New era begins. MoS2 - 35000 mobility. SdH oscillations. Very recent Preprint.

[Денис Александрович Бандурин]

Hi, guys. 

                                                           To begin with: YOU BETTER READ THIS PREPRINT and this is why:

I know, that we were going to discuss magnetism in graphene ribbon edges but 2 days ago another VERY important preprint appeared in arxive so I thought it would be extremely useful for most of you especially for Mario since he is working with this material. 

The preprint is about MoS2. One of the authors is P.Kim. These guys for the first time (!!!) observed Shubnikov - de Haas oscillations in few-layers of MoS2. In addition they showed that the mobility can be as high as 35000 cm2V-1s-1. This is enormous! Before that it was 200. Now this is comparable with graphene! So as you might expect that will lead to the reorientation of the research to molly. At leas I would anticipate it. 

1. How did they manage to do so.

First of all the encapsulated MoS2 with boron nitride. AND they made contacts from graphene which was crucial. Very beautiful. In addition they made 1D contacts between graphene and outer electrodes so the contact resistance went to zero (50-100 Ohms).

2. So what?

a) As you remember the story with graphene started from high mobility of 2D electron gas. The problem for transistor application was that graphene has no gap. Now we have MoS2 with high mobility and a gap!

b) In MoS2 people have already observed optically valley hall effect DOI: 10.1126/science.1250140. 

Now accompanied by high mobility devices that will lead not only to the conventional electronics but to the growth of TMDCs valleytronics. 

Would be nice to discuss that. What do you think, guys? Shall we start working on TMDCs?

With Best Regards,

Denis.

[Joaquín Fernández Rossier]

Hi Denis,

if you think this is a better paper for the first session of the journal club, let's go for it.  I had no time to read it yet. If is the one I saw in the arXiv the other day,  the high mobility is for a multilayer, right?

[Денис Александрович Бандурин]

Hi, guys! 

I hope you all have read the article. Now let's start the discussion. Actually I have got several questions - so maybe those of you who understand the problem can help me to understand that. In addition in order to make sure that you have read it I have to ask you couple more question :) I hope, you will try to answer. Anyway it can be useful for all of us to discuss that. Ok, let's get started:

1. What is the role of graphene in this device? This is very important question. Recently I was measuring similar device with single layer of TMDC with graphene contacts - it was quite bad. Why did graphene helped here?

2. Why they didn't make just standard gold contacts? 

3. What is the role of boron nitride? Especially if we are talking about thick flakes of MoS2? The layers would screen themselves? Why do we need to encapsulate?

4. Why thin MoS2 flakes have less mobility than 6 layers?

5. I somehow don't understand. How can you dope 6 layers? Do you change the concentration just by doping one of the layers?

6. Question for theoretician to get familiar with the technique: Please, describe what is 1D contacts (or so called side-contatcs)? Who was the first who made 1D contacts to graphene? Why they are nice?

Would you be so kind, guys, to reply asap, please.

Many thanks!

With Best Regards,

Denis.

[marioaoribeiro]

Ok!

Here goes a couple of questions I got some answers to (please someone check this because I am not convinced my self of some answers, lol): 

1. Role of graphene: Gate tunable fermi level of graphene: beeing a semi-metal you can use field effect (back gate or top gate) to align the work function of graphene with the MoS2 electron affinity. So you reduce the schottky barrier and make a "perfect ohmic contact". 

2. Same as 1, but the only issue this time is that gold, beeing a metal (huge DOS), will have it's intrinsic carrier density basically unnafected by the field effect, and you will not align the work function with MoS2, and thus a schottky barrier is formed, and your conduction will be mainly tunneling and thermoionic, and that is non-linear (non-ohmic I-V)

3. Cleans interfaces and self-heals electron traps. Mobility gives you the the average speed of your assemble of electrons in the channel under a field effect, which means that, under the relaxation time approximation, the scattering mechanisms are the responsible for constraining the channel mobility. Beeing 2D material, anything at the interface will act as a possible scatterer and might constrain the mobility (Mathiessen's Rule). Note: if you put a BN flake over a 2D material and inspect it with a microscope, you will see that some whitish "spots" appear on the BN - those spots represent all the junk that once was over the 2D channel; you might want to avoid them when you contact your flakes!

4. Hum...

5. Doping or gating? If it is gating, you can gate 6 layers do that due the low DOS (semiconductor); the field can penetrate the layers without getting fully screened until you have a bunch of them.

