## Ga- and N-rich condition

The bottom-up method employing either MBE or MOVPE technique provides different possibilities, for growing the epilayer crystal which is decided by what growth condition is used. In this case, let us consider one of the III-V material: GaN crystal growth on our substrate.

To grow GaN, we need Ga and N atoms being supplied from the respective source, where Ga source cell and nitrogen gas or ammonia for MBE or TMGa and ammonia for MOCVD. In here, we can choose either the grown crystal is situated in Ga-rich or N-rich condition.

Depending on the what environmental that GaN crystal is grown, its structure is largely influenced by the majority of atoms dominating the growth of the crystal. It is well-established that Ga-rich condition prefers formation of GaN planar film-2D grow (for example a paper from Ramachandran C, et al from Carnegie Mellon University), while N-rich condition promotes GaN nanowire-3D grow (for example a paper from Callarco R and Marso M from Research Center Julich). There is an important point to be understood in here. What is actually Ga- and N-rich conditions?

I notice there are two important factors in determining how the growth is either Ga-rich or N-rich condition. First is the growth temperature and second is the flux contributing to the growth of GaN epilayer.

Growth temperature can be designed from the very beginning and we can directly assume what is actually the preferred condition is. Ga start desorbing at temperature around 600 C, both for GaAs (source) and GaN (source) system. Then Ga atoms situated at the growth above this range of temperature (higher than 600 C) will start to desorb from the surface of the substrate, and at the same time, only N atoms stay there. As a result, we have more N atoms and therefore this condition is referred as N-rich condition. For the growth conducted at the temperature below 600 C, Ga atoms will likely to stay in the surface of the substrate. This situation is called Ga-rich condition.

Determining flux is rather bit hard. One has to calibrate with the GaN planar film growth, where two condition has to be applied (Ga- and N-rich). To calculate Ga growth rate, the condition has to be in N-rich. Just imagine when the surface is saturated with N, then the only factor that governs the growth is limited Ga atoms due to the desorption. In the other hand, N growth rate can be calculated by using Ga-rich condition. Too much Ga atoms will saturate the substrate surface resulting Ga atoms can’t do much in controlling the structure growth. In fact, the limited presence of N will direct the growth of GaN. I learnt this from Heying et al (2000) and Koblmueller (2003). Next, one has to divide the ratio of Ga/N. If the value is more  than 1, it means it is Ga-rich condition, while value less than 1 is N-rich condition.

Growth of GaN nanowire itself is normally done at high temperature and Ga/N<1, implying the growth being done in N-rich condition. I encountered papers from Calleja’s group from Spain, where there is a possibility of having nanowire at Ga-rich condition (1, 2). Despite grown on high substrate temperature, Ga/N is more than 1. I am still looking the answer for this question. It might be that high growth temperature is more dominant?

This is approximately the same with other III-V semiconductor material, such as GaAs in Ga- or As-rich condition.

## Well, it is a nanowire!

No nanowire growth has been done this week. Since there are two of my friends planning to use MBE with nitrogen-free chamber next week, the engineer decided to let growth chamber of MBE in the idle state or no nitrogen-related growth takes place for two-three days. Based on his experience, the decided recovery time is supposed to be sufficient enough to get nitrogen away from growth chamber, indicated from the pressure as low as 10E-10 or even lower. It means the growth chamber is in the ultra high vacuum state. The reason is because of my friends will grow in arsenic rich condition where the presence (even the small portion) of nitrogen is not desirable. Even with small portion of nitrogen, the growth sample will have diluted-nitride on it, a well-known method to alter energy band-gap of semiconductor.

No growth means characterization. I brought few of the grown samples to the scanning electron microscopy laboratory in the material department. I went training two weeks ago and did some two measurements where the results are not well-adjusted, according to my friends who has expertise in this area. In order to fix my weakness, I asked them, not once but twice to come with me but of course with different persons as I know they have their own work. Well, I think my efforts are fruitful in the sense of achieved better resolution image resulted from less distortion from astigmatism, focus and aperture optimization. Some tips and tricks were given to me , such as finding the beam location, the proper working distance (it is not in-lens type), in-plane and out-plane stage rotation.

