = v d<br />

E<br />

(3)<br />

= dL<br />

t d V<br />

(4)<br />

<strong>The</strong> flash of light creates an excess of both minority and majority carriers, n = p (where n is the<br />

number of electrons created, p the number of holes created). However, the relative increase in the<br />

majority carrier concentration is much less than the relative increase in the minority charge carrier<br />

concentration. <strong>The</strong>refore, the arrangement is much more sensitive to minority charge carriers. <strong>The</strong><br />

sign of the minority carriers can be determined by reversingthe polarity V of the battery and observing<br />

the conditions under which the minority carriers propagate towards the contact C.<br />

<strong>The</strong> <strong>Haynes</strong>-<strong>Shockley</strong> experiment also provides information on two other very important processes<br />

that occur in semiconductors, namely diffusion and recombination. <strong>The</strong> pulse on the oscilloscope is<br />

much broader in time than the flash of light that generated the carriers. Furthermore, if the pulse is<br />

monitored as a function of the drift time t d (which can be varied by changing the distance, d), it will<br />

be seen that the pulse becomes broader as the drift time increases (figure<br />

<strong>The</strong> broadening of the pulse is due to diffusion, which is a movement of charge carriers due to the<br />

presence of a concentration gradient. <strong>The</strong> diffusion of charge carriers gives rise to a diffusion current, as<br />

distinct from drift currents that arise from teh presence of a voltage gradient. We can write equations<br />

for the electron diffusion current density, J e , and the hole diffusion current density, J h , respectively,<br />

J e = eD e<br />

dn<br />

dx<br />

(5)<br />

and<br />

J h = −eD h<br />

dn<br />

dx . (6)<br />

Here, D e is the electron diffusion coefficient and D h is the hole diffusion coefficient. In contrast, the<br />

equations for the drift current density of electrons and holes respectively are<br />

and<br />

J e = env d (7)<br />

J h = −epv d . (8)<br />

Beware of confusion between these current densities! Make sure you’re explicit about which one you’re<br />

referring to.<br />

<strong>The</strong> diffusion coefficients are related to their associated carrier mobilities according to the Einstein<br />

relation:<br />

2


D e = kT e µ e (9)<br />

and<br />

D h = kT e µ h. (10)<br />

Thus, the pulse broadening is simply a consequence of the minority charge diffusing outwards from<br />

a region of high concentration at the centre of the pulse of the excess minority charge to regions of<br />

lower charge concentration.<br />

<strong>The</strong> area under the trace is proportional to the charge transferred through the contact point C. If the<br />

only processes occurring where due to diffusion effects, we would expect that while the trace height<br />

decreases with distance from the contact point, its width should increase so that its total area remains<br />

constant. However, there is a second process occurring - recombination. Due to the recombination<br />

of holes and electrons, the number of minority charge carriers is decreased. This effect shows itself<br />

as a decrese in the total area under the trace. Thus, the rate of recombination can be measured by<br />

monitoring the variation of the area under the trace as it propagates from the laser flash point to the<br />

contact point (C).<br />

2.2 Summary of <strong>Experiment</strong>al Work<br />

(1) Perform the <strong>Haynes</strong>-<strong>Shockley</strong> experiment on the slightly doped germanium sample provided.<br />

You have to<br />

(a) determine the type of minority carriers (electrons or holes, generated by the laser pulse<br />

(b) characterise the semiconductor by determining the drift velocity, mobility, diffusion and<br />

recombination rate of the minority charge carriers.<br />

(2) Watch the video tape on the <strong>Haynes</strong>-<strong>Shockley</strong> experiment and go through its description in J.R.<br />

<strong>Haynes</strong> and W. <strong>Shockley</strong>, Phys. Rev. 81, 85 (1951).<br />

2.3 Procedure<br />

<strong>The</strong> experimental circuit diagram is presented in figure <strong>The</strong> germanium sample is of the following<br />

dimensions:<br />

Length<br />

Width<br />

Thickness<br />

30.0 mm<br />

3.0 mm<br />

0.3 mm<br />

<strong>The</strong> light flash is produced by the diode laser which generates light pulses with frequency varied in<br />

the range between 100kHz and 2kHz. In this experiment the collector point C is fixed. <strong>The</strong> distance<br />

d between the point C and the point A of the minority charge generation is varied by moving the<br />

laser beam along the sample length. <strong>The</strong> laser is mounted on a moving platform supplied with a<br />

micrometer. <strong>The</strong> laser power supply is connected to an oscilloscope to provide triggering signals,<br />

so the oscilloscope beam starts its sweep at the instant the laser light is flashed. <strong>The</strong> 27 V batterh<br />

produces an electric field which moves the charges in the sample. <strong>The</strong> oscilloscope needs to be set to<br />

