## Abstract

Temperature-dependent photoreflectance (PR) measurements are employed to characterize the conduction band structure of In0.54 Ga0.46 P1-y Ny (y=0 and 0.02) grown on GaAs substrates. The band gap and the upper subband E+ transition are observed in InGaPN as predicted by the band anticrossing (BAC) model. To investigate the energetic positions of the features in the PR spectra, a Kramers-Kronig analysis is proposed. Based on the PR data and the BAC model, we find that the energy EN of isolated nitrogen states shifts significantly to higher energies with decreasing temperature. Simultaneously, the interaction potential V between the nitrogen states and the unperturbed conduction band also rises to higher values. At 293 K, EN =2.054 eV and V=1.513 eV are determined. The thermal shifts of EN and V are d EN /dT≈-0.43 meV/K and dV/dT≈-0.67 meV/K, respectively. The temperature-dependent EN level and interaction potential V are attributed to the lattice distortions, which can be affected by temperature-induced changes in deformation potential. This information is important for overall validity of the BAC model to dilute nitride InGaPN alloys.

Original language | English |
---|---|

Article number | 016109 |

Journal | Journal of Applied Physics |

Volume | 104 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2008 |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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*Journal of Applied Physics*,

*104*(1), [016109]. https://doi.org/10.1063/1.2952514

**Temperature-dependent parameters of band anticrossing in InGaPN alloys**. In: Journal of Applied Physics. 2008 ; Vol. 104, No. 1.

}

*Journal of Applied Physics*, vol. 104, no. 1, 016109. https://doi.org/10.1063/1.2952514

**Temperature-dependent parameters of band anticrossing in InGaPN alloys.** / Lin, K. I.; Wang, T. S.; Tsai, J. T.; Hwang, J. S.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Temperature-dependent parameters of band anticrossing in InGaPN alloys

AU - Lin, K. I.

AU - Wang, T. S.

AU - Tsai, J. T.

AU - Hwang, J. S.

