The Photo-Oxidation of Black

Phosphorus at Intrinsic Defects

Kainen L. Utt

An Honors Thesis submitted in partial fulfillment of the

requirements of Honors Studies in Physics

Spring 2016

Physics

J. William Fulbright College of Arts and Sciences

The University of Arkansas

i

Acknowledgements

I would like to thank Dr. Salvador Barraza-Lopez for his continued support of

my research and for the opportunity to gain valuable research experience under his

direction.

Additionally, I would like to thank the members of my thesis committee for

taking the time out of their schedule to be a part of this exciting process.

Finally, I would like to thank the Honors College for the facilitation and

encouragement of undergraduate research as well as its financial support.

ii

Contents

Acknowledgements ........................................................................................................ i

Introduction .................................................................................................................. 1

Methods ......................................................................................................................... 2

Results ........................................................................................................................... 4

Conclusions ................................................................................................................... 9

References ....................................................................................................................11

iii

Figures

Figure 1. Triangular area formed by edge vectors used in calculation of the discrete

metric and curvature tensors. ...................................................................................... 3

Figure 2. The activation energy for oxidation depends heavily on the local structural

features. Intrinsic structural defects lower the energy barrier for both planar (a) and

conical (b) structures. The yellow bar represents the energies accessible by visible

light. .............................................................................................................................. 4

Figure 3 The dissociation of oxygen dimers at the pentagonal defect (a) and the line

defect (b). ....................................................................................................................... 6

Figure 4. Energetics of oxidation at defect A (a) and defect B (b). .............................. 7

Figure 5. Analysis of the effects of chemisorption of a single oxygen dimer (a) and

two oxygen dimers (b) at defect A on the local geometric invariants, charge transfer,

the electronic bandgap, and simulated STM images. .................................................. 8

Figure 6. Analysis of the effects of the defect itself and the chemisorption of a single

oxygen dimer (a) and two oxygen dimers (b) at defect B on the local geometric

invariants, charge transfer, the electronic bandgap, and simulated STM images. .... 9

file:///C:/Users/Kainen/Documents/University%20of%20Arkansas/Honors%20College/Thesis/Rough%20Draft.docx%23_Toc447633955file:///C:/Users/Kainen/Documents/University%20of%20Arkansas/Honors%20College/Thesis/Rough%20Draft.docx%23_Toc447633955

1

Introduction

Since the discovery and exfoliation of graphene, or atomically-thin carbon, in

2004, the condensed matter physics community has been increasingly interested in

the synthesis and properties of similarly atomically-thin materials. [1] The most

recently synthesized two-dimensional (2D) material, phosphorene, was discovered in

2014. [2] Phosphorene’s bulk structure, black phosphorus (BP), exhibits high carrier

mobility – a property which is retained at the monolayer limit. [3] Like graphene,

phosphorene can be exfoliated mechanically with ease. However, phosphorene

presents a monolayer semiconducting bandgap of 1.88 eV whereas graphene exhibits

a 0 eV bandgap at the monolayer limit. [4] [5] In addition, phosphorene’s direct

semiconducting bandgap is tunable by layer dependency and strain. [6]

Despite the aforementioned advantages, phosphorene is currently difficult to

study experimentally due to its propensity for rapid deterioration in ambient

conditions. [7] If preventative measures are not taken, black phosphorus sometimes

degrades in as little as half an hour. In normal laboratory conditions, black

phosphorus reacts with atmospheric oxygen resulting in a non-constant height

profile and locally increased curvature. [8] In order to combat this degradation, it is

necessary to either cap the material with a less reactive layered material or to work

in an inert environment. [9] While these methods are effective for short-term study,

a permanent solution is imperative to the continued function of phosphorene-based

devices. Standing in the way of permanent degradation prevention is a dearth of

studies regarding the mechanisms of oxidation in BP. In order to continue the

productive study of phosphorene and enable the future production of phosphorene-

based devices, the oxidation process in monolayer black phosphorus must be well

understood. Throughout this paper, we demonstrate that photonic excitations within

the visible spectrum are sufficient to induce oxidation at local intrinsic structural

defects.

The existence of intrinsic structural defects in BP is indicated by the presence

of variations in height even in newly exfoliated, pristine samples. [10] In turn, these

intrinsic defects induce changes in the local curvature of the material which can be

measured experimentally. [11] These height and curvature fluctuations are

exacerbated when the material is exposed to air, which implies that the areas of the

2

material most vulnerable to the effects of oxidation are the intrinsic defects. As such,

we claim that the local geometric structure of the material is linked to oxidation.