3


pick up the AC component corresponding to the minority carriers’ pulse. <strong>The</strong> push button is to be<br />

switched on for a short period fo time during the taking of measurements to prevent overheating of<br />

the semiconductor sample due to the DC component.<br />

a. Change the polarity of the 27 V battery to determine the type of minority charge carriers in the<br />

sample under investigation.<br />

b. Make sure that the trace height is proportional to the laser beam intensity which means that<br />

the oscilloscope vertical deflection is proportional to teh number of the minority charge carriers<br />

passing under the detector. This is done by simultaneously reducing the light intensity using the<br />

film screen supplied and increasing the gain of the oscilloscope by the same factor. <strong>The</strong> pulse<br />

obtained should match exactly the original pulse.<br />

c. Record the distance d between the points A and C, the corresponding values of the drift time t d ,<br />

the pulse height and its full width at half maximum. Conduct this analysis of the trace profile<br />

every 0.5 mm from the collection point C. <strong>The</strong> micrometer range is ∼ 10 mm, so you will be able<br />

to get 19 or 20 experimental points.<br />

d. Plot the graph of t d versus d and determine the drift velocity v d from the graph.<br />

e. Calculate the minority charge mobility, µ h .<br />

<strong>The</strong> diffusion current for charge carriers (electrons or holes) is related to the concentration gradient<br />

according the the diffusion equation<br />

J = eD δn<br />

δx<br />

(11)<br />

Note that this is just a restatement of equations (5) and (6).<br />

<strong>The</strong> diffusion current can also be written<br />

J = env diff (12)<br />

where v diff is the diffusion velocity with which the pulse is broadened with time. From the above<br />

relations we can find an expression for the diffusion coefficient:<br />

D = nv diff<br />

δn<br />

δx<br />

<strong>The</strong> diffusion velocity is defined as the pulse broadening per unit time:<br />

. (13)<br />

v d iff = x f − x i<br />

t f − t i<br />

(14)<br />

where x f and x i are the half-widths of the pulse in meters at teh final and intial instants t f and<br />

t i respectively. <strong>The</strong> oscilloscope unfolds the pulse along the time axis and hence it measures the<br />

half-width of the pulse t p in seconds. Since the pulse passes the collection point C with the drift<br />

velocity v d one can see that the width of the pulse x is related to its time width t p as monitored by<br />

the oscilloscope at the point C according to the relation x = v d t p . For two successive moments t f and<br />

t i we have respectively x f = v d t pf and x i = v d t pi , so<br />

4


x f − x i = v d (t pf − t pi ) (15)<br />

= v d ∆t p (16)<br />

where ∆t p = t pf − t pi is the change in the time half-width between the successive travel times t i and<br />

t f . <strong>The</strong>n<br />

v diff = x f − x i<br />

t f − t i<br />

= v d∆t b<br />

∆t<br />

(17)<br />

where ∆t = t f − t i .<br />

Assume that the charge concentration is an approximately linear function of the distance from the<br />

central part of the pulse. <strong>The</strong>n<br />

δn<br />

δx ≃ n x<br />

(18)<br />

where n is the mean concentration and x = v d t p is the half-width. Combining the equations (13) and<br />

(17) yields<br />

D = (v d ) 2 t p∆t p<br />

∆t . (19)<br />

In this equation ∆t p is the change in the time half-width during the time interval ∆t, whereas t p is the<br />

average time half-width of teh pulse within the time interval ∆t. That is, t p = ¯t p = (t pf +t pi )<br />

2<br />

. <strong>The</strong>n<br />

te quantity t p ∆t p = (t pf +t pi )(t pf −t pi )<br />

2<br />

= ((t pf ) 2 −(t pi ) 2 )<br />

2<br />

= ∆(tp)2<br />

2<br />

, so that the diffusion coefficient can be<br />

presented in the form<br />

D = (v d ) 2 ∆(t p) 2<br />

2∆t<br />

(20)<br />

You should note that this expression is obtained by assuming that the concentration gradient is<br />

constant. That is, the recombination rate is not taken into account. In general, we have to introduce<br />

the a constant, a, which takes these effects into account:<br />

D = a(v d ) 2 ∆(t p) 2<br />

∆t<br />

(21)<br />

where for our sample and arrangement the constant a = 0.242.<br />

f. Plot the graph of the squares of the half-widths of the pulses observed on the oscilloscope, (t p ) 2<br />

versus their corresponding delay times t d , and use the slope of the resulting straight line to<br />

calculate the diffusion constant.<br />

g. Compare your result with that given by the Einstein relation (equations (9) and (10)).<br />

