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Electronic and optical properties of Zn-doped InGaAs emission layer with vacancy defects: A DFT study
Accepted Manuscript Title: Electronic and Optical Properties of Zn-doped InGaAs Emission Layer with Vacancy Defects: A DFT Study Authors: Jing Guo, Minhua Zhou, Jing Zhao, Lei Zhou, Liansong Xiong PII: DOI: Reference:
S0030-4026(17)30725-8 http://dx.doi.org/doi:10.1016/j.ijleo.2017.06.056 IJLEO 59319
To appear in: Received date: Accepted date:
20-3-2017 15-6-2017
Please cite this article as: Jing Guo, Minhua Zhou, Jing Zhao, Lei Zhou, Liansong Xiong, Electronic and Optical Properties of Zn-doped InGaAs Emission Layer with Vacancy Defects: A DFT Study, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.06.056 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Electronic and Optical Properties of Zn-doped InGaAs Emission Layer with Vacancy Defects: A DFT Study
Jing Guo a, b,*, Minhua Zhoub, Jing Zhaoa, Lei Zhoua, Liansong Xionga
a b
School of Automation, Nanjing Institute of Technology, Nanjing 211167, China Institute of Electronic Engineering and Optoelectronic Technology, Nanjing
University of Science and Technology, Nanjing 210094, China
Corresponding author at: School of Automation, Nanjing Institute of Technology Tel: + 86 13770672896
E-mail: [email protected]
Abstract In0.53Ga0.47As is an important material for the shortwave near-infrared negative electron affinity photocathodes. Zn atoms were doped in the intrinsic InGaAs to form p-type In0.53Ga0.44 Zn0.03As emission layer. Models of Zn-doped In0.53Ga0.44 Zn0.03As bulk with In, Ga or As vacancy defect were built in the article. Emphasis was put on how the defects influence the microstructure and the optical properties of the Zn-doped InGaAs emission layer. Combined effect of both vacancy defects and doped Zn atoms for the photoelectron emission performance was further studied. It is indicated that the In or Ga vacancy defect is easier to be generated than the As from the analysis of formation energy. However, As vacancy defect is more benefit for photoelectrons emission considering the material polarity because As vacancy defect interacting with doped Zn atoms is a positive center and generates acceptor level to narrow the energy gap. At the same time Zn ion will be easier to accept electrons when the As vacancy defect appears. The absorption coefficient of the InGaAs emission layer with As vacancy defect is also bigger than that with In or Ga defect. In conclusion, As vacancy defect is benefit and will promote the photoemission of InGaAs photocathode while the In or Ga vacancy defect should be avoided when the
emission layer is grown. Keywords: InGaAs emission layer; Vacancy defect; Zn doping; Photoemission
1. Introduction Doping is adopted to form most of p-type photoemission materials and the point defect is unavoidable during the growth process [1-5]. The small amount of the doping atoms and the point defects are the critical factor for photoemissions and photocathodes quality [6-8]. The InGaAs material doped by Zn atoms has been discussed in Ref. [9]. The doped atoms and the vacancy defects will break the periodicity potential field and generate new energy levels to narrow the energy gap. The impurity and defect levels cannot be occupied by two electrons spinning in the opposite direction, which is different from that in the energy bands [10]. There are three kinds of point defects in InGaAs emission layer, such as vacancy defect, antisite defect and interstitial defect. Among these, the vacancy defect is most common and easiest to be generated. Excess carriers are captured and accepted by the vacancy defect center, which is just like a trap. As a result, the transport and escape of photon-generated carriers are influenced by the vacancy defects [11, 12]. In 1970, E. Monoz observed GaAs material and found that acceptor level at generated by As vacancy defects and
E V 0 . 01
eV and
E V 0 . 12 E V 0 . 18
eV was eV were
generated by Ga vacancy defects [13]. The typical photoemission materials GaAs or InGaAs have been discussed as a cluster or a surface [14-16]. However, Zn-doped InGaAs bulk with vacancy defects has not been discussed theoretically. InGaAs is a ternary semiconductor and polar covalent bonds are formed among In, Ga and As atoms. The electronegativity of In and Ga atoms differs from each other although they both have 3 peripheral electrons. Meanwhile，the doping Zn atoms and the appearing vacancy change the InGaAs emission layer together. Therefore the InGaAs emission layer with In, Ga or As vacancy defect show more complicated physical and chemical properties than GaAs. The article focuses on Zn-doped InGaAs emission layer with vacancy defect. The formation energy, bonding structure, energy levels, charge
