1. Electric Fields in Polarized GaInN/GaN heterostructures

Transcription

1 IN III-NITRIDE SEMICONDUCTORS: OPTICAL PROPERTIES II, EDITED BY M.O. MANASREH AND H.X. JIANG (TAYLOR & FRANCIS NEW YORK 2002) P Electric Fields in Polarized GaInN/GaN heterostructures 2. C. Wetzel 1,a, T. Takeuchi 2, H. Amano 2, and I. Akasaki 2 1 High Tech Research Center, Meijo University, Shiogamaguchi, Tempaku-ku, Nagoya , Japan 2 High Tech Research Center and Department of Electrical and Electronic Engineering, Meijo University, Shiogamaguchi, Tempaku-ku, Nagoya , Japan 3. Table of contents 4. Introduction 4.1. Polarization and Electric Field 5. Experimental 5.1. Sample Growth 5.2. Experimental Techniques 5.3. Strain Analysis and Pseudomorphy 5.4. Lateral Homogeneity of Optical Properties 5.5. Principle of Photo- and Electroreflectance 5.6. Electric Field in GaInN/GaN 5.7. Franz-Keldysh Oscillations and Franz-Keldysh Effect 6. Polarization in Pseudomorphic GaInN/GaN Thin Films 6.1. Photoreflection in GaInN/GaN Single Heterostructures 6.2. Band Gap Energies 6.3. Derivation of Electric Field Strength 6.4. Piezoelectric Field by Pseudomorphic Strain 6.5. Luminescence in Polarized Thin Films 6.6. Electric Field and Bandedges 7. Polarization in Quantum Well Structures 7.1. Polarity of Polarization Field in the Barrier 7.2. Balanced Polarization Dipoles 7.3. Screening of Polarization Charges 8. Polarization Controlled Bandstructure 8.1. Composition Dependence 8.2. Well Width Dependence 8.3. Electric Field in Quantum Well 8.4. Tuned Three Dimensional Critical Point 8.5. Polarization Dipole and the Bandstructure 9. Conclusions 10. Acknowledgements 11. References 12. Figure Captions

2 4. Introduction By the recent development of the wide band gap group-iii nitrides as fully functional Group-III nitride semiconductors come with a set of rather unusual properties that render them most advantageous performance in a very wide range of applications. Key achievements 1,2 in terms of crystalline quality 3-8 and full n and p-type conduction 9, initiated the development of high luminance light emitting diodes covering the entire visible spectrum and the near UV, 10 blue and UV laser diodes, solar blind photodetectors, 14 high temperature electronics, 15 high power electronics 16 as well as high frequency electronics 17, e.g., microwave power in the 20 GHz range 18. In this phase of this most successful development it is essential to develop a clear picture of the electronic band structure in this system and its peculiarities to take full advantage of its capabilities 19,2 and to elucidate the fundamental principles leading to those dearly soughtfor properties. One of the significant differences of group-iii nitrides with respect to other commercial semiconductors like Si, GaAs, or InP is the fact that the nitrides crystallize predominantly in the wurtzite structure. The associated space group P6 3 mc is characterized by a unique axis of rotational symmetry [0001], which coincides with the typical growth direction <0001> for GaN in metal organic vapor phase epitaxy (MOVPE). Group-III elements and N are located on the sites of two hexagonal closed packed (hcp) sublattices, which for ideal wurtzite structure are offset by u = 3/8 of the c lattice constant along [0001]. Due to this asymmetry (u = 3/8 rather than u = 1/2), the big difference in the atomic charge of the constituents, and the strongly polar binding conditions of group-iii nitrides, or Ga-N in particular, there is no inversion symmetry along this axis. Similar to the magnetic moments in a ferromagnet the electric dipoles add up to a macroscopic polarization P of the crystal along this axis. The polarization is dependent on biaxial strain conditions (piezoelectricity) and on the alloy constituents, i.e., GaN, AlN, InN, or their respective alloys The polarization itself does not reflect in the electronic band structure but its discontinuity does and it is therefore important to consider this properly within heterostructures. A discontinuity of polarization at the crystal surface or between layers of different composition or strain induces locally fixed net electrostatic polarization charges. The proper sign of charges is dependent on the direction of the discontinuity. Charge neutrality is maintained by the fact that ultimately a vacuum level connects both ends of the structure. In the consequence electric fields act