Characterization of a Helium Gas-DischargeLamp

Christian StiegerSemester-Thesis

September 14, 2012

Abstract

The goal of this experiment was to characterize a helium gas-discharge lamp bymeans of angle resolved photoemission spectroscopy on a tungsten sample. In thisway the spectrum of tungsten was measured for two different photon energies emittedby the helium lamp and a measure of the lamps intensity for each photon energy asa function of helium pressure and plasma current was determined at the same time.

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Contents

1 Introduction 3

2 Theory 32.1 Photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Workfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Experimental Setup 53.1 UHV Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.2 Pirani gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.3 Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4 Helium Gas-Discharge Lamp . . . . . . . . . . . . . . . . . . . . . . . . . 73.5 Energy analysator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.5.1 The Lens System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.5.2 The Hemispherical Analyzer . . . . . . . . . . . . . . . . . . . . . . 9

3.6 The CCD Imaging Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 103.6.1 Computer Equipment and Software . . . . . . . . . . . . . . . . . . 113.6.2 Software for Image Analysis . . . . . . . . . . . . . . . . . . . . . . 113.6.3 C++ Code Edit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Results 144.1 Scans over the 70eV and 90eV regions for different pressures and currents 14

4.1.1 56mA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.1.2 16mA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2 Pressure in the Measurement Chamber . . . . . . . . . . . . . . . . . . . . 194.3 Lamp Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Discussion 22

6 Conclusion 23

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1 Introduction

Gas-discharge lamps produce light very efficiently. On the downside the light is consid-ered to be of low quality, yet still sufficient for large scale lighting where efficiency ismore important than quality such as street lighting. In this case a sodium-vapor lampor a mercury-vapor lamp is used. As the name says this type of lamp uses sodium ormercury vapor in an excited state to produce light. In the case of sodium the lightstems from a sharp line at about a wavelength of 590 nm which appears yellow to thehuman eye. The sodium-vapor lamp is often preferred in cities hosting astronomical ob-servatories because they produce less light pollution. Other types of gas-discharge lampsusually use a noble gas such as neon, argon, krypton, xenon or a mixture of these toproduce light. If the radiation lies in the ultraviolet regime a fluorescent coating can beapplied to the inside of the glass tube holding the gas which converts ultraviolet light tovisible light. The best known of these lamps are sodium-vapor lamps for street lightingand neon tubes often used for signs which can be found all over the place in big cities,especially in Asia.For the purpose of this experiment a helium gas-discharge lamp was used because of thehigh ionization energy of helium resulting in a high photon energy of the emitted radi-ation which is needed for photoemission. The goal was then to characterize the lamp,that is to investigate its behaviour for different currents in the plasma and different gaspressures. This was achieved by means of angle resolved photoemission spectroscopy(ARPES) on a tungsten sample. Two different spectral lines of helium in the UV regimewere used to measure the spectrum of tungsten using an energy analyzer, aswell as get-ting a measure for the lamps intensity for a given pressure and current at the same time.This effectively allows a characterization of the lamp and a comparison of the spectrumof tungsten for two different photon energies.

2 Theory

2.1 Photoemission

Photoemission is the process of emitting photons from a sample through absorption ofa photon by an electron in the sample. If the photons energy is high enough the excitedelectron may escape the sample. There are however also secondary processes involved.An electron may scatter many times on its way to the surface, resulting in a very sharppeak just above the vacuum level called the cascade as most electrons only just manage toovercome the workfunction. Additionally there are Auger electrons. These electrons areejected when an electron from a higher level occupies a newly vacant (due to absorptionof a photon), lower level. Energy conservation then dictates that another electron canbe emitted. These so called Auger peaks depend on the material under investigationand may therefore be used to identify chemical elements.Electrons that are directly ejected may be used to determine the bandstructure of asample. This process is described by equation (1).

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hν = Ekin +W + EB (1)

Where hν is the photonenergy, W = Evac − EF the work function, EB the bindingenergy and Ekin the kinetic energy of the electron after emission. See also Figure (1)on the left for an illustration of the workfunction, binding energy, kinetic and vacuumenergies.

