First-Principles Study of the Doping of InAs Nanowires - American

ARTICLE pubs.acs.org/JPCC

First-Principles Study of the Doping of InAs Nanowires: Role of Surface Dangling Bonds Haibo Shu,†,‡ Xiaoshuang Chen,†,* Zongling Ding,† Ruibing Dong,† and Wei Lu† †

National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, 200083 Shanghai, People’s Republic of China ‡ College of Optical and Electronic Technology, China Jiliang University, 310018 Hangzhou, China

bS Supporting Information ABSTRACT: The effect of surface dangling bonds (SDBs) on the doping of InAs nanowires is investigated by first-principles calculations within density functional theory. The result of the formation energies shows that the dangling bonds of In atom on the surface of nanowires are a kind of stable defect. Moreover, the surface dangling bonds prefer to be charged and form trap centers of carriers. For the ultrathin nanowires, both the positively and negatively charged SDBs can be produced. With the increase of size, the stable energy region of the negatively charged SDBs has diminished gradually and disappeared, but the positively charged SDBs keep a high stability. The result originates from the quantum confinement effect that makes stronger influence on the conduction band than the valence band of InAs nanowires. The higher stability of the positively charged SDBs means that the SDBs have an ability to capture the holes from the p-type dopants, resulting in the deactivation of dopants. Thus, the SDBs could be fundamental obstacles for the p-type doping of InAs nanowires. On the basis of our results, the surface passivation can be considered as an effective way to suppress the effect of SDBs on the doping of InAs nanowires.

I. INTRODUCTION One-dimensional semiconductor nanowires have attracted much attention in recent years due to their unique physical properties and superiority as the building blocks for the fabrication of the nanoscale devices. Recent progress in nanoelectronic and nano-optoelectronic devices has been demonstrated based on semiconductor nanowires such as lasers,1 field-effect transistors,2,3 photodiodes,4 sensors,5 and solar cells.6 Successful realization of most these applications requires a high carrier concentration so as to reach sufficient conductivity. Unfortunately, pure semiconductor nanowires have low concentration of carriers due to the increasing band gap with the decrease of the nanowire size.7
9 Doping is an important way to provide free carries. The density of carriers is controlled by the addition of doping atoms. However, it is fairly difficult to control effectively doping of semiconductor nanowires. For example, the concentration of carriers in doping Si and III
V nanowires is still far less than that expected.10,11 InAs nanowires are potential candidate materials for the applications in nanoscale electronic and optoelectronic devices since bulk InAs is known to have narrow band gap (354 meV), high electron mobility (20 times higher than that of Si at room temperature), and high-saturation drift velocity.12 To realize the application in nanoscale devices, the doping of InAs nanowires is required step. However, the doping of InAs nanowires is less efficiency, especially for the p-type doping. There are several factors that could limit the doping efficiency. One is the so-called r 2011 American Chemical Society

self-purification effect.13 The doping atoms tend to segregate to surfaces and/or interfaces as the size of the semiconductor nanomaterials decreases. To overcome the limitation, Erwin et al.14 have developed a concept of kinetic doping in which doping can be controlled by adsorption of impurties on the suitable surface of nanostructures during growth. The second factor is high ionization energy of dopants. Generally, the ionization energy of dopants in the nanowires increases with the decrease of size due to the dielectric confinement, resulting in lower conductance. For example, the resistance of InAs nanowires with 20 nm diameter is 2 orders of magnitude larger than that of the nanowires with 40 nm diameter.15 Surface functionalization of nanowires is considered as the most useful way to lower the effect of dielectric confinement.16 The last factor is also the most important factor that InAs surface Fermi-level is pined above the conduction band edge, resulting in a surface accumulation layer of electrons.17,18 The Fermi level pinning makes it difficult to achieve p-channel conductivity in InAs nanowires. It is generally believed that the Fermi-level pinning is caused by a large number of surface states on InAs nanowires.19,20 However, the intrinsical physical mechanism for the doping of nanowires inhibited by the surface states is still unclear. Received: December 17, 2010 Revised: June 28, 2011 Published: June 28, 2011 14449