distribution and optical properties of the Zn-doped InGaAs with In, Ga or As defect are analyzed to explain how the vacancy defect impact the photoemission on the micro level. 2. Models and methods According to the analysis from Ref. [9], In0.53Ga0.44Zn0.03As with Ga atom substituted by doping Zn atom was chosen as Zn-doped InGaAs emission layer model, shown in Fig. 1. Three kinds of vacancy defects models were built based on the Zn-doped InGaAs model. An In atom around the doped Zn atom was taken away from In0.53Ga0.44 Zn0.03As model to form In vacancy defect model. The Zn-doped InGaAs model with Ga or As vacancy defect was generated in the same way. The three models of Zn-doped InGaAs with vacancy defect were calculated with the Vienna Ab-initio Simulation Package (VASP) [17-20], which was based on density functional theory (DFT) combined with PW91 general gradient approximation (GGA) exchange-correlation functional [21]. Vanderbilt ultrasoft pseudopotentials, as supplied by VASP [22] was used to optimize Atoms. The number of Monkhorst-Pack [23] k points was 6×6×6 in calculation of InGaAs models. 400eV was set as the plane wave cut-off energy. The error in these calculations is estimated to be ± 0.1eV. Valence electrons in orbit of Ga (3d, 4s, 4p), In (4d, 5s, 5p), As (4s, 4p) and Zn (3d, 4s) were only considered during the calculations and the analysis. 3. Results and discussion 3.1 Formation energy and bonding structure Formation energy represents the stability of atomic structure. The formation energy of Zn-doped In0.53Ga0.44Zn0.03As was -3.854 eV [9]. The negative value means that energy was released when the Zn atom substituted the Ga atom to form stable In0.53Ga0.44Zn0.03As. The formation energies of Zn-doped In0.53Ga0.44Zn0.03As with In, Ga or As vacancy defect are shown in Table. 1. The formation energies of the models with vacancy defect are all negative, which indicates vacancy defects can be generated stably with the energy released. In or Ga vacancy defect is formed more easily than As, as more energy is released. As we all know, Zn doping is essential for InGaAs emission layer. As a result, it is also studied
how the vacancy defects impact on the doping Zn atom based on the analysis of bonding structure, shown in Table. 2. Table. 2 shows the bonding among In, Ga, As and Zn atoms nearest vacancy defect. Compared with 2.521 Å in the perfect In0.53Ga0.44Zn0.03As [9], the bonding length of Zn-As in that with vacancy defect becomes longer. In the meanwhile, the bonding length of In-As or Ga-As is also stretched and longer than 2.665 Å or 2.530 Å of that in perfect In0.53Ga0.44Zn0.03As. It shows that a collapse happened and the bonding length became longer when the In, Ga or As atom was taken away to form a vacancy defect. However, the collapse and the length change don’t depend on the atomic volume. The volume of In atom is biggest, Ga is followed and the As is smallest. But the bonding length of In-As and Ga-As in InGaAs with As vacancy defect is longer than that with In or Ga vacancy defect. But beyond that, some other factors such as charge distribution and energy levels should also be taken into account to measure the stability of emission layer and bonding situation. 3.2 Energy levels and polarity The charge center after the generation of In, Ga or As defect in InGaAs emission layer is shown in Fig. 2 The In or Ga atom in the InGaAs emission layer is a cation and the negative charge center is formed when the cation is taken away. However the positive charge center is generated on account of an anion defect of As atom vacancy. The electrons are constrained around when the positive charge center is still at neutral state. Change of energy levels follows the charge centers formation. The bound electrons are excited easily up to the conduction band and then the positive charge center is formed. Therefore the donor levels are generated in the energy gap because the positive charge center plays a role of donor. In the same way, the holes are constrained around negative charge center at neutral state. The bound holes are excited down to the valence band and then the negative charge center is formed. The acceptor levels are generated in the energy gap because the negative charge center plays a role of acceptor. So the donor or acceptor levels are generated in the energy gap when the vacancy defect is formed.
The energy bands of the Zn-doped InGaAs without vacancy defect are shown in Ref. [9]. The InGaAs is still direct gap semiconductor with the top of valence-band and bottom of conduction band both at the Γ energy valley although new energy levels are generated because of the doped Zn atom. The energy levels change again when the vacancy defect appears. The energy levels of the emission layer with In, Ga or As vacancy defect are shown in Fig.3 The doped Zn atom is a negative charge center since it needs to trap an electron to form covalent bond during the process of substituting Ga atom to form Zn-doped InGaAs. The In or Ga vacancy defect is the negative charge center too. Theoretically, the InGaAs emission layer are influence by two negative charge centers, the doped Zn and the In or Ga vacancy defect, which seems to be benefit to generate p-type semiconductor. The result shows in Fig.3 appears something different. New energy levels are generated indeed because of the In or Ga vacancy defect. But the top of the valence band and the bottom of the conduction band are not at the same position, which means the Zn-doped InGaAs emission layer with In or Ga vacancy defect is not a direct-gap semiconductor any