Figure 1: Illustration of the principle of photoemission on the left, a typical photoe-mission spectrum on the right. Note the cascade, Auger electrons and theelectrons from the bandstructure. Figure from [1]

On the right of Figure (1) we can see a typical photoemission spectrum including thebeforementioned cascade electrons and Auger peaks.

2.2 Workfunction

Often it is not quite clear if the workfunction of the sample or the analysator should beused in the calculations. If we assume an electron absorbs a photon of energy hν theemitted electron will have a kinetic energy of

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Ekin,sample = hν − EB −Wsample (2)

where Wsample is the workfunction of the sample. Since the sample and the detectorare electrically connected the fermi level of both the sample and the detector equalizes(See Figure (2)).

Figure 2: Workfunction of the sample and the detector individually in the upper half, theFermi energy for the sample and the detector is on two different levels. If thesample and the detector are connected electrically the Fermi energy equalizesthroughout the system, as seen in the lower half. Figure from [1]

Therefore since the electron directly enters the analysator we get the following kineticenergy

Ekin = Ekin,sample +Wsample −Wanalysator (3)

Inserting equation (2) into equation (3) then leads to

Ekin = hν − EB −Wsample +Wsample −Wanalysator = hν − EB −Wanalysator (4)

The workfunction of the sample drops out and we may use the workfunction of theanalysator. This has the great advantage that we may use any sample without knowingits workfunction once we know the workfunction of the analysator.

3 Experimental Setup

In order to perform Angle-resolved photoemission spectroscopy (ARPES) one needs anultra-high vacuum (UHV) chamber, a sample therein, a light source (in this case ahelium gas-discharge lamp), an energy analysator for the ejected electrons, a detectorand computer equipment to make sense of the data. Each part shall be discussed brieflyhere.

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3.1 UHV Chamber

A ultra-high vacuum chamber (UHV) chamber was used in this experiment. Throughthe use of various different pumps the pressure inside the chamber can stepwise belowered to the low 10−11mbar-regime. The chamber consists of a measurement chamberwhere the sample is placed during the experiment and a preparation chamber wherethe sample is prepared. The two sections are seperated by a valve meaning that themeasurement section can be vented without affecting the preparation chamber. Thisstep was needed to install the helium gas-discharge lamp prior to the measurements. Toensure a sufficiently low vacuum inside the chamber after resealing it, it is mandatoryto heat the entire UHV chamber to about 180◦C for several days. This process called”baking” was performed by wrapping heating wire all around the chamber and thenwrapping it in aluminium foil. Its purpose is mainly to get rid of any water vapor thatgot into the chamber while it was unsealed.

3.2 Pirani gauge

The Pirani gauge is an instrument used to measure very low pressures by measuring thethermal conductivity of the gas causing the pressure. It must therefore be calibrated tothe substance at hand.It consists of an electrically heated filament (usually platinum) in a tube connected tothe system whose vacuum is to be measured. The resistance of the filament is dependenton its temperature. Since the heatflow from the filament to the gas is described by thethermal conductivity of the gas which in turn depends on its pressure, we may indirectlymeasure the pressure in the gas by measuring the resistance of the filament. Hoeweverusually the resistance is kept constant using a bridge circuit and the current needed tokeep this balance is measured.

3.3 Sample

The previously mentioned preparation chamber was used to perform a cleaning procedureon the sample, which for the case of this experiment was a block of tungsten. A currentis passed through a filament behind the sample causing it to eject thermally excitedelectrons which in turn heat the sample upon impact to a temperature well over 2000◦C.In a first step the sample is heated while oxigen is released into the chamber at the sametime to burn of carbon. During the second step called ”flashing” the sample is againheated by the filament but without any oxygen added. In this manner any CO or CO2

remaining from the first step as well as any other impurities at the surface are removedfrom the surface by effectively shaking them off.It is noteworthy that the preparation chamber may also be used to evaporate thin filmsof iron onto the block of tungsten, however this step was omitted for this experiment.

