Role of the surface density of states in understanding size-dependent surface band bending in GaN nanowires

Applied Surface Science 510 (2020) 145502

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Role of the surface density of states in understanding size-dependent surface band bending in GaN nanowires Santanu Paridaa, a b

⁎,1

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, Aloka Ranjan Sahoob,1, Kishore K. Madapua, S. Mathi Jayab, , Sandip Dharaa,

T

⁎

Surface and Nanoscience Division, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam 603102, India Materials Physics Division, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam 603102, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Surface states Kelvin probe force microscopy Surface band bending Nanowire GaN DFT

In semiconductor nanostructures, surface states play a very important role in determining the surface potential or contact potential difference (CPD). We measure the CPD value of individual GaN nanowires (NWs) using Kelvin probe force microscopy (KPFM). The corresponding surface band bending (SBB) is calculated from the measured CPD value and is found to increase with a decrease in the NW size. In order to investigate the size dependence of the SBB, the electronic density of states of the surface atoms of the nanowires at different values of the diameter are calculated using the first-principle density functional theory (DFT). The calculated density of states of the nanowires revealed size-dependent occupancy and shift of conduction band edge. The relative position of the conduction band edge corroborates with size-dependent SBB values obtained from KPFM measurements.

1. Introduction Group III nitride semiconductors have raised a lot of interest for the past few decades because of their direct and tunable bandgap and high electron mobility. These properties have led to the emergence of the light emitting diode, photodetectors and high-power transistors [1–3]. Particularly the nanowires (NWs) of group III nitride emerged as a potential candidate for the high-performance optoelectronic devices because of the unidirectional conduction of charge carriers and absence of extended defects in the nanostructures [2–4]. Dopants and incorporation of defect atoms control the electronic property of semiconductor materials. Moreover, the surface states also play a crucial role in governing the electronic property. In a semiconductor, surface states exist because of the termination of lattice periodicity. The unpaired electrons in the dangling bonds of surface atoms interact with each other forming an electronic state with a very narrow energy band at the semiconductor band gap. In the case of the n-type semiconductor, bulk Fermi level, EF (bulk) is closer to the conduction band. The EF (bulk) is placed higher than the surface Fermi level (EF (surf)) under nonequilibrium. Thus, there will be a transfer of charge carriers in order to match both the EF. In the n-type semiconductor, the electrons will transfer from the bulk to the surface. As a result, the value of EF (bulk) drops and that of EF (surf) rises until an equilibrium is achieved. At equilibrium, the energy bands bend upward

as one move toward the surface. Similarly, in the case of the p-type semiconductor EF (bulk) is closer to the valance band and lies below the surface Fermi level (EF (surf)) under nonequilibrium. Holes transfer from the bulk to the surface, and at equilibrium, the energy bands bend downward as one move toward the surface [5,6]. In the nanostructures, the surface states affect the band structure of the semiconductor significantly because of the presence of a higher number of unpaired electrons in the dangling bonds of surface atoms as compared to that for the bulk [7]. Therefore, the electronic properties of the nanostructure semiconductors are influenced by the surface density of states [5,8]. Moreover, for practical electronic device applications, the semiconductor material must be connected through the metal contact to the external circuit. The electronic conduction through metal-semiconductor interfaces is of great importance in electronic devices. The contact behavior of metal-semiconductor is well understood based on work function difference. Depending on the value of work function, the contact can be Ohmic or Schottky type [5,9]. Substantial advances have been made in the past to understand the contact formation in case of bulk material. Nevertheless, some aspects need further understanding and clarification, particularly in the case of nanostructures, where the surface states at the interface play a prominent role. The contact behavior and carrier transport in the devices are completely dependent on the semiconductor surface states and the nature of band bending near the surface. Therefore, complete

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Corresponding authors. E-mail addresses: [email protected] (S. Parida), [email protected] (S. Mathi Jaya), [email protected] (S. Dhara). 1 Authors has contributed equally. https://doi.org/10.1016/j.apsusc.2020.145502 Received 24 September 2019; Received in revised form 12 December 2019; Accepted 21 January 2020 Available online 23 January 2020 0169-4332/ © 2020 Elsevier B.V. All rights reserved.