more. The conduction band moves to the low energy region as the As vacancy defect, which is positive charge center, appears at the Zn-doped In0.53Ga0.44Zn0.03As layer. The top of the valence band and the bottom of the conduction band are still at position Γ, showing the properties of direct-gap semiconductor. It is indicated that the acceptor level, the blue dotted line shown in Fig. 3, is mainly influenced by the doping Zn atom when the InGaAs emission layer are both impacted by the doping Zn atom and the As vacancy defect as a positive charge center. The As vacancy defect narrows the energy gap further and enhances the photoemission. In conclusion, the energy band of the In0.53Ga0.44Zn0.03As with In or Ga vacancy defect changes a lot although they are both negative charge centers. The Zn-doped InGaAs changes to be an indirect-gap semiconductor and is not good for the photoemission. However, the Zn-doped InGaAs with As vacancy defect is also a p-type semiconductor and is benefit for the generation of a photocathode as As vacancy defect is a positive charge center, which is different from the negative charge
center generated by doping Zn atom. Therefore, the As vacancy defect won’t affect the In0.53Ga0.44Zn0.03As to be an indirect-gap semiconductor while generation of the In or Ga vacancy takes uncertain factors to the emission layer. The partial densities of states (PDOS) are shown in Fig. 4 to assist to analyze the energy bands further. The energy bands and the PDOS of the Zn doped InGaAs with In vacancy defect look similar to that with Ga vacancy defect from Fig. 3 and Fig. 4 (a) and (b). The energy levels turn up in the energy gap from 0 to 1 eV are mainly occupied by s state electrons of As atoms and then by the s and p states electrons of In and Ga atoms. The amount of doped Zn atoms is small. As a result it contributes little to the energy level directly. In Fig.4 (c), it makes clear that the minimum PDOS of In, Ga and As atoms arise during 0 to 0.5 eV and the electrons at the conduction band move to the low energy region integrally influenced by the As vacancy defect. In addition, p state electrons contributes more to the energy levels than the s state in the region of 0 to 1 eV because of the negative charge center created by the doped Zn atom. The acceptor level is contributed by the s and p states electrons of In, Ga and As atoms on account of the combined effect of As vacancy defect and the doping Zn atom. 3.3 Mulliken population and charge distribution Zn doping is essential for the InGaAs emission layer. Therefore the charge distribution of the doped Zn atom is analyzed when the emission layer has vacancy defect. Table. 3 shows mulliken bonding population between the doping Zn atom and the other atoms and the charge distribution of the doping Zn atom. Mulliken bonding population indicates the bonding strength. Positive value means covalent bonding. The bigger the value is, the stronger the covalent bonding is. Zn atom has two peripheral electrons, one less than In or Ga atom. As a result, the covalent bonding of Zn-As becomes weaker and the mulliken bonding population is 0.86 when the Zn atom substitutes the Ga atom for doping. Meanwhile the atoms around the vacancy will collapse. The mulliken population of the covalent bonding between the Zn atom and the other atoms around reduces more or less because of the vacancy defect. The vacancy defect also makes the bond ionicity of the doped Zn enhanced and the covalency weakened. The mulliken population of the bond Zn-As1
in InGaAs with As vacancy defect reduced to 0.59, which means the bond covalency is weakest among the three types of vacancy defects. As the charge distribution, 0.02 electrons are lost from Zn atom in the perfect InGaAs model. The Zn atom gains 0.05 electrons and the charge of Zn atom is -0.03 in the Zn-doped InGaAs model with In vacancy defect. 0.02 electrons are gained when the Ga vacancy defect is generated. However, 0.03 electrons are lost and the charge of Zn atom changes to 0.05 in the Zn-doped InGaAs model with As vacancy defect. Based on the analysis above, the As vacancy defect enhances the ability of doped Zn atom to accept electrons, which is benefit for the photoelectrons transport. 3.4 Optical properties According to the three-step photoemission proposed by Spicer [24], the photoelectrons diffuse and escape from the bottom of the conduction band. InGaAs with Zn doping is a p-type semiconductor. The electrons excited to the conduction band are unbalance minority carriers and will thermalize at the bottom of conduction band following the law of carrier diffusion. The one-dimensional equation of continuity is shown in Eq. (1), which is the theoretical base of the carrier diffusion. n( x ) t
where g( x )
n( x ) t
g( x )
n( x )
J
(1)
q
is the change rate of the electron density in time in any position x,
is carrier generation function (generation rate of photoelectrons) relevant to
spatial position,
n( x )
is carrier recombination velocity,
J
is diffusion term, J is
q
electronic current density, q is electron charge. Photoelectrons generation rate
g( x )
shown in Eq. (2) is defined as the