The ultimate role of the defects in the oxidation process is similar to that of a

catalyst in a macroscopic chemical reaction. For a pristine phosphorene monolayer,

the energy required for chemisorption of an O2 dimer is on the order of 10 eV (or

1000 kJ/mol). Such a large activation energy barrier is beyond the scope of ambient

thermodynamic and optical excitations. To see this more clearly, one must only

consider that energy barriers on the order of a couple electronvolts are only

overcome by temperatures greater than 1,000 K. At intrinsic defects, however, the

activation energy is greatly attenuated and falls within the energy range accessible

by visible (1.6 to 3.2 eV) and ultraviolet light.

This study proceeds by creating both planar and conical finite phosphorene

monolayers in addition to isolated O2 molecules as the reference structures. The

phosphorene structures were then excited by passing the oxygen dimers through

various points in the structures. In order to determine the energy barriers for

oxidation, the total energy of the system was calculated at each distance step and

subsequently compared to the total energy of the aforementioned reference

structures. After the energy profile had been thoroughly characterized, we utilized

ab initio energetic optimization or relaxation to demonstrate the process of oxygen

chemisorption and calculate the energies of the resulting structures.

Methods

The reference structures were structurally or geometrically characterized

using discrete geometry. Specifically, we consider three edge vectors, 𝒆1, 𝒆2, and 𝒆3

such that 𝒆1 + 𝒆2 + 𝒆3 = 0. (see Figure 1) The quantity 𝑄𝑙I ∶= 𝒆𝑙 ∙ 𝒆𝑙 (where 𝑙 = 1, 2, 3)

is defined to be the square of the smallest finite distance between component atoms.

[12] Additionally, we project variations in orientation of normal vectors �̂�1and �̂�2

onto the shared edge, 𝒆𝑙. Similarly, the we define 𝑄𝑙II ∶= (�̂�k − �̂�j) ∙ 𝒆𝑙 where 𝑖, 𝑗, 𝑘 =

1, 2, 3. Here, we set �̂�𝑙 to be the average of the individual normal vectors for the

triangular area elements within the shape formed by the next-nearest neighbors to

atom l. The shared edge is defined to be 𝒆𝑙∗ ∶= 𝑣 × 𝒆𝑙, where 𝑣 is the normal vector to

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the plane formed by atoms 1, 2, and 3. The area of the triangle is given by the edge

vectors and the normal to the plane in which it lies. 𝐴𝑇 =1

2𝑣(−𝒆1 × 𝒆2).

Under this set of definitions, the discrete metric tensor is expressed by:

𝑔 = −1

8𝐴02 ∑ (𝑄𝑗

I − 𝑄𝑘I − 𝑄𝑙

I)𝒆𝑗∗ ⊗ 𝒆𝑗

∗

(𝑗,𝑘,𝑙)

where 𝐴0 is the area of the triangle formed by atoms 1, 2, and 3 in the planar case.

Similarly, the discrete curvature tensor takes the form:

𝑘 = −1

8𝐴𝑇2 ∑ (𝑄𝑗

II − 𝑄𝑘II − 𝑄𝑙

II)𝒆𝑗∗ ⊗ 𝒆𝑗

∗

(𝑗,𝑘,𝑙)

In the above equations, (𝑗, 𝑘, 𝑙) indicates a sum of the terms (1, 2, 3), (2, 3, 1),

and (3, 1, 2). The results of these equations are in the form of 3 × 3 matrices with

values for 𝑄𝑗I , 𝑄𝑗

II, and 𝒆𝑗 for each atomic position.

From this framework, we derive five geometric invariants with which to

analyze any two-dimensional lattice structure: det(𝑔) , tr(𝑔), Gaussian curvature (𝐾),

mean curvature (𝐻), and out-of-plane thickness (τ). Here, 𝐾 ≔ 𝑘1𝑘2 and 𝐻 ≔(𝑘1 + 𝑘2)

2,

where 𝑘1, 𝑘2 are the non-trivial eigenvalues of the discrete curvature tensor.

Figure 1. Triangular area formed by edge vectors used in calculation of the discrete metric and curvature tensors.

