The study of nanocrystalline cerium oxide by X-ray absorption spectroscopy

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(1)Jpn. J. Appl. Phys. Vol. 42 (2003) pp. 375–383 Part 1, No. 2A, February 2003 #2003 The Japan Society of Applied Physics. Band Gap Reduction in InAsN Alloys Ding-Kang SHIH1 , Hao-Hsiung LIN1 , Li-Wei S UNG1 , Tso-Yu C HU1 and T.-R. Y ANG2 Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C. 1 Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan, R.O.C. 2 Department of Physics, National Taiwan Normal University, Taipei, Taiwan, R.O.C. (Received May 7, 2002; revised manuscript received September 9, 2002; accepted for publication September 17, 2002). We report the structural, electrical and optical properties of bulk InAsN alloy with various nitrogen contents deposited on (100) InP substrates using plasma-assisted gas-source molecular beam epitaxy. From absorption measurements, it is found that the fundamental absorption energy of InAsN is higher than that of InAs due to the Burstein–Moss effect resulting from the high residual carrier concentration in InAsN. To deduce the ‘real’ band-gap energy of InAsN samples, the energy shift due to the Burstein–Moss effect and the band-gap narrowing effect are calculated by using a self-consistent approach based on the band-anticrossing (BAC) model [Shan et al.: Phys. Rev. Lett. 82 (1999) 1221]. After correction, the ‘real’ band-gap energy of InAsN samples decreases as N increases. The electron effective mass of InAsN is also investigated by plasma-edge measurement. We found a sizeable increase of the electron effective mass in these InAsN alloys, which is consistent with the theoretical predictions based on the BAC model. [DOI: 10.1143/JJAP.42.375] KEYWORDS: InAsN, gas source MBE, nitride, Burstein–Moss effect, localized state, infrared reflectivity, effective mass. 1.. increases. Furthermore, the fundamental absorption edge of InAsN, compared to that of InAs, shifts to higher energies due to the Burstein–Moss (BM) effect.14) To deduce the ‘real’ band-gap energy of InAsN samples, the energy shift due to the BM effect and the band-gap narrowing (BGN) effect is considered using a self-consistent approach based on the BAC model. After the correction, the ‘real’ band-gap energy of InAsN samples decreases as N increases, and obeys the bowing effect. In addition, we found a dramatic increase of the electron effective mass in these InAsN alloys, which is consistent with the theoretical predictions based on the BAC model.. Introduction. Low-nitrogen-content zincblende III–V alloys have received much attention in the past few years.1–3) The large difference in atomic size and electronegativity between N and As has motivated the development of many theoretical approaches to understand the huge bowing parameter, and to ascertain the semiconducting or semimetallic nature of these alloys.4–6) Over the last few years, there have been numerous attempts to explain the large band-gap reduction properties of III–V–N alloys.7–10) It has been demonstrated recently that a band anticrossing (BAC) model in which localized N states interact with the extended states of the conduction band can explain the unusual properties of III–V–N alloys.10,11) The diluted III–V–N alloys are also very promising for long-wavelength optoelectronic device and high-efficiency hybrid solar cell applications. In the mid-infrared 2–5 mm wavelength region, the InAsN alloy may be a very promising material. In a previous study, we demonstrated a highquality 2.2 mm InAs/InGaAs/InP highly strained multiple quantum well (MQW) laser grown by gas-source molecularbeam epitaxy (GSMBE).12) Using InAsN to replace InAs can alleviate the critical thickness limitation of the quantum well because of its small lattice constant. In addition, the bandgap energy of the quantum well can also be reduced further because of the huge bowing effect. These two features reveal the possibilities of extending the wavelength of lasers on InP substrates to the longer infrared range. The first InAs0:97 N0:03 /InGaAs/InP quantum well laser lasing at 2.38 mm under pulse operation at 260 K, which was grown by GSMBE, has recently been reported.13) Although the InAsN laser has been already demonstrated, unlike the extensively studied InGaAsN, GaAsN and other III–V–N compounds, there are still substantial physical properties that remain to be elucidated for the InAsN alloy. In this study, we have investigated a series of unintentionally doped InAsN bulk layers with various N contents grown on InP substrates using GSMBE. We found that these samples have high residual carrier concentration that increases as N content. 