Nitrogen-induced perturbation of the valence band states in $\mathrm{Ga}{\mathrm{P}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ alloys

Nitrogen-induced perturbation of the valence band states in $Ga P_{1 - x} N_{x}$ alloys

S. V. Dudiy, Alex Zunger, M. Felici, A. Polimeni, M. Capizzi, H. P. Xin, and C. W. Tu

Phys. Rev. B 74, 155303 – Published 4 October 2006

Abstract

The effects of diluted nitrogen impurities on the valence- and conduction-band states of $Ga P_{1 - x} N_{x}$ have been predicted and measured experimentally. The calculation uses state-of-the-art atomistic modeling: we use large supercells with screened pseudopotentials and consider several random realizations of the nitrogen configurations. These calculations agree with photoluminescence excitation (PLE) measurements performed for nitrogen concentrations $x$ up to 0.035 and photon energies up to $1 eV$ above the GaP optical-absorption edge, as well as with published ellipsometry data. In particular, a predicted nitrogen-induced buildup of the $L$ character near the valence- and conduction-band edges accounts for the surprising broad-absorption plateau observed in PLE between the $X_{1 c}$ and the $Γ_{1 c}$ critical points of GaP. Moreover, theory accounts quantitatively for the downward bowing of the indirect conduction-band edge and for the upward bowing of the direct transition with increasing nitrogen concentration. We review some of the controversies in the literature regarding the shifts in the conduction band with composition, and conclude that measured results at ultralow N concentration cannot be used to judge behavior at a higher concentration. In particular, we find that at the high concentrations of nitrogen studied here $(\sim 1 %)$ the conduction-band edge (CBE) is a hybridized state made from the original GaP $X_{1 c}$ band-edge state plus all cluster states. In this limit, the CBE plunges down in energy as the N concentration increases, in quantitative agreement with the measurements reported here. However, at ultralow nitrogen concentrations $(< 0.1 %)$ , the CBE is the nearly unperturbed host $X_{1 c}$ , which does not sense the nitrogen cluster levels. Thus, this state does not move energetically as nitrogen is added and stays pinned in energy, in agreement with experimental results.

Received 28 June 2006

DOI:https://doi.org/10.1103/PhysRevB.74.155303

Authors & Affiliations

S. V. Dudiy and Alex Zunger

National Renewable Energy Laboratory, Golden, Colorado 80401, USA

M. Felici, A. Polimeni, and M. Capizzi

CNISM and Dipartimento di Fisica, Università “La Sapienza,” Piazzale A. Moro 2, I-00185 Roma, Italy

H. P. Xin and C. W. Tu

Department of Electrical and Computer Engineering, University of California, La Jolla, California 92093, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 74, Iss. 15 — 15 October 2006

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Photoluminescence excitation spectra of $Ga P_{1 - x} N_{x}$ epilayers at $T = 10 K$ . The short-dashed vertical lines indicate the energy of N single centers and N-related complexes $N N_{i}$ . The long-dashed vertical lines indicate the energy of GaP critical points. Upward-pointing arrows indicate weak features in the PLE spectra. PLE detection energy is set on the low-energy side of PL spectra.Reuse & Permissions
Figure 2
Fits (dotted lines) of a linear-energy dependence to the square of photoluminescence excitation data in samples with different N concentration, $x$ . The extrapolated values of the effective optical band-gap energy $E_{g}$ are shown also.Reuse & Permissions
Figure 3
(a) Calculated energy dependence of the square of the “transition probability” (namely, the dipole-matrix element squared, see text) for optical transitions between the states of the valence- and conduction-band edges in 1728 atom $Ga P_{1 - x} N_{x}$ random-alloy supercells. A Gaussian smearing of $0.02 eV$ is used. Fits of a square-root law (dotted lines) to the calculated dipole matrix squared and values of the extrapolated optical-energy gaps $E_{g}$ are given. (b) Comparison of the measured values of the shift of $E_{g}$ as obtained from the fits to the PLE data reported in Fig. 2 (open circles), and from the fits to the theoretically calculated dipole-matrix element squared shown in panel (a) (full dots). The error bars in panel (b) show the uncertainty of the fits in panel (a) and in Fig. 2.Reuse & Permissions
Figure 4
Calculated energy dependence of the dipole-matrix-element squared density for the case of 18 random-alloy atomic configurations of (a) 4 $(x = 1.56 %)$ and (b) 9 $(x = 3.51 %)$ N atoms in a 512 atom $(4 \times 4 \times 4)$ GaPN supercell. The dashed lines describe the $(Γ − Γ)$ transitions from the three valence-band maximum (VBM) states to the conduction-band states. The solid lines show the energy distribution of the dipole-matrix-element squared density as obtained by including in the above estimate the additional transitions from states below the three VBM states. Gaussian smearing of $0.02 eV$ is applied. Vertical dashed lines indicate the energies of bulk GaP critical points. The resonance around $2.7 eV$ in (a) is an artificial supercell-size effect and disappears for larger supercells (e.g., 1728 atom cells in Ref. 18).Reuse & Permissions
Figure 5
(Color online) Calculated $Γ$ , $L$ , and $X$ character for N concentrations 1.56% (upper panels) and 3.51% (lower panels) is shown for the valence band (left panels) and for the conduction band (right panels). The eigenstate energies are given with respect to the VBM of pure unstrained GaP, namely, the (weak) VBM bowing is not incorporated. The calculations use 512 atom GaPN $(4 \times 4 \times 4)$ supercells. The results are averaged over 18 random-alloy configurations, after receiving a Gaussian smearing of $0.02 eV$ .Reuse & Permissions
Figure 6
Energy shift $Δ E$ of the $Γ_{1 c}$ critical point as estimated in the present work (full dots) from supercell-empirical pseudopotential calculations for different N concentrations compared to the corresponding shift in the present PLE measurements (open circles) and the shift of the $E_{0}$ transition as determined by ellipsometry in Ref. 9 (open squares).Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Nitrogen-induced perturbation of the valence band states in $Ga P_{1 - x} N_{x}$ alloys

S. V. Dudiy, Alex Zunger, M. Felici, A. Polimeni, M. Capizzi, H. P. Xin, and C. W. Tu

Phys. Rev. B 74, 155303 – Published 4 October 2006

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Nitrogen-induced perturbation of the valence band states in GaP1−xNx alloys

S. V. Dudiy, Alex Zunger, M. Felici, A. Polimeni, M. Capizzi, H. P. Xin, and C. W. Tu

Phys. Rev. B 74, 155303 – Published 4 October 2006

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Nitrogen-induced perturbation of the valence band states in $Ga P_{1 - x} N_{x}$ alloys