I learned scanning-tunneling electron microscopy in Nanolab. It is bit different than the one in the material department where a transmission can be done in the same machine. Of course there is a dedicated machine to do transmission electron microscopy. As a result, such a small sample is required before it is loaded into the sample holder. I am impressed with this machine because it has way much faster venting and pumping time owing to the small chamber volume compared to the scanning electron microscopy in the material department. One of my friend always jokes that in order to get the machine in high vacuum, the user has to pay 75-100 NOK. In addition, scanning-tunneling electron microscopy in the Nanolab uses in-lens objective lens meaning the users do not have to bother much adjusting working distance as this parameter is the fixed value. With this type of lens, the resolution can go down to 0.5 nm but the drawback is located in the very limited sample size. Overall, both machine has similarities.

To use this wonderful machine, there is a theory, practical, self-training and examination part that I had to participate and pass. Generally, I did not have any difficulty in adapting with this machine. Just… The way of removing and inserting the sample holder is new for me. I have to rotate a bit, pull, rotate all the way, pull again, press “Air” button. The same method with opposite direction when I have to put it back. In one occasion of inserting the sample holder, after “Vac” button was press, I forgot to wait until the LED blink. I just force it to rotate and as a result, an alarm was beeping >_< I just realized my mistake after 5 minutes :p During this time, I was really afraid that I broke the machine XD

I showed my scanning electron microscopy images to the one who assisted me growing the first 7 samples. I suggested that no nanowire was observed in these samples, even with the help of AlN buffer layer. Before meeting with him, I knew that he would be disappointed with these results. Surprisingly, he did not show that sign at all and said that those short things were actually the nanowire, especially his own growth! Well, those words are in fact what I needed for the efforts we have put in the first attempts of GaN nanowire growing. Though they were not properly forming as a nanowire due to its short length. He suggested that the next growth with higher nitrogen flow. I am thinking to grow with much longer time, probably 2-3 times than what I did in the last 7 samples.

As for the last growth, I used double Ga flux rate to confirm whether the nanowire will increase its height by double. It did not turn to the expectation. It had the same height approximately with the the others. Of course, as the Ga flux was doubled, the physical mechanism on GaN nanowire formation was slightly changed. For instance, the edge has more two dimension growth (see picture below) resulting in higher non-uniformity toward the center. What a bad sample unfortunately, but I learned something at least. Maybe a lower growth rate can be planned as well? Such extreme growth rate was done by Galopin et al, almost half of the assigned Ga flux rate I set.

## Further GaN growth experience with MBE

Another two weeks, from the last week of July to the first week of August were scheduled with the attempt to grow nanowire structure of GaN material on the substrate of Si. There were five samples in total I could grow within these period. Considering the normal workload, the number of grown samples were quite normal.

I think I will not have any growth chance for the next 3-4 weeks ahead, since there are other person who also will use this MBE requiring different chamber condition. That is why the MBE system need to be stabilized for some time, 2-3 days before a cleaning and purifying stage are conducted from Nitrogen environmental condition.

I was thinking to grow two-three samples each day last week. But I guess it was impossible to do, since the growth itself took 3 hours added with another 2-3 hours calibrating the flux of the source, outgassing the sample and preparing the chamber in such way to favorably grow in suppressed contaminated environment which can destruct the growth of GaN. Moreover, I am not confident enough and officially not allowed to transfer substrate from one chamber to another, or else I mess up with the machine. Fallen substrate holder in any chamber is not really good idea, since the engineer has to vent the chamber, pump back to vacuum, bake the chamber to remove the contaminants-oxides and another source calibrations here and there. Believe it or not, this sequence will take around 3-4 weeks. That is why I do not want to mess up. Simple reason why I can’t grow more than one sample is because of the available substrate holder for the 2 inch wafer is only one. Well, at the same time I am relieved.

Normally, I start ramp down the load-lock chamber at 9 AM. While it is ramping down, I calibrated the required source fluxes to be met at certain number so that it equivalents to the growth rate I want. Well, It takes like one hour. Then my friend helped me to transfer the sample from load lock chamber to heater station located in buffer chamber. Another hour spent to let the sample heated to remove any possible contamination, until the pressure is low enough. Finally the sample is transferred from buffer chamber to growth chamber. Yet the growth can’t be started directly. The real outgassing is done in the growth chamber. Why is it real? Because this process undergoes very high temperature up to 900 °C. It can’t be done in the buffer chamber, as the highest temperature is limited up to 600 °C. It is taken to avoid As evaporation on the substrate holder which has been used previously with the As based sample or growth. The evaporated As atoms can make the viewport to be darkened, making the grower can’t really see and therefore disturbing the transfer process. While in the growth chamber, not much to be seen and it is ok to let the outgassing being done in the very high temperature.