2.. Experiments. The samples were grown on semi-insulating (100) InP substrates using a VG V-80H GSMBE system. Elemental In source and thermally cracked AsH3 and PH3 sources were used. The active N species were generated from an EPI UNIbulb RF plasma source. The RF power and nitrogen flow rate used for these growths ranged from 300 W to 480 W and from 0.5 to 1.9 sccm, respectively. Detailed growth conditions are summarized in Table I and described elsewhere.15) To start the growth, the InP substrate was desorbed at 500 C under P2 flux. Then, a 0.3-mm-thick undoped InP buffer layer was deposited at 460 C at a rate of 1.5 mm/h. A 2-mm-thick undoped InAs(N) was subsequently overgrown on the buffer. Table I. Growth conditions and nitrogen composition of InAsN on InP substrate. Sample no.. . Corresponding author. E-mail address: [email protected] 375. RF plasma power. Flow rate of N2. Nitrogen. (W). (sccm). composition (%). C937. 0. 0. 0. C1076. 300. 1.2. 0.5. C1077 C1078. 400 480. 1.2 1.2. 1.6 2.8. C1117. 300. 1.9. 0.8. C1118. 300. 1.5. 1.2. C1129. 480. 0.5. 0.1. C1130. 480. 0.9. 0.5. C1132. 480. 1.8. 2.8.

(2) Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 2A. D.-K. SHIH et al.. layer without growth interruption and the AsH3 flow rate was fixed at 4 sccm. High-brightness mode N2 plasma was ignited for the N-containing growth. The RF power was turned off immediately after finishing the InAsN growth. Besides the InAsN sample, a controlled InAs sample was also grown. Their growth conditions were kept the same except the irradiation of active N species. The structural properties of the InAsN layers were characterized using a Bede D3 high-resolution X-ray diffractometer (HRXRD), a Bede QC1a X-ray double crystal X-ray diffractometer (DXRD), an SPM Solver P47 atomic force microscope (AFM), and a CAMECA IMS-5F secondary-ion-mass spectroscope (SIMS). All the XRD spectra in this study were measured in the =2 mode. AFM measurements were carried out in ambient environment with a scan size of 4 mm 4 mm. The electrical properties of the samples were investigated by Hall-effect measurements. The Van der Pauw geometry with soldered indium dots as ohmic contacts was used. Infrared reflectivity and transmission measurements were performed at room temperature using a Bruker IFS 120 HR Fourier-transform infrared (FTIR) spectrometer. 3.. Results and Analysis. Since phase separation has been reported in III–V–N alloys, the structural properties of these InAsN films were studied first. Figure 1 is a typical (004) HRXRD scan profile of an InAsN sample (C1077). From the figure, we can see that there are no X-ray peaks associated with cubic InAs, cubic InN, or hexagonal InN, which indicates no phase separation (namely poly-phase) in the InAsN film and confirms the formation of a single InAsN crystal in this study. Figure 2 shows the (004) DXRD rocking curves of InAs and InAsN samples. Upon increasing the plasma power or the N2 flow rate, the diffraction peak of the InAsN, compared with that of InAs sample, shifts toward the InP substrate peak, demonstrating the reduction of the lattice constant due to N incorporation. The alloy compositions of the InAsN layers were determined from the DXRD spectra fittings using a commercially available dynamic simulator, RADS. The N compositions determined from RADS fitting are summarized in Table I. Since the film thickness is much. InP_SUB C1078. count intensity (arb. units). 376. C1077. C1118. C1117. C1076. C937. -6000 -5000 -4000 -3000 -2000 -1000. 0. Diffraction Angle θ (arc second) Fig. 2. DXRD spectra of a series of InAs1x Nx bulk samples with x ranging from 0 to 0.028.. larger than the critical layer thickness calculated from Matthews and Blakeslee’s model16) (4 nm and in some nonequilibrium growth conditions it might be two times larger) and the thermal expansion coefficient of InAs is very close to that of InP,17) the InAsN samples are assumed to be fully relaxed. Although N was successfully incorporated into InAs, its incorporation significantly degrades the DXRD linewidths as compared to the reference InAs sample. In order to examine the N content in the InAsN crystal, SIMS depth measurement was performed. Figure 3 shows an indepth SIMS profile. The In, As, N, P and O signals were analyzed. It can be seen that a clear nitrogen signal was detected in the InAsN layer and there is no detectable P in. 10 4. X-ray intensity (arb. units). InP sub. (002). 10 3. InP sub. (004) InAsN (004). InAsN (002). 10 2. 10 1. C1077 10 0. 20. 30. 40. 50. 60. 70. 80. 2θ (deg) Fig. 1. Typical X-ray –2 scan profile of an InAsN sample (C1077), showing no phase separation.. Fig. 3. Depth profile of InAsN sample analyzed by SIMS..