<strong>The</strong> pulse area<br />

5


A = Ht b , (22)<br />

where H is the pulse height. It is possible to use this quantity to determine the lifetime of the minory<br />

charge carriers, τ.<br />

Assume that when excess carriers are present, the rate of recombination is proportional to the excess<br />

carrier concentration. That is,<br />

− ∂n<br />

∂t<br />

∝ n. (23)<br />

<strong>The</strong> minus sign indiates that, as t increases, the excess concentration decreases. We can integrate the<br />

above equation to give<br />

n(t) = n 0 e ( −t<br />

τ<br />

) . (24)<br />

Here, τ is the time required for the number of excess carriers to drop to 1/e times their original value.<br />

We call this characteristic time the lifetime of the minority charge carriers.<br />

<strong>The</strong> pulse area is proportional to the excess charge concentration, so it follows the same form as<br />

equation (24) above:<br />

Hence,<br />

A(t) = A 0 e ( −t<br />

τ<br />

) . (25)<br />

ln A(t) = ln A 0 − t τ<br />

ln e (26)<br />

= ln A 0 − 1 τ<br />

.t (27)<br />

h. Plot the graph of the logarithm of the pulse area A versus the drift time t d .<br />

i. From the graph, find the lifetime of the minority charge carriers, τ.<br />

3 Optical Characterisation and Band Gap of Materials<br />

References - the optical properties handout and kittel...<br />

So far we have used the electrical properties of semiconductors to help characterise them, but the<br />

electronic structure of materials can also be investigated by considering their optical properties. Light<br />

incident on a sample may be reflected, absorbed and/or transmitted. Each of these processes is<br />

governed by the electronic structure of the material. For example, the dominant absorption mechanism<br />

in semiconductors and insulators is usually the excitation of an electron from the valence to the<br />

conduction band across the forbidden band gap.<br />

(a) Before proceeding, make sure that you understand the following terms:<br />

(i) band gap<br />

6


(ii) valence band<br />

(iii) conduction band<br />

(iv) direct transition<br />

(v) indirect transition<br />

(vi) crystalline material<br />

(vii) amorphous material<br />

You should provide an explanation of each of them in your log book.<br />

(b) Based on your results from section (2), discuss the mechanism of charge recomination in direct<br />

and indirect band semiconductors.<br />

3.1 Background<br />

<strong>The</strong> complete optical characterisation of a solid both in bulk and thin film form involves a knowledge<br />

of its complex refractive index:<br />

N ∗ = n − jk (28)<br />

where j = √ −1. Here, n is the real part of the refractive index. This should already be a familiar<br />

concept. It is important in the design of optical components as it is this quantity which primarily<br />

determines the refracting power of lenses etc. It is also important when designing anti-reflection<br />

coatings, optical fibres and modern electro-optical devices.<br />

<strong>The</strong> imaginary or loss part of the refractive index, k, is crucial in the determination of the absorption<br />

properties of materials. In practice, this quantity when measured as a function of frequency can give<br />

a direct measure of the band gap of solids.<br />

As mentioned above, when light strikes a sample it may be absorbed, reflected or transmitted (see<br />

figure (We define a transmission coefficient, given by<br />

and a reflection coefficient,<br />

T = I T<br />

I 0<br />

, (29)<br />

R = I R<br />

I 0<br />

. (30)<br />

Here, I 0 is the intensity of the incident lifht, I T is the intensity of the transmitted light and I R is<br />

the intensity of the reflected light. Optical absorption is usually defined in terms of an absorption<br />

coefficient, α, such that<br />

I T = (I 0 − I R ) e −αd . (31)<br />

Here (I 0 − I R ) is the intensity of the light that actually propagates into the crystal (with second order<br />

corrections for reflections from the back face and from repetitive crossings of the crystal as a result),<br />

and d is the thickness of the sample.<br />

<strong>The</strong> absorption coefficient is in turn related to the imaginary part of N ∗ by<br />