Outgassing process itself takes time and once more, very low pressure or good vacuum pressure indicates less and less contamination exist on the surface of the sample. Once it is done, then the growth can be started. Generally, these steps are the same for all typical growth using MBE, no matter what substrate and kind of structure. One thing to remember is that the different sample may undergo different outgassing temperature. For instance GaAs substrate must not exceed than 650 °C to avoid evaporation of As even in the As chamber condition. Without As help, the temperature for GaAs must not exceed more than 400 °C. If it being done, the sample will be ruined even before the growth has not started.

Now what I did for the past two weeks actually can be divided into two different methods. First was directly grown on Si and the second part was helped by buffer layer of Al. The first growth was exactly similar with the previous weeks with the differences in the nitridation treatment and growth temperature. The reasons for changing these two growth conditions were to put more nitrogen incorporation in the nanowire structure and further increase the probability of getting nanowire structure instead of thin film. Well, after scanning electron microscopy measurement, I had a feeling of what the nanowire looks like, better than the last growth but the problem located on how short the grown nanostructure was. The growth time was almost two and half hours, but the height was less than 200 nm where I expected to be at least 400 nm.

Then at the second growth, as my friend suggested me that using Al deposition forming AlN after nitridation can increase the probability of getting nanowire structure, way much better than directly on bare Si. There are many reports using this method and one example is by Songmuang et al. After some discussion, in what sequence the Al and N shutter should be opened and the expectation of what formation will be occurred, finally the plan was written down. Few considerations have been taken to avoid and suppress the formation of SiN by our plan. The growth process was observed using reflective high energy electron diffraction where the formation of AlN and GaN can be witnessed.

The result was not as I was expecting. The grown structure was the same with the structure without AlN buffer layer: short grown nanostructure. I knew there was an issue on the inhomogeneous heating where I could find different structure from the edge to the center of the wafer. The first of two last growth experienced different substrate temperature during AlN formation and slightly higher growth temperature. For the last growth which I have not checked using scanning electron microscope, I increased the growth rate for Ga source. Why? I want to re-confirm my understanding whether I will be getting higher height of grown nanostructure. By using this growth rate, I may get planar thin film instead of nanowire structure. Well, my objective for this sample is not to get the nanowire structure, but to obtain different nanostructure and if it is proven, then I will be happy 😀

I will show the “giant” foot step mark I found in my sample during measurement using scanning electron microscope. I am not quite sure why there is suppressed growth on these area and I can find quite a lot structure similar like these actually. Many factors such as contamination or fracture can give rise to such kind of suppressed growth.

## My first GaN growth experience

After a year and four months waiting, last week I had a chance to actually grow GaN nanowires on Si substrate. Yep, it was my initial episode of my experimental work in this field.

As that time was my debut, actually and honestly, I did not expect something big to happen. I did not put any pressure on myself on getting “proper” nanowire structure. However, I put my best in choosing what parameter to choose with reference from Wierzbicka’s work.

“Growing GaN nanowire growth is more straightforward than GaAs nanowire.” That was a statement I received from my three friends who are much more experience than me. Such words encouraged and challanged me at the same time. I did not know which side I should take, but I choose to take both of them.

The growth of GaN nanowire needs two sources: Ga and N. Ga adatoms, in this case is the flow rate, can be controlled by determining the temperature in the Knudsen cell. N atoms in the other hand, are supplied in the form of plasma from the plasma source. The N atoms flow rate can be adjusted by setting forward power and N gas flow rate. Another important parameter is substrate temperature, where Si substrate sits during the growth. In this substrate, the reaction of Si substrate, Ga adatoms and N atoms interact with each other. Depending on the growth parameters, such growth can result either nanowire or thin film structure.

On Monday, the first day of growth, we made a slight mistake. After nitridation process, we did not notice any Ga adatoms were deposited on the nitrided silicon surface due to the too high substrate temperature. The observation of Ga adatoms are made possible thanks to the reflection high energy electron diffraction. The diffraction pattern were the same before and after 1 hour growth, which was diffused in the background pointing an amorphous surface. We decided to use the same sample for the second attempt.