between these charges across the crystal or heterostructure. Throughout insulating materials polarization effects are rather the rule than the exception. Also for semiconductors polarization properties are well known for the case of II-VI compounds like ZnSe, ZnS, CdTe, CdS, CdSe and their alloys and heterostructures Also the well-studied systems of strained GaInAs quantum wells has been considered for its piezoelectric properties along the [111] direction In group-iii nitrides, however, a number of favorable conditions are combined. Polarization effects are very large. Associated fields range in the MV/cm - about an order of magnitude higher than in [111] zincblende structures. 2

3 There is a large controllable lattice mismatch within heterostructures of Ga 1-x In x N (0 x 1) by tuning of the InN fraction x. Large strain in pseudomorphic heterostructures is readily supported. Strain-thickness products amount up to the range of 6 Å most likely due to strong bonding forces and reduced glide plane symmetries. There is a large polarization difference in GaN and AlN and polarization can be tuned by the AlN fraction y in Al y Ga 1-y N Group-III nitrides constitute a versatile, fully functional semiconductor system with a long list of application advantages. The pivotal relevance the polarization and its associated fields play in the electronic and optoelectronic properties of group-iii materials and devices became evident by the observation of the quantum confined Stark effect (QCSE) in the luminescence of GaInN/GaN quantum wells. 29,30 From an emission wavelength variation in response to an externally applied bias voltage a finite polarization was concluded from a built-in electric field within the active layers of the order of 1.2 MV/cm. 30 The QCSE had been established in AlGaAs/GaAs devices in the early 1980's at Bell Labs for fields in the range of a few 10 kv/cm. 31,32 The finding of fields in the range of MV/cm for nitride layers, however, opens up highly desired properties, challenges, and opportunities for new ways of electronic bandstructure design. Also in theory first principles calculations 21 have found large polarization effects comprising large equilibrium polarization and large piezoelectric coefficients for AlN, GaN, as well as for InN. Piezoelectric coefficients have experimentally been derived in piezoresistivity 20 and electromechanical experiments. 22 This situation has prompted experimental quantification of polarization charges and associated fields as well as exploration of their affects on the properties of thin films, heterostructures and on device performance. Only on the basis of such information will it be possible to correctly describe the electronic band and defect structure. This in turn is of pivotal relevance for the design optimization of high efficiency light emitting devices and power electronics. To this end, we studied series of pseudomorphically strained Ga 1- xin x N /GaN thin films and multiple quantum well (MQW) structures by combination of optical modulation spectroscopy and photoluminescence (PL). By comparison of photomodulated reflection (PR) and electromodulated reflection (ER) we derive direct and accurate readings of band edge energies, interband transition energies, and electric field strength acting within the individual layers. An independent approach to derive polarization charges in AlGaN/GaN heterostructures by means of capacitance-voltage characteristics has been applied in Ref. 33 On the basis of this coherent information we derive models of the electronic bandstructure in thin films and quantum wells. This chapter is based on the current status of the literature and our own work as cited Polarization and Electric Field In general the polarization P within a heterostructure sample is the sum of several components and it is important to distinguish primary from secondary effects. The local arrangement of charges in the core levels is a primary effect while screening by mobile carriers at the fundamental band gap occurs only in response to this initial polarization. This distinction, of course is not a physical but more a practical one since a complete 3