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The structural relaxations were performed using the SIESTA density

functional theory code with spin polarization and the PBE exchange-correlation

potential. [13] [14] [15]

Results

In order to understand the energy required for the chemisorption of O2, we

determine the net energy needed for the molecule to pass through the phosphorene

monolayer. To this end, we consider two finite monolayer structures as our

reference: a planar structure consisting of approximately 600 phosphorus atoms and

a conical structure of about 500 atoms. The structures are then relaxed to obtain an

accurate energy baseline before they are pierced by the oxygen molecule. The energy

of the system is calculated at finite distance steps starting from a vertical distance of

±6 Å from the material, where 0 Å represents the midpoint between the two sub-

layers 𝑠1 and 𝑠2 that comprise the monolayer. This activation energy landscape was

calculated using ab initio calculations without structural relaxation. (see Figure 2)

Figure 2. The activation energy for oxidation depends heavily on the local structural

features. Intrinsic structural defects lower the energy barrier for both planar (a) and

conical (b) structures. The yellow bar represents the energies accessible by visible light.

5

In Figure 2, darker colors in the det(𝑔) and tr(𝑔) plots indicate a larger

distance between atoms. Similarly, darker colors in the H and K plots indicate

increased local mean and Gaussian curvature, respectively. As illustrated by the

figure, the energy barrier 𝐸𝑎 for an oxygen dimer to pierce an ideal planar monolayer

(shown in black) is approximately 12 eV. Such a large energy barrier makes

chemisorption of oxygen into an ideal planar monolayer extremely unlikely. At

intrinsic defects, however, the energy barrier is significantly reduced. For example,

the maximum value of 𝐸𝑎 is nearly halved at the pentagonal defect (defect A) in the

planar structure -- shown in red on the left side of the figure. This value of

approximately 6 eV is accessible by near-ultraviolet light, paving the way for

oxidation at the defect. This lowering of the energy barrier is related to the

increased metric invariants as the larger distance between atoms reduces the

electronic forces exerted on the oxygen dimer.

Conversely, we see both structural compression and large curvature values

near the top of the conical structure, which increases the maximum value of 𝐸𝑎. At

the top of the cone, 𝐸𝑎 assumes a value of approximately 18 eV as a result of the

increased electronic forces imparted by this compression. However, while

constructing the cone, the defect shown on the far right of the figure was found to be

metastable and likely similar to defects that occur during phosphorene growth or

exfoliation. This larger defect (defect B) significantly reduces the energy barrier; 𝐸𝑎

at the defect is approximately one-fourth the magnitude of the value at the cone’s

apex. Indeed, the energy profile lies nearly entirely within the band of energies

accessible by photons of visible light. Hence, the energy barrier reduction at both

examined structural defects supports the hypothesis that phosphorene oxidation

occurs at least initially at structural defects.

After a sufficiently large optical excitation has provided the necessary energy

for the placement of the O2 molecule within the phosphorene structure, the repulsive

force exerted on the oxygen dimer by the monolayer results in the dissociation of the

molecular oxygen into its two component oxygen atoms. To demonstrate this, we

placed a static oxygen molecule within the structural defects with the lowest values

of 𝐸𝑎. Though the situation presented does not reflect the fact that in most cases the

oxygen dimer in question would possess some finite amount of kinetic energy, the

6

static case represents the minimum energy of the molecule and is thus uniformly

applicable. Upon the structural relaxation shown in Figure 3, the distance between

the component atoms of the molecular oxygen increases to a value greater than the

bond tolerance of the molecule. The process illustrated in the figure represents the

first proposed mechanism for the dissociation of oxygen molecules in phosphorene.

At defect A, the final distance between the oxygen atoms was 2.96 Å – more than

twice the reference bond length of 1.25 Å. The effect is magnified at defect B, where

the final distance was 3.08 Å. In both cases, the separation is sufficient for the

dissociation of the oxygen dimers.

Figure 3 The dissociation of oxygen dimers at the pentagonal defect (a) and the line defect

(b).

Moreover, a detailed study of the energetics of the phosphorene oxidation

process including the dissociation of molecular oxygen indicates that the reaction is

highly exothermic. The released energy was determined to be sufficient to induce

further oxidation even in the absence of photonic excitation. To further illustrate

this point, consider placing an initial oxygen dimer into defect A. (see Figure 4a) As

the oxygen bonds to the phosphorene, the system increases in energy by 4.3 eV due

to the initial optical excitation. The subsequent dissociation of the oxygen releases

approximately 7 eV of energy, which provides sufficient energy for a secondary

oxygen molecule to overcome the energy barrier and continue the oxidation process.