Tuesday, the second day, our experiment was conducted at the same growth condition with the previous one, except lower substrate temperature. As a comparison to the earlier growth, after like 20 minutes of growth, I could notice that the diffraction pattern were slightly changed where a weak spot were aroused among the diffuse background. I was quite happy at that time, and decided to continue the growth up to another 1 hour and 40 minutes. After one hour, I came back to the lab and observed the diffraction pattern: a stronger spots arranging themselves as it is called as hexagonal or wurtzite crystal structure. Just before the growth was finished, I decided to take another diffraction pattern. I got more convinced that I will get nanowire structures, as Sobanska has proved in her work.

Wednesday, inspection was conducted using scanning electron microscope. Unfortunately, it did not show any nanowire along the surface we have investigated through. It just like random islands trying to coalescence with the nearest islands. Well, eventhough I did not expect too much from my first growth, I was dissappointed at that moment.

Thursday, after thinking what went wrong, I remembered that we set too much growth rate to get the desired structure (based on Calleja’s observation). It was not intentional though. We made miscalculation when considering the length of 450 nm for one hours from Wierzbicka’s work. It was for two hours.

Friday, the second growth using a new sample was conducted, of course with higher expectation. We decided to use the same growth condition, but altered only the growth rate of Ga adatoms. As a consquence of lower growth rate, the diffraction pattern did not show any interesting bright spot after even one hour growth. It was just… nothing compared with the higher growth rate. It was understandable though, but I was becoming really skeptical with my result. A slight changes on the diffraction pattern before and after growth was able to be noticed. Not bad.

Growth was done in 2 hours and 30 minutes. Regarding the diffraction pattern, weak spots appeared and their intensities were nothing compared to the growth with higher growth rate.

In the evening, the same day, we did scanning electron microscopy measurement on this grown sample. Well, it was not a prefect nanowire structure found on the substrate surface, but at least a slightly nanowire-look alike-structure was there! It was better than the first growth at least.

The nanowire were standing very close to each other. I believed it was in the order of 5-10 nm with the closest vicinity. It was so densed and more uniform compared to the GaAs growth, from my point of view. Nevertheless, the growth was inhomogeneous across the wafer. The better nanowire structure was observed close to the edge and getting worse as it located in the center part. My friend thought it was because of the non-homogeneous heating from the sample holder. I just need to talk with the lab engineer.

Hmm… I wonder what to change in order to get more space between nanowire? I hope I can get a better one this week!

## Igniting Nitrogen Plasma

This is my first note on stuff related with my research on molecular beam epitaxy or MBE for short, a technique I will be using for next 3-4 years ahead to make epitaxial grown gallium nitride nanowires on silicon.

Ok, where should I begin? To describe it in simple way, MBE takes place in really huge machine (compared to other techniques like metal organic chemical vapor deposition). One advantage of using this technique is the higher purity of the grown material compared to other technique or in fact, the highest purity quality that we can get. This fact is supported by the condition that need to be maintained inside the MBE machine itself, so-called high vacuum to ultra high vacuum pressure. As an illustration, we live in the atmospheric pressure, where this pressure is equal to 1.000-1.000.000.000.000 lower than atmospheric pressure. It implies the number of contaminants is getting less and less as the pressure goes to ultra high vacuum. Actually, ultra high vacuum provides “the straight pathway”, where intended gas can travel long enough reaching surface of the material without any collision with other gases.

Growing epitaxial layer on top of the substrate can be depicted easily with lego blocks. Imagine you have green big plate and you want to make something on top of it, say a house (Figure 1). The lego house is made of many block components and colors. It can be a 2D house or detailed house, depending the creativity and what passion one has. The same thing goes with MBE.

Now think like this:

Green big plate = substrate

Block components = gas

How the machine looks like, I will write another post for it. This method of growth, where you start from the scratch of substrate where there is nothing on top of it and putting one by one intended component on the substrate, we call it as bottom-up method. Another method is called top-down method, which is similar with carving a statue from single block of stone. Bottom-up method requires more time than top-down method, but guarantee better structural quality.

===

Back to the title. Honestly, this is my first time for me to be trusted with one component of MBE. Since my research is gallium nitride, it means that I need nitrogen to be introduced in the process later on, and the MBE in my professor’s lab is introducing nitrogen by using a plasma.