generation of electrons and holes pairs in proportion to the reduction ratio of light intensity I in the thin layer from x to x+Δx. g( x )
dI dx
(2)
where α is light absorptivity. The light intensity I at the point with a distance x from the surface in the semiconductor is described as
I I0e
light intensity. For the reflection-mode photocathode,
x
, where I0 is the incident
g( x )
is deduced as Eq. (3)
considering only the reflectivity R. g( x ) ( 1 R )I 0 e
x
(3)
The generation of photoelectrons is closely related to the absorptivity α and the reflectivity R. However, the cesium and the oxygen alternating adsorption on the InGaAs emission layer are essential to form InGaAs photocathode and then the discussion of R is not very meaningful for just emission layer [25, 26]. So just only the absorptivity α of the Zn-doped InGaAs with vacancy defect is shown in Fig. 5. The absorption peak appears at 3.86 eV in InGaAs emission layer with As or In vacancy defect. And the curve peak in that with Ga vacancy defect is at 4.05 eV, moving slightly to the high energy region. The absorptivity of InGaAs with In vacancy defect is almost the same as that with Ga when the photon’s energy is lower than 2.77 eV. In addition, the absorptivity in InGaAs with As vacancy defect is bigger than that with Ga or In vacancy defect in the energy region lower than the peak. Three types of InGaAs models with defect have almost the same absorptivity from 4.05 eV to 4.90 eV. But the InGaAs with As vacancy defect also has bigger absorptivity than that with In or Ga vacancy defect in the region of 4.05 eV to 8.83 eV. As we all know, the InGaAs photocathode are sensitive to the photons with lower energy in the infrared region. As a result, the Zn-doped InGaAs emission layer with As vacancy defect is more suitable than that with In or Ga vacancy defect for the InGaAs photocathode from the analysis of absorptivity. 4. Conclusions The In, Ga or As vacancy defect models are built based on the Zn-doped In0.53Ga0.44Zn0.03As bulk model in this article. The formation energy, bonding structure, energy bands, material polarity, charge distribution and the absorptivity are analyzed when the models with vacancy defect. Emphasis is put on the properties of InGaAs both with doping Zn atom and vacancy defect. In experiments, evaporation
rates of As atoms is bigger than In or Ga atoms during the photocathode activation with high and low temperature and the As vacancy defect is easier to be generated. Then from the theoretical analysis above, the acceptor level is generated by the doping Zn atom and As vacancy defect while the InGaAs emission layer with In or Ga vacancy defect is changed to be indirect band gap which is bad for the generation and transition of photoelectrons. In addition, As vacancy defect in Zn-doped InGaAs is benefit for photoemission from material polarity, charge distribution and the absorptivity although the In or Ga vacancy may be easier to be formed in respect of formation energy. In conclusion, As vacancy defect is good for photoemission and In or Ga vacancy should be avoided during the generation of InGaAs emission layer.
Acknowledgements This work is supported by the innovation important research fund of NJIT (Grant No: CKJA201508, CKJA201409), the startup foundation for introducing talents of NJIT (Grant No: ZKJ201610, ZKJ201508), National Natural Science Foundation of China for youth (Grant No: 61305011 and 61601198), the Major Research Plan of the National Natural Science Foundation of China (Grant No: 91433108), Shandong provincial natural science foundation (Grant No: ZR2015FL010) and the startup foundation for introducing talents of NUIST（Grant No. 2016r39）.
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oxynitride thin films by x-ray photoelectron spectroscopy, J. Vac. Sci. technol. 17 (1999) 1086~1090. [13] G. P. Srivastava, The electron counting rule and passivation of compound semiconductor surfaces, Appl. Phys. Lett. 252 (2006) 7600~7607. [14] M. Saavedra, A. Buljan, M. Muñoz, Theoretical study of methanethiol adsorbed on GaAs(100) surface, Comput. Theor. Chem. 906 (2009) 72–77. [15] Z. Syum, H. Woldeghebriel, The structure and electronic properties of (GaAs)n and Al/In-doped (GaAs)n(n=2–20) clusters, Comput. Theor. Chem. 1048 (2014) 7–17. [16] J. S. Zhang, H. C. Liu, F. Shi, F. Yu, Y. Liu, C. Xiao, Q. Lan, Adsorption and dissociation of H2O on the Ga-rich GaAs(001)-(4×2) surface: DFT and DFT-D computations with a Ga7As8H11 cluster model, Comput. Theor. Chem. 1064 (2015) 51–55. [17] G. Kresse, VASP, Technische University at Wien (1993). [18] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comp. Mater. Sci. 6 (1996) 15-50. [19] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B. 54 (1996) 11169. [20] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B. 47(1993) 558. [21] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77(1996) 3865. [22] G. Kresse, J. Hafner, Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements, J. Phys-Condens. Mat. 6 (1994) 8245. [23] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B. 13(1976) 5188. [24] W.E. Spicer, Photoemissive, photoconductive, and absorption studies of alkali antimony compounds, Phys. Rev. 112 (1958) 114–122. [25] M. Z. Yang, M. C. Jin, Photoemission of reflection-mode InGaAs photocathodes