After preparation the sample is moved from the preparation chamber into the mea-surement chamber where it has to placed precisely into the light beam from the heliumgas-discharge lamp to ensure the geometry of the experiment is well defined. During theexperiment there is a voltage applied to the sample to help the electrons enter the energy

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analysator since they are easily influenced by magnetic fields at low kinetic energy. Forthis experiment however no magnetic fields were applied. The discrepancy hails from thefact that the aperature is usually used to examine time-resolved magnetization dynam-ics of the sample which can be magnetized by a pulser for this purpose and is thereforesubject to relatively strong magnetic fields. The effect the magnetic field has on theemitted electrons from the sample is unwanted, thus a voltage is applied to minimizeits effect. The electron fluence the lamp causes is too weak to cause spacecharge effects.They do not play a role for this reason.

3.4 Helium Gas-Discharge Lamp

A gas-discharge lamp consists of a cathode, an anode and an ionized gas in betweencalled a plasma. The ionization degree may vary anywhere from 100% to 10−4 − 10−6

i.e. from fully to partially ionized gases. Plasmas are cathegorized in high-temperatureor fusion plasmas and low-temperature plasmas or gas discharges. The latter are ofrelevance for this experiment.The general principle of the basic plasma processes for the case of an argon-plasma aresketched in Figure (3).

Figure 3: Schematic of the basic plasma processes. In the upper half the process relevantfor this experiment is sketched for the case of an argon-plasma. In the lowerhalf ”sputtering” is sketched by which additionally to the processes abovematerial from the cathode dubbed M is released into the plasma by impactingargon ions. Figure from [2]

When a potential difference is applied between two electrodes the gas in between willbreak down into electrons and positive ions. The process starts off when a few electronsare emitted at the cathode. They are accelerated due to the potential difference andcollide with the gas atoms. The inelastic collisions lead to excitation and ionization ofthe gas, followed by de-excitations accompanied by emission of radiation. These colli-sions create themselves new ions which are accelerated towards the cathode, where theyrelease new electrons which then in turn again ionize the gas. In this way we get a self

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sustaining plasma.At sufficiently high voltages another process called sputtering sets in. The ions are ac-celerated fast enough so that they not only release secondary electrons at the cathodebut also some of the material the cathode is made of. This can be used for spectrochem-istry or for deposition of the cathode material onto the anode, i.e. for deposition of thinfilms. For the purpose of this experiment the voltage was relatively low so no sputteringoccured.In this experiment the gas used was pure helium, since it requires a lot of energy toionize. Its spectrum features spectral lines at about 20eV and about 40eV which is inthe UV regime in addition to its well know visible spectrum (for comparison: visiblelight is on the order of 1eV). These two lines were used for ARPES in this experiment.Since a low pressure corresponds to a long mean free path of the electrons they areaccelerated to higher speeds meaning they can excite helium to higher levels which thenin turn emits radiation of higher energy. As an indication of the pressure in the lampwe used that the visible light was biased more towards blue when the pressure was lowand more towards red when the pressure was high (see also Figure (4)) due to the effectdescribed above. However the actual radiation used for ARPES is in the UV range.

Figure 4: The visible spectrum of helium [3]

Unfortunately pictures of the spectrum of helium in the UV range relevant for thisexperiment are hard to come by, but a search in the Nist Atomic Spectra Database [4]reveals several lines at 32.02926nm (38.7135eV) coming from different transissions fea-turing a shared relative intensity of 10, this corresponds to the 40eV region. Additionalya sharp line at 58.43339nm (21.22012eV) featuring a relative intensity of 1000 is found,which corresponds to the 20eV region. During this experiment the Characteristics ofour helium lamp were determined by measuring the intensity of both the emitted elec-trons from the 20eV region and those of the 40eV region for different gas pressures anddifferent currents between the electrodes.