N1 - Funding Information: Lin K. I. a) Wang T. S. Tsai J. T. Hwang J. S. Department of Physics, National Cheng Kung University , Tainan 701 Taiwan a) Author to whom correspondence should be addressed. Electronic mail: xlight_1108@yahoo.com.tw. 01 07 2008 104 1 016109 04 04 2008 06 05 2008 11 07 2008 2008-07-11T10:45:29 2008 American Institute of Physics 0021-8979/2008/104(1)/016109/3/ $23.00 Temperature-dependent photoreflectance (PR) measurements are employed to characterize the conduction band structure of In 0.54 Ga 0.46 P 1 − y N y ( y = 0 and 0.02) grown on GaAs substrates. The band gap and the upper subband E + transition are observed in InGaPN as predicted by the band anticrossing (BAC) model. To investigate the energetic positions of the features in the PR spectra, a Kramers–Kronig analysis is proposed. Based on the PR data and the BAC model, we find that the energy E N of isolated nitrogen states shifts significantly to higher energies with decreasing temperature. Simultaneously, the interaction potential V between the nitrogen states and the unperturbed conduction band also rises to higher values. At 293 K, E N = 2.054 eV and V = 1.513 eV are determined. The thermal shifts of E N and V are d E N / d T ≈ − 0.43 meV / K and d V / d T ≈ − 0.67 meV / K , respectively. The temperature-dependent E N level and interaction potential V are attributed to the lattice distortions, which can be affected by temperature-induced changes in deformation potential. This information is important for overall validity of the BAC model to dilute nitride InGaPN alloys. NSCT NSC96-2112-M-006-020-MY2 NSCT NSC95-2112-M-006-026 Incorporation of small amounts of nitrogen (N) into conventional III-V semiconductors causes a profound reduction of the fundamental band gap energy, which results in a large composition-dependent bowing coefficient. 1 Therefore, the band anticrossing (BAC) model is introduced to describe the influence of N incorporation on the band structure of the dilute nitrides, such as (In)GaAsN and GaPN alloys, 2–7 which have recently attracted considerable attention. It is well known that an isolated N introduces highly localized states in these nitrides, which interact with the extended conduction band states of the host semiconductor matrix. The interaction splits the conduction band into two subbands defined as the upper subband E + and the lower subband E − , which corresponds to the conduction band edge. Recently, temperature dependence of the parameters, i.e., the localized states energy E N introduced by the isolated N and the interaction potential V , of the BAC model in GaAsN epilayers has been reported. 6 This has largely been overlooked in the earlier BAC analysis of the temperature behavior of the band gap energies in (In)GaAsN alloys, where the E N level is believed to be temperature independent based on the localized nature of the N-related states. 7 More recently, dilute nitride In x Ga 1 − x P 1 − y N y alloys have been grown by gas source molecular beam epitaxy on GaAs substrates. 8 There are published reports of the band gap properties in InGaPN analyzed by the BAC model, 9–11 but some doubts on the temperature dependence of E N and V and overall validity of the BAC model have been raised. Therefore, temperature-dependent measurements of the band structure and verifications of the BAC model of InGaPN alloys are necessary and important. In this work, temperature-dependent photoreflectance (PR) measurements are employed to characterize the conduction band structure of In 0.54 Ga 0.46 P 1 − y N y grown on GaAs substrates. The band gap, i.e., E − transition, and the upper subband E + transition are observed in InGaPN, as predicted by the BAC model. To investigate the energetic positions of the features in the PR spectra, a Kramers–Kronig analysis is proposed. Based on the PR data and the BAC model, we find E N = 2.054 eV and V = 1.513 eV at 293 K. With decreasing temperature, the energy of E N shifts significantly to higher energies. Simultaneously, the interaction potential V between the N states and the unperturbed conduction band also rises to higher values. The thermal shifts of E N and V are d E N / d T ≈ − 0.43 meV / K and d V / d T ≈ − 0.67 meV / K , respectively. The In 0.54 Ga 0.46 P 1 − y N y / GaAs heterostructures are grown on a (001) GaAs semi-insulating substrate by gas source molecular beam epitaxy. The growth sequence involves the growth of a 0.5-μm-thick undoped In 0.54 Ga 0.46 P 1 − y N y ( y = 0 and 0.02) layer on a 0.2-μm-thick GaAs buffer layer. The growth temperature is maintained at approximately 420 ° C , with N plasma ignited. A standard arrangement of the PR apparatus is used. 11 The probe beam consists of a tungsten lamp and a quarter meter monochromator combination. The 325 nm line of a He–Cd laser serves as the pumping beam. The detection system comprises a Si photodetector and a lock-in amplifier. The PR measurements are performed in a helium-closed cryostat at temperatures ranging from 25 to 293 K. According to the BAC model, the interaction of the conduction band edge with the dispersionless N level results in a splitting of the conduction band into two subbands, E − and E + , described by the equation at Γ point (Refs. 3–6, 9, and 11 ) E ± = 1 2 { E N + E Γ ± [ ( E N − E Γ ) 2 + 4 V 2 y ] 1 / 2 } , (1) where E Γ and E N represent the energies relative to the top of the valence band of the unperturbed conduction band and of the localized N states, respectively, V is the interaction potential between the conduction band E Γ and the E N level, and y is the N content. The downward shift of the lower E − subband is responsible for the band gap reduction. Based on the temperature dependence of the E − , E Γ , and E + transitions obtained from the PR spectra and Eq. (1) , E N and V as a function of temperature can be directly determined by (Ref. 6 ) E N = E + + E − − E Γ , (2) V = ( E + − E − ) 2 − ( E N − E Γ ) 2 4 y . (3) Figures 1(a) and 1(b) depict the temperature-dependent PR spectra of the E − and the E + transitions in the In 0.54 Ga 0.46 P 0.98 N 0.02 alloy, respectively. The features of the PR spectra are marked by the arrows. In addition, the spin-orbit splitting E − + Δ SO is indicated in Fig. 1(a) . 12 The line shape of the PR spectrum is usually fitted to (Ref. 11 ) Δ R R ( E ) = Re [ A e i θ ( E − E j + i Γ ) − m ] , (4) where E is the photon energy and A , θ , E j , and Γ are the amplitude, phase factor, transition energy, and broadening parameter, respectively. The parameter m depends on the dimensionality of the critical point. The band gap energies of the In 0.54 Ga 0.46 P alloy at various temperatures determined from the PR measurements are reported elsewhere. 