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understanding and characterization of the surface states are important in the optoelectronic devices. Unfortunately, the direct experimental admittance to characterize these surface states is very difficult. Moreover, the surface states are prone to change with the surrounding conditions and instrumental artefacts [7,10]. In recent years, scanning tunneling microscopy (STM) is proven to be an ideal tool for the investigation of individual bulk defects and dopant atoms in semiconductors [11]. However, STM measurements are limited to conducting, and heavily doped semiconductors only [12]. Moreover, it also suffers from tip-induced band bending phenomena [13]. On the other hand, the AFM based Kelvin probe force microscopy (KPFM) technique demonstrated its utility as a powerful tool for measuring electrostatic forces and electric potential distribution with nanometer resolution [14,15]. Due to its promise of high spatial resolution surface potential measurements, the KPFM found many miscellaneous applications in just a few years. In previous studies, the doping distribution and deep traps in Si NWs are measured using KPFM [16,17]. Moreover, the effect of defects on the surface potential or contact potential difference (CPD) value of different diameter emphasizing on the charge transfer mechanism in GaN NWs [18], and the effect of free electron distribution on the size-dependent surface potential in the degenerate InN NWs [19], are also explored from the insight of KPFM measurements. In all these reports, the role of surface states is only qualitatively discussed as the origin for the observed variation in the surface potential. However, there is hardly any effort to establish the correlation of surface potential with the available surface states in single nanostructure and its size dependence. In the present report, we intend to study the effect of surface states on the band bending of unintentionally doped n-GaN NWs using KPFM with high spatial resolution. The CPD value of the individual NWs is measured, and the corresponding surface band bending (SBB) value is calculated for the NWs with different diameter. The variation in the SBB is observed as a function of NW diameter and is corroborated with the calculated surface density of states and conduction band edge values of the individual NWs using ab initio density functional theory (DFT).

Fig. 1. Typical Raman spectra of as-grown GaN NWs. The inset shows typical scanning electron micrograph of the NWs.

the unwanted interaction between periodic images of the NWs. DFT as implemented in Vienna Ab initio simulation package (VASP) [21], was used to carry out the calculations, and the results were used to examine the thickness dependence of the electronic structure of these NWs. All the NW structures were fully relaxed to force tolerance of 0.02 eV/Å. Energy cut-off was fixed at 520 eV, and a 1 × 1 × 5 K-point mesh was used for sampling the Brillouin zone. The generalized gradient approximations (GGA) functional of Perdew, Burke and Ernzerhof (PBE) [22], was used to treat the exchange-correlation potential.

3. Results and discussions Typical Raman spectrum of as-grown GaN NWs is shown in Fig. 1. The peaks at ~567 and ~725 cm−1 correspond to the symmetry allowed E2(high) and A1(LO) modes for wurtzite GaN, respectively [23]. Along with the symmetry allowed modes, peak observed at ~420 cm−1, corresponds to zone boundary phonon mode. The peak centred at ~520 cm−1 is originated from the crystalline Si substrate. The inset of Fig. 1 shows the typical scanning electron micrograph of asgrown NWs. The NWs are of diameter in the range of 30–150 nm with lengths of micron. The KPFM measurements are carried out for the simultaneous mapping of CPD and AFM micrograph. Typical topographic and corresponding CPD map of a single GaN NW is depicted in Fig. 2. The diameter of the NW is ~80 nm (Fig. 2(c)) with a smooth and uniform surface. The corresponding line profile of the CPD (Fig. 2(d)) map shows a difference of ~50–60 meV between the tip and the NW. Several measurements are performed on NWs with different diameter, and a variation of CPD value is observed. Since the NWs are taken from a single sample for the measurements, they are expected to show similar values of CPD with respect to the KPFM tip. On the contrary, the measured CPD with significant variation as a function of NW size is depicted in Fig. 3. The variation of CPD can arise from the same material due to several reasons like, because of the presence of absorbent, the difference in work function or electron affinity of the material and change in the surface band bending (SBB). Since the measurements are performed under high vacuum condition, the effect of absorbent on the measurement of CPD can be discarded. Similarly, the NWs will have equal value of electron affinity since the growth conditions are the same for all the NWs and have an approximately similar value of carrier concentration (~1017/cm−3) [20]. In the nanoscale regime, however, there may be a significant effect of surface states on the measured CPD of the NWs. In the introduction, we have already qualitatively discussed

2. Experimental GaN NWs were synthesized on crystalline Si (1 0 0) substrate by chemical vapor deposition technique at 900 °C using Au nanoparticles as a catalyst in the vapor-liquid-solid growth process. Ga metal as the precursor, NH3 as the reactant, and Ar as carrier gases were used for the growth of NWs, and the complete growth process were detailed in our earlier report [20]. The as-grown NWs were mechanically transferred to an Au coated Si substrate for the KPFM measurements. The CPD value was measured by KPFM technique (MultiView 4000, Nanonics Imaging Ltd.). The measurements were carried out at high vacuum (~10−7 mbar) to avoid the effect of surface adsorbents with the help of ion pump, backed with turbo molecular pump. Sufficient care was taken to minimize the effect of impurity which might have incorporated while the sample was exposed to the atmosphere. For ensuring so, the sample was heated at an elevated temperature (> 100 °C) under high vacuum (~10−7 mbar) inside the chamber just prior to the KPFM measurement. This process ensures minimization of the effect of most likely impurities of absorbed gases or water molecule on the CPD measurements. Singlepass imaging was adopted for the simultaneous measurement of topography, and the CPD with the help of two lock-in amplifiers. Pt-Ir coated Si tip with the resonance frequency in the range of 36–98 kHz was used for the present measurements. The work function of the tip was calibrated with respect to the electron beam coated Au film before the measurement. DFT based first-principle calculations were performed for interpreting the experimental results obtained from KPFM measurements. GaN NWs with different diameters were considered in the calculations. The supercell technique is used to obtain the NW structures. A vacuum of 12 Å along X and Y-directions are used in the calculations to remove 2