(3) Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 2A. D.-K. SHIH et al.. Table II. Room-temperature Hall mobility and residual carrier concentration of the InAsN samples.. 377. 4500 N=0. 4000. Sample no.. N (%). Residual carrier conc. nD (cm3 ). Mobility (cm2 /Vs). C937 C1129. 0 0.1. 2:64 1016 9:87 1017. 7660 3530. C1130. 0.5. 1:69 1018. 2140. C1076. 0.5. 1:91 1018. 1740. C1117. 0.8. 1:21 1018. 2690. C1118. 1.2. 8:85 1017. 3290. C1077. 1.6. 3:24 1018. 1280. 1000. C1132. 2.8. 18. 2:80 10. 1010. 500. C1078. 2.8. 1:69 1019. 38.1. mobility (cm2/ Vs). N=0.1%. 3500 3000 2500. N=0.5%. 2000 1500 N=2.3% N=4.1%. 0. 20. 40. 60. 80. 100. 120. 140. rms roughness (Å) Fig. 4. Relationship between rms surface roughness and mobility. N content of each sample is also indicated in the figure.. only when the layer thickness is comparable to the surface roughness, such as in the case of silicon inversion layers. In this study, the rms surface roughness of InAsN films is between 3 and 14 nm and the film is 2 mm thick, which is much larger than the rms surface roughness. Therefore, the effect of surface roughness scattering on electron transport could be neglected. Figure 5 shows the near band edge absorption spectra at room temperature. The absorption coefficient is obtained from FTIR transmission measurements. Two points are worth noting from this figure. First, the energy of the absorption edge of InAsN samples is always higher than that of InAs. Second, when the N content is lower than 1.6%, a higher N content leads to a higher absorption edge. However, the trend reverses for InAsN with higher N content. The phenomenon seems to contradict the theoretical prediction. To interpret the results, the BM effect should be taken into account owing to the high residual carrier concentration in these InAsN samples. Samples with lower N concentration have smaller effective mass and thus display more BM shift. The two high N content samples, however, have larger effective mass and thus their BM effects are less. 1.0x10 8. InAs1-xNx. α2(cm-2). the InAsN epilayer. Table II shows the Hall results of the samples at room temperature. All the intentionally undoped samples exhibit n-type conduction, and the larger the N content, the higher the carrier concentration. The origin of the high background n-type doping in N-containing sample is still under investigation. However, because of the large InAs crystal lattice constant and the small N atom size, nitrogen interstitial defects could be a possible candidate. Furthermore, since the band gap is very narrow, the defect levels in these materials could be ionized to result in high residual carrier concentration. In these samples, the electron mobility drops from 7:66 103 cm2 /Vs in the reference InAs sample to 38.1 cm2 / Vs in sample C1078 (x ¼ 0:028 with a residual carrier concentration of 1:69 1019 cm3 ). This phenomenon can be attributed to the nitrogen incorporation into the alloy. As mentioned above, the incorporation drastically deteriorates the material quality, which may introduce scattering centers for residual carriers. In addition, the increase of electron effective mass due to the nitrogen incorporation should also be taken into account. According to the BAC model, the dispersion relation of the nonparabolic subbands becomes flatter as the nitrogen content is increased. This indicates a large increase of the effective mass in the subbands.18,19) Among these N-containing samples, C1078 has the highest residual free carrier concentration and an extraordinarily low mobility. The very high residual free carrier concentration in C1078 may make the nonparabolic effect on the subband much more significant, and therefore results in very low mobility. Similar results have been reported by Skierbiszewski et al.19) The surface roughness was determined by tapping-mode AFM using SiN tips. The AFM images of these InAsN films indicate that the root mean square (rms) surface roughness is between 3 and 14 nm, depending on the nitrogen compositions of the samples. In fact, as plasma power increased (indicating more N was generated and incorporated into the InAs), the reflection high-energy electron diffraction (RHEED) pattern observed during the growth became spottier and dimmer, indicating a three-dimensional growth mode. Figure 4 shows the relationship between the rms surface roughness and mobility. N content of each sample is also indicated in the figure. As indicated in the figure, the mobility decreases as N content increases. Surface roughness scattering has a significant influence on the mobility. 