after Cs, O activation and recaesiations, Opt. Mater. 62 (2016) 499-504. [26] M. Z. Yang, M. C. Jin, B. K. Chang, Spectral response of InGaAs photocathodes with different emission layers, Appl. Optics. 55 (2016) 8732-8737
Fig. 1 Zn-doped InGaAs emission layer model
(a)
(b)
Fig.2 The charge center after defect generation (a) negative charge center because of cation defect (b) positive charge center because of anion defect
Fig.3 The energy bands of the Zn-doped InGaAs models with vacancy defect
(a)
(b)
(c) Fig.4 The PDOS of the Zn-doped InGaAs emission layer with vacancy defect (a) PDOS of the InGaAs with In vacancy defect (b) PDOS of the InGaAs with Ga vacancy defect (c) PDOS of the InGaAs with As vacancy defect
Fig. 5 The absorptivity α of InGaAs emission layer with vacancy defect
Table.1 Formation energies of Zn-doped In0.53Ga0.44Zn0.03As with vacancy defect Defect type
In vacancy defect
Ga vacancy defect
As vacancy defect
Formation energy（eV）
-4.469
-4.156
-2.742
Table. 2 Bonding of models with vacancy defect Defect type
In vacancy defect
Ga vacancy defect
As vacancy defect
In-As（Å）
2.687
2.702
2.725
Ga-As（Å）
2.529
2.535
2.593
Zn-As（Å）
2.543
2.554
2.560
Table. 3 Mulliken bonding population and charge distribution of the doped Zn atom mulliken population
bonding and
charge
no vacancy
In vacancy
Ga vacancy
As vacancy
Zn-As1（e） 0.86
0.63
0.64
0.59
Zn-As2（e） 0.86
0.63
0.67
0.69
Zn-As3（e） 0.86
0.66
0.69
0.64
Zn-As4（e） 0.86
0.67
0.79
0.78
-0.03
0.00
0.05
distribution mulliken bonding population Zn charge（e）
0.02
S0030-4026(17)30725-8 http://dx.doi.org/doi:10.1016/j.ijleo.2017.06.056 IJLEO 59319
To appear in: Received date: Accepted date:
20-3-2017 15-6-2017
Please cite this article as: Jing Guo, Minhua Zhou, Jing Zhao, Lei Zhou, Liansong Xiong, Electronic and Optical Properties of Zn-doped InGaAs Emission Layer with Vacancy Defects: A DFT Study, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.06.056 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Electronic and Optical Properties of Zn-doped InGaAs Emission Layer with Vacancy Defects: A DFT Study
Jing Guo a, b,*, Minhua Zhoub, Jing Zhaoa, Lei Zhoua, Liansong Xionga
a b
School of Automation, Nanjing Institute of Technology, Nanjing 211167, China Institute of Electronic Engineering and Optoelectronic Technology, Nanjing
University of Science and Technology, Nanjing 210094, China
Corresponding author at: School of Automation, Nanjing Institute of Technology Tel: + 86 13770672896
E-mail: [email protected]
Abstract In0.53Ga0.47As is an important material for the shortwave near-infrared negative electron affinity photocathodes. Zn atoms were doped in the intrinsic InGaAs to form p-type In0.53Ga0.44 Zn0.03As emission layer. Models of Zn-doped In0.53Ga0.44 Zn0.03As bulk with In, Ga or As vacancy defect were built in the article. Emphasis was put on how the defects influence the microstructure and the optical properties of the Zn-doped InGaAs emission layer. Combined effect of both vacancy defects and doped Zn atoms for the photoelectron emission performance was further studied. It is indicated that the In or Ga vacancy defect is easier to be generated than the As from the analysis of formation energy. However, As vacancy defect is more benefit for photoelectrons emission considering the material polarity because As vacancy defect interacting with doped Zn atoms is a positive center and generates acceptor level to narrow the energy gap. At the same time Zn ion will be easier to accept electrons when the As vacancy defect appears. The absorption coefficient of the InGaAs emission layer with As vacancy defect is also bigger than that with In or Ga defect. In conclusion, As vacancy defect is benefit and will promote the photoemission of InGaAs photocathode while the In or Ga vacancy defect should be avoided when the
emission layer is grown. Keywords: InGaAs emission layer; Vacancy defect; Zn doping; Photoemission
1. Introduction Doping is adopted to form most of p-type photoemission materials and the point defect is unavoidable during the growth process [1-5]. The small amount of the doping atoms and the point defects are the critical factor for photoemissions and photocathodes quality [6-8]. The InGaAs material doped by Zn atoms has been discussed in Ref. [9]. The doped atoms and the vacancy defects will break the periodicity potential field and generate new energy levels to narrow the energy gap. The impurity and defect levels cannot be occupied by two electrons spinning in the opposite direction, which is different from that in the energy bands [10]. There are three kinds of point defects in InGaAs emission layer, such as vacancy defect, antisite defect and interstitial defect. Among these, the vacancy defect is most common and easiest to be generated. Excess carriers are captured and accepted by the vacancy defect center, which is just like a trap. As a result, the transport and escape of photon-generated carriers are influenced by the vacancy defects [11, 12]. In 1970, E. Monoz observed GaAs material and found that acceptor level at generated by As vacancy defects and
E V 0 . 01
eV and
E V 0 . 12 E V 0 . 18