4 picture should include the feedback, i.e., the screening onto the origin of polarization. But with respect to the current problem to describe the electronic bandstructure in polarized semiconductors it is useful to differentiate the major components inducing polarization and the effects induced by that. The primary polarization P can be parameterized in terms of an equilibrium polarization P eq (also somewhat misleadingly labeled spontaneous polarization) and its partial derivatives with respect to temperature P/ T, composition P/ x, strain P/ ε, as well as their spatial derivatives. Pyroelectricity thus describes the contributions associated with temperature variations, ( P/ T) δt, while piezoelectricity accounts for the strain dependent part, ( P/ ε) δε. Historically, however, the name pyroelectricity has also been used to describe the total polarization. Polarization furthermore may arise from extrinsic contributions of surface terminations, surface charges, fixed dopant charges, charged defects, and applied voltages. For a capacitor-like geometry with paired surface area charge densities σ + and σ -, (σ + = - σ - ) the resulting polarization P measured in Coulomb per area is given by P = σ e. e is the electron charge and has a negative value for electrons. This polarization will induce an electric field F according to 1 F = P 0 r (1) In thermodynamic equilibrium P is balanced macroscopically by rearrangement of mobile charges, such as free electrons in the sample or mobile ions at the surfaces. For homogenous structures, i.e., vanishing spatial gradients, this screening will cancel the electric field provided, that sufficient mobile charges can be rearranged. The piezoelectric properties of GaN have been derived from piezoresistive 20 and interferometric 22 measurements. A complete set of the polarization matrix elements has been obtained in first principles calculations treating polarization within the Berry phase approach. 21 In these results for the binary components AlN, GaN, and InN values of the equilibrium polarization have been derived as well as piezoelectric coefficients. In contrast our work focuses on the derivation of actual fields strengths. For inhomogeneous layers, on the other hand, such as heterostructures and quantum wells involving different alloys and strain conditions net polarization charges arise across the discontinuity of polarization at the individual interfaces (Fig. 1). The screening of the associated fields is then closely determined by the capability to accumulate sufficient mobile charges for the compensation. Such a system is best described by considering undoped structures and a subsequent consideration of screening effects. According to the first principles theory spontaneous polarization in InN and GaN varies by a small amount of 10 % whereas the values for AlN are 3.5 times that of GaN. 21 On the other hand piezoelectric coefficients for all components are similar in value and the very large a-plane lattice mismatch of InN and GaN makes piezoelectric effects more important than in the closely lattice matched case of pseudomorphic AlN on GaN. In combination of both we expect the piezoelectric effect to dominate in the GaN-InN range 34 while discontinuity of the equilibrium polarization should dominate in the AlN- GaN system. 35,36 4

5 Combining imaginary heterostructures A/B of the components AlN, GaN, InN as well as their respective alloys a wide range of huge electric fields in both polarities can be achieved in theory according to Pz Pz 0 r Fz = Pz, A Pz, B = Pz = δx + δε zz. x ε zz (2) Fig. 2 illustrates an interpretation of theory values in terms of field strength achievable in heterostructures of ternary layers as indicated by their composition x, y, z on either AlN, GaN, or InN relaxed epilayers. Fields as large as 15 MV/cm may be expected for GaN/AlN or InN/GaN structures. Data for ternary layers shown here is based on the arbitrary assumption that piezoelectric coefficients and equilibrium polarization in the alloys as well as the elastic constants and the lattice constants follow a simple Vegard law as a linear interpolation of the values of the binary components. This assumption, however, is not further substantiated and bowing effects similar to the band gap energy in GaInN might be significant. The piezoelectric component can be related to the individual strain components in wurtzite by means of matrices of the piezoelectric coefficients. The polarization along the z-axis is given by P z = e 31 (ε xx + ε yy ) + e 33 ε zz, (3a) P z = [d 31 (c 11 + c 12 ) + d 33 c 13 ] (ε xx + ε yy ) + [2 d 31 c 13 + d 33 c 33 ] ε zz. (3b) using either of the two sets of piezoelectric coefficients {e 31, e 33 } (linking to strain) or {d 31, d 33 } (linking to stress) and the elastic constants {c 13, c 33 }. For biaxial strain ε xx = ε yy = (-2 c 13 /c 33 ) -1 ε zz this reduces to P z = (2 e 31-2 e 33 c 13 /c 33 ) ε xx, (4a) P z = 2 d 31 (c 11 + c 12-2 c 2 13 /c 33 ) ε xx. (4b) It will be part of this chapter to derive actual values for this polarization and associated fields within experiment. 