3.5 Energy analysator

In any photoemission experiment the measurement consists of an analysis of the kineticenergy of the emitted electrons. In this experiment a hemispherical energy analysatorcalled Phoibos by Specs was used. It consists of two parts:

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3.5.1 The Lens System

The emitted electrons first pass an adjustable iris aperture which restricts the angle ofthe incoming electrons relative to the entry slit which is needed since the lens system canonly process a limited angular range. Before entering the system however an additionalslot aperture is passed which allows us to plot the energy of the electrons on one axisand the angular or spacial dependence on the other. The lens system allows for severaldifferent lens modes. Among other things it is possible to analyze either the angulardispersion or to get a real space image in one dimension. The second task of this systemis to retard the electrons by the difference Ekin − Epass so that if an electron had theenergy Ekin when entering the system, it will leave the system with Epass. These twoparameters may be set by the experimenter. Ekin is the kinetic energy of the electronswe are interested in analysing and Epass is the energy at which the electrons will passthe spherical analysator exactly parallel to both hemispheres (see Figure (5)).

Figure 5: Schematic view of the energy analyzer showing the lens system and the spher-ical analyzer. Note that our setup deviates from this one in that a heliumgas-discharge lamp was used instead of an electron gun and in that a simplerdetector that isn’t spin sensitive was used. The analysator on the right is thesame however. Figure from [1]

3.5.2 The Hemispherical Analyzer

The hemispherical analyzer consists of two concentric hemispheres each on a differentelectric potential. Epass is proportional to the potential difference on the two hemi-spheres:

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Epass = −qk(Vouter − Vinner) (5)

Where q = 1.602 ∗ 10−19C is the elementary charge and k = 1516 = 0.9375 a calibration

constant [1]. Electrons that deviate too much from Epass upon entering the energyanalysator crash into one of the hemispheres. The deviation in energy ∆E at which theelectrons reach the detector is found to be proportional to Epass [1]:

∆E =∆R

Rinner +RouterEpass (6)

Where electrons with Epass arrive at position R and electrons with Epass±∆E arriveat R ± ∆R. From this we see immediately that the energy resolution of the energyanalysator is directly connected to Epass i.e. the smaller Epass the better the energyresolution. In conclusion we get on the horizontal axis the angular dispersion or a realspace image depending on the lens mode and on the vertical axis an energy resolution.Note however that this only corresponds to the analysator. Since the detector wasmounted in such a way that the images taken are rotated by 90◦ the axis are actuallyreversed in the measurements. Keep this in mind when considering Section 4.

3.6 The CCD Imaging Detector

The detector was placed right at the exit of the energy analysator for this experimentsince no additional tools were needed such as a spin detection system. This also providesthe advantage that the imaging properties of the analysator were well known beforehandas they were already elaborated when this experiment started. The detector consists ofthree parts: a micro-channel plate (MCP), a phosphor plate and a charge-coupled device(CCD) camera.The MCP consists of glass capillaries coated with molybdenum which act as electronmultipliers. The maximum amplification depends on the applied voltage and is usuallyaround 106. The geometry of the plate is that of a small cylinder with a diameter of49mm and a thickness of 12µm. [1]The cascade of electrons behind the MCP hits the phosphor plate which consists of typeP 43 phosphor (Gd202S:Tb) [1] and emits green light when struck by electrons. Thislight is then captured by a CCD camera which consists of an array of capacitors.The camera used in this experiment was a 14bit mono CCD camera with Peltier coolingwhich reduces the noise. In order to subtract the background of the camera an imagewith a high integration time and closed shutters (called a ”darkfield”) is taken and thensubtracted from the subsequent measurements. The images obtained using this detectorhave a resolution of 1280x1024 pixels and are saved in the Nexus-HDF5 format by thescan server. Note that the exit slit of the energy analysator is larger than the MCP andslightly conical in the upper half (see Figure (6)). This is visible in the measurements(see Section (4))

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Figure 6: Comparison of the size of the exit slit and the MCP on the left and an exampleof a measurement in false colors on the right. Note the edge of the MCP isclearly visible in the corners.