7


α = 4πk<br />

λ , (32)<br />

where λ is the wavelength of the light used.<br />

For normal incidence of light on the sample, the reflection coefficient, R, is related to the refractive<br />

index by<br />

R = (n − 1)2 + k 2<br />

(n + 1) 2 + k 2 (33)<br />

and if the sample thickness is many times the wavelength of the light (i.e. if d ≫ λ), the transmission<br />

coefficient is<br />

T =<br />

(<br />

1 − R 2) e −αd (<br />

1 + k2<br />

n 2 )<br />

. (34)<br />

From these equations it is clear that a measurement of R and T enables the determination of n and k,<br />

and if R and T are measured as a function of wavelength then a complete optical characterisation of<br />

the material is possible. When k 2 ≪ n 2 , which is usually the case for many materials in the wavelength<br />

region of high transparency, equations (33) and (34) aquire a simplified form:<br />

and<br />

T =<br />

R =<br />

(n − 1)2<br />

(n + 1) 2 (35)<br />

(<br />

1 − R 2) e −αd . (36)<br />

Of particular importance to us in this final equation is the absorption coefficient, α. It depends directly<br />

on the electronic band structure of the material involved. For a direct band gap semiconductor,<br />

α = B 1 (hν − E g ) 1/2 (37)<br />

where E g is the band gap energy, whereas for an indirect band gap semiconductor<br />

α = B 2 (hν − E g ± E p ) 2 (38)<br />

where E p is the phonon energy associated with the indirect transition. When E p ≪ E g , then equation<br />

(38) reduces to<br />

α = B 3 (hν − E g ) 2 . (39)<br />

For many amorphous semiconductors, the dependence of α on E follows the relationship<br />

αhν = B 4 (hν − E g ) 2 . (40)<br />

8


By monitoring the absorption coefficient as a function of wavelength one can not only determine the<br />

value of the band gap energy, but also whether or not the material is a direct, indirect or amorphous<br />

semiconductor.<br />

3.2 A note on the equipment...<br />

Of particular importance in this experiment is the determination of the band gap of some specific<br />

solids. <strong>The</strong> spectrophotometer used in this prac has a wavelength range between 190 nm and 900 nm.<br />

Germanium has its absorption edge outside this range, so its band gap cannot be investigated with<br />

this instrument. <strong>The</strong> same is true of other important materials like silicon and diamond.<br />

(c) What spectrophotometer range would be required to enable the band gap of these materials to<br />

be analysed? You may need to consult your references to answer this question...<br />

Instead, in this prac we will use ZnSe, single crystal MgO and soda-lime glass, which have their absorption<br />

edges in the visible-UV part of the spectrum (i.e. the part covered by our spectrophotometer).<br />

You will also find a range of other materials available (e.g. quartz, sapphire (crystalline Al 2 O 3 ) and<br />

glassy (i.e. diamond-like) carbon).<br />

Note: Details of the optical path of the spectrophotometer and its operation are described in the<br />

appendices.<br />

3.3 Determination of Absorption Coefficient and Band Gap - Background<br />

<strong>The</strong> absorption coefficient, α, can be determined from a simple transmission experiment. <strong>The</strong> measurement<br />

will turn out to be very simple, but we’ll consider the background in some detail.<br />

Consider the case where we have two different samples of the same material but of differing thicknesses,<br />

d 1 and d 2 . <strong>The</strong>n, from equation (36) above, the ratio of the transmission coefficients for each sample<br />

will be<br />

T 1<br />

T 2<br />

= e −α(d 1−d 2 )<br />

(41)<br />

where, from equation (29), T 1 = I 1<br />

I 0<br />

, T 2 = I 2<br />

I 0<br />

, and I 1 and I 2 are the intensities transmitted through<br />

sample 1 and sample 2 respectively. By placing sample 1 in the reference cell and sample 2 in the<br />

sample cell, one can measure the absorbance<br />

( ) I1<br />

A = log . (42)<br />

I 2<br />

However, the reference and sample beams are of different intensity, so the spectrophotometer reading<br />

is<br />

( ) T1 I 01<br />

A = log<br />

T 2 I 02<br />

(43)<br />

where I 01 and I 02 are the intensities of the beams incident on samples 1 and 2 respectively. To find<br />

one needs to take the spectrophotometer reading without the samples, which is<br />