5.0x10 7. x=0 x=0.5% x=0.8% x=1.2% x=1.6% x=2.8%. T=300K 0.0 0.3. 0.4. 0.5. 0.6. Energy (eV) Fig. 5. Plots of the square of the absorption coefficient (2 ) vs the photon energy deduced from 300 K IR transmission spectra recorded on a series of InAs1x Nx ..

(4) 378. Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 2A. D.-K. SHIH et al.. significant. In these two samples, C1078 (2.8%) and C1077 (1.6%), the bowing effect on the band-gap may have overcome the BM effect, resulting in the red-shifted absorption edge, although the carrier concentration of the former is five times higher than that of the latter. To deduce the ‘real’ band-gap energy of our InAsN samples, the energy shift due to the BM effect and the BGN, which is always accompanied by the BM effect, are considered using a self-consistent approach based on the BAC model. According to the BAC model, the interaction of the conduction band edge with the highly localized N states leads to a splitting of the conduction band into two highly nonparabolic subbands E and Eþ with dispersion relations given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 ½EM ðkÞ þ EN ½EM ðkÞ EN 2 þ 4VNM E ðkÞ ¼ ; 2 ð1Þ where EN is the energy of the nitrogen state, EM ðkÞ is the dispersion relation for the conduction band of the N-free semiconductor matrix, and VNM is the matrix element coupling those two types of states. All energies are measured relative to the top of the valence band. The downward shift of the lower subband E can account well for the reduction of the fundamental band gap observed in these III–V–N alloys. It is evident from eq. (1) that the initial rate of the Ninduced band gap reduction depends on the coupling parameter VNM and on the energy difference EM EN . Therefore, the dependence of EN , EM , and VNM on the nitrogen content of the InAsN bulk layer should be duly taken into account. In the case of InAsN, we determined the EN based on the following assumptions: The existing experimental results on the location of EN in different III– V group materials indicate that, similar to many other highly localized centers, the energy of the nitrogen level is constant relative to the common energy reference or vacuum level.20,21) Using the known conduction band offset we can determine EN in InAs. It is well known that in GaAs, EN lies at about 0.23 eV above the conduction band edge. Therefore, the energy of the highly localized nitrogen level (EN ¼ 1:48 eV) relative to top of the valence band maximum in InAs was estimated from the valence band offset, EV ðGaAs/InAsÞ ¼ 0:17 eV.22) Concerning the dispersion relation EM ðkÞ for the conduction band of InAs, we adopted the calculated results of ref. 23, which are based on the tripleband effective-mass approximation, and EM ð0Þ ¼ 0:35 eV at room temperature. For VNM , it has been shown previously that the square of the matrix elements is proportional to the concentration of nitrogen atoms, i.e., VNM ¼ CNM x1=2 , where CNM is a constant that depends on the semiconductor matrix10,24) and is treated as a fitting parameter in this study. In the present case, according to the schematic band structure of InAsN shown in Fig. 6, the absorption edge Eabs is Eabs ¼ E þ EBM EBGN ;. ð2Þ. where EBM is the energy shift due to the Burstein–Moss effect, and EBGN is the reduction energy due to the band-gap narrowing effect. To estimate EBM , we solve the Fermi. Fig. 6. Schematic of the band structure of a heavily doped n-type InAsN. The conduction band (CB) and the valence band (VB) were assumed to be parabolic. Shaded areas denote the regions occupied by electrons.. energy EF in the