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Fig. 2. (a) Topographic and (b) CPD map of GaN NW with their corresponding (c) and (d) line profile. The scale in (a) and (b) corresponds to 220 nm.

conduction band minima and position of the EF level of the semiconductor at equilibrium, respectively. However, the CPD value gets modified in the presence of surface states at the semiconductor surface. Therefore, the Eq. (1) gets modified with an extra term, which accounts for the contribution from the band bending due to the surface states and is given by Eq. (2) [6,24,25],

eVcpd = Φm − χs − eVs − (Ec − EF )

(2)

where Vs is the surface potential of the semiconductor arises because of the presence of surface states. From the above relation in Eq. (2), the SBB value is estimated by

SBB = eVs = Φm − χs − eVcpd − (Ec − EF )

Using Eq. (3) the corresponding SBB of the NWs are calculated and plotted as a function of NW diameter in Fig. 3. The variation in the SBB arises because of the difference in the number of surface states in the NWs with different diameter. In order to investigate the surface density of state in the NWs with different diameter, we have performed the DFT calculation. Since there is a restriction in handling the number of atoms in the DFT calculation, we have chosen the NWs in the diameter range of ~0.95–3.5 nm without any defect incorporation and investigated the variation of the surface density of state with respect to the diameter. As evident from Raman spectroscopic measurement, GaN NWs posses wurtzite-type structure. Therefore, the bulk GaN possessing the wurtzite structure was used to construct the supercells required to obtain the NW structures. The bulk structure was first relaxed to obtain the equilibrium lattice parameters. In the calculation, Brillouin zone is sampled by a 9 × 9 × 5 Monk-horst Pack [26], K-point mesh and the energy cut-off is fixed at 520 eV. The calculated values of the equilibrium lattice parameters are respectively a = b = 3.24 Å, and c = 5.28 Å, which are in good agreement with experimental lattice

Fig. 3. Variation of CPD and SBB with respect to NW diameter. Lines shown in the figure are guide to eye.

the effect of surface states on the surface band bending of the NWs, which in turn modify the measured CPD value. For the quantitative analysis, we consider the metal (KPFM tip) and semiconductor (GaN NW) contact. When a semiconductor comes to contact with metal, there is a SBB because of the EF mismatch. The CPD value between the semiconductor and the metal is the measure of band bending. In the case of n-type semiconductor, the CPD value between the metallic tip and the sample is given by [5,6,24],

eVcpd = Φm − χs − (Ec − EF )

(3)

(1)

where, Φm and χs are the work function of the metal and the electron affinity of the semiconductor, respectively. Ec and EF correspond to the 3

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Density of states (states/eV)

(d)

1.15

1.20

1.25

1.30

1.35

1.5 nm

2.0

1.0

1.0

0.5

0.5

0.0

0.0 0

1

(e)

2

3 -3

-2

-1

0

1

(f)

2.8 nm

2

3 2.0

3.5 nm

1.5

1.5

1.0

1.0

0.5

0.5

0.0

0.0 -3

-2

-1

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Energy (eV)

2

3 -3

-2

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Energy (eV)

2

3 -3

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(c)

1.5

2.2 nm

1.50

figures that the occupancy of the surface density of states and surface barrier height increases with a decrease in the diameter of the NW. In order to inspect the variation of the surface barrier height with NW diameter, we have plotted the density of states in a narrow energy range of 1.1 to 1.5 eV (Fig. 5), which show the conduction band edges of the NWs with different diameters. The conduction band edges of the NWs with diameters of 0.95, 1.5, 2.2, 2.8, 3.5 nm are found to be at ~1.330, 1.260, 1.210, 1.175, 1.165 eV, respectively. The conduction band edge shifts to higher energies (potential) when the NW diameter is decreased. Since we have fixed the EF at 0 eV in our calculation, the shift of the conduction band edge with respect to the NW diameter is due to the relative change in the position of the EF when

0.95 nm

-1

1.45

Fig. 5. Surface density of states range of plotted in a narrow energy range of 1.1–1.5 eV to represent the conduction band edge of GaN NW with different diameter.