3.6.1 Computer Equipment and Software

The computer equipment consists of a whole array of software. Most important is thescan server which saves images taken by the CCD camera and saves them in Nexus-HDF5 format and a library written in C++ to analyze these images using a Pythonwrapper for easy access.

3.6.2 Software for Image Analysis

The software used for this experiment takes a scan over different kinetic energies andcombines the images into a larger panorama picture. In the process the data is averagedwhere the individual images overlap. See Figure (7) for an example of a scan over kineticenergies starting from 70eV to 72eV on the x-axis vs angular dispersion on the y-axis.Note the clearly visible fermi-edge which is moving to the left as the scan progresses.

The software creates a panorama image using such a scan. See Figure (8) for anexample. Note the panorama is much grainier on the left edge where no averaging waspossible.

Additionally the software also computes the spectrum of the panorama where eachpoint corresponds to the integral over the angular dispersion (i.e. a column) on thepanorama. For examples see Section 4.

3.6.3 C++ Code Edit

While I didn’t initially write the C++ code used for this experiment I did find a fewbugs and also helped in making the source code more easily maintainable by removingunnecessary parenthesis, typecasts, declared variables that were never used and more. I

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Figure 7: Example of a scan over kinetic energies starting from 70eV to 72eV.

Figure 8: Example of a panorama corresponding to the scan in Figure (7).

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also introduced assertions which can be a tremendous help in bugtracking. While thisis not directly connected to the physics in this experiment I spent a lot of time on it sothought it worth mentioning.Compare the code in Listing (1) to the one in Listing (2). Note that the code in Listing(2) is much shorter and more inviting to look at, yet it provides the same functionalityand better bugtracking.

Listing 1: unedited code

Image2D<dataType> bin(int newSizeX, int newSizeY) {

double binX = (double) getSizeX() / (double) newSizeX;double binY = (double) getSizeY() / (double) newSizeY;

Image2D<dataType> binnedImage = Image2D<dataType>(newSizeX, newSizeY);Image2D<int> counter = Image2D<int>(newSizeX, newSizeY);

for (int i = 0; i < newSizeX; i++) {for (int j = 0; j < newSizeY; j++) {

binnedImage.set(i, j, 0);counter.set(i, j, 0);

}}for (int x = 0; x < sizeX; x++) {

for (int y = 0; y < sizeY; y++) {int indexX = (int) ((double) x / binX);if (indexX >= newSizeX)

indexX = newSizeX;int indexY = (int) ((double) y / binY);if (indexY >= newSizeY)

indexY = newSizeY;binnedImage.set(indexX, indexY,

binnedImage.get(indexX, indexY) + get(x, y));counter.set(indexX, indexY, counter.get(indexX, indexY) + 1);

}}for (int i = 0; i < newSizeX; i++) {

for (int j = 0; j < newSizeY; j++) {if (counter.get(i, j) == 0) {

binnedImage.set(i, j, 0);} else {

binnedImage.set(i, j,binnedImage.get(i, j) / (double)counter.get(i, j));

}}

}

return binnedImage;}

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Listing 2: edited code

Image2D<dataType> bin(int const newSizeX, int const newSizeY) const {assert(!isempty());assert(0 < newSizeX && newSizeX <= sizeX);assert(0 < newSizeY && newSizeY <= sizeY);

double binX = (double)newSizeX / sizeX;double binY = (double)newSizeY / sizeY;

Image2D<dataType> newImage(newSizeX, newSizeY, dataType(0));Image2D<int> weight(newSizeX, newSizeY, 0);

for (int x = 0; x < sizeX; ++x)for (int y = 0; y < sizeY; ++y) {

int newX = x * binX;int newY = y * binY;newImage(newX, newY) += (*this)(x,y);++weight(newX, newY);

}

for (int i = 0; i < newSizeX; ++i)for (int j = 0; j < newSizeY; ++j)

if (weight(i,j) != 0)newImage(i,j) /= weight(i,j);

return newImage;}

It is not up to me whether this code will be used in the future. However I wouldrecommend it on the grounds that it also provides additional functionality such as theability to edit images individually before appending them into a panorama.