eV was eV were
generated by Ga vacancy defects [13]. The typical photoemission materials GaAs or InGaAs have been discussed as a cluster or a surface [14-16]. However, Zn-doped InGaAs bulk with vacancy defects has not been discussed theoretically. InGaAs is a ternary semiconductor and polar covalent bonds are formed among In, Ga and As atoms. The electronegativity of In and Ga atoms differs from each other although they both have 3 peripheral electrons. Meanwhile，the doping Zn atoms and the appearing vacancy change the InGaAs emission layer together. Therefore the InGaAs emission layer with In, Ga or As vacancy defect show more complicated physical and chemical properties than GaAs. The article focuses on Zn-doped InGaAs emission layer with vacancy defect. The formation energy, bonding structure, energy levels, charge
distribution and optical properties of the Zn-doped InGaAs with In, Ga or As defect are analyzed to explain how the vacancy defect impact the photoemission on the micro level. 2. Models and methods According to the analysis from Ref. [9], In0.53Ga0.44Zn0.03As with Ga atom substituted by doping Zn atom was chosen as Zn-doped InGaAs emission layer model, shown in Fig. 1. Three kinds of vacancy defects models were built based on the Zn-doped InGaAs model. An In atom around the doped Zn atom was taken away from In0.53Ga0.44 Zn0.03As model to form In vacancy defect model. The Zn-doped InGaAs model with Ga or As vacancy defect was generated in the same way. The three models of Zn-doped InGaAs with vacancy defect were calculated with the Vienna Ab-initio Simulation Package (VASP) [17-20], which was based on density functional theory (DFT) combined with PW91 general gradient approximation (GGA) exchange-correlation functional [21]. Vanderbilt ultrasoft pseudopotentials, as supplied by VASP [22] was used to optimize Atoms. The number of Monkhorst-Pack [23] k points was 6×6×6 in calculation of InGaAs models. 400eV was set as the plane wave cut-off energy. The error in these calculations is estimated to be ± 0.1eV. Valence electrons in orbit of Ga (3d, 4s, 4p), In (4d, 5s, 5p), As (4s, 4p) and Zn (3d, 4s) were only considered during the calculations and the analysis. 3. Results and discussion 3.1 Formation energy and bonding structure Formation energy represents the stability of atomic structure. The formation energy of Zn-doped In0.53Ga0.44Zn0.03As was -3.854 eV [9]. The negative value means that energy was released when the Zn atom substituted the Ga atom to form stable In0.53Ga0.44Zn0.03As. The formation energies of Zn-doped In0.53Ga0.44Zn0.03As with In, Ga or As vacancy defect are shown in Table. 1. The formation energies of the models with vacancy defect are all negative, which indicates vacancy defects can be generated stably with the energy released. In or Ga vacancy defect is formed more easily than As, as more energy is released. As we all know, Zn doping is essential for InGaAs emission layer. As a result, it is also studied
how the vacancy defects impact on the doping Zn atom based on the analysis of bonding structure, shown in Table. 2. Table. 2 shows the bonding among In, Ga, As and Zn atoms nearest vacancy defect. Compared with 2.521 Å in the perfect In0.53Ga0.44Zn0.03As [9], the bonding length of Zn-As in that with vacancy defect becomes longer. In the meanwhile, the bonding length of In-As or Ga-As is also stretched and longer than 2.665 Å or 2.530 Å of that in perfect In0.53Ga0.44Zn0.03As. It shows that a collapse happened and the bonding length became longer when the In, Ga or As atom was taken away to form a vacancy defect. However, the collapse and the length change don’t depend on the atomic volume. The volume of In atom is biggest, Ga is followed and the As is smallest. But the bonding length of In-As and Ga-As in InGaAs with As vacancy defect is longer than that with In or Ga vacancy defect. But beyond that, some other factors such as charge distribution and energy levels should also be taken into account to measure the stability of emission layer and bonding situation. 3.2 Energy levels and polarity The charge center after the generation of In, Ga or As defect in InGaAs emission layer is shown in Fig. 2 The In or Ga atom in the InGaAs emission layer is a cation and the negative charge center is formed when the cation is taken away. However the positive charge center is generated on account of an anion defect of As atom vacancy. The electrons are constrained around when the positive charge center is still at neutral state. Change of energy levels follows the charge centers formation. The bound electrons are excited easily up to the conduction band and then the positive charge center is formed. Therefore the donor levels are generated in the energy gap because the positive charge center plays a role of donor. In the same way, the holes are constrained around negative charge center at neutral state. The bound holes are excited down to the valence band and then the negative charge center is formed. The acceptor levels are generated in the energy gap because the negative charge center plays a role of acceptor. So the donor or acceptor levels are generated in the energy gap when the vacancy defect is formed.