5. Experimental 5.1. Sample Growth The good definition of the material studied is crucial for the comparison of results. For the case of GaInN a wide rage of experimental observations in the literature are being attributed to material with large spatial fluctuations especially for the InN fraction or phase separation. 41 The work presented here, however, concentrates on material where such inhomogeneities are minimized in order to study best-most defined material and sample structures. Great effort has been spent to optimize the film properties with respect to microscopic homogeneity and smooth morphology. Ga 1-x In x N/GaN structures have been grown by metal organic vapor phase epitaxy (MOVPE) on (0001) basal plane sapphire using the technique of low temperature deposited buffer layers of AlN and GaN. 4,7,42,43 A first set of Ga 1-x In x N/GaN single heterostructures was grown at thicknesses of 400 Å onto 2 µm GaN epilayers. The InN fraction x was continuously varied in a rather wide commercially relevant range (0 < x < 0.2). Typical growth temperatures for GaInN layers range from o C. Typical source fluxes are as follows: TMGa 2 µmol/min, 5

6 TMIn µmol/min, NH 3 2 slm. 42,43 Pseudomorphic growth conditions and x were determined from high-resolution x-ray diffraction of a and c lattice constants taking into account the deformation of the unit cell. 7 Next a set of GaInN/GaN multiple quantum wells (MQWs) with variable x, (0 < x < 0.2) and fixed well width L w = 30 Å, barrier width L b = 60 Å was grown. 44 A third set comprises nominally fixed compositions (x = 0.13) and variable well width L w, 23 Å L w 70 Å. A fourth set consists of Ga 1- xin x N/GaN MQW with Si doping in the barriers at concentrations of 3x10 18 cm -3 (L w = 30 Å, L b = 60 Å, x = 0.15) Experimental Techniques For photoreflection (PR) and electroreflection (ER) the spectral reflectivity was measured using the continuum light of a Xe-arc lamp in near-to-perpendicular reflection. For photomodulation light of a 325 nm, 40 mw HeCd laser was employed at a typical flux of 0.1 W/cm 2. In above-band gap excitation internal electric fields would be modulated by the generated photocarriers. A mechanical chopper at 1.4 khz and lock-in technique was employed for the detection. In the electromodulation mode of ER an external bias voltage was applied through an aqueous electrolyte and Cu or C electrodes. Atop a variable bias a sinusoidal modulation voltage of 2-10 V amplitude was applied. To form the PR or ER signal the AC component was normalized to the DC part. Due to the excitation geometry thickness interference fringes did not occur in the AC part nor in the DC part 45 except for some cases where noted. Time integrated photoluminescence (PL) was performed using the same 325 nm HeCd laser at the same low fluxes of 0.1 W/cm 2. Spatially resolved PL mapping was performed in a confocal UV microscope at typical power densities of 10 6 W/cm 2. Alloy compositions were determined using a dynamical analysis of x-ray rocking data in the QWs and x-ray diffraction of both lattice constants for the thicker layers. Details have been given in Refs. 42,43,46. All data were taken at room temperature. This condition is justified by the large exciton binding energy in GaN of 33 mev compared to a thermal energy of k B T = 25 mev at 300 K. Room temperature characterization in GaN therefore corresponds to spectroscopy at some 30 K in the case of GaAs and therefore should be most suitable for a detailed analysis 5.3. Strain Analysis and Pseudomorphy Heteroepitaxy of wurtzite nitride layers along the unique c-axis on thick GaN leads to large biaxial compressive (tensile) strain within the basal plane of the ternary GaInN (AlGaN) layer. From detailed x-ray diffraction analysis of high indexed lattice planes in GaInN/GaN as well as AlGaN/GaN single heterostructures involving both lattice constants a and c pseudomorphic growth at the basal plane lattice constant of GaN could be established for our material. 