4 Results

The results for this experiment consist of a whole array of images consisting of thespectra for both lines of the helium lamp mentioned in section 3.4 for different pressuresand currents between the electrodes. Only a small amount of them will be shown hereto illustrate what exactly was measured and how the results could be interpreted.

4.1 Scans over the 70eV and 90eV regions for different pressures andcurrents

As mentioned in section 3.4 the helium gas-discharge lamp features two spectral linesof interest for this experiment. Together with a voltage applied to the sample of -50Vthe resulting kinetic energy for the 20eV line was around 70eV, hence 70eV region. Andanalogous to this around 90eV for the 40eV line.For each setting on the pressurevalve of the lamp a scan from 70eV to 72eV and onefrom 90eV to 92eV was performed, thereby catching the spectra for both the 20eV andthe 40eV line. This was done for 14 different pressure settings and two different currents

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on the lamp, resulting in 14 ∗ 2 ∗ 2 = 56 scans in total. The purpose of this was tocompare the spectra in both regions to each other and to find the intensity of the lampfor each line as a function of the current and the pressure (more on this in section 4.3.)

4.1.1 56mA

In this section the panorama for each region is presented along with their correspondingspectra (obtained by integrating over the angular dispersion) for a few selected pressures.For a pressure of 1.5mbar (which was the lowest pressure before the lamp died for bothcurrents) see Figure (9) and Figure (10). Note that the spectra are suggestively coloredred and blue to indicate which line they correspond to, i.e. 20eV ”the red line” and40eV ”the blue line”.

Figure 9: The panorama for the 70eV region above and the 90eV region below for asetting of 56mA and 1.5mbar. Note the difference in intensity indicated by thecolorbar to the right of about a factor 20. Also note that the fermi edge foreach region is not exactly 20eV apart.

The Spectrum seen in Figure (10) corresponds to a convolution of the density of states(DOS) and the fermi-dirac distribution. Close to the fermi edge the DOS is almost con-stant which means that the fermi edge is actually a pretty nice fermi-dirac distribution,at least for the 70eV region. Also since there is no peak at the fermi edge we mayconclude that tungsten is not ferromagnetic (accoring to the Stoner criterium).If we compare the spectra we notice mainly three differences:

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Figure 10: The spectrum for the 70eV region above and the 90eV region below for asetting of 56mA and 1.5mbar. Again the fermi edge is not exactly 20eVapart. For the sake of better comparison the spectra are shifted so that thefermi edges are right on top of each other. Note that plot shows only therelative intensity, the red line is shifted up for comparison. Also note thatthe upper scale corresponds to the red line and the lower scale to the blueline.

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There appears to be a less prominent shoulder at the fermi edge for the 90eV region,secondly there is a second peak towards the beginning of the 90eV region and third thereis still a drop in intensity for the 70eV region after the fermi edge but not for the 90eVregion. The first effect could be due to the greater penetration depth of the 40eV line,the second could be some sort of resonance only present for the blue line and the thirdis the cascade of the blue line seen in the 70eV region.Since there are no new physical effects of interest occuring at higher pressures the follow-ing Figures will be kept smaller and are simply to demonstrate the effect of increasingthe pressure. See Figure (11) for a pressure of 4.8mbar. Note the decay of the blueline and the massive difference in intensity of about a factor 150. Figure (12) shows thespectra for a pressure of 95mbar. The blue line has reduced to noise and the factor inintensity has gone up to 164 where it saturates. The cascade of the blue line howeveris still visible in the 70eV region. This is because the cascade absolutely dwarfs thebandstructure in intensity.

Figure 11: Panorama and spectra for both regions for a setting of 56mA and 4.8mbar.Note the decay of the blue line and the difference in intensity of a factor 150.The red line is also less noisy and the cascade of the blue line is smaller.

