Project: 3.3 Si band structure [detailed explanation] | Quantum Espresso Tutorial 2019

Project: 3.3 Si band structure [detailed explanation] | Quantum Espresso Tutorial 2019

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00:00
hello everyone welcome back to my channel in this video I will talk about how to calculate the band structure of silicon crystal and in the last video I have shown you how to calculate the tensile state of silicon but that is much simpler than the calculation of the band structure because the attends of state is just a one-dimensional function so x axis is the energy and y axis is the dance of state and and information of the of the reciprocal lattice has
00:31
been integrated out but here in in reality for for every point in the reciprocal space you get a discrete array of of energies for example at at this L point here you can see from the band structure here at our point you have an array of discrete energy levels and that array is basically the energy of different bands and if you change
01:00
your if you move your K points in the in the k space those array of those array of energy will also change with respect to the position in a tech space so basically now the problem is not a one-dimensional function but it is a three dimensional function and and several three different dimensional function so in this case it is it is not possible to represent all of the
01:33
information on paper so so you need to come up with a smarter idea how to represent your calculation so the common way to do it is to Ursula is to find out high symmetry points in the in the Brillion zone and what I show here is is the first Brillouin zone for FCC lattice and you know that silicon crystal is two FCC lattice shifted by one fourth of the
02:05
crystal of the unit cell so so here the earned the highest symmetry points are labeled here with different names for example the L point is the center of the hexagon here and the gamma point is the like center of the Brillion zone and this X point is the center of the square here and you point is the is the Center for this edge here so so on right hand side this is the this is one reference
02:39
of the pen structure for silicon and it actually goes from our 2 comma 2 X 2 u 2 comma so it goes so it chooses a path from L to gamma and from gamma to X that is the center of the square and then from X to u there's the center of this edge and then from you directly to come a straight Lee ok so if you search search the literature you can find
03:12
different ways to define the K path and it's totally fine that you that if you include this K point here or in you include the W point here indeed you can find some literature also using other other K paths so but in today's video I will never follow the same path as the reference here from how to command gamma to X X to you and u2 comma and what we
03:44
notice here is that the size and the length of the segments of the of this plot is different so so I also try to reproduce that by setting the number of points to be different so we see that in hacked from X to u that is this in this segment we set the points to be smaller so that in the output it is also proportional to what we see in the reference so the basic steps are the
04:16
same you first need to do the case of consistency calculation and then you need to pants calculation and to do some post-processing and then to plot the pant however things you since when you want to put a plot depend you need to specify the Fermi energy and and in the in the step status that before it is not unlike the from energy is not automatically obtained so there are two ways to obtain
04:46
the Fermi energy either you add a smearing term in self-consistency calculation part or you you keep you keep the self-consistency part the same but you add another known self-consistency calculation with a tensor of k k points as we did last time for the sense of state so if you follow the second possibility it is and it's usually more accurate like the fermi energy and also the north of consistency
05:17
calculation would help a little bit on an advanced calculation because you you already refined the calculation then intenser okay k point grid however the left possibility with the smearing has has one step less so that you don't have to calculate that's K point so this will be faster so in this video I will show show you so what does it mean by adding smearing or not but
05:49
then we will follow the second possibility to calculate energy pad okay so as usual I have already written down the input files and yeah and then we need to first source the pair of studio and we first checked the self-consistency input file and
06:22
everything is is more as the same it's just that I add and kind of kinetic energy for the charge to be eight times thicker WFC here so to be more accurate and then and then I specified a number of pens calculated here so if you don't specify this line it will it will be a half of the electrons in half of the total electrons
06:54
in the system and and the total electrons calculated are specified by by this pseudo potential file how do you find out there are how many electrons are there you can comment out you can so if you don't know you can comment out one line in in the input file by this exclamation mark you know so so basically though and this line and this line are are commented out so they will not be they will not be run okay so so