This end of June was the second opening of the MBE made by Veeco, namely GEN930. Opening in here was done because the some sources (for gases) were nearly finished and repairing electronics of the substrate holder. After opening was finished, then we baked (put lot of panel on it, basically cover the whole surface of the MBE system) it for nearly one week. The baking was done to reduce as much as possible unwanted particles (because of the opening: exposing some part to the atmospheric pressure) and make sure the pressure can go down low enough to ultra high vacuum.

At first week of July, we turned off the baking mode and removed the panel. After connecting all necessary cables, the source outgassing part was done. Once again, the outgassing is required to make sure that the contaminants are minimized to the lowest point. Afterward, dedicated baking for the nitrogen line source was carried out, but no big panel was required. We simply cover it with conductive heating element. After another two days, the baking was finished and it was removed. We need two weeks to do all of these work. Finally, the last step must be done before getting the MBE ready to work: source calibration.

Before doing calibration, my professor would like to test the plasma source, since there was a change in aperture plate (nozzle). The reason to replace with the new one was the attempt to get high brightness mode of nitrogen plasma. This mode is required to grow gallium nitride efficiently. Honestly, I have not tried the growth with low brightness mode of nitrogen plasma source. Probably it would not be appearing as I wanted.

However, there were two main problems which we encountered. First, as we turned on the chiller (for cooling the plasma source), my friend noticed a leakage on input and output of the hose, from the autotuner to the plasma source. Not only leakage in that part, but there was noticed as well on the OD stainless pipe in the plasma source. We discovered the caused which was deformed O-rings, which we forgot to take them out before baking of nitrogen line source. After I got the required O-rings from workshop near my home (great exercise though ^^), we managed to install them and run the chiller with the cooling system not being leaked.

Now, the second problem. We got the plasma at the first time (mediated with argon gas owing to its lower ionization energy than nitrogen gas) and after decreasing the power, suddenly the plasma was off and no plasma was observed since that time. It took about 5 minutes for us to recognize a burnt smell on the autotuner unit and the worse thing was the accumulated heat on the surface near the RF shield. My friend was afraid that he broke the autotuner, but discovered afterward that the smell actually came from the remnant of the leakage liquid that had happened before. The heat was found to be high inside the RF shield itself.

The day ended as my friend sent an e-mail to Veeco engineer, describing the situation. Next day, my friend took a day off and I was the only one left in the lab. The Veeco engineer replied the message with several questions, meaning that I was the responsible person to answer those questions. I was not really familiar with the things like required flow rate, cooling flow direction and RF reflected power, so I needed a bit of time to adapt with it. It took me almost 2 hours to understand the questions, compose the answer and send it back to him.

After I had replied the e-mail, the lab engineer came to the lab and I forwarded the message from my friend. He suggested to clean the copper electrode inside the RF shield, since it was oxidized during nitrogen line baking. As a note oxidized copper is insulating. He used sand paper to remove the oxide from copper electrode. He also explained another electrode which connects to the copper is made from silver and oxidized silver is conductive, so he need to clean the copper electrode only. After putting everything back, we tried to ignite the plasma, but we failed. Still, there was abnormal heat in the same place.

Returning back to my office, I received an e-mail from the Veeco engineer. We talked a bit over the phone and he asked me to send a graph of the forward power, tuning cap and load cap over time.

The day after, I did as he requested. Based on the user manual, I tried to re-ignite the plasma and oberved the important parameter of the graph. Afterward, I sent the exported data of the information, for the two days measurement duration. It took no more than 1 hour for him to analyze the graph! That was such fast response, especially during lunch time. He called me once more and suggested to me that the chiller temperature need to be lowered. He also sent me the procedure to do regarding the difficulty in igniting the plasma.

Well, I was bit skeptic with the new procedural document. In that time, my friend who took day off the day before, coming to my office and encouraging me back to do the new step. I was surprised as the first time and so did my friend, that the required flow rate of the nitrogen was really high, 4 times higher than the highest flow rate we used in the previous experiments. We were afraid of having much high pressure as a result of massive nitrogen flow rate in the plasma source chamber. However, the document said the limit that should be kept an eye for, so we did that and it was fine actually, the pressure still in the safe zone.

After about one minute introducing such high flow rate, I stood close to the autotuner and heard a motor moved. I did not know what it mean though, but I saw a slight RF reflected  power changed. I went to the computer and observed the graph. There was a slight change in tuning and load cap over time. Without any further second thought, I peeked the viewport and voila! The nitrogen plasma source was successfully ignited! You can see how the nitrogen plasma looks like in Figure 2.