4.1.2 16mA

The physics here are the same however the factor in intensity is even larger (about36) for the lowest pressure of 1.8mbar. This can easily be explained since the lowercurrent causes less collisions between electrons and therefore less intensity of the emittedradiation. The difference between the two currents will become apparent in section 4.3.For now we notice that the blue line decays even faster, see Figure (13) and Figure (14).Note the factor in intensity of about 94 in Figure (14). We conclude that the blue linedecays faster but the red line also builds up much slower compared to 56mA.

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Figure 12: Panorama and spectra for both regions for a setting of 56mA and 95.0mbar.Note that the blue line has reduced to noise while its cascade is still visible,this is because the intensity of the cascade absolutely dwarfs the one fromthe bandstructure.

Figure 13: Panorama and spectra for both regions for a setting of 16mA and 1.8mbar.Note the weaker blue line compared to 56mA and the factor in intensity ofabout 36.

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Figure 14: Panorama and spectra for both regions for a setting of 16mA and 4.9mbar.Note the blue has already pretty much reduced to noise and the factor inintensity of about 94 compared to a factor 150 in Figure (11). We concludethat while the blue line decays faster, the red line also builds up much slower.

4.2 Pressure in the Measurement Chamber

As described in Section 3.1 the pressure in a UHV chamber is usually as low as 10−11mbar.This was not achieved in this experiment because the helium gas-discharge lamp ismounted directly onto the UHV chamber and needs to be fed helium to work. Some ofthis helium leaks into the chamber, increasing the pressure. This is of little consequencefor this experiment since helium is nonreactive. However for exactly the same reasonit can be hard to get it out of the chamber. See Figure (15) for a plot of the pressureinside the chamber versus the pressure on the lamp.

The pressure in the chamber increases only by a factor of about 1.35 for over twoorders of magnitude in pressure on the lamp. There should be no disturbance in themeasurements because of this increase. It should be noted that the Pirani gauge (seeSection 3.2) used to measure the pressure in the chamber is calibrated for air, not forhelium. Since the vast majority of pressure comes from helium it can only give a roughestimate of the pressure in the chamber, which in our case is enough to preclude anyinfluence of the pressure in the chamber on the measurements.

4.3 Lamp Characterization

The relative intensity for both the red and the blue line for both currents are plotted infigure (16). Each point on one of these lines corresponds to an integral over the spec-trum such as in Figure (10). This is repeated for all pressures on each energy region andcurrent until we finally end up with a plot of intensity versus pressure.

For comparison four different ratios of maximum intensity are given:

• Γ70eV = I56mA70eV /I16mA

70eV = 1.77

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Figure 15: Pressure in the measurement chamber as a function of the pressure on thelamp. The pressure on the lamp changes by a factor of only about 1.35 overtwo orders of magnitude in pressure on the lamp. Note the logarithmic scaleon the x-axis.

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Figure 16: Intensity of the emitted light for both the red and the blue line versus pressure.Additionally four different ratios of maximum intensity are given. Γ70eV andΓ90eV compare the maximum for 56mA vs 16mA for a given energy region.Γ56mA and Γ16mA compare the maximum for 70eV vs 90eV for a given current.

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• Γ90eV = I56mA90eV /I16mA

90eV = 4.38

• Γ56mA = I56mA70eV /I56mA

90eV = 146.16

• Γ16mA = I16mA70eV /I16mA

90eV = 361.09

From Γ70eV we can see that the saturation intensity for 56mA is roughly two timesas high as the one for 16mA. Note that for the case of 16mA the measurement wasdiscontinued shortly before saturation was achieved. A rough estimate is therefore allwe can give here.Γ90eV does not correspond to saturation but instead shows the intensity of the blue linefor the minimal pressure the lamp needs to work. The intensity is 4.38 times higher fora current of 56mA than for 16mA which is roughly comparable to the increase in currentwhich is 3.5 times. We should note here that the lowest pressure at which the intensitywas measured is not exactly the same. For the 16mA case the lowest pressure is slightlyhigher than for 56mA. We may therefore assume that the value for Γ90eV is a bit too highand that the correspondence to the increase in current is in reality even better than wecan see here. We could be tempted to assume a linear relationship between current andmaximum intensity. Validation of this hypothesis would require further measurementshowever.Γ56mA and Γ16mA demonstrate the massive difference in intensity of the red line comparedto the blue line. The effect for the 16mA case is about 2.5 times higher than for the56mA case.