6. Edge contacts: 2D materials have dangling bonds at the edges, and so it's fairly more reactive and you can bond the metal and the graphene more easily and make shure that you have a interface properly set to inject your electrons! If you do it the traditional way, you can have junk in between, and since the surface is chemically inert, the likelihood of having a good bond is even lower (therefore bad contact). (Hint: Christian Alvino knows this better)!

[Jose Luis Lado Villanueva]

4. Why thin MoS2 flakes have less mobility than 6 layers?

Umh, I also don't know. Maybe additional layers help to screen impurities. Or maybe it is related with some change between the different bandstructures of the different multilayer systems (however due to commensurate stuff they might be decoupled in terms of electronic bandstructure). What do you think?

[José Luis Sambricio]

1,2 & 6. Very related topics, I guess you are already familiar with that... shall it be left to theoreticians?

3. Isolation from the oxide and keeping things clean, Mario wrote it better than I did. Only thing I want to add is that the crap appears in hBN before putting it over/below graphene, but you always have more after. Very obvious in dark-field images.

4. Check how the single layers were made and you will have the answer. Also, I want to see the supplementary info on how they distinguish MoS2 with Raman & photoluminescence up to 6 layers... And in the STEM image (figure 1c), I don't see the difference between hBN and graphene -they have the same interlayer distance and they put a stupid false color that doesn't allow to see the real contrast-.

5. I didn't see any mention to any doping...

[Jose Luis Lado Villanueva]

4. Check how the single layers were made and you will have the answer.

Only the monolayer was made by CVD, the other were all exfilated, however you see an increasing trend in mobility also in between the others (Fig 3a), so the synthetization technique cannot be the only reason.

[José Luis Sambricio]

Jose Luis, check figure 3.a again, look specifically to the red dots and their "supposed" fit. I don't buy that. Also, it's quite interesting to observe that the temperature they achieved was lower in the case of the 6L...

So summing up:

-6L measurement is, at least weird, and the fitting highly doubtful.

-1L is crap (CVD)

-I am nut sure they can really differentiate the number of layers of 2L, 3L and 4L with only Raman and photoluminescence.   

So the table must read as: CVD is bad (but nor incredibly bad), every other measurement you can trust (2,3,4L) is in the order of a few thousands for mobility. The 6L measurement is... weird.

[Jose Luis Lado Villanueva]

I agree that the fit is far from perfect, however the points could still have a correct value, right?. I mean I don't really know, I don't have an intuition about those measurements are!

Regarding how to characterize the different multilayers, do you all think that is hard to do it just by Raman and photoluminescence?

By the way, I agree with the points that Mario said

[sowmya.ssomanchi]

Revolving around the same "mobility" discussion- Why would 3L have lesser mobility than 2L ? And then it increases from 4 to 6L again!

[josepingla]

To answer Sowmya,

Even in the case they were 100% sure of the number of layers of every sample there must be a dispersion in the mobilities. Not all the samples have the same mobility even if they are made using the same technique (I have seen that in mines) I guess that, if there is not a fundamental reason for that (lower density of states close to the gap for 2 than 3... This should be commented by a theoretician or someone who knows...)  it may be just a matter of making statistics with a lot of samples. 

Cheers 

Pep

[Francesca Finocchiaro]

Hi everybody. After an afternoon of hard work, misunderstanding, doubts about the fundamentals, all fortunately shared with Luis, here I come with questions, doubts and answers (mostly questions) (I want to anticipate that to the experimentalists most of my questions might sound really basic but I thought: what better occasion than this to finally clarify all of these things?):

1) Why to use a four terminal device when it seems clear that all the issues due to non-ohmic contacts and semiconductor/metal (or graphene, in this case) resistance increase proportionally with the number of contacts? I mean, there must be a clear advantage in using multi-terminal devices, but I can’t see it straightforwardly.

2) Am I right in guessing that the “non-metallic” behaviour of the contact resistivity for back-gate biases smaller that 20 V is due to in-gap states produced by the impurities or defects which make the system stay insulating for low carrier concentration since with the first electrons you “inject" it is these in-gap levels that you are populating instead of the conduction band?

3) I don’t see clearly why using hBN is better than the substrate itself. Why do Si-SiO2 induce so many interfacial impurities while hBN does not, and, what’s more, it even arrives to the point of cleaning the sample, that is, grabbing and trapping itself the impurities it finds on the MoS2 surface? From what I red I got (maybe wrongly, I don’t know) that hBN has a high dielectric constant and that makes the impurities more screened, is that it? But is it all? Or are there more fundamental reasons? And how come the hBN accepts all of the junk accumulated by the sample? (or the junk you see on the microscope is not grabbed from the sample, but from the substrate?)