13,14 However, the analysis of the derivativelike line shape in Eq. (4) is more debatable for our samples, which possess a valence band splitting (VBS) caused by strain and ordering effects because there will be many variables in the fitting procedure. 12 Rather than the method of Eq. (4) , in this work, we consider a modulus spectrum obtained from the Kramers–Kronig analysis, which is less troublesome. 6,14,15 The complex PR function is defined as Δ ρ ( E ) = Δ R R ( E ) + i Δ ρ I ( E ) , (5) where Δ R / R ( E ) and Δ ρ I ( E ) are the real part and the imaginary part of this function, respectively. The imaginary part can be calculated from the Kramers–Kronig relations. 6,14,15 Knowing the imaginary part of the complex PR function enables us to determine the modulus spectrum through the following equation: | Δ ρ ( E ) | = [ Δ R R ( E ) ] 2 + [ Δ ρ I ( E ) ] 2 = A [ ( E − E j ) 2 + Γ 2 ] − m / 2 . (6) The advantage of such analysis is that neither further assumptions nor fitting procedures are required when the transition energy E j is determined. The peak position gives the transition energy directly. For example, the modulus spectra of the complex PR function for the In 0.54 Ga 0.46 P 0.98 N 0.02 alloy at 120 and 270 K are shown in Fig. 2 . The transition energies E − , E − + Δ SO , and E + are determined from the peak positions of the modulus spectrum and are indicated by the arrows. Although the VBS caused by the strain and ordering effects exists in the y = 2 % sample, it remains unresolved in the modulus spectra due to the broadening effect on the spectral line of alloy scattering with high N content. As a simplification, the VBS is left aside in this work. For details on the VBS and spin-orbit splitting of the valence band of InGaPN, the reader is referred to Ref. 12 . The energy E Γ is the band gap of In 0.54 Ga 0.46 P 0.98 N 0.02 considering only the strain and ordering effects but neglecting the anticrossing with E N . 11,12 It is well known that the temperature dependence of the direct band gap of semiconductors can be described by the Varshni equation, E Γ ( T ) = E Γ ( 0 ) − α T 2 / ( β + T ) , where E Γ ( 0 ) is the band gap at T = 0 K and α and β are the Varshni coefficients. For the sample with y = 0 , the fitting parameters are E Γ ( 0 ) = 1.906 eV , α = 0.83 meV / K , and β = 652 K obtained from our previous study. 13 Assuming that E Γ ( T ) of the y = 2 % sample follows the temperature dependence of the band gap of In 0.54 Ga 0.46 P and therefore shares the same Varshni coefficients as In 0.54 Ga 0.46 P , the values of E Γ ( T ) of the y = 2 % sample at various temperatures can be evaluated with E Γ (293) assigned as 1.738 eV, which is obtained in Ref. 11 . Figure 3 displays the E − and E + transitions obtained from the modulus spectra and the evaluated E Γ transitions for the In 0.54 Ga 0.46 P 0.98 N 0.02 alloy at different temperatures. Using these data and Eqs. (2) and (3) , the temperature-dependent energies of E N and V are obtained and plotted in Fig. 4 . At 293 K, E N = 2.054 eV and V = 1.513 eV are obtained and are close to previous reports. 9,11 With decreasing temperature, the energy of E N shifts significantly to higher energies. Simultaneously, the interaction potential V between the N states and the unperturbed conduction band also rises to higher values. Since no theoretical models of the temperature dependence of E N and V are reported, a linear fit is used tentatively to describe the temperature tendency of E N and V in InGaPN as used in Ref. 6 for GaAsN. The thermal shifts of E N and V are d E N / d T ≈ − 0.43 meV / K and d V / d T ≈ − 0.67 meV / K , respectively. In Ref. 4 for GaPN, the authors reported that in addition to electronegativity difference between N and phosphorus (P) atoms, the lattice distortions in the vicinity of N are shown to play a decisive role in determining the strength and the range of the N potential and thus the energy level of the related bound state. To a certain degree, this local distortion can be affected by temperature-induced changes in deformation potential, leading to the shift of the E N level. In this work, not only the temperature-dependent E N level but also the temperature-dependent interaction potential V is attributed to the temperature-induced changes in the deformation potential. This information is important for overall validity of the BAC model to dilute nitride InGaPN alloys. Although temperature-independent E N or V has been reported in some studies of (In)GaPN alloys, 4,9–11 the discrepancies in the temperature dependence can be explained by the lack of complete temperature-dependent E + transitions in those studies. For example, the E + transition cannot be discerned in the samples with y = 0.005 and 0.01 in our previous report. 11 Temperature-dependent properties of E N and V in the samples with y = 0.005 and 0.01 cannot be obtained directly from Eqs. (2) and (3) , and therefore the discrepancy is made. In this work, the sufficient data of the E + transition improve the accuracy of temperature properties of the BAC parameters. In conclusion, we utilize temperature-dependent PR measurements to characterize the conduction band structure of In 0.54 Ga 0.46 P 1 − y N y ( y = 0 and 0.02) alloys grown on GaAs substrates. The band gap and the upper subband E + transitions are observed in InGaPN as predicted by the BAC model. To investigate the energetic positions of the features in the PR spectra, a Kramers–Kronig analysis is proposed. Based on the PR data and the BAC model, we find E N = 2.054 eV and V = 1.513 eV at 293 K. Since no theoretical models of the temperature dependence of E N and V are reported, a linear fit is used tentatively to describe the temperature tendency of the two parameters. The thermal shifts of E N and V are d E N / d T ≈ − 0.43 meV / K and d V / d T ≈ − 0.67 meV / K , respectively. The temperature-dependent E N level and interaction potential V are attributed to the lattice distortions, which can be affected by temperature-induced changes in deformation potential. This work was supported by the National Science Council of Taiwan under Grant Nos. NSC96-2112-M-006-020-MY2 and NSC95-2112-M-006-026. FIG. 1. Temperature-dependent PR spectra of (a) the E − and (b) the E + transitions in the In 0.54 Ga 0.46 P 0.98 N 0.02 alloy, respectively. FIG. 2. Modulus spectra of the complex PR function for the In 0.54 Ga 0.46 P 0.98 N 0.02 alloy at 120 and 270 K. The transition energies E − , E − + Δ SO , and E + are determined from the peak positions of the modulus spectrum and are indicated by the arrows. FIG. 3. Energies of the E − , E Γ , and E + transitions for In 0.54 Ga 0.46 P 0.98 N 0.02 plotted as a function of temperature. FIG. 4. Temperature dependence of E N and V for the In 0.54 Ga 0.46 P 0.98 N 0.02 alloy. The dashed lines represent a linear fit, which is used tentatively to describe the temperature tendency of E N and V .