conduction band from the following equation, Z nD ¼ f ðE ÞDðE ÞdE ; ð3Þ where nD is the residual carrier concentration from the Hall measurements, f ðE Þ is the Fermi–Dirac distribution, and DðE Þ is the density-of-states function in the lower subband conduction band, E . The BM shift in the valence band is EV ðkF Þ ¼. h 2 kF2 ; 2mh. ð4Þ. where kF is the Fermi wave number and is given by kF ¼ ð32 nD Þ1=3 , mh is the effective mass of the heavy-hole (assuming that heavy-hole valence band is parabolic), and h is Planck’s constant. Using photomodulation spectroscopy, Shan et al. found that the energetic location of the valence band was nearly independent of the nitrogen content in GaAs1x Nx (x < 3%) alloys.10,25) Furthermore, the theoretical calculations by Bellaiche et al.26) showed that the valence band discontinuity between GaP1x Nx and GaP was almost zero within x < 5%. Therefore, we assume that the perturbation induced by N on the valence band can also be omitted in InAsN. The absorption from the light-hole band is neglected because of its very low density of states. In addition, the band-gap narrowing due to band tails is not considered either.27) Now, the band-gap widening EBM for carrier concentration nD is expressed as EBM ¼ EF þ EV ðkF Þ:. ð5Þ. Concerning the BGN due to the residual carrier, the shrinkage in energy is proportional to the carrier concentration and an empirical relation28,29) can be represented by 1. EBGN ¼ InAsN nD3 ;. ð6Þ.

(5) Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 2A. D.-K. SHIH et al.. 379. Table III. Summary of the computed and experimental energies involved in the self-consistent approach as described in the text. (All energies are given in eV.) Sample no.. N (%). Eabs. EF. EV (kF ). EBM. EBGN. E. C1076 C1077. 0.5 1.6. 0.439 0.439. 0.129 0.157. 0.010 0.019. 0.139 0.176. 0.034 0.038. 0.334 0.301. C1078. 2.8. 0.434. 0.255. 0.061. 0.316. 0.061. 0.179. C1117. 0.8. 0.419. 0.106. 0.010. 0.116. 0.028. 0.331. C1118. 1.2. 0.406. 0.094. 0.009. 0.103. 0.021. 0.324. C1129. 0.1. 0.409. 0.094. 0.008. 0.102. 0.026. 0.333. C1130. 0.5. 0.415. 0.117. 0.012. 0.129. 0.031. 0.317. C1132. 2.8. 0.423. 0.142. 0.017. 0.159. 0.036. 0.300. Fig. 7. Block diagram illustrating the procedure that was used in this study to solve the unknown values EBM , E , EBGN , and VNM .. where InAsN is the band-gap narrowing coefficient. To solve E from eq. (2), we adopted the following procedure that is shown in Fig. 7. The parameter VNM is the only fitting parameter. With a given VNM , the lower subband E ðkÞ can be calculated using eq. (1). Once E ðkÞ is determined, we can calculate the density of states DðE Þ and solve EF using eq. (3) with measured nD . EBM is thus found by using eqs. (4) and (5). With the calculated E ðkÞ, we may also calculate the conduction band effective mass, 2. mInAsN ¼. 1 d E : h 2 dk2. ð7Þ. The band-gap narrowing coefficient InAsN can be expressed as30) InAsN ¼ ð"InAsN ="InAs ÞðmInAs =mInAsN Þ InAs ; ð8Þ where "InAs(N) is the static dielectric constant of InAs(N), and we suggest that "InAsN ¼ "InAs since the nitrogen content is small in the present alloy. For InAs, mInAs ¼ 0:024m0 , where m0 is the electron rest mass, and "InAs ¼ 15:15.17) Based on the three effects proposed in ref. 27, the estimated band-gap narrowing energy of InAs increases from

(6) 40 meV to

(7) 100 meV when carrier concentration increases from n

(8) 4 1018 cm3 to

(9) 5 1019 cm3 . By using the empirical formula, eq. (6), the BGN coefficient InAs should be