5 Discussion

The purpose of this work was a characterization of the helium lamp, that is to findout how the intensity of the emitted light scales with the pressure in the lamp andthe current applied to the lamp. The expectation beforehand was that the intensityshould scale exponentially with pressure at least in an intermediate region, i.e. not inthe saturation region. This effect is demonstrated quite nicely for both the red and theblue line for both currents. However at least for the red line this behaviour seems tobe followed better for higher current. For a current of 16mA higher pressure is neededto achieve saturation and an odd hitch at about 6.5mbar is observerd. There seems tobe a systematic error underlying this effect since the whole curve appears to be slightlyshifted down from this point on. If there were just one faulty measurement the curvewould correct itself to its originally expected trajectory. While this may be unfortunatewe may still observe a different behaviour upon approaching the saturation region, asthe curve is still increasing where the other already saturates. The minimum requiredcurrent for the lamp to sustain emission of radiation could not be determined using thissetup since 16mA was the lowest possible setting. It is possible however that 16mA isclose to the minimum current and therefore the emission could be somewhat unstablecompared to the 56mA which was the maximum setting. This could be a source oferrors.A secondary purpose of this experiment was to measure the spectrum of tungsten using

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two different photon energies. The expectancy here was that there should only be a slightdiscrepancy when comparing the two spectra in the 70eV and the 90eV region. The maindifference in using two different photon energies is the penetration depth. If we comparethe spectra for example in Figure (10) we immediately notice a steeper increase afterthe fermi edge for the blue line, aswell as a peak in energy for slightly higher energiesbelow the fermi edge and an increase with dropping energy for the blue line whereas thered line drops with decreasing energy. There are a lot more discrepancies found in themeasurements than were expected beforehand. It is hard to say what exactly causes thesedifferences as spectroscopy is a very complex subject. We could for example speculatethat in the low energy region there may be certain resonances present which depend onthe photon energy and not just the penetration depth. This would explain the differentbehaviour for the two lines. A thorough investigation of this however is not the scopeof this experiment. It should also be noted that for the red line the intensity is stilldropping after the fermi edge. This is because the cascade (mentioned in section 2.1)from the blue line overlaps the spectrum of the red line since the red line corresponds toa lower photon energy. This observance cannot explain any of the discrepancies above.

6 Conclusion

The task of roughly characterizing the lamp for different pressures and currents wasachieved. It is of course always possible to measure for more currents than was performedhere. Since there was no drastic difference observed for the maximum setting of 56mAand the minimum setting of 16mA it was decided that these two setting should sufficeto get a characterization of the helium gas-discharge lamp. It is also worth noting thatthe spectral difference between the two lines may be worth investigating in additionalexperiments.

References

[1] D. Perriard, Master Thesis at ETH Zurich, 2012Characterization of a Novel Spin Detector Based on Spin Diffraction on a Crystal

[2] Annemie Bogaerts, Erik Neyts, Renaat Gijbelsm Joost van der MullenGas discharge plasmas and their applicationshttp://www.sciencedirect.com/science/article/pii/S0584854701004062

[3] http://mail.msad35.net/~rluciano/Chemistry/FOV1-00017B5C/

FOV1-00018356/

[4] Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2012). NISTAtomic Spectra Database (ver. 5.0), [Online]. Available: http://physics.nist.gov/asd [2012, August 10]. National Institute of Standards and Technology,Gaithersburg, MD.

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