6,7 Pseudomorphic growth had been well-established in short period superlattices of other III-V compounds like AlGaAs/GaAs and GaInAs/InP. According to theoretical models such conditions can be supported when the product of stress and layer thickness remains below a critical value which typically limits such conditions to structures where quantum size effects are highly relevant. It is a surprising fact of the group-iii nitride heterostructures, however, that ternary Ga 1-x In x N as well as Al y Ga 1-y N layers remain pseudomorphically strained to GaN at layer thicknesses of 400 Å and beyond for composition values of 0 x 0.20 or 0 y These thicknesses supersede the values predicted by current models of Matthews and Blakeslee 47 and that of 6

7 Fischer et al.. 48 A tentative explanation for this effect can be found in the large angular variation of the amplitude of possible Burger vectors in this wurtzite structure. 49 According to this picture dislocations are predominantly oriented along the growth direction and cannot contribute to relax the in-plane stress. Our interpretation of the strain conditions is based on the linear interpolation of the lattice constant for hypothetically freestanding unstrained Ga 1-x In x N material (Vegard's law) c(x) = c GaN (1 - x) + c InN x = Å (1 - x) Å x, a(x) = a GaN (1 - x) + a InN x = Å (1 - x) Å x (5a) (5b) and the linear interpolated values of the elastic constants (in dyn/cm 2 ): c 13 =11.4 (9.4), c 33 =38.1 (20.0) in GaN (InN), respectively. 50,51 Under pseudomorphic conditions such GaInN is forced onto 2 µm GaN/sapphire with lattice constants c 1 = Å, a 1 = Å. The resulting strain leads to forced lattice constants c s and a s = a 1, and a new relation between x and c s that is essentially different from the linear interpolation values for the relaxed bulk values. The new relation is x = c s Å -1, a s = Å. (6) The induced strain within the ternary layer is given by: (7) a1 ε xx = 1 < 0. as As a consequence within Hook's law an elongation along the c-axis occurs, c c13 ε > zz = = ε xx 0. cs c33 (8) (elastic constants c 13, c 33 ; values of GaN). For x = 0.2 we therefore induce strain ε zz = 0.015, ε xx = Despite these large values and a thickness of 400 Å corresponding to a large strain-thickness product of 6 Å GaInN films are found to remain a single alloy component and unrelaxed as observed from high resolution x-ray diffraction of both lattice constants. 6 This deformation effect of the unit cell strongly affects the interpretation of the composition from x-ray data of one lattice constant alone, i.e., the c- lattice constant. It appears that in many previous works the InN-fraction has been overestimated by roughly a factor of two due to the misinterpretation of the actual strain conditions (for a discussion see Ref. 42) Lateral Homogeneity of Optical Properties The spatial homogeneity in our material was also tested in high resolution PL. Fig. 3a) presents a typical statistical analysis of 2500 spectra taken on a Ga 1-x In x N/GaN (x = 0.187) layer over an area of µm Spatial resolution and sampling interval were fixed at 1 µm 2. Test spectra taken at different excitation power densities from

8 W/cm 2 did not show any variation. The emission energy in the peak of each spectrum is shown in Fig. 3a) and reveals a very narrow distribution of 25 mev at ev (full width at half maximum, FWHM). In some locations, however, the peak intensity occurs at energies some 50 mev below. According to the concept of preferred luminescence in localized states 53,40 these lower energy tail states would be expected to dominate the PL intensity distribution. Fig. 3b) represents the same distribution weighed by the respective peak intensity. In this case the high-energy side is strongly favored over the low energy tail and the distribution exhibits a distribution of 28 mev (FWHM). This result indicates that spatial inhomogeneities on the length scale of 1-50 µm do not induce a variation of the peak energy of the most intense PL transitions. In turn, the narrow PL distribution itself defines a clear effective PL band gap energy. This property can be explained by either the absence of any significant fluctuation or the absence of any efficiency enhancing localization process in our material. At the same time the PR spectrum (Fig. 3c) shows a very