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The Journal of Physical Chemistry C Experimentally, some studies have found that surface passivations can adjust the concentration of carriers and increase the efficiency of p-type doping in InAs nanowires. For example, the p-channel characteristics have been observed when Cd-doped InAs nanowires are passivated by surface ligands.21 Du et al.22 have demonstrated that InAs nanowires can be considered as one of best candidate materials for the applications in gas sensor. They have found that surface adsorption of most chemical molecules can reduce electron density in nanowires and enhance the electron mobility greatly at the same time. Recent experiment has found that the electron mobility of InAs nanowires passivated by with 1-octadecanethiol (ODT) is significantly superior to that of unpassivated nanowires.19 The XPS characterization has indicated that the ODT molecules are bound to the InAs nanowires through In
S bonds. All these experimental results suggest that the elimination of surface states by passivating surface atoms is an important way to improve the transport properties and activate the p-type dopant in InAs nanowires. It is well-known fact that the dangling bond (DB) defects are abundant at the surface of InAs nanowires without the surface processing and consist of the main source of surface states of InAs nanowires. Therefore, it is important for understanding the role of surface dangling bonds in the doping of InAs nanowires, which is the key to realize the effective p-type doping. Theoretical investigations of the effect of surface dangling bonds (SDBs) on the electronic properties and doping of semiconductor nanowires have been performed extensively in the past few years. Fern
andez-Serra et al.23 have shown that a large proportion of dopants would be trapped and electrically neutralized at SDBs, significantly reducing the density of carriers of Si nanowires. Hong et al.24 have investigated the effect of SDBs on the doping of Si nanostructures using the first-principles calculations. They have found that SBDs could be fundamental obstacles in the asymmetry doping of Si nanostructures. On the basis of the density functional calculations, Miranda-Dur
an et al.25 have demonstrated that molecular passivation could be a good way to activate the dopants and increase the doping efficiency of Si nanowires. For III
V semiconductor nanowires, Fang et al.26 have performed the first-principles approach to investigate the effect of surface passivations on the electronic properties of GaN nanowires with various functional groups. They have shown that the partial hydrogenated GaN nanowires have small band gaps due to the effect of dangling bond states. Recent theoretical study of first-principles calculations has be performed on the stability and electronic properties of unpassivated GaAs nanowires.27 They found that the band gaps of nanowires are ruled by surface states of edge atoms and do not follow the trend by the quantum confinement effect. To the best of our knowledge, the theoretical studies on the role of SDBs in the electronic properties and doping of InAs nanowires have not yet been reported. In this work, we have reported the results of ab initio calculations for the effect of surface dangling bonds on the doping of InAs nanowires. We first investigate the stability of various charged SDBs on both zinc-blende (ZB) and wurtzite (WZ) InAs nanowires by comparing their defect formation energies. Then we show the p-type doping limitation from the charged SDBs. Finally, we further investigate the size effect of nanowires on the formation energies and trap density of the DB defects. Our results suggest that the charged traps caused by surface dangling bonds are also a fundamental factor for limiting p-type doping of InAs nanowires.

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Figure 1. Atomic structures of (a) zinc-blende and (b) wurtzite InAs nanowires. Left and right panels represent top and side views, respectively. Red, blue, and green balls denote In, As, and H atoms, respectively. Yellow balls 1 and 2 represent the removed H atoms from In and As atoms of nanowire surfaces when surface dangling bonds are considered, respectively.