07:27
we first see if we do it without without the specification for the number of pens and then we take a look in the output file and in the header of the whole profile you can find the number of number of electrons here so there are eight electrons in the in the system and the band and it only uses half of the
07:59
electrons as the number of bands so for so in in the case of insulator of semiconductor it will be exactly half of the half of the number of electrons but in the case of of metal or you a dance at a smearing term it could be a little bit more than half but here we want to calculate eight the reason is that if you just calculate for it is all of them are the valence band and there is no
08:32
conduction spent if you if you see from output file still you can find out that in the end it only specifies the is occupied arrival because there is no information about the conduction band so it doesn't doesn't know what is the what is the lowest unoccupied level so we can add this on communities and set bands to p8 and then we start we run again and see in our profile here we first go
09:12
and going to the heater to see that the number number of electrons are still 8 but the band is successfully increased to 8 bands okay and if we scroll down there there is more information here because now we include the conduction bands so it knows what is the highest occupied level what is also what is the lowest unoccupied level and the the difference between those two numbers is more or
09:43
less and band gap the reason why I say more or less instead the K point grid is still not very dense here so the estimation could be a little bit off but well I guess this is more and more or less there okay but still you see no no matter whether you you add at a specification for the band number you don't get a Fermi energy inside this file to get the Fermi energy inside this
10:16
file you need a smearing term here the reason is that if you don't have a smearing term you are basically calculate adds at zero temperature at zero temperature you you know there's a there's a band gap the Fermi energy could be anything's at a band gap so to solve that you need you need some smearing under Fermi honor Fermi level and then if you do the calculation again and it opened on fire and you see that
10:56
it outputs the Fermi energy however here you see that it doesn't output the highest occupied level or lowest unoccupied level the reason is that you add a smearing so so not everything below the Fermi energy is occupied or everything under laughter from an energy is occupied so this is no longer true because of the smearing okay so this is one way that you can get the Fermi
11:27
energy but but in in this video I will I will just not use that if you if you do it like that you can skip the SCF calculation and and then directly go to the bands and bands P P and plot band calculation you know so we commented out and do the calculation do the self-consistency calculation again so it's finished and
11:59
we check again yeah so now in it is back the highest occupied and lowest unoccupied level and then we want to do a know Suffolk insist consistency calculation to calculate the Fermi level and yeah so this is quite familiar to you and we just do this unless yeah one do this calculation and in the output file you can always
12:44
find the Fermi energy so yeah so the third step is to run bands calculation so still the PW tax program and the only difference is that you change the calculation type to be bands and everything else you keep the same except that you change the K points to the through capers and points that you manually that we manually define and this is the K points the K path that you want and want to define here okay I need
13:18
to make this so so basically it is the first high point is l and second is gamma and xu gamma and it specify the path from L to gamma from gamma to X X to u u2 comma and and this number is is the total number of K points which is just a number of lines here and then for
13:54
each line the first three numbers are the K X KY and KZ and the fourth line of the fourth number is the weight and the weight here means that missed number of points starting from that starting from that path so basically it means that from L to gamma there are 20 points from gamma to X there are 30 points from X to you there are 10 points from you to gamma there are 30 points and this trend here
14:25
has no meaning here oh you can set it to whatever you like okay and then the question is how do you like you know you know that you want to specify a path from our 2 comma 2 from gamma to X and from X to you from u2 comma but now the question is that how do you get these numbers you know so one very useful software is X Kristin and you can open the input file or opera fire whatever you want
14:56
for example the odd profile for the SCF calculation here for example and it's just a single point calculation just to get the structure of of silicon crystal and then you choose in the tools there's ok pass a selection yeah and then you see the first boolean zone so maybe I
15:31
need to move it a little bit so that I can see yeah I can show you both at the same time ok so we first so we rotate it to the to the same way as soon as this one and then we want to get from from L to gamma and L is the center of this hexagons of this one and then to gamma gamma is the center of the boolean zone