broad oscillation in energy without any narrow (10-20 mev, 54,55 ) features typically indicating the presence of excitons. Altogether this indicates that homogeneous material such as presented in this study, can be obtained. These results are in important contrast to work on 500 nm layers of GaInN/GaN 38 where several components were identified in symmetric x-ray scattering of the c-planes. Those were associated with the coexistence of phases with different alloy composition. While this picture may hold for a variety of GaInN material it is our intention to point out that it is also possible to grow homogenous material as described above. A similar analysis of GaInN/GaN quantum wells typically reveals a line width in both modes of as little as 2 mev (FWHM) Principle of Photo- and Electroreflectance The principle of PR is based on the fact that photogenerated free charge carriers will contribute in the screening of any existing electric fields within the sample. This reflects in the electronic bandstructure, the joint density of states (DOS), and in the associated dielectric function. This in turn can be detected in the spectral reflectivity of the layer as measured by a second weak probe beam. High sensitivity can be achieved by periodic modulation of the excitation beam and synchronous lock-in detection. In ER the modulation is achieved by direct application of an external bias voltage. Both methods have widely and successfully been used in the literature for detailed and quantitative description of semiconductor layers and structures The signal of such reflection methods directly probes the joint density of states (DOS). Luminescence in contrast is sensitive to radiative transitions at the end of a possibly long chain of thermalization processes into potential minima. There is no direct correspondence to the DOS band gap. Modulated reflectivity measurements such as PR are therefore the most successfully employed methods to determine band gap energies. The analysis and interpretation of PR spectra has been performed on a wide variety of compound and alloy systems in the literature 59,60,58 and its theory mainly distinguishes cases of localized (i.e., excitons, states of spatial confinement) and states of free carriers (i.e., band electrons). The primary process of photo modulation is a local variation of the screening conditions leading to a variation of an electric field and quasi Fermi levels. 8

9 5.6. Electric Field in GaInN/GaN PR of the GaInN/GaN thin film heterostructures with different composition is shown in Fig. 4. A strong oscillatory signal is seen above a clearly marked onset at a certain threshold energy. Towards higher energies several oscillations appear with decreasing amplitude and decreasing period. For comparison ER and PR in the x = 0.19 GaInN/GaN sample are shown together. Also in the case all of the above features appear, yet with a stronger damping of the amplitude towards higher energies. Most importantly ER and PR produce the identical spectrum and we conclude that in both cases the mechanism responsible for the observation of oscillations is the same. Oscillatory behavior in PR of nitride layers has been observed in several cases 54,61-63 and it is mandatory to distinguish several effects to identify the proper mechanism. The following have been considered and discussed in the present case: thickness interference fringes, piezoelectrical thickness variations, thermo-modulation, electric field effects acting on a series of discrete electronic levels or on a continuum. The major criteria of distinction lie in the dependence on layer thickness, excitation power dependencies and the fact of a single continuous line shape describing the observations over a large energy range. From a careful assessment of the associated effects as discussed in Ref. 43 all of the above could be distinguished from an effect of a large electric field acting in the layer. The good correspondence indeed indicate that we can perform the interpretation of PR spectra along the established mechanisms for ER, 64 i.e. a direct modulation of the dielectric function by the electric field. We therefore explain the signal as Franz-Keldysh oscillations (FKOs) where the reflection signal of the interband absorption at the band gap energy is controlled by the electric field. 