II. MODELS AND COMPUTATIONAL METHODS Our calculations are performed within density functional theory (DFT) as implemented by the Vienna ab initio Simulation Package (VASP).28,29 The exchange-correlation energy is described in the generalized-gradient approximation (GGA) using the PW91 functional.30 The energy cutoff for the plane-wave expansion is set to 360 eV, using the projector augmented wave (PAW) potentials31 to describe the electron-ion interaction. The nanowires are created on the basis of the optimized bulk structures. Although the bulk InAs can be crystallized to a ZB structure, the InAs nanowires often exhibit hexagonal WZ crystal phase or the rotational twin structure including both ZB and WZ segments.32,33 Therefore, we consider both ZB- and WZstructured InAs nanowires with the surfaces passivated by hydrogen. The ZB-structured nanowires are oriented along [111] direction with the range of diameter from 1.32 to 2.20 nm. The WZ-structured nanowires are oriented along [0001] direction with the range of diameter from 1.28 to 2.91 nm. The distance between the neighboring nanowires is set to be larger than 10 Å to eliminate the interaction between adjacent nanowires. The Monkhorst-Pack k-point mesh of 1  1  6 is found to provide sufficient accuracy in the Brillouin-zone integration. For the geometry optimization, all atoms have been relaxed until the force acting on each atom is less than 0.01 eV/Å. Figure 1 shows the typical atomic structures of ZBstructured and WZ-structured nanowires. Surface dangling bonds are formed by removing hydrogen atoms from the surface of InAs nanowires, as shown in Figure 1. The binary InAs nanowires induce three different types of SDBs: DBIn, DBAs, and DB pair. The DBIn and DBAs are obtained by removing the hydrogen atom from In and As atoms of nanowire surface, respectively. DB pair is formed by In
As DB pair. In order to study the effect of the surface dangling bonds on the doping of InAs nanowires, we calculate the defect formation energies of the surface dangling bonds (ΔHf(q)) with the charge states q by the following expression34 ΔHf ðqÞ ¼ EDB ðqÞ
ET ð0Þ þ μH þ qðEVBM þ EF Þ 14450

ð1Þ

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Figure 2. The formation energies of surface dangling bonds on (a) 1.32 nm diameter ZB-structured and (b) 1.28 nm diameter WZ-structured InAs nanowires with respect to the Fermi level. The numbers +1, 0, and
1 represent the positively charged, neutral, and negatively charged InAs nanowires with the surface DBs, respectively. The trap density of charged SDBs is obtained by the Boltzmann statistics for (c) 1.32 nm diameter InAs nanowire with the ZB structure and (d) 1.28 nm diameter nanowires with the WZ structure.

Where EDB(q) and ET(0) are the total energy of q-charged and uncharged InAs nanowires with and without surface dangling bonds, respectively. Ef is the Fermi level relative to the valence band maximum (VBM) of InAs nanowires. μH is the chemical potential of hydrogen atom extracted from the H2 molecule.

III. RESULTS AND DISCUSSION Figure 2a,b shows the formation energies of each SDB for the 1.32 and 1.28 nm diameter InAs nanowire with the ZB structure and the WZ structure as a function of the Fermi energy, respectively. The range of the Fermi energy corresponds to the calculated band gap value. Although the well-known fact that DFT/GGA underestimates the band gap of semiconductors, the trends elucidated by the DFT results are proved to be still valid, as shown in the previous numerous studies on the band gap of semiconductor nanostructures.24,25,35 We also have performed hybrid density functional calculations for small InAs nanowires to confirm the reliability of our DFT calculations. The corresponding results are summarized in Figure S1 (Supporting Information). Although DFT calculations underestimate the band gap and result in relatively shallow transition energies and higher formation energies of SBDs, the general trend can be confirmed to be reasonable. As shown in Figure 2, the formation energies of SDBs on the positively charged, neutral, and negatively charged InAs nanowires are marked by (+1), (0), and (
1), respectively. For both ZB and WZ-structured nanowires, it is found that the charged DBIn is the most stable defect with the Fermi energy being close to the valence band maximum (VBM) or conductional band minimum (CBM), while the neutral DB pair is the most stable defect for the Fermi energy around the midgap. The transition from the positively charged DBIn to neutral DB pair occurs at ε(+/0), while the transition from the negatively charged DBIn to neutral DB pair occurs at ε(
/0). For the DBAs, it is still

Figure 3. Band structures of the ZB-structured InAs nanowires with (a) Zn dopant and (b) SDB-Zn complex, respectively. The horizontal dashed lines denote the position of the Fermi level.