1.5

-2

1.40

Energy (eV)

(b)

2.0

-3 2.0

1.10

Density of states (states/eV)

(a)

0.95 nm 1.5 nm 2.2 nm 2.8 nm 3.5 nm

Density of states (states/eV)

parameters (a = b = 3.18 Å, c = 5.16 Å) and other reported values [27]. This optimized structure is then used to construct the supercells required for making the NWs. The band gap value of bulk GaN is obtained as 1.63 eV, which is found to be underestimated compared to the experimental value of ~3.47 eV. It is well-known that Local-density approximations (LDA) and GGA functional used in the DFT underestimate the band gap for semiconductors [28,29]. Several correction schemes such as hybrid functional [30,31], self-interaction correction (SIC) [32], GW approximations [33,34], are available to overcome this underestimation of the band gap. However, we have restricted to GGA functional alone as our interest is to evaluate the relative changes in the band edges with respect to the NW diameters. Further, these corrections are computationally expensive. NWs with diameters ranging from 0.95 nm to 3.5 nm and hexagonal cross-sections were made from appropriate supercells. Five different values of the diameters of the NWs were considered in our studies. The values of the diameters are respectively 0.95 nm, 1.5 nm, 2.2 nm, 2.8 nm, and 3.5 nm. The number of atoms that are considered in the supercells corresponding to the above said diameters values are respectively 48, 108, 192, 300 and 432. The geometry of each of the NWs was fully relaxed, and the electronic structures were then obtained. In the case of the NW with 0.95 nm diameter (Fig. 4(a)), the Ga-N bond length is 1.877 Å which is found to be reduced compared to that of the bulk (1.99 Å). The reduction is due to the surface reconstruction of the NW in the optimized geometry, leading to a contraction of 5–6% in the bond length. The similar contraction in the Ga-N bond length occurs for the other NWs with different diameters too (Fig. S1; supporting information). It is also found that there is no significant change in Ga-N bond length for the inner layers of the NWs (Fig. 4(a)). Hence, the surface effect is confined predominantly to the outermost layer only. The contraction in bond length is found to alter the bond angle between Ga and N (Fig. 4(a)). The projected density of states of surface atoms of the NWs with different diameters are plotted in Fig. 4(b)–(f). It is observed from the

3

Energy (eV)

Fig. 4. (a) The stick and ball representation of GaN NW of diameter 0.95 nm. (b)-(f) Surface density of states of NW with different diameter. 4

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the diameter of the NW is changed. The SBB occurs when the NW is contacted with the metal tip in KPFM measurement and is related to the mismatch of EF of the NW and the tip. Hence the value of SBB is determined by the position of the conduction band edge of the NW when it is contacted by the metal tip. As the density of state of the surface atoms is the one that is important in this process, shift of the conduction band edge to higher energy with decreasing NW diameter indicates an increase in the SBB when the NW diameter is decreased. We also try to understand diameter dependence of surface band bending in the presence of point defects in the GaN NW. It is well known that, in GaN nitrogen vacancy (VN) is the most stable defect and resides on the surface of the sample with a charged state of −3 [35,36]. In the presence of charged VN defects, the NWs with smaller diameter will have higher surface band bending as compared to the higher diameter NW, because of the creation of deeper depletion region in smaller diameter NW. This is in fact consistent with the obtained result from the KPFM measurement. DFT calculation for the surface density of states in GaN considering presence of VN, however, was limited by the requirement of large number atoms. In our calculations, we have used a supercell containing 432 atoms for the largest diameter NW (3.5 nm) beyond which it becomes extremely difficult for DFT calculations. Now to incorporate defects, still larger supercell is required which will drastically increase the number of atoms in the supercell.

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4. Conclusion Kelvin probe force microscopy (KPFM) measurements are carried out on individual GaN nanowire (NW) with different diameters. The contact potential difference between the KPFM tip and the GaN NW is found to be increased with the increase in the NW diameter. The corresponding surface band bending (SBB) is calculated and found to be increasing with a decrease in NW diameter. The surface density of states calculated with the help of density functional theory (DFT) reveal the blue shift of conduction band edge position with a decrease in NW diameter, and it is related to the increase in the SBB. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We thank R. Pandian of SND, IGCAR, for his help in the FESEM study. We also thank P. Sahoo of IIT, Kharagpur and A. Patsha of Tel Aviv University for their valuable suggestions and useful discussions. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apsusc.2020.145502. References [1] S. Nakamura, T. Mukai, M. Senoh, Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes, Appl. Phys. Lett. 64 (1994) 1687–1689. [2] F. Qian, Y. Li, S. Gradečak, H.-G. Park, Y. Dong, Y. Ding, Z.L. Wang, C.M. Lieber, Multi-quantum-well nanowire heterostructures for wavelength-controlled lasers,

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