Nitrogen-induced enhancement of the electron effective mass in InN[sub x]As[sub 1-x]

Nitrogen-induced enhancement of the electron effective mass

in InN

As

W. K. Hung, K. S. Cho, M. Y. Chern, and Y. F. Chena)

Department of Physics, National Taiwan University, Taipei, Taiwan, Republic of China D. K. Shih and H. H. Lin

Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, Republic of China C. C. Lu and T. R. Yang

Department of Physics, National Taiwan Normal University, Taipei, Taiwan, Republic of China 共Received 6 September 2001; accepted for publication 14 November 2001兲

The electron effective mass in n-type InNxAs1⫺x 共with x up to 3.0%兲 grown by gas-source

molecular-beam epitaxy was obtained from infrared reflectivity and Hall-effect measurements. The large increase of the effective mass due to the incorporation of nitrogen is attributed mainly to the nitrogen-induced modification on the electronic states near the conduction-band edge. The well-known band anticrossing共BAC兲 model for the electronic structure of the III-N-V alloys cannot well describe the experimental data, especially in the region of higher electron concentration. This result provides an opportunity to examine the ‘‘universality’’ of the BAC model. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1436524兴

III-N-V alloys such as Ga共In兲NAs, GaNP, and InNP have been found to exhibit particular physical properties and po-tential applications in long-wavelength optoelectronic devices.1– 6The incorporation of nitrogen into the host III–V crystal causes a significant reduction 共giant bowing兲 in the fundamental band gap,4,5 reduced temperature and pressure dependence of the band-gap energy,7,8and a large increase in the electron effective mass.9–11These unusual behaviors are usually explained in terms of the band anticrossing 共BAC兲 model in which the localized N resonant states interact with the extended conduction-band 共CB兲 states, leading to the splitting of the CB into two nonparabolic subbands.7 Alter-natively, the theoretical calculations based on the pseudopo-tential local density approximation indicates that the N-induced mixing between the ⌫ and L states is responsible for these phenomena.12

InNxAs1⫺x should be a promising material for infrared

technology since InAs has a narrow band gap of 0.36 eV at room temperature. Up to now, there were only very limited efforts directed to this alloy.13–15Naoi, Naoi, and Sakai grew InNAs films on GaAs substrates by metalorganic chemical-vapor deposition and found the band gap reduced to 0.12 eV with nitrogen composition up to 6%.13However, except for a photoluminescence study on InNxAs1⫺x/InGaxAs1⫺x single

quantum wells,15no further experimental studies on the elec-tronic properties of InNAs were reported. Knowledge of the carrier effective mass provides valuable information on the fundamental nature of the band states in the alloy and is also important for a full exploration and optimization of this ma-terial system in device applications. In this work, we report measurements of the electron effective mass in InN_xAs_1⫺x with various N contents and electron concentrations. The ef-fective mass is greatly enhanced due to the N incorporation. However, in contrast to the case of Ga共In兲NAs, we find that

the simple BAC model may be not suitable to describe the effective mass in the InNAs alloy systems.

The InNAs films were grown on semi-insulating 共001兲 InP substrates using a VG V-80 gas-source molecular-beam epitaxy system. An element In source and thermally cracked AsH3 were used for producing molecular beams. The active

N species were generated from an EPI UNI-bulb rf plasma source. The growth temperature for InNAs was 460 °C. De-tails of the growth conditions are reported elsewhere.16The films are about 2.5␮m thick and intentionally undoped. The samples were examined with a high-resolution x-ray diffrac-tometer using the Cu K␣1 line 共with wavelength 1.54 Å兲.

The N compositions were determined by assuming that the InNAs films are fully relaxed and Vegard’s law holds. The former assumption is justified by the fact that the film thick-ness is much larger than the critical thickthick-ness calculated from the Matthews and Blakeslee model.17 The lattice con-stants of InP, InAs, and cubic InN are taken to be 5.8688, 6.0584, and 4.98 Å, respectively. The electrical properties were investigated by Hall-effect measurements in the Van der Pauw configuration. The results are summarized in Table I. The samples containing nitrogen are intrinsically n type and the electron concentration increases with the incorpo-rated N concentration. The possible origin of the high carrier concentration in these samples is not yet clear.

The infrared reflectivity measurements were performed

a兲_{Electronic mail: yfchen@phys.ntu.edu.tw}

TABLE I. Parameters of the studied samples. All measurements were per-formed at room temperature.

Sample number N共%兲 Thickness 共nm兲 n共cm⫺3兲 Mobility 共cm2_V⫺1_s⫺1_兲 m */m0 共experiment兲 A 0 ¯ 2.64⫻1016 _{7660 0.024} B 0.2 2465 1.91⫻1018 _{1740 0.063} C 2.2 2670 2.80⫻1018 _{1010 0.058} D 2.4 2460 3.24⫻1018 _{1280 0.068} E 3.0 2580 1.69⫻1019 38 0.326

APPLIED PHYSICS LETTERS VOLUME 80, NUMBER 5 4 FEBRUARY 2002

796

at room temperature with a Bruker IFS 120 HR Fourier transform infrared spectrometer. Figure 1共a兲 shows the re-flectivity spectra of three InN_xAs_1⫺xsamples. The features at about 307.2 and 347.5 cm⫺1 correspond to InP transverse optical共TO兲 and longitudinal optical 共LO兲 phonons, respec-tively. We attribute the peak at about 225 cm⫺1to the InAs-like TO mode, and the peak at about 440 cm⫺1 to the InN-like TO mode. The plasma reflection edge is evidently observed and shifts to higher energy with increasing electron concentration.