energetically unfavorable due to the stronger As
H bonds in InAs nanowires. The charged DBIn with the high stability brings the surface states into band gap and forms the trap centers of carriers. In other word, the surface dangling bonds have the ability to capture electrons from the conduction band of n-type InAs nanowires and capture holes from the valence band of p-type InAs naowires. It can be proved by the result of electronic structures. Figure 3a shows the band structure of the hydrogen passivated ZB-structured InAs nanowire with a substitutional Zn dopant. It is shown that there is a typical p-type characteristic. In contrast, the electronic structure of the nanowire undergoes a significant change when one DBIn is introduced. The formation of SDB-Zn complex yields an intrinsic semiconductor characteristic, as shown in Figure 3b. The reason is that the holes from Zn dopant are captured by the SDBs, thus the nanowire loses its 14451

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Figure 4. (a) Formation energies of the most stable surface dangling bonds and (b) the corresponding trap density of charged SDBs for ZBstructured InAs nanowires with the range of diameter from 1.32 to 2.20 nm. Ev and Ec represent the position of valence band maximum and conduction band minimum of the nanowires, respectively.

acceptor characteristic. The similar phenomenon also has been observed in WZ-structured nanowires. Generally, the defect density Nd follows the Boltzmann statistics, namely24 Nd µ expð
ΔHf ðqÞ=KB TÞ

ð2Þ

where ΔHf(q) is the formation energy of the charged surface dangling bonds, KB and T are Boltzmann constant and temperature, respectively. It is found that the density of charged DBIn increases exponentially with the decrease of the formation energy, as shown in Figure 2c,d. For the ZB-structured InAs nanowire (see Figure 2c), the density of negatively charged DBIn is slightly higher than that of positively charged DBIn. It suggests that the SDBs of ZB-structured InAs nanowire can deactivate asymmetrically n-type dopants (such as Se and Te) by capturing electrons and p-type dopants (such as Zn and Cd) by capturing holes. For the WB-structured InAs nanowire, the density of positively charged DBIn is more than that of negatively charged DBIn, as shown in Figure 2d. Therefore, DBIn can deactivate the p-type dopants, but has a relatively small limitation for the n-type doping. The dopant deactivation induced by the surface dangling bonds is thus responsible for the low doping efficiency of InAs nanowires. To examine the size effect on the formation energies of charged SDBs in InAs nanowires, we have repeated the calculations for both ZB- and WZ-structured InAs nanowires with various sizes. With different sizes, the formation energies of the most stable SDBs and the trap densities of charged SDBs for ZBand WZ-structured nanowires as a function of Fermi level are shown in Figures 4 and 5, respectively. For the ZB-structured nanowires (see Figure 4), the stability of SDBs are similar to that of the 1.32 nm nanowire. Charged DBIn is stable for the Fermi level close to VBM or CBM, while neutral DB pair is stable for the Fermi level around the midgap. As the diameter of nanowires increases, the stable energy region (SER) for both positively and negatively charged DBIn becomes narrow. However, the energy

Figure 5. (a) Formation energies of the most stable surface dangling bonds and (b) the corresponding trap density of charged SDBs for WZ-structured InAs nanowires with the range of diameter from 1.28 to 2.91 nm. Ev and Ec represent the position of valence band maximum and conduction band minimum of the nanowires, respectively.