(10) 2:67 108 meV cm. This value is adopted in this study to estimate InAsN for the determination of the energy shift caused by the BGN effect, i.e., EBGN . Once the E , EBM , and EBGN are determined, Eabs can be obtained from eq. (2). If the difference between the calculated Eabs and the experimental result is larger than 104 eV, a new VNM is chosen using the bisection method to calculate a new Eabs . Table III gives the values of E , EBM , EBGN , EF and VNM obtained from the above calculation, along with the residual. Fig. 8. Dependence of interaction potential, VNM , on nitrogen content for InAs1x Nx . The solid line is the best fit of VNM ¼ CNM x1=2 to the data (CNM ¼ 1:68 eV).. carrier concentration nD and absorption edge Eabs from the experiments. A plot of VNM versus the square root of nitrogen composition (x1=2 ) is shown in Fig. 8. The solid line is the best fit of VNM ¼ CNM x1=2 to the data. The result of the fitting parameter CNM , the coupling parameter in InAs, is 1.68 eV. This value is smaller than those found in InGaAsN with low indium concentration (2.3–2.7 eV),10,31,32) and that found in InPN (3.5 eV).33) Since the interaction energy VNM is the matrix element coupling the state of the unperturbed conduction band edge at point and a localized state introduced by nitrogen, it is reasonable that the extent of coupling should be weaker in a semiconductor matrix with EM at point far from the localized EN level. The dispersion relation of InAs0:97 N0:03 calculated by the BAC model is shown in Fig. 9 as an example. The parameters used in this calculation [eq. (1)] include the known EM ðkÞ of InAs, the highly localized nitrogen level EN ¼ 1:48 eV relative to the top of the valence band maximum in InAs, and the best fit value of CNM ¼ 1:68. As can be seen in Fig. 9, both E and Eþ transitions exhibit a classical anticrossing behavior. Additionally, a distinct flattening of the E ðkÞ curves for energies approaching EN is clearly demonstrated, which implies a significant increase of the effective mass of both the subbands as compared to that of InAs. Deducting the effect of EBM and EBGN on the band gap.

(11) 380. Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 2A. 1.8. D.-K. SHIH et al.. E+(k). 1.6. EN. Energy (eV). 1.4 1.2 1.0 0.8. E-(k). EM(k). 0.6 0.4 0.2 0. 2. 4. 6. 8. 10. 12. Wave vector, k (106 cm-1) Fig. 9. Calculated dispersion curves for E subbands (solid lines) of the InAs0:97 N0:03 using the BAC model as described by eq. (1). The dotted lines represent the unperturbed energies of the N level (EN ) and the InAs matrix. It should be noted that a distinct flattening of the E ðkÞ curves for energies approaching EN is clearly demonstrated.. 0.55 dielectric method predicted (ref. 4) tight binding method predicted (ref. 35) BAC model this work Naoi et al. (ref. 34). 0.50. Band gap energy (eV). 0.45 0.40. binding method.35) As can be seen, our experimental results are close to the theoretical curve calculated from the BAC model. The estimated transition energy shrinkage coefficient of our bulk InAsN is 15 meV/at.% N. We note that this coefficient is smaller than 31 meV/at.% N in our earlier photoluminescence study on strained InAs1x Nx /InGaAs(P)/ InP quantum wells (QWs).36) The difference due to the strain effect37,38) is small, about 3 meV/at.% N in this study. Therefore, we considered two other possibilities to interpret this phenomenon. The first is the quantum confinement effect. It is well known in the QW case that the quantum confinement of electrons and holes creates a larger transition energy than that of the bulk, and hence it corresponds to an allowed higher wave number k in the dispersion relations. With a decrease in the width of the well, the quantum levels become higher, and the allowed k values become larger. As mentioned earlier, the interaction between the extended conduction band and the highly localized N states leads to a reduction of the band gap in the III–V–N alloys, and the interaction becomes pronounced as the extended states approach the EN level. In the InAsN case, EM (k ¼ 0) is 0.36 eV and the localized nitrogen level EN ¼ 1:48 eV, all relative to top of the valence band maximum. As can be seen in Fig. 11, the position of EM (k ¼ 0) is far below the EN state when compared with that of the other III–V–N alloys, such as (In)GaAsN or GaPN alloys. Therefore, less nitrogeninduced perturbation on the band states of InAs is expected. However, in some higher k (QW case) regions for the states located close to EN , the interaction will be much stronger than that in the lower k region (bulk case). Consequently, the transition energy difference EW between with and without nitrogen in the QW case is larger than that of Eb in bulk case. These may explain the reason why we. 0.35 0.30 0.25 0.20 0.15 0.10 0.05. T=300K. 0.00 0.00. 