4) By doping you mean inserting different atomic species able to donate electrons to the system, right? While by gating you mean putting a specific substrate (back-gating) or a overlayer (top-gating) (how is the material chosen, btw?) and then connect it to the metallic contacts (drain and source) in order to move the Fermi level of the sample?

5) What does José Luis Lado mean by “commensurate stuff”? In any case, I'm attaching a file that explains a little how the band structure changes while increasing the number of layers, maybe it can be helpful.

6) What’s the difference between Hall mobility, Field Effect mobility and “true” mobility (if any)? What’s the more realiable measurement?

7) I haven’t got clear why a 2L/3L “inversion” is obtained, and why they seem (people who performed the experiment) nontheless able to state that there is a clear trend of the mobility with both carrier concentration (that I see, and there’s a clear and unanimously recognized cause, that is the enhanced screening) and with layers (in this case the trend is not monotonous). In any case my (veeeeery naive) idea is barely that if the charged impurities are mostly superficial (correct me if I’m wrong here) than it’s clear that the more layers you add, the more “clean system” you get, meaning that the percentage of dirty sample over clean sample grows with the number of layers, being maximum in the case of a monolayer.

8) I don’t have any idea of how these characterizations of the number of layers are done (Raman and photoluminescence) and I imagine that the subject is huge so if you have some useful (yet simple) references I would be grateful.

9) Does anybody know what’s the state of the art of the QHE in these systems, both experimentally and theoretically?

10) Does anybody have access to the supp info? If yes, can you send them to us?

I could go on to infinity (it’s amazing to have the possibility of “exploiting” experimentalists for clarifying these evergreen doubts -waiting for you to do the same with us as soon as it will be our turn). I’m about to read references on the 1D contact thing, I don’t even have a clue of what you mean by 1D in this case.

Hope I haven’t been too pedantic, feel free to skip as many questions as you wish.

[Francesca Finocchiaro]

[Francesca Finocchiaro]

Errata corrige:

point 7): the correct thing is: "the more layers you add, the more “clean system” you get, meaning that the percentage of clean sample over dirty sample grows with the number of layers, being minimum in the case of a monolayer."

and not the other way around

[Jose Luis Lado Villanueva]

3) I don’t see clearly why using hBN is better than the substrate itself. Why do Si-SiO2 induce so many interfacial impurities while hBN does not, and, what’s more, it even arrives to the point of cleaning the sample, that is, grabbing and trapping itself the impurities it finds on the MoS2 surface? From what I red I got (maybe wrongly, I don’t know) that hBN has a high dielectric constant and that makes the impurities more screened, is that it? But is it all? Or are there more fundamental reasons? And how come the hBN accepts all of the junk accumulated by the sample? (or the junk you see on the microscope is not grabbed from the sample, but from the substrate?)

Apparently O defect in a SiO2 substrate are able to easily create hole dopand in graphene http://arxiv.org/pdf/1107.3001.pdf. On the other hand, I think there is no charge transfer between graphene and BN, so that defects on BN are not so critical.

5) What does José Luis Lado mean by “commensurate stuff”? In any case, I'm attaching a file that explains a little how the band structure changes while increasing the number of layers, maybe it can be helpful.

Depending on the angle between two graphene layers, their electronic structure can be the one of the bilayer or the can also behave simply as two uncoupled monolayers (even though they are quite close!) http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA590798. The same can happen with BN and graphene, graphene can suffer a BN induced gap at certain angles, or it can behave as free graphene at other angles. So, the same might happen in MoS2 a bilayer can behave as an typcal bilayer (like the one of your picture), or just as two uncoupled bilayers.

[Luis González]

A few remarks to summarize:

1) It seems clear and trustworthy that the electron mobility does increase with carrier density. 

2) It is not clear AT ALL that electron mobility increases with sample thickness. As Sowmya pointed out, the 2-layer has greater electron mobility than the 3-layer, this seems like an important exception (and by the way Pep, I´m not sure I understood your explanation). Also when they study the temperature dependence of the mobility for samples of different thickness (Fig. 3a) finding that they all follow a power law T^(-gamma), it turns out that the thicker the sample the more steeply the mobility decreases with T (the greater the gamma parameter), again, with the exception of the 2-layer!!!. So, in my humble opinion: further inquiry needs to be done to assess the dependence of mobility with respect to sample thickness. 