region of the negatively charged DBIn shows more rapid decrease than that of positively charged DBIn. When the diameter of nanowires increases to 2.20 nm, the SER of negatively charged DBIn is disappeared and the positively charged DBIn keeps a high stability with relatively small decrease in SER (see Figure 4a). It can be found that the calculated trap density of positively charged DBIn is far larger than that of negatively charged DBIn when the diameter of nanowires is larger than 1.76 nm, as shown in Figure 4b. For the WZ-structured nanowires, the similar behavior for the stability of the charged SBDs has also been observed. As shown in Figure 5a, the calculated formation energies indicate that the positively charged DBIn and neutral DB-pair are still two stable defects with the increase of size. Moreover, it is found that the trap centers consisted of charged SBDs are completely determined by the positively charged DBIn when the diameter of nanowires is larger than 1.28 nm (see Figure 5b). The results imply that the SDBs of InAs nanowires can restrain the p-type doping but has fewer roles in the n-type doping with the increase of size. It should be mentioned that the size of nanowires in the present calculations is smaller than 3 nm, but the sizes of most InAs nanowires in experiments are about 20
40 nm. To prove that the charged SDBs are a fundamental limitation for the p-type doping of InAs nanowires, we have also calculated the formation energies of SDBs on InAs(110) thin slab.25 The calculated results are summarized in Figure S2 (Supporting Information). The two-dimension InAs(110) thin slab can be considered as the larger-size InAs nanowires due to the reduced quantum confinement effect. It is found that the positively charged DBIn and neutral DB-pair are stable for the Fermi energy close to the VBM and CBM, respectively. For DBAs and the negatively charged DBIn, they are energetically unfavorable for the allowed range of Fermi level. The result suggests that the p-type doping could be restricted by the positively charged DBIn even for larger-size InAs nanowires or InAs thin slabs. 14452

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The Journal of Physical Chemistry C The above results indicate that the surface dangling bonds are a fundamental obstacle for p-type doping of InAs nanowires but have few effects on the n-type doping as the size of nanowires increases. Three main factors are responsible for the results. One is the electron counting rule (ECR). Generally, the energy minimization of semiconductor surfaces is often governed by the ECR.36
38 The surface of nanowires with the positive charged DBIn satisfies the ECR and shows a higher stability. It supports that the SDBs can capture holes from valence band of p-type InAs naowires. The surface of nanowires with the negatively charged DBIn shows relatively weak stability due to the deviation of ECR. Although the surface of nanowires with neutral DB pairs satisfy the ECR, they have no effect on the doping of InAs nanowires. The second factor is quantum confinement effect. As shown in Figures 4 and 5, the variation of the transition energy levels ε(+/0) and ε(
/0) is smaller than that of VBM and CBM with the change of size. However, the quantum confinement effect leads to a stronger effect on the conduction band than the valence band of InAs nanowires.39 Thus, we can observe that the positively charged DBIn keeps a relatively high stability but the stable energy region of the negatively charged DBIn has diminished rapidly and disappeared as the size of InAs nanowires increases. Finally, the DBIn is a kind of deep level defect, its energy level is not much affected by the size variation of InAs nanowires, as shown in Figure S3 (Supporting Information). Thus, DBIn can keep a limitation for the p-type doping of InAs nanowires. To overcome the p-type doping limitation from the SDBs and increase the doping efficiency of InAs nanowires, it is required to avoid the formation of SDBs. Surface passivation of nanowires is a good way to hinder the formation of SDBs. Moreover, the unpinning of the Fermi level from the conduction band in InAs nanowires can be caused by choosing appropriate pasivation materials.20 The choice of the appropriate passivation materials and the passivation effect on the electronic properties and the doping of InAs nanowires will be discussed in our future work.

IV. CONCLUSIONS In summary, we have performed the detailed investigations for the effect of the surface dangling bonds on the doping of InAs nanowires based on the first-principles calculations. We find that the surface dangling bonds prefer to be charged and deactivate asymmetrically p-type and n-type doping in the ultrathin nanowires. With the increase of nanowire sizes, the positively charged SDBs keep a high stability, but the negatively charged SDBs are gradually degenerated. The result indicates that the charged SDBs are a fundamental obstacle for realizing the effective p-type doping of InAs nanowires but have less influence on the n-type doping. The surface passivation can be good way to suppress the effect of SDBs. We expect that our calculations can contribute to the realization of p-type doping of InAs nanowires and the fabrication of nanodevices. ’ ASSOCIATED CONTENT

bS

Supporting Information. The formation-energy calculation with hybrid density functional theory for a 1.32 nm diameter of InAs nanowire with the zinc-blende crystal structure, formation energies of various surface dangling bonds on InAs(110) thin slab, and the band structures of DBIn on the InAs nanowires

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with different sizes. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Phone: +86-21-25051403. Fax: +86-21-65830734.