16:00
and from gamma to 2x from gamma to X exit the center of the square from X to u use the center of this edge from u2 comma again yeah and then you get reciprocal coordinates here and an in principle you could just copy all of the coordinates from here from here to here
16:34
and of course you see that it's it's it's different the reason is that there there is a very high symmetry of the first Brillouin zone so even if you get different numbers as here but but they are more or less symmetric so you will get the same band structure out you know ok so I will just close this one and and this is the k path that we want
17:04
to specify and let's just do the calculation so to do the calculation you also have to also use the Peter brutal x3 no sorry there's not three but you okay and now it's finished and you know and now the Barons are calculated but they are not in a way that is readable
18:03
so we need to post processed the result and then you need to use another another or sub program which is called bent dot X to do post process the result and this is the input file for bent on X and you need to specify the name of the of the output data so this output file will contain the data of the pants and afterwards you can you can use gene you plot you can use Python you can you know
18:36
or you can use as I will show later the plot bent to a pen etat X in quantum espresso to plot the depend okay and then we just run the bandit or X remember that you need your changes depend two x plus three okay I'm in mistake it is not caught band directs but bends and directs
19:35
okay so now it's finished and you see this is the fire that contains the data of the Bands you know and it is a structured but still we cannot directly put plotted what I what I want to use is not this one is the P is the plot bandit order and Daleks so for the broadband don't acts you can do the interact interactively you can just type in plot
20:08
bandit or X and then it will prompt you for different inputs what I do here is that I constructed a input file for the broadband drugs and and for the input file the first line is the is the fire that contains the data of the bands which is the output of the of the last step and then the second line specifies the the window of energy so this is the minimum energy this is a maximum energy
20:39
plotted so how do you get these numbers you can go to whatever output file for example an output file for the SCF or a tall profile of that unless CF or even the pants I will just show you the profile of the pants and then scroll down and take a look at at the energy of different K points so basically this means there are one two three and there are eight energy bands and at this K
21:10
point and energy is from minus 4a action bar to 13 electron volt and you may scroll down a little bit and you will see that okay it's more as from minus six to 215 in extreme world so here we say minus 7 to 16 in action were two to take into account of everything and this is the name of the output file and these are also the name of the output file for this one you need a special and special software to be open in whooping to and
21:41
this way you can directly open in open to and so basically those are the plots of the pans and this is the Fermi energy you have to specify and in our case we can just copy it from from here from the output you can either copy it from the output of the nest and SCF or if you use smearing in the ass here you can also
22:11
copy it from there okay so this is and this one is its spacing of the while APIs you know of the of the labels on the energy axis and and this number here we usually set it to the Fermi energy this is the energy that you you were ship it to be to be zero energy so the Z this defines the Fermi energy as a
22:43
street and zero energy in the plot so then we can do the plot and usually I don't use MPI run here plot and toe tags and the name is floor okay yeah
23:25
in this case you shouldn't use - I am P because it doesn't accept that you need to use this this lesser sign okay and then this is the ultra as I adore pen store PS open this PS file maybe you want to rotate it and this is actually the energy band so so this one means the
23:56
spacing of the energy axis so this is a nine eight seven if you if you change it to two for example maybe we should cross this one first we have 22 you are see it on a spacing changes to 2 and 0 is the Fermi energy
24:25
okay so so if you see from from here to here we successfully reproduced the pen structure calculation in the reference and you see this is a this is the Fermi energy and there is a band gap here and and the first line is is what we specified an arrow gamma X U and gamma and the shape and everything is the same mass and as the reference okay
25:07
so into this video I have shown you how to do Ben structure calculation of of silicon crystal and and I've shown you how to obtain the Fermi energy in in two different ways and how to how to obtain K paths if you know that we want to plot from our 2 gamma 2 ax 2 u 2 gamma how to convert the name here to the actual coordinates by x Kristin okay so thank
25:39
you for watching and I hope to see you next time

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