This secondary oxygen dimer causes the system to increase in energy by 3.1 eV by

bonding to the structure. While the second dimer did not dissociate, its introduction

caused the severance of a P-P bond, which is characteristic of the degradation the

material undergoes in laboratory conditions.

7

Figure 4. Energetics of oxidation at defect A (a) and defect B (b) .

Similarly, the addition of an initial oxygen dimer within defect B resulted in

a gross energy gain of 3.5 eV as shown in Figure 4b. This increase in system energy

is accessible via adsorption of light with a wavelength of 354 nm. Upon structural

relaxation and oxygen dissociation, approximately 7 eV of energy is again released.

Unlike the oxidation process at defect A, an ultraviolet excitation corresponding to

an energy of 6.8 eV is needed for the introduction of a secondary oxygen molecule.

However, nearly 7 eV of energy is released upon structural optimization and

subsequent dissociation. The large energy cost for the introduction of a second

oxygen molecule at defect B points to increased stability in the oxidized structure

with respect to a pristine reference. Despite the vast differences between the planar

and conical reference structures and between defects A and B, the similarity of the

energy barriers and oxidation processes implies that this process can be applied

generally to explain the degradation of phosphorene.

The final aspect of phosphorene oxidation examined within this study is its

effect on the structural and electronic properties of the material. Defect A, a line

defect, induces periodic stretching and compression of the inter-atomic distances

along the axis of the line defect. As shown in Figure 5a, this compression and

elongation manifests as the periodic reduction and increase in the trace and

determinant of the metric tensor. The variations in Gaussian curvature, mean

curvature, and thickness, while visible, are not large enough to be significant. In

order to account for the buckled structure of monolayer phosphorene, plots for both

sublayers 𝑠1 and 𝑠2 are shown. Figure 5b shows the same structure after the

8

chemisorption of the second oxygen dimer. Here, we see a marked increase in the

trace and determinant of the metric tensor for the top sublayer, while the curvature

remains unchanged. However, the most significant difference between the two

structures is the electronic gap. After the second dimer is chemisorbed into the

phosphorene, we see that the local bandgap is approximately 70% of the gap for the

structure with a single oxygen dimer.

Figure 5. Analysis of the effects of chemisorption of a single oxygen dimer (a) and two

oxygen dimers (b) at defect A on the local geometric invariants, charge transfer, the

electronic bandgap, and simulated STM images.

As for the conical structure, Figure 6 illustrates the tendency for the

oxidation process to enhance any existing curvature. This pre-existing curvature has

the effect of slightly reducing the local bandgap along the axis of the defect.

Additionally, defect B itself results in larger distances between atoms at the site of

the defect. This is illustrated by the large values for the trace and determinant of

the metric tensor in the top sublayer in Figure 6a. When a single oxygen dimer is

permitted to chemisorb into the material, the inter-atomic distances and curvature

increases as shown clearly in Figure 6b. This increase in curvature and inter-atomic

distance further reduces the local bandgap to approximately 60% of its reference

value. As a second oxygen dimer is added to the structure in Figure 6c, the increase

of the stress and curvature geometric invariants is exacerbated. In addition, we

observe increased charge transfer coupled with a further reduction of the local

electronic gap. The creation of what can only be described as a hole in the structure

9

by the addition of a second oxygen dimer illustrates the disastrous consequences of

uncheck degradation in the material.

Figure 6. Analysis of the effects of the defect itself and the chemisorption of a single oxygen

dimer (a) and two oxygen dimers (b) at defect B on the local geometric invariants, charge

transfer, the electronic bandgap, and simulated STM images.

Conclusions

Despite increased interest in the study of phosphorene, the inability to

produce air-stable devices will significantly hamper the continued development of

the field unless the processes of its degradation are better understood. To this end,

this study presents a viable mechanism for the oxidation of the material in ambient

conditions via intrinsic structural defects. Such intrinsic defects work to lower to

oxidation energy barrier to a level accessible via visible and ultra-violet light

exposure, which in turn allow for the chemisorption and subsequent dissociation of

oxygen molecules. The energetics of oxidation and the effects of oxidation on the

structural and electronic properties were also discussed. While this study focused

solely on atmospheric oxygen, there exists the exciting opportunity for further study

of degradation in the presence of other contaminants such as water. Additionally,

further study may be conducted on the procession of degradation throughout multi-

10

layer phosphorene. The work presented here sheds light on the previously unknown

degradation dynamics of layered black phosphorus and suggests one plausible

mechanism for the degradation of the material when exposed to external

illumination.