Electron effective mass m* is obtained by fitting the reflectivity spectra with a three-layer structure共air–InNAs– InP兲 model. The dielectric function of InP is taken from the literature. Dielectric function ⑀ of InNAs can be modeled with an additive form18

⑀⫽⑀⬁⫹

兺

where⑀_⬁ is the high-frequency dielectric constant共taken to be 12.25, the same as InAs兲; ␻_{T j}, ⌫_j, and S_j are the reso-nance frequency, damping constant, and strength of the jth TO mode共InAs and InN-like兲, respectively. The last term in Eq. 共1兲 represents the free-carrier contribution with

frequency-independent damping constant ␥ and plasma fre-quency␻p. The electron effective mass at the Fermi energy

can be determined from18,19

m*⫽4␲ne

2

⑀⬁␻p

2 , 共2兲

where e is the electron charge, and n is the electron concen-tration. The obtained values of the film thickness and effec-tive mass are also listed in Table I. We see that the effeceffec-tive mass increases largely as nitrogen atoms are introduced into the InAs host.

The experimental effective mass obtained above is plot-ted against the electron concentration in Fig. 2. It is well known that due to the CB nonparabolicity the electron effec-tive mass in heavily doped narrow-band-gap semiconductors strongly depends on the electron concentration. To evaluate this effect, we use the simple two-band Kane model20,21to calculate the InAs effective mass mMat the electron

concen-tration of our samples. The momentum matrix element P2in the Kane model is taken to be 11.9 eV, as in Ref. 20, and the results are consistent with the values found in the literature.20 The calculated mM, also plotted in Fig. 2, is too small to

account for the experimental data. Thus, it is clear that the enhancement of the effective mass should be mainly due to the N-induced modification of the CB structure.

The BAC model is known to predict a large increase of the electron effective mass.10,22In the model, the interaction of N states with the extended states of the semiconductor matrix results in the formation of two conduction subbands E_⫺and E_⫹ given by7

E_⫾共k兲⫽1

2兵关EM共k兲⫹EN兴⫾

冑

N M

2 _x其,

共3兲 where E_N is the energy of the N state, E_M(k) is the disper-sion relation for the CB of the host crystal, and C_{N M} is the matrix element describing the coupling between these two types of states. All the energies are relative to the top of the valence band. Due to its localized nature, the energy ENof

the N level can be estimated to be 1.48 eV from valence-band offset ⌬ (GaAs/InAs)⫽0.17 eV and from EN FIG. 1. 共a兲 Reflectivity spectra for three InNxAs1⫺xsamples.

FIG. 2. Effective mass vs electron concentra-tion n. Closed circles denote the experimental data for InNxAs1⫺x, while open circles denote

the calculated effective mass for InAs.

797 Appl. Phys. Lett., Vol. 80, No. 5, 4 February 2002 Hunget al.

⫽1.65 eV in GaAs.7,23 _C

N M is taken as 1.92 eV to fit the

band-gap energy measured by Naoi, Naoi, and Sakai.13 It should be noted that in the simple BAC model only the an-ticrossing interaction between the extended states of the ⌫ CB and the localized N level is considered. The interaction between L 共or X兲 and the N level is neglected due to the symmetry selection rules.24

From Eq.共3兲 an analytic expression for the k dependence of the inverse effective mass can be written as 共considering only the E_⫺branch兲10

1 m*共k兲⫽ 1 2mM共k兲

再

冑

冎

the two-band Kane model, as mentioned above. The effective mass is calculated at the Fermi surface, i.e., at k⫽kF

⫽(3␲2_n)1/3_{. One notes that due to the relatively large}

en-ergy difference between EN and EM 关EN⫺EM(kF)⬃1 eV,

here兴, the composition-dependent term C_{N M}2 x has little effect on the effective mass. That is, m* should approximately ap-proach mM for InAs. Furthermore, one should note that

ef-fective mass m*(k) calculated from Eq.共4兲 never exceeds 2mM(k) if EM(k)⬍EN. However, as shown in Fig. 2, the

measured effective mass either approaches 2mM, which

cor-responds to extremely large CN M, or exceeds 2 mM

共espe-cially for the sample with the highest electron concentration兲. Thus, the simple BAC model fails to describe the experimen-tal data.

According to our experimental results, it seems more plausible to view the CB edge of InNxAs1⫺x as a mixing

state which has components of the⌫, L, and X states of InAs. Such a mixing is caused by the strong perturbation intro-duced by substitution of N on an As site.12As illustrated in the case of GaN_xAs_1⫺x, the CB edge shows a reduced 共in-creased兲 ⌫(L) character as x increases 共for x approaches 0.8%, the L component approaches 12%兲.12Since the L elec-trons have much heavier mass than the ⌫ 关for InAs, mt(L)

⬃0.05, ml(L)⬃0.64兴, effective mass m*(kF) has the

possi-bility to exceed 2mM.

In summary, the effective mass of InNxAs1⫺x with

dif-ferent N compositions and electron concentrations was ob-tained from infrared reflectivity and Hall-effect measure-ments. We point out that the large increase of the effective mass is probably due to the N-induced modification on the

electronic structure near the conduction-band edge. Our re-sults, therefore, calls for further theoretical efforts in order to clarify the role of the nitrogen state in the perturbation of the band structure.

This work was supported by the National Science Coun-cil and Ministry of Education of the Republic of China.

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