’ ACKNOWLEDGMENT This work was supported in part by the State Key Program for Basic Research of China (2007CB613206), the National Natural Science Foundation of China (10725418, 10734090, 10990104, and 60976092), Key Fund of Shanghai Science and Technology Foundation (09DJ1400203, 09DZ2202200, 10JC1416100, and 10510704700), Zhejiang Provincial National Natural Science Foundation of China (Y1110777), and the Knowledge Innovation Program of the Chinese Academy of Sciences (Q-ZY-6). Computational resources from the Shanghai Supercomputer Center are acknowledged. ’ REFERENCES (1) Agarwal, R.; Lieber, C. M. Appl. Phys. A 2006, 85, 209. (2) Lind, E.; Persson, A. I.; Samuelson, L.; Wernersson, L. E. Nano Lett. 2006, 6, 1842. (3) Dayeh, S. A.; Aplin, D. P. R.; Zhou, X. T.; Yu, P. K. L.; Yu, E. T.; Wang, D. L. Small 2007, 3, 326. (4) Hayden, O.; Agarwal, R.; Lieber, C. M. Nat. Mater. 2006, 5, 352. (5) Heremans, J. Nanometer-scale thermoelectric materials. Springer Handb. Nanotechnol. 2007, 345, 345. (6) Tian, B.; Zheng, X.; Kempa, T. J.; Fang, Y.; Yu, N.; Yu, G.; Huang, J.; Lieber, C. M. Nature 2007, 449, 885. (7) Li, S.; Yang, G. W. Appl. Phys. Lett. 2009, 95, 073106. (8) Nolan, M.; O’Callaghan, S.; Fagas, G.; Greer, J. C.; Frauenheim, T. Nano Lett. 2007, 7, 34. (9) Shu, H. B.; Chen, X. S.; Zhao, H. X.; Zhou, X. H.; Lu, W. J. Phys. Chem. C 2010, 114, 17514. (10) Bjork, M. T.; Schmid, H.; Knoch, J.; Riel, H.; Riess, W. Nat. Nanotechnol. 2009, 4, 103. (11) Ford, A. C.; Chuang, S.; Ho, J. C.; Chueh, Y. L.; Fan, Z. Y.; Javey, A. Nano Lett. 2010, 10, 509. (12) Tomioka, K.; Motohisa, J.; Hara, S.; Fukui, T. Nano Lett. 2008, 8, 3475. (13) Dalpian, G. M.; Chelikowsky, J. R. Phys. Rev. Lett. 2006, 96, 226802. (14) Erwin, S. C.; Zu, L.; Haftel, M. I.; Efros, A. L.; Kennedy, T. A.; Norris, D. J. Nature 2005, 436, 91. (15) Scheffler, M.; Nadj-Perge, S.; Kouwenhoven, L. P.; Borgstr€om, M. T.; Bakkers, E. P. A. M. J. Appl. Phys. 2009, 106, 124303. (16) Leu, P. W.; Shan, B.; Cho, K. Phys. Rev. B 2006, 73, 195320. (17) Noguchi, M.; Hirakawa, K.; Ikoma, T. Phys. Rev. Lett. 1991, 66, 2243. (18) Khanal, D. R.; Yim, J. W. L.; Walukiewicz, W.; Wu, J. Nano Lett. 2007, 7, 1186. (19) Hang, Q. L.; Wang, F. D.; Carpenter, P. D.; Zemlyanov, D.; Zakharov, D.; Stach, E. A.; Buhro, W. E.; Janes, D. B. Nano Lett. 2008, 8, 49. (20) Sørensen, B. S.; Aagesen, M.; Sørensen, C. B.; Lindelof, P. E.;  Martinez, K. L.; Nygard, J. Appl. Phys. Lett. 2008, 92, 012119. (21) Hang, Q. L.; Wang, F. D.; Buhro, W. E.; Janes, D. B. Appl. Phys. Lett. 2007, 90, 062108. (22) Du, J; Liang, D; Tang, H; Gao, X. P. Nano Lett. 2009, 9, 4348. (23) Fern
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