PY - 2008

Y1 - 2008

N2 - Temperature-dependent photoreflectance (PR) measurements are employed to characterize the conduction band structure of In0.54 Ga0.46 P1-y Ny (y=0 and 0.02) grown on GaAs substrates. The band gap and the upper subband E+ transition are observed in InGaPN as predicted by the band anticrossing (BAC) model. To investigate the energetic positions of the features in the PR spectra, a Kramers-Kronig analysis is proposed. Based on the PR data and the BAC model, we find that the energy EN of isolated nitrogen states shifts significantly to higher energies with decreasing temperature. Simultaneously, the interaction potential V between the nitrogen states and the unperturbed conduction band also rises to higher values. At 293 K, EN =2.054 eV and V=1.513 eV are determined. The thermal shifts of EN and V are d EN /dT≈-0.43 meV/K and dV/dT≈-0.67 meV/K, respectively. The temperature-dependent EN level and interaction potential V are attributed to the lattice distortions, which can be affected by temperature-induced changes in deformation potential. This information is important for overall validity of the BAC model to dilute nitride InGaPN alloys.

AB - Temperature-dependent photoreflectance (PR) measurements are employed to characterize the conduction band structure of In0.54 Ga0.46 P1-y Ny (y=0 and 0.02) grown on GaAs substrates. The band gap and the upper subband E+ transition are observed in InGaPN as predicted by the band anticrossing (BAC) model. To investigate the energetic positions of the features in the PR spectra, a Kramers-Kronig analysis is proposed. Based on the PR data and the BAC model, we find that the energy EN of isolated nitrogen states shifts significantly to higher energies with decreasing temperature. Simultaneously, the interaction potential V between the nitrogen states and the unperturbed conduction band also rises to higher values. At 293 K, EN =2.054 eV and V=1.513 eV are determined. The thermal shifts of EN and V are d EN /dT≈-0.43 meV/K and dV/dT≈-0.67 meV/K, respectively. The temperature-dependent EN level and interaction potential V are attributed to the lattice distortions, which can be affected by temperature-induced changes in deformation potential. This information is important for overall validity of the BAC model to dilute nitride InGaPN alloys.

UR - http://www.scopus.com/inward/record.url?scp=47749139289&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=47749139289&partnerID=8YFLogxK

U2 - 10.1063/1.2952514

DO - 10.1063/1.2952514

M3 - Article

AN - SCOPUS:47749139289

VL - 104

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 1

M1 - 016109

ER -