The energy bands of the Zn-doped InGaAs without vacancy defect are shown in Ref. [9]. The InGaAs is still direct gap semiconductor with the top of valence-band and bottom of conduction band both at the Γ energy valley although new energy levels are generated because of the doped Zn atom. The energy levels change again when the vacancy defect appears. The energy levels of the emission layer with In, Ga or As vacancy defect are shown in Fig.3 The doped Zn atom is a negative charge center since it needs to trap an electron to form covalent bond during the process of substituting Ga atom to form Zn-doped InGaAs. The In or Ga vacancy defect is the negative charge center too. Theoretically, the InGaAs emission layer are influence by two negative charge centers, the doped Zn and the In or Ga vacancy defect, which seems to be benefit to generate p-type semiconductor. The result shows in Fig.3 appears something different. New energy levels are generated indeed because of the In or Ga vacancy defect. But the top of the valence band and the bottom of the conduction band are not at the same position, which means the Zn-doped InGaAs emission layer with In or Ga vacancy defect is not a direct-gap semiconductor any more. The conduction band moves to the low energy region as the As vacancy defect, which is positive charge center, appears at the Zn-doped In0.53Ga0.44Zn0.03As layer. The top of the valence band and the bottom of the conduction band are still at position Γ, showing the properties of direct-gap semiconductor. It is indicated that the acceptor level, the blue dotted line shown in Fig. 3, is mainly influenced by the doping Zn atom when the InGaAs emission layer are both impacted by the doping Zn atom and the As vacancy defect as a positive charge center. The As vacancy defect narrows the energy gap further and enhances the photoemission. In conclusion, the energy band of the In0.53Ga0.44Zn0.03As with In or Ga vacancy defect changes a lot although they are both negative charge centers. The Zn-doped InGaAs changes to be an indirect-gap semiconductor and is not good for the photoemission. However, the Zn-doped InGaAs with As vacancy defect is also a p-type semiconductor and is benefit for the generation of a photocathode as As vacancy defect is a positive charge center, which is different from the negative charge
center generated by doping Zn atom. Therefore, the As vacancy defect won’t affect the In0.53Ga0.44Zn0.03As to be an indirect-gap semiconductor while generation of the In or Ga vacancy takes uncertain factors to the emission layer. The partial densities of states (PDOS) are shown in Fig. 4 to assist to analyze the energy bands further. The energy bands and the PDOS of the Zn doped InGaAs with In vacancy defect look similar to that with Ga vacancy defect from Fig. 3 and Fig. 4 (a) and (b). The energy levels turn up in the energy gap from 0 to 1 eV are mainly occupied by s state electrons of As atoms and then by the s and p states electrons of In and Ga atoms. The amount of doped Zn atoms is small. As a result it contributes little to the energy level directly. In Fig.4 (c), it makes clear that the minimum PDOS of In, Ga and As atoms arise during 0 to 0.5 eV and the electrons at the conduction band move to the low energy region integrally influenced by the As vacancy defect. In addition, p state electrons contributes more to the energy levels than the s state in the region of 0 to 1 eV because of the negative charge center created by the doped Zn atom. The acceptor level is contributed by the s and p states electrons of In, Ga and As atoms on account of the combined effect of As vacancy defect and the doping Zn atom. 3.3 Mulliken population and charge distribution Zn doping is essential for the InGaAs emission layer. Therefore the charge distribution of the doped Zn atom is analyzed when the emission layer has vacancy defect. Table. 3 shows mulliken bonding population between the doping Zn atom and the other atoms and the charge distribution of the doping Zn atom. Mulliken bonding population indicates the bonding strength. Positive value means covalent bonding. The bigger the value is, the stronger the covalent bonding is. Zn atom has two peripheral electrons, one less than In or Ga atom. As a result, the covalent bonding of Zn-As becomes weaker and the mulliken bonding population is 0.86 when the Zn atom substitutes the Ga atom for doping. Meanwhile the atoms around the vacancy will collapse. The mulliken population of the covalent bonding between the Zn atom and the other atoms around reduces more or less because of the vacancy defect. The vacancy defect also makes the bond ionicity of the doped Zn enhanced and the covalency weakened. The mulliken population of the bond Zn-As1
in InGaAs with As vacancy defect reduced to 0.59, which means the bond covalency is weakest among the three types of vacancy defects. As the charge distribution, 0.02 electrons are lost from Zn atom in the perfect InGaAs model. The Zn atom gains 0.05 electrons and the charge of Zn atom is -0.03 in the Zn-doped InGaAs model with In vacancy defect. 0.02 electrons are gained when the Ga vacancy defect is generated. However, 0.03 electrons are lost and the charge of Zn atom changes to 0.05 in the Zn-doped InGaAs model with As vacancy defect. Based on the analysis above, the As vacancy defect enhances the ability of doped Zn atom to accept electrons, which is benefit for the photoelectrons transport. 3.4 Optical properties According to the three-step photoemission proposed by Spicer [24], the photoelectrons diffuse and escape from the bottom of the conduction band. InGaAs with Zn doping is a p-type semiconductor. The electrons excited to the conduction band are unbalance minority carriers and will thermalize at the bottom of conduction band following the law of carrier diffusion. The one-dimensional equation of continuity is shown in Eq. (1), which is the theoretical base of the carrier diffusion. n( x ) t