I 01<br />

I 02<br />

9


( ) I01<br />

A 0 = log . (44)<br />

I 02<br />

<strong>The</strong>n, from expressions (41) and (43),<br />

α = 2.3 (A − A 0)<br />

(d 2 − d 1 ) . (45)<br />

- really need the schematic/principles of operation, because I think the taking of the baseline measurement<br />

involves the calculation and removal of I 01<br />

I 02<br />

in software, so that the quoted A is the (A − A 0 )<br />

from the original notes... Have just transcribed them for now, until I can get hold of a proper manual<br />

for the machine.<br />

- don’t forget to talk about what an absorption edge actually *is*!!<br />

theory theory theory... all the stuff about the differnet thicknesses and linking A to alpha<br />

- yes, you do have to do different thicknesses because you have to be able to cancel off<br />

the reflection term from the simplified T equation!<br />

3.4 Taking Spectra<br />

For this experiment you will be using the Varian 2215 UV-Vis Spectrophotometer. <strong>The</strong>re are two main<br />

modes - an automatic mode, which will allow you to take spectra relatively quickly, and a manual<br />

mode, for when you want to take high resolution measurements.<br />

You will need to turn on the machine 5 to 10 minutes before you begin taking spectra. <strong>The</strong> switch is on<br />

the front left-hand side, next to the chart recorder. <strong>The</strong> spectrophotometer will run through a series<br />

of self-tests before the default screen (showing the instrument settings and the current absorbance<br />

measurement) appears.<br />

3.4.1 Buttons Beneath the Screen!<br />

Menus are accessed via a series of buttons (eg Instrument Settings). Once you’re in a menu, you can<br />

change particular settings by pressing the number for that item on the menu (eg on the Instrument<br />

Settings screen, press 4 to change the chart resolution) and then pressing Enter.<br />

Most of the menus won’t concern you, but you should find the following basic controls (starting top<br />

left of console):<br />

1. RAPID: ABSORBANCE vs WAVELENGTH<br />

2. ADVANCED: INSTRUMENT SETTINGS<br />

3. ENTER (bottom left of the numbers)<br />

4. START, STOP (under the numbers)<br />

5. BASELINE SETUP<br />

6. GO TO WAVELENGTH<br />

7. AUTOMATIC BALANCE<br />

10


3.4.2 Loading Samples<br />

On the right of the machine there are two lids which you can remove to give you access to the sample<br />

chamber. Removing either of these lids results in a shutter automatically blocking the beam, but you<br />

should make sure you know where the beam path travels through the chamber. You will find a sample<br />

holder which contains 6 “turrets” (ie spots into which samples can be placed) - the holder can be<br />

rotated using the knob on the outside of the machine to bring particular samples into the beam path<br />

without opening the chamber, but this should only be done with care. Your demonstrator will show<br />

you how to mount your samples securely.<br />

3.4.3 Low Resolution Spectra<br />

In the first instance (see section 3.5 below) you will be interested in taking spectra over a wide range<br />

of wavelengths in order to ascertain the position of the absorption edge for your particular sample.<br />

You can do this by using the “RAPID” mode.<br />

(i) Press “ABSORBANCE vs WAVELENGTH”<br />

(ii) Enter upper wavelength (e.g. 890 nm)<br />

(iii) Enter lower wavelength (e.g. 210 nm). Note that this machine claims to be able to scan down<br />

to 180 nm, but in fact it will be out of range (and will start complaining!) once you get below<br />

200 nm.<br />

(iv) At this point the machine should ask you to take a “baseline” measurement - this is a measurement<br />

of the absorbance of a standard (in your case, the absorbance of air) over the specified<br />

wavelength range. <strong>The</strong> machine automatically subtracts this background from the measurements<br />

of your sample’s absorbance. It should just be a case of pressing “BASELINE SETUP”, and<br />

then “START”.<br />

(v) Rotate the sample holder (it may be safest to do this manually...) so that your sample is in the<br />

beam path. Ideally at this point you should zero your detector. <strong>The</strong> spectrophotometer should<br />

be at the high wavelength end (i.e. far from the absorption edge of the sample) where you would<br />

not expect it to absorb. Press “AUTOMATIC BALANCE”. Note that a couple of the samples<br />

are rather opaque, in which case the spectrophotometer will probably complain when you try to<br />

do this part of the process. Don’t worry too much. All that will happen is that there will be a<br />

constant offset introduced into your data, which shouldn’t ultimately affect your analysis.<br />