0.01. 0.02. 0.03. 0.04. 0.05. 0.06. 0.07. Nitrogen composition Fig. 10. Composition dependence of the band gap of InAsN. Empty circles represent experimental data, whereas the solid line represents calculated results using the BAC model. Filled triangles are experimental data published in the literature (see ref. 34). Results from dielectric calculations (see ref. 4) and the tight-binding method (see ref. 35) are shown by a dash-dotted line and a dotted line, respectively.. from the absorption peak edge gives the corrected band-gap energy E of each InAsN sample. Figure 10 shows the composition dependence of the corrected band-gap energy of InAsN. It is clear that the bowing effect reappears in these samples. Besides our own results, the figure also includes a previously published result from another research group.34) The three curves represent calculated band gaps based on the BAC model in this study, the dielectric model4) and the tight. Fig. 11. Schematic of dispersion curves for the lower and upper conduction subbands E in InAsN. The dotted lines represent the unperturbed conduction band of InAs EM ðkÞ and the nitrogen level EN . Arrows indicate possible experimental optical transition. As a result of the quantum confinement effect, the allowed wave number kw in the quantum well case is larger than that of in bulk case, kb . The transition energy difference Ew between with nitrogen and without nitrogen perturbed in the QW case is obviously larger than the Eb in bulk case..

(12) Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 2A. D.-K. SHIH et al.. observed a significant band-gap reduction in the QW structure. The second possibility is the ordering effect. Recently, Bellaiche et al. reported the effect of short-39) and long-range6) ordering on the band gap of GaAsN. They pointed out that ordered alloys have larger bowing effect than random alloys. This large difference in the bowing coefficient is especially prominent for low nitrogen concentrations. Since the nitrogen concentration in this study is low, the effect may take place in these InAsN alloys. As compared with the previous coherent strained InAs1x Nx / InGaAs(P) QW, all of the samples in this study are fully relaxed, perhaps indicative of a low degree of ordering. A similar phenomenon has also been observed in GaAsN alloys by Francoeur et al.38) It has been predicted that the nitrogen alloying should increase the electron effective mass of the E state. Although a large enhancement of the electron effective mass in InGaAsN and GaAsN as compared to its parental III arsenides without nitrogen, has been recently demonstrated,18,40) no experimental determination of the InAsN alloy has been reported so far. To verify the effective mass increment predicted by these models, we performed measurements of the infrared reflectivity and Hall effect from which the plasma frequency, !p , and the Hall electron concentration, nD , in these InAsN samples were determined. Typical examples of reflectivity spectra for InAsN samples of different nitrogen compositions and residual carrier concentrations are shown in Fig. 12. As can be seen, the onset of the plasma reflection edge is at 470 cm1 and 617 cm1 , respectively. The thin line represents the fitting curve using the method described in ref. 41. The electron effective mass at the Fermi energy can be determined from. 1.0. (a). Ne ðkF Þe mexp ðkF Þ"1 "0. Reflectance. ωp =471 cm-1. 0.6. 0.4. 0.2. C1076 T=300K 0.0 300. 400. 500. 600. wavenumber(cm-1) 1.0. experimental fitting ωp=617cm-1. Reflectance. 0.8. 0.6. 0.4. 0.2. C1078 T=300K 0.0 500. (b). 600. 700. 800. 900. wavenumber (cm-1). ;. ð9Þ. where e is the electron charge, Ne (kF ) is the free electron concentration, "1 is the high frequency dielectric constant (here we assume an "1 of 12.2517)), and "0 is the permittivity of free space. We also calculated the effective mass using the following equation as described in ref. 23: Z1 Z1 2 q f ðE ÞDðE ÞdE !2p ¼ d!2p ðEÞ ¼ ; ð10Þ mopt ðE Þ"1 EC. experimental fitting. 