11

References

[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, "Electric Field Effect in Atomically Thin

Carbon Films," Science, vol. 306, no. 5696, pp. 666-669, 2014.

[2] H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tomanek and P. D. Ye,

"Phosphorene: A New 2D Material with High Carrier Mobility," ACS Nano, vol.

4, no. 4, pp. 4033-4041, 2014.

[3] D. Warschauer, "Electrical and Optical Properties of Crystalline Black

Phosphorus," Journal of Applied Physics, vol. 34, no. 1853, 1963.

[4] D. R. Cooper, B. D'Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N.

Majlis, M. Massicotte, L. Vandsburger, E. Whiteway and V. Yu, "Experimental

Review of Graphene," ISRN Condensed Matter Physics, vol. 2012, 2012.

[5] V. Tran, R. Soklaski, Y. Liang and L. Yang, "Layer-controlled band gap and

anisotropic excitons in few-layer black phosphorus," Physical Review B, vol. 89,

no. 235319, 2014.

[6] M. Mehboudi, K. Utt, H. Terrones, E. O. Harriss, A. A. P. SanJuan and S.

Barraza-Lopez, "Strain and the optoelectronic properties of nonplanar

phosphorene monolayers," Proceedings of the National Academy of Sciences of

the United States of America, vol. 112, no. 19, pp. 5888-5892, 2015.

[7] R. A. Doganov, E. C. T. O’Farrell, S. P. Koenig, Y. Yeo, A. Ziletti, A. Carvalho,

D. K. Campbell, D. F. Coker, K. Watanabe, T. Taniguchi, A. H. Castro Neto and

B. Özyilmaz, "Transport properties of pristine few-layer black phosphorus by

van der Waals passivation in an inert atmosphere," Nature Communications,

vol. 6, no. 6647, 2015.

[8] S. P. Koenig, R. A. Doganov, H. Schmidt, A. H. Castro Neto and B. Ozyilmaz,

"Electric field effect in ultrathin black phosphorus," Applied Physics Letters,

vol. 104, no. 10, pp. 103106/1-103106/4, 2014.

[9] J. D. Wood, S. A. Wells, D. Jariwala, K.-S. Chen, E. Cho, V. K. Sangwan, X.

Liu, L. J. Lauhon, T. J. Marks and M. C. Hersam, "Effective Passivation of

Exfoliated Black Phosphorus Transistors against Ambient Degradation," Nano

Letters, vol. 14, no. 12, pp. 6964-6970, 2014.

[10] Y. Liu, F. Xu, Z. Zhang, E. S. Penev and B. I. Yakobson, "Two-Dimensional

Mono-Elemental Semiconductor with Electronically Inactive Defects: The Case

of Phosphorus," Nano Letters, vol. 14, no. 12, pp. 6782-6786, 2014.

[11] A. Castellanos-Gomez, L. Vicarelli, E. Prada, J. O. Island, K. L. Narasimha-

Acharya, S. I. Blanter, D. J. Groenendijk, M. Buscema, G. A. Steele, J. V.

Alvarez, H. W. Zandbergen, J. J. Palacios and H. van der Zant, "Isolation and

characterization of few-layer black phosphorus," 2D Materials, vol. 1, no. 2, pp.

25001/1-25001/19, 2014.

[12] C. Weischedel, A. Tuganov, T. Hermansson, J. Linn and M. Wardetzky,

"Construction of discrete shell models by geometric finite differences," in The

2nd Joint Conference on Multibody System Dynamics, Stuttgart, Germany,

2012.

12

[13] R. Car and M. Parrinello, " Unified approach for molecular dynamics and

density-functional theory," Physical Review Letters, vol. 55, no. 22, pp. 2471-

2474, 1985.

[14] J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon and D.

Sanchez-Portal, "The SIESTA method for ab initio order-N materials

simulation," Journal of Physics: Condensed Matter, vol. 14, no. 11, pp. 2745-

2779, 2002.

[15] E. Artacho, E. Anglada, O. Dieguez, J. D. Gale, A. Garcia, J. Junquera, R. M.

Martin, P. Ordejon, J. M. Pruneda, D. Sanchez-Portal and J. M. Soler, "The

SIESTA method; developments and applicability," Journal of Physics:

Condensed Matter, vol. 20, no. 6, pp. 064208/1-064208/6, 2008.