1. First principles calculation on field emission of boron/nitrogen doped carbon nanotube
I’m going to talk about the first principles calculation on field emission of carbon nanotube. Especially on the effect of boron/nitrogen doping on electronic structure.
Hyo-Shin Ahn1,2, Seungwu Han3, Kwang –Ryeol Lee1 and Doh-Yeon Kim2
1 Korea institute of science and technology
2 Department of materials science and engineering, Seoul national university
3 department of physics, Ehwa womans university

2. Field emission Carbon nanotube for field emission device Definition:
CNT-FED by Samsung
when a material is placed under a high electric field, electrons are extracted from parent material to the vacuum space by tunneling. it is called field emission.
Using field emission, we can make a thin flat panel display of high efficiency. Field emission display. Many researches on FED are in progress
The intrinsic mechanical and electronic properties of carbon nanotube is suitable for FED application.
CNT with high aspect ratio makes stronger effective field
What we focus on this study is that by incorporating foreign elements, the property of CNT can be changed.
Definition:
the emission of electrons stripped from parent atoms by a high electric field via quantum mechanical tunneling  
Carbon nanotube
for field emission device
Structural advantage
- Property modification by doping

3. Experimental measurement
“Role of extrinsic atoms on the morphology and field-emission properties of carbon nanotubes”
L.H.Chan et al., APL., Vol.82, 4334(2003) B
Here is a previously reported result of CNT FE.
Nitrogen and boron is doped to multi-wall CNT.
Compared with undoped CNT, nitrogen doping shows enhanced emission, while boron doping reduces field emission current.
From the view point of dopant effect, we calculated the field emission of carbon nanotube.
B/N doping on multiwall Carbon nanotube
Nitrogen doping on CNT enhances emission, while boron suppresses

4. Calculation method –fist step
Information of wave function shapes and state energy under applied electric field
(5,5) Caped CNT, 250atoms
Relaxation of the wave function
Basis set is changed to plane wave to emit the electrons
Time evolution
Evaluation of transition rate by time dependent Schrödinger equation
Ab initio tight binding calc To obtain self-consistent potential and initial wave function
with the explanation of calculation method, I will show you the result of undoped CNT first.
For the calculation, I used the same method of han, which is a kind of direct calculation of field emission.
Calculation is two step process. first step is to obtain the initial state of emission.
I used (5,5) metallic armchair type CNT of 250 atoms.
After the first step, we can get the information of ‘spatial distribution of electrons and the shape of wave functions’.
Localized basis
Plane wave
“First-principles study of field emission of carbon nanotubes”, S. Han et al., PRB, Vol.66, (2002)

5. Electronic states of Carbon nanotube
p and p* bonds,
Extended states
Due to the graphene structure of nanotube wall
Extended states
<No bias>
<Under bias>
Localized states
Energy EF
<shapes of orbital>
left figures shows the shape of wave functions , orbitals.
CNT has two kinds of wave function shapes. one is extended state, originated from the wall structure.
wall structure is similar to the single graphite layer and graphite has pi bonding state and anti-bonding states, pi *.
and this state is spread all over the wall, so it is called extended state.
the other is localized state, originated from the defective sites on cap of CNT.
Normally, ES locates in all range of energy levels, LS lies above and below Fermi level when there is no applied bias.
when bias voltage is applied, all the states move down, and LS moves close to fermi level.
In field emission of CNT, states around the fermi level have the major contribution to the total emission current, because the potential wall is thin. (easiest place for emission)
localized state is important because it is on the end of CNT, electrons are easy to move and high probability of tunneling.
For the larger emission current, how easy to pull down the localized state energy close to the fermi level is the key of determining the amount of emission current.
If LS is easily pulled to fermi level, field emission is ea
Localized state:
Due to the defective structure of nanotube cap
S. Han et al., PRB, Vol.66, (2002)

6. Calculation method – second step
(5,5) Caped CNT, 250atoms
Relaxation of the wave function
Basis set is changed to plane wave to emit the electrons
Time evolution
Evaluation of transition rate by time dependent Schrödinger equation
Ab initio tight binding calc To obtain self-consistent potential and initial wave function
In second step of calculation, we can do the real simulation of field emission.
From the first step, initial electronic structure is obtained, calculated with localized basis.
by changing the basis from localized to plane wave, electrons are free to move.
By calculating the time dependent schroedinger equation, we get the probability of tunneling and then integrating the number of emitted electrons we can estimate the emission current of each state.
Localized basis
Plane wave

7. Emission current of undoped CNT
Total current: 67.17mA
Cutoff radius 80Ry, Electric field: 1.0V/Å, Energy selection : E-Ef= -1.5eV ~ 0.5V
Localized states
Extended states EF
This is the emission diagram. Y axis represents the energy w.r.t. fermi level. we can see energy states.
X axis represents the emitted current of each state.
energy states near fermi level gives large emission current compared with the others.
These two are localized states.

8. Emission current vs. Bias voltage
From this graph we can see the contribution of LS on field emission clearly.
emission current increases rapidly than that of extended states.
In undoped system, electron emission by localized state is main.

9. Emission current of N doped CNT
Cutoff radius 80, Applied field 1.0V/Å, Energy selection : E-Ef= -1.5eV ~ 0.5V
Total current: 87.59μA
Localized state
Extended state
Now, Let’s look at the nitrogen effect on field emission.
I applied exactly the same procedure to the structure; one carbon atom is substituted by nitrogen then I obtained the emission diagram.
we also can see 4 states around the fermi level have large portion on emission.
Its distribution is slightly different from undoped one.
however, nitrogen doped system shows totally different electronic structure. undoped CNT, 2 localized states exists around the fermi level.

10. Shape of wave functions in N-doped CNT
π*+localized state
By nitrogen doping, noticeable change is observed.
The mixing of localized and extended structure.
In case of undoped system, even when LS and ES have the same energy, mixing does not occur.
Nitrogen gives perturbation of e–structure.
Localized state
π extended state
mixing of localized and extended states;
large contribution to electron emission

11. Emission current vs. Bias voltage
From this figure, we can see the role of mixed states. the other states are similar to undoped one.
orange colored one is mixed state, we can see it act like localized states giving larger emission current.
and according to bias voltage, it has more emission than LS.

12. Increase of emission current
Undoped CNT
Total current: 67.17mA
23% increase by N doping
I substituted only one atom to nitrogen, emission current increased 23% under the same bias voltage.
we can see the enhancement of FE by N-doping
N-doped CNT
Total current: 87.59μA

13. Nitrogen position vs. emission current
Applied electric field : 0.7V/Å, Energy selection : E-Ef= -1.5eV ~ 0.5V
undoped CNT
I changed the position of substitution. as nitrogen position goes along axial direction, emission current increases.
the reason for emission current increase, is originated from the energy of localized state.
As I mentioned before, LS is the main fact for FE and to pull down LS around fermi level is to initiate the FE

14. Boron doping
exactly opposite effect - raising the localized state energy
350atoms, (5,5) armchair-type, applied electric field: 0.5V/Å
undoped CNT

15. Conclusion
Emission of undoped carbon nanotube is mainly due to the localized states
Nitrogen doping :
mixing of the extended and localized states
lowers the energy of localized state
emission current increase
Boron doping :
no hybridization of states
raises localized state energy
emission current decrease