where g( x )
n( x ) t
g( x )
n( x )
J
(1)
q
is the change rate of the electron density in time in any position x,
is carrier generation function (generation rate of photoelectrons) relevant to
spatial position,
n( x )
is carrier recombination velocity,
J
is diffusion term, J is
q
electronic current density, q is electron charge. Photoelectrons generation rate
g( x )
shown in Eq. (2) is defined as the
generation of electrons and holes pairs in proportion to the reduction ratio of light intensity I in the thin layer from x to x+Δx. g( x )
dI dx
(2)
where α is light absorptivity. The light intensity I at the point with a distance x from the surface in the semiconductor is described as
I I0e
light intensity. For the reflection-mode photocathode,
x
, where I0 is the incident
g( x )
is deduced as Eq. (3)
considering only the reflectivity R. g( x ) ( 1 R )I 0 e
x
(3)
The generation of photoelectrons is closely related to the absorptivity α and the reflectivity R. However, the cesium and the oxygen alternating adsorption on the InGaAs emission layer are essential to form InGaAs photocathode and then the discussion of R is not very meaningful for just emission layer [25, 26]. So just only the absorptivity α of the Zn-doped InGaAs with vacancy defect is shown in Fig. 5. The absorption peak appears at 3.86 eV in InGaAs emission layer with As or In vacancy defect. And the curve peak in that with Ga vacancy defect is at 4.05 eV, moving slightly to the high energy region. The absorptivity of InGaAs with In vacancy defect is almost the same as that with Ga when the photon’s energy is lower than 2.77 eV. In addition, the absorptivity in InGaAs with As vacancy defect is bigger than that with Ga or In vacancy defect in the energy region lower than the peak. Three types of InGaAs models with defect have almost the same absorptivity from 4.05 eV to 4.90 eV. But the InGaAs with As vacancy defect also has bigger absorptivity than that with In or Ga vacancy defect in the region of 4.05 eV to 8.83 eV. As we all know, the InGaAs photocathode are sensitive to the photons with lower energy in the infrared region. As a result, the Zn-doped InGaAs emission layer with As vacancy defect is more suitable than that with In or Ga vacancy defect for the InGaAs photocathode from the analysis of absorptivity. 4. Conclusions The In, Ga or As vacancy defect models are built based on the Zn-doped In0.53Ga0.44Zn0.03As bulk model in this article. The formation energy, bonding structure, energy bands, material polarity, charge distribution and the absorptivity are analyzed when the models with vacancy defect. Emphasis is put on the properties of InGaAs both with doping Zn atom and vacancy defect. In experiments, evaporation
rates of As atoms is bigger than In or Ga atoms during the photocathode activation with high and low temperature and the As vacancy defect is easier to be generated. Then from the theoretical analysis above, the acceptor level is generated by the doping Zn atom and As vacancy defect while the InGaAs emission layer with In or Ga vacancy defect is changed to be indirect band gap which is bad for the generation and transition of photoelectrons. In addition, As vacancy defect in Zn-doped InGaAs is benefit for photoemission from material polarity, charge distribution and the absorptivity although the In or Ga vacancy may be easier to be formed in respect of formation energy. In conclusion, As vacancy defect is good for photoemission and In or Ga vacancy should be avoided during the generation of InGaAs emission layer.
Acknowledgements This work is supported by the innovation important research fund of NJIT (Grant No: CKJA201508, CKJA201409), the startup foundation for introducing talents of NJIT (Grant No: ZKJ201610, ZKJ201508), National Natural Science Foundation of China for youth (Grant No: 61305011 and 61601198), the Major Research Plan of the National Natural Science Foundation of China (Grant No: 91433108), Shandong provincial natural science foundation (Grant No: ZR2015FL010) and the startup foundation for introducing talents of NUIST（Grant No. 2016r39）.
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Fig. 1 Zn-doped InGaAs emission layer model
(a)
(b)
Fig.2 The charge center after defect generation (a) negative charge center because of cation defect (b) positive charge center because of anion defect
Fig.3 The energy bands of the Zn-doped InGaAs models with vacancy defect
(a)
(b)
(c) Fig.4 The PDOS of the Zn-doped InGaAs emission layer with vacancy defect (a) PDOS of the InGaAs with In vacancy defect (b) PDOS of the InGaAs with Ga vacancy defect (c) PDOS of the InGaAs with As vacancy defect
Fig. 5 The absorptivity α of InGaAs emission layer with vacancy defect
Table.1 Formation energies of Zn-doped In0.53Ga0.44Zn0.03As with vacancy defect Defect type
In vacancy defect
Ga vacancy defect
As vacancy defect
Formation energy（eV）
-4.469
-4.156
-2.742
Table. 2 Bonding of models with vacancy defect Defect type
In vacancy defect
Ga vacancy defect
As vacancy defect
In-As（Å）
2.687
2.702
2.725
Ga-As（Å）
2.529
2.535
2.593
Zn-As（Å）
2.543
2.554
2.560
Table. 3 Mulliken bonding population and charge distribution of the doped Zn atom mulliken population
bonding and
charge
no vacancy
In vacancy
Ga vacancy
As vacancy
Zn-As1（e） 0.86
0.63
0.64
0.59
Zn-As2（e） 0.86
0.63
0.67
0.69
Zn-As3（e） 0.86
0.66
0.69
0.64
Zn-As4（e） 0.86
0.67
0.79
0.78
-0.03
0.00
0.05
distribution mulliken bonding population Zn charge（e）
0.02