I can’t describe how happy I was that time. Probably it can be described like an adventurer who finds a treasure after several days wandering in the desert. I let the nitrogen plasma on for one hour, to make it stable. At the beginning, I feared of the unusual accumulated heat in the RF shield. I monitored the heat in every 5 minutes. Surprisingly, the RF shield went warm at stable temperature. A second happiness 🙂

I stayed in the lab for another two hours, just to make sure that I can re-ignite the nitrogen plasma again and again and again and again… Well, several times. The nitrogen plasma was actually reproducible and I can play a bit with the forward current and flow rate from the set point, running from high brightness mode to low brightness mode.

That Friday evening was one of the best Friday I have ever had in my life :))

## The Wave Equation

This is what I want to write since a long time ago: The wave equation, derived from Maxwell’s equations in free space. Finally! I can write now 🙂

To start with, we need to realize that an electromagnetic field is described by two vector fields, both are functions of position and time:

1. The electric field, $\vec{\varepsilon}(\vec{r},t)$
2. The magnetic field, $\vec{H}(\vec{r},t)$

The famous Maxwell’s equations in free space are defined by

the $\nabla \times$ and $\nabla \cdot$ are the curl and divergence. the constants of $\epsilon_0$ and $latex \mu_0$ represents the electric permitivity and the magnetic permeability in the free space.

Basically, we can express the wave equation based on the described Maxwell’s equation above. So, here we go

Next, we need to use the vector identitiy (curl of the curl) of $\nabla \times \left( \nabla \times \vec{\varepsilon} \right)=\nabla \left( \nabla \cdot \vec{\varepsilon} \right)-\nabla^2 \vec{\varepsilon}$. From (3), we arrive to the equation of $\nabla \times \left( \nabla \times \vec{\varepsilon} \right)=\nabla \left( 0 \right)-\nabla^2 \vec{\varepsilon} \longrightarrow \nabla \times \left( \nabla \times \vec{\varepsilon} \right)=-\nabla^2 \vec{\varepsilon}$. Therefore, we will have

By applying the speed of light equation in free space $c_0=\frac{1}{\sqrt{\varepsilon_0 \mu_0}}$, we arrive to the wave equation in the free space according to the Maxwell’s equation

If we start with (1) i.e $\nabla \times \left( \nabla \times \vec{H} = \epsilon_0 \frac{\partial \vec{\varepsilon}}{\partial t} \right)$ and follow the same step, the final result for the wave equation will be

When we speak about scalar wavefunction, the electric ($\vec{\varepsilon}(\vec{r},t)$) and magnetic field ($\vec{H}(\vec{r},t)$) can be represented in the scalar wavefunction ($u(\vec(r),t)$), and we will have the wave equation as it is explained below,

Great! Now I am satisfied enough 😀

## Plasma Optics (I)

When we talk about optics, we always relate it with the interaction between light and matters. The interaction will give varying result as it depends on what kind of material are being interacted with. One important properties of material is called dielectric function $\epsilon(\omega,K)$, a function whose frequency and wavevector has impact on the physical interaction between light and matters.

We have two fascinating interaction probabilities in here: the light can be reflected or propagate from/through matter. Before we start with everything, it is better to have understanding of what plasma is. Basically, plasma, one of the fundamental state of matters (others are solid, liquid and gas), is medium with equal concentration of positive and negative charges, of which at least one charge type is mobile. Plasma takes form in gas which composed of free electrons and ions. Plasma has high energy.

Plasma has frequency, called plasma frequency $\omega_{p}$ which becomes a guideline for deciding whether the light will be reflected or propagate. I will try to explain this later. All of us know the relation between energy E and wavelength $\lambda$: $E=h\frac{c}{\lambda}$. It is also obvious that metal, in the visible light, is reflecting incoming light. But how does it can be explained by plasma optics?

The answer lies on the value of incoming wavelength light $\lambda$. When $\lambda>\lambda_{p}$, incident light will be reflected. In the other hand, as $\lambda<\lambda_{p}$, incident light will propagate through matter. Illustration in figure \ref{fig:vis} will give a brief explanation of where should the light get reflected or propagate through material. The example is group of alkali metal, with wavelength ranging from 155 – 362 nm.

We will come back later to this concept in the next section.