0.8. 2. !2p ¼. 381. EC. where mopt (E ) is the optical effective mass defined as mopt ¼ ½1=h 2 kðdE =dkÞ 1 . A detailed definition of the above quantities can be found elsewhere.42) Substituting plasma wavelength into eq. (9), one can find the electron effective mass. The plasma frequency and the calculated electron effective mass of InAsN samples are summarized in Table IV. As can be seen, a very large increase of the effective mass is found in samples with higher N composition, which is qualitatively in good agreement with the predictions of the BAC model. The electron effective mass of C1078 is extraordinarily larger than those of the other samples. This result supports the arguments we used to interpret the extraordinarily low mobility for the same sample in previous Hall results. To illustrate the dependence of the effective mass on the electron energy and the nitrogen content, the values of the. Fig. 12. FTIR-measured plasma reflectance spectra (bold lines) for two samples with different residual carrier concentrations. The thin lines show the best fit using the methods described in ref. 41.. Table IV. Carrier concentration, plasma frequency, and experimental, theoretical calculated electron effective masses of the studied samples. Sample no.. !p (cm1 ). Residual carrier concentration nD (cm3 ). m (m0 ) exp.. m (m0 ) cal.. C937. —. 2:64 1016. —. 0.024a). 18. C1076. 471. 1:91 10. 0.063. 0.044. C1077. 590. 3:24 1018. 0.068. 0.052. C1078. 617. 1:69 1019. 0.326. 0.123. C1117. 390. 1:21 1018. 0.055. 0.039. C1118. 360. 8:85 1017. 0.051. 0.036. C1129. 395. 9:87 1017. 0.046. 0.037. C1130 C1132 a) ref. 17. 475 593. 1:69 1018 2:80 1018. 0.055 0.058. 0.043 0.046. experimental effective mass at different electron concentrations are shown in Fig. 13. Solid squares and empty triangles represent experimental data and theoretical values, which span the range of the alloy compositions of the investigated samples. Basically, the experimental results are qualitatively in good agreement with the theoretical results and support.

(13) 382. Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 2A. 0.30. m*/m0. 0.25. anticrossing model.. experiment theory. 0.35. Acknowledgements. 0.070. This work was supported by the National Science Council and the Ministry of Education of the Republic of China under Contract nos. NSC 89-2215-E-002-034 and 89-NFA01-2-4-3, respectively.. 0.065 0.060 0.055 0.050. 0.20. 0.045 0.040. 0.15. 0.035. 1018. 0.10 0.05 1018. 1019. carrier concentration (cm-3) Fig. 13. Electron effective mass versus residual carrier concentration from the present experimental data for InAs1x Nx samples with different nitrogen compositions. The open triangles are the theoretically calculated mass. The inset shows the magnified part of the region marked by the dotted circle.. the BAC model that predicts an enhancement in the electron effective mass of the III–V–N alloys. The discrepancy between the calculated and the experimental data might be due to (i) the nonparabolicity effect in the degenerate semiconductors. Since in our samples the Fermi level EF is located at least 90 meV above the conduction band minimum, one should take into account the contribution of the nonparabolicity effect to the value of m and the effect is expected to be more pronounced in this small band-gap energy InAsN material. It may cause an increase of the effective mass with respect to m at the bottom of the conduction band [m (0)]. (ii) Nitrogen-induced –L–X intermixing on the conduction band edge.9,43) The X and L electrons of InAs have heavier mass than the conduction band edge of InAs. However, the exact reason for the discrepancy is still not clear and is under further investigation. 4.. D.-K. SHIH et al.. Conclusions. In summary, the structural, electrical, and optical properties of bulk InAsN alloys grown using GSMBE were investigated. When N composition increases, InAsN film has broader linewidth in the DXRD spectrum and higher residual carrier concentration. 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