A few questions: 

1) This might be an amateur-like on my part, but here it goes: Why do they need ohmic contacts???. Apparently, this is crucial, since Mario said that this is the reason why they used graphene contacts in the first place. Also can someone explain why the low density of states of graphene  (as compared to gold) makes it easier to tune its work function to whatever value you need to reduce the Schottky barrier???. Please, if you have an answer, don´t underestimate my ignorance, keep the answer as simple as possible. 

Thank you

[Julian Peiro]

Sorry to come late:

@Luis: 1. The ohmic contact is also often called transparent contact in the sense that we need as much as possible a weak temperature dependent and linear with bias resistance of contact so that you can easily interpret your measurements, reduce the level of noise and attribute features to the material you interested in.
Why graphene: I guess but not sure that

@Jose-Luis: For photoluminescence I don't know, but for raman I know the signal is a bit worse than in MoS2 and you can already distinguish specific signals for 1, 2 and sometimes 3 layers.

@Francesca:
3. You're right about the dielectric constant but also the roughness of your substrate wafer of Si/SiO2. Even for a thermally grown oxide the roughness is large enough to induce local strain reducing the mobility (early measurements in graphene). In a general case you have nothing better than a 2D layered material as substrate deposited on top to smooth a large part of this roughness. I don't really understand what you mean by hBN accepting junk, but all the art of transferring and staking the flakes is to do it slowly with the less bubbles possible, but this may happen between every layer of your microscope, and create the discrepancy you can observe on 2 devices made out of the same stack.
4. Yes about the difference between doping and gating, but in 2D material world, guys call doping the direct tuning of carrier density by gate voltage. Anyway maybe I misunderstand but no point in connecting it directly to source or drain. You only apply a difference of potential between the ground reference of the sample and the gate, and enjoy the difference of behaviour of conduction between source and drain for instance, that's all.
7. About the behaviour of the mobility mu_imp with the number of layers: I agree with Jose-Luis that we cannot actually trust quantitatively the mobility curve, some statistics is crucial.
This idea of uncoupled layer is very interesting, but isn't it quite unlikely to happen with exfoliation? Never heard about this case here.
Unfortunately we don't have the 5 layers curve either, but, very naive question: would it be possible (maybe theoreticians know) for few layers to expect a different "quality" of screening due to a difference of repartition of conductive channels between odd and even number of layers?

Plus for the 1D contact, It concerns etched stacked structures (like hBN/graphene/hBN), which after etching present generally a not perpendicular edge but a small slope where the very edge of your graphene appears. So you deposite your metal on that to make the contacts, I guess the 1D simply comes from the intersection between this amount of metal and your plane of graphene (contact itself should be a 1D nanowire in wonderful perfect world)

I hope I could help, I stay interested in your other question, I don't want to be too adventurous to answer my self now.

[Julian Peiro]

Errata: @Jose-Luis: For photoluminescence I don't know, but for raman on WSe2 I know the signal is a bit worse than for MoS2 and you can already distinguish specific signals for 1, 2 and sometimes 3 layers

[sowmya.ssomanchi]

@Francesca-

1)      If you are referring the use of Hall bar geometry and the 4 probe measurements- 2 for sending in the current and 2 transverse probes to measure the Hall voltage, then I think its because its easy to extract the conductivity and mobility from the same experiment. I mean, in general too, 4 probe measurements are preferred because there is no current through the voltage measuring contacts, so they are more accurate because they measure the potential drop and not any contact resistance. May be there is more to this.
3) As far as I know- hBN is atomically flat like graphene, free from any dangling bonds and charge traps and has only a  a little lattice mismatch with graphene which makes it a good and clean substrate. SiO2 induces a lot of disorder, charge traps and can lead to a lot of scattering. Julian explained it well. More Fundamental reasons- Experienced experimentalists in the group, please help!

4) You are right about gating. You move from hole to electron carrier regime by playing with gate voltage around the Fermi energy and thereby the doping and charge carrier density- typically what you will see in a Hall conductivity measurement

6) Conductive mobility- It comes from the 2 probe conductivity measurements directly.

Hall mobility is the mobility when the electron is under a magnetic field and therefore might experience different scattering mechanisms. So Hall mobility can be different from regular mobility. But its easy to measure and compare.

Field effect mobility- This is measured in transistors obviously and refers to operational device mobility. It should be smaller than the Hall/drift mobility due to even more scattering from the gate oxide and various interfaces, leakage current etc.

8) You characterize the no. of layers in graphene by fitting the 2D peak of the Raman spectrum to a Lorentzian. The FWHM and no. of Lorentzians that can be fitted to the 2D peak determine the no. of layers. This paper explains it well. http://fscimage.thermoscientific.com/images/D19504~.pdf