(vi) <strong>The</strong> spectrophotometer should now be showing the first screen (i.e. the screen from step (i)<br />

above) again - press “ABSORBANCE vs WAVELENGTH” if it isn’t. Now, press “START” to<br />

begin recording.<br />

3.4.4 High Resolution Spectra<br />

<strong>The</strong> low resolution scan’s main purpose is to allow you to identify the wavelength range over which<br />

your samples absorb strongly. Once you have done so, you will need to take data at higher resolution<br />

in order to characterise the absorption process. Although for this section it is possible to simply record<br />

a series of charts and read the data from them, you will get more precise data if you digitise your<br />

results manually - that is, if you do the scan slowly, stopping and starting it and writing down the<br />

absorbance at a series of (well known) wavelengths.<br />

11


1. Press “INTRUMENT SETTINGS” and adjust the scan rate and chart resolution as required.<br />

You may also wish to change to pen range, depending on your sample.<br />

2. Press “GO TO WAVELENGTH”, and enter the upper wavelength of your chosen range.<br />

3. Remove the sample from the beam path.<br />

4. Press “BASELINE SETUP” and “START”. <strong>The</strong> spectrophotometer will keep scanning until<br />

you press “STOP”, so keep an eye on the wavelength and stop the baseline measurement at (or<br />

slightly below) the lower end of your chosen range.<br />

5. Place the sample in the beam path. Press “GO TO WAVELENGTH” to go to a wavelength far<br />

from the absorption edge, and then “AUTOMATIC BALANCE” to zero the detector.<br />

6. Press “GO TO WAVELENGTH” and enter the upper wavelength of your chosen range.<br />

7. Press “START” to begin the scan. You can press “STOP” periodically to allow you to take<br />

down the value of the absorbance for a series of wavelengths. Press “STOP” to finish the scan<br />

once you reach the end of your chosen wavelength range.<br />

3.5 Determination of Absorption Coefficient and Band Gap - Procedure<br />

Before you begin, you should be aware of the fact that you will be taking lots of scans in the course of<br />

this experiment. You will end up with a long roll of paper with lots and lots of curvy lines on it. You<br />

should take care to label these carefully. Do this by actually writing things onto the chart paper<br />

next to the scan. You will need to take note of things like<br />

- what sample this spectrum is for<br />

- what the starting wavelength was<br />

- what the final wavelength was (It’s a good idea to write these near the start and end of the scan<br />

itself (as if on the scan’s independent axis), so that you know which direction the scan was made<br />

in.)<br />

- what the chart resolution was<br />

- the cause of any discontinuities in the spectrum (e.g. changes in lamp/filter or pen range).<br />

Provided you know the resolution, you should be able to read absorbances straight off the charts, but<br />

it is a good idea to write down a few pairs of (wavelength, absorbance) data so that you don’t have<br />

to rely on whether the chart paper’s zero exactly matches the detector’s zero. You should be able to<br />

press “STOP” and “START” during the scan, so taking this sort of backup data should be easy.<br />

(d) Measure α as a function of λ for MgO, ZnSe, glass, quartz and sapphire crystals using a 20 nm/cm<br />

scale. Use the instructions in section 3.4.3 above for this low resolution scan.<br />

(e) Comment on the usefulness of these materials as windows or as protective screens for radiation.<br />

Explain what limits the window width at the lower and upper ends of the transparency range,<br />

and thus explain the difference in the absorption characteristics of the materials tested.<br />

(f) Plot the absorption edge for MgO, ZnSe and glass using a higher resolution (i.e. a 1 nm/cm<br />

scale. Use the instructions in section 3.4.4 above for these scans.<br />

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You can find a rough value for the band gap energy by noting the wavelength at which a line drawn<br />

through the steepest part of the absorption edge intersects with the axis. Discuss this with your<br />

demonstrator.<br />

(g) Analyse the shape of the edge, and try to fit one of the appropriate equations above (equations<br />

(37) to (40)) to your data. Thus determine the type of the material (direct, indirect or<br />

amorphous).<br />

(h) Discuss the nature of the band gap for these materials. How does the value compare with that<br />

given in the literature?<br />

(i) Describe the absorption characteristics of a good pair of sunglasses. If you have time, you<br />

could measure the absorption characteristics of your sunglasses - are they living up to their<br />

manufacturers’ claims?<br />

References:<br />

S. Sze, “Semiconductor Devices”, Unimelb Physics, 621.38152 SZE.<br />

Kittel in all his editions!<br />

the handout on optical properties<br />

<strong>The</strong> band gap prac paper<br />

T.R.Mackin 7MAY03 (Version 0.1)<br />

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