Band-offsets of Single-wall Carbon / Boron Nitride NanotubesYen-Chen Lin, Der-Hua Liu, Yu-Ru Hsieh, and Ming-Hsien Lee

Department of Physics, Tamkang University, Taipei 25137, Taiwan

We investigate the band offsets of single wall (n,0) C / BN nanotubes and study their variation with respect to different tube diameters. Since a C-BN nanotube unit is polar, a reverse tube section is prepared in our model, making the size of the super-cell doubled. We plotted macroscopically averaged potential to study the interface dipole between C and BN tube sections. It has been reported that the electron distribution due to top of valence band states of different n can makes the polarisability of electron cloud different at tube junction [1]. Our results provide a check to such interpretation. In the current study, a static electric field is also applied perpendicular to the tubes axis to study the band offset modulation under the influence of such external electric field. The doubled length supercell construction makes our methodology more transparent and results easier to understand.

FIG.1. Semi-infinite tube junction of BN-C (with N-C bonded interface), B (pink), N (blue), C (gray).

II. Two types of single-wall BN/C tube junctions

I. Motivation

III. Super-cell models for band-offset calculations

FIG.3. Supercell (periodic, extended) models of tubes from (3,0) to (8,0) , with colours of B (pink), N (blue), C (gray).

IV. Obtaining band-offsets

FIG.6. Schematic figure showing how are eigenvalues, and potentials of tube and moving slab averaged potentials related to conduction and valence band offsets. (This is the method we used to get band offets.)

FIG.2. Semi-infinite tube junction of NB-C (with B-C bonded interface) ,with colours of B (pink), N (blue), C (gray).

(3,0)

(4,0)

(7,0)

(5,0)

(8,0)(6,0)

FIG.5. Planar and moving slab averaging results, for all zero field tubes (potential vs. z plots).

FIG.4. Band structure plots of pure tubes (region near fermi-level)

TABLE.1. Since there are polarisation field inside BN tube sections, the moving-slab averged potential in the region is not flat. We use mid-point value as reference position of potential background for band structure eigenvalues. The convergence tests of mid-point BN value w.r.t. tube section length don't affect the band offset values obtained.

V. Calculated band offset values at two types of junction

TABLE.2. Band offsets at BN-C interfaces of (n,0) tubes (comparing with available data in Ref.[1]).

TABLE.3. Band offsets at interfaces of (n,0) NB-C tubes.

VI. Band offset value from PDOS method

FIG.7. PDOS of pure C, pure BN to show where are PDOS edges of VB and CB.

2 BN unit cells band offset 　VB -1.04 eV 　CB 1.62 eV 　

3 BN unit cells band offset err w.r.t. the original (%)VB -1.054 eV 1.577 CB 1.60 eV -1.013

4 BN unit cells band offset err w.r.t. the original (%)VB -1.04 eV 0.017CB 1.62 eV -0.011

BN-C (n,0) (3,0) (4,0) (5,0) (6,0) (7,0) (7,0) [1] (8,0) (8,0) [1]

VB offset (eV) -0.30 0.46 1.08 1.04 0.88 0.82 0.94 1.12

CB offset (eV) -0.32 -0.84 -0.81 -1.62 -2.15 -2.09 -2.13 -2.50

(3,0) (4,0) (5,0) (6,0) (7,0) (8,0) (9,0)

VB offset (eV) -0.12 0.79 0.71 1.33 1.48 1.42 0.42

CB offset (eV) -0.15 -0.51 -1.17 -1.32 -1.54 -1.66 -3.02

FIG.8. Bulk-zone selected PDOS of BN-C to emphasize CB offsets and VB offsets. (7,0) tube (left), (8,0) tube (right).

FIG.9. Bulk-zone selected PDOS of NB-C to emphasize CB offsets and VB offsets.(7,0) tube (left), (8,0) tube (right).

BN-C (7,0) error w.r.t. [1] (%) (8,0) error w.r.t.

[1] (%)VB offset

(eV) 0.65 -20.7 0.88 -21.3

CB offset (eV) -1.25 -40.2 -1.55 -38

TABLE.4. Band offsets of (7,0) and (8,0) BN-C tubes extracted from PDOS (with % error comparing with [1]).

VIII. Band offset variation with respect to applied static E-field

FIG.12. Band structure plots of pure tubes of (5,0) tube under different E-fields. (Moving slab potential averaging plots are not shown here.)

(5,0) BN

(5,0) C

0.0 V/A 1.25 V/A 2.5 V/A 3.75 V/A 5.0 V/A

TABLE.5. Band offsets at N-C interface and B-C interface of (5,0) tube, under different E-field . From zero E-field to 1.25 V/A, magnitude of band offsets are reduced, and the sign of CB offsets are revered.

E-field (V/Å) 0.0 1.25 2.50 3.75 5.0

N-C interface

VB Off (eV)

CB Off (eV)

1.08-0.81

0.440.41

-0.001-0.035

-0.021-0.017

-0.034-0.044

B-C interface

VB Off (eV)

CB Off (eV)

0.71-1.17

0.230.19

0.0460.017

0.0340.038

0.0130.003

IX. Discussion and Conclusion

Reference [ 1] Meunier, Roland, Bernholc and Nardelli, Applied Physics Letter, Vol.80, 40, (2002)

We would like to investigate the possibility of obtaining band offset values of single-wall BN/C tube junction of different tube diameters, using a more "traditional methods", namely moving-slab averaging potential and bulk- zone PDOS matching-up, other than the one suggested in Ref.[1].

We are also interested to know how band offsets of these tubes are modulated under a static electric field perpendicular to tube axis.

(1) Band offsets of nanotube junction can be obtained by using traditional moving-slab approach, PDOS approach is less robust in this application unless better sampling of k-points is used, which is computationally demanding. (2) For all tube size investigated, B-C interface has a bigger band offset magnitude (both VB and CB offsets) than those at N-C tubes junctions. (3) Perpendicular static E-field does have an effect on VB and CB offsets on both B-C and N-C interfaces, making them smaller in magnitude. (Preliminary results.) (4) In the present work, we can not find the (7,0), (8,0) specific orbital orientations reported as the FIG.2 in Ref. [1] 　 (please see the mini-figure on the right). Further investigation is in progress.

3 BN unit cells

4 BN unit cells

2 BN unit cells