45, Franz-Keldysh Oscillations and Franz-Keldysh Effect The principle of FKOs is the fact that in the presence of an electric field F the band edges in a layer extending along the field will be inclined along this direction (see schematic in Fig. 5. In contrast to field free conditions (Fig. 5a) the band edge here acts as barrier for electrons at any given energy (Fig. 5b). The associated wave functions of reflected electrons at different energies thereby establish a phase factor that scales with the tilting of the band edges, i.e., the magnitude of F. This then reflects in oscillatory behavior at and above the bandedge energy. These Franz-Keldysh oscillations are accompanied by the Franz-Keldysh effect, which describes the effective band edge shrinking within an electric field. The field-induced tilting of the bands in real space creates a triangular tunnel barrier for spatially indirect transitions below the gap (Franz-Keldysh effect, photon assisted tunneling) (Fig. 5c). 65 This can be expressed by an exponentially decaying effective DOS with a slope parameter again determined by the electric field amplitude. A closed description of the expected signal has been given by Aspnes 56 in the form of Airy functions with extrema above, at, and below the band gap. This can be expressed by means of the electro-optical functions F(η) and G(η). The scaled function G(η), (η reduced energy) is shown as a fit to the spectra in Fig. 4 and demonstrates the excellent description by theory. Above the band gap the PR modulation can be approximated by an exponentially decaying cosine: 56 9

10 3 / 2 R 1 2Γ E E g 4 E Eg exp cos + χ 2 3 / 2 R E ( E Eg ) ( hθ) 3 hθ Extrema in E = E i (i 0) are given by integer multiples of π of the phase argument in the cosine function. Index i = 0 (χ = π) marks the dominant minimum which in the limit of vanishing damping Γ corresponds to the DOS band gap E g (see ticks and labels in Fig. 4). hθ is the electro-optical energy 57 and related to the electric field. 3 / 2 2µ F = ( hθ). eh (10) In this µ is the joint DOS mass and the only material parameter. The relation to the reduced energy is given by η = (E - E g )/(hθ). This allows for a very accurate determination of the actual electric field strength in the layers. (9) 6. Polarization in Pseudomorphic GaInN/GaN Thin Films 6.1. Photoreflection in GaInN/GaN Single Heterostructures PR in some 40 Ga 1-x In x N /GaN thin film samples with different composition has been investigated. PR of 13 samples with various x is presented in Fig. 6a) (offset for clarity). The typical signal is in the range of R/R = At 3.42 ev signal of the GaN layer is seen indicating that the entire thickness of the ternary layer is sampled. Similar narrow features of the excitons in GaN have been obtained in PR 54 and ER 66 and have been used to describe the valence band splitting as a function of strain. 67,55 We ascribe the dominant feature in the range from 3.1 ev to 2.7 ev to the DOS band gap in the GaInN layer. 42,59 The very large spectral width of the feature increases and the band gap decreases for higher x or c-values. Both properties show a clear correlation. Furthermore, PR oscillations are seen on the high-energy side with a decreasing amplitude and period for higher energies within each of the spectra (see also Fig. 7), offset in energy for clarity). These subsidiary oscillations could be observed in about half of the samples studied. In the other samples PR signal below the GaN band gap was in the range of R/R = In order to distinguish individual contributions to the PR signal we independently varied the following parameters by about a factor of ten: flux of UV light, flux of white light, modulation frequency, and sampling area. Within these limits there was no observable variation in the obtained spectra Band Gap Energies The band gap energy E g corresponds to the dominant minimum in the GaInN PR signal (Fig. 6a). 42 Due to the high symmetry of the signal the DOS band gap energy is directly derived from the minimum energy. Within the range 0 < x < 0.2 we can interpolate the band gap with InN (E g = 1.89 ev 68 ) and define an effective bowing parameter b: 10

11 E g (x) = E g (GaN) (1 - x) + E g (InN) x - b x (1 - x). (11) We obtain a best least-square-fit description of the PR data for b = 2.6 ev (pseudomorphic). The contribution of biaxial strain shift in the band gap energy can be approximated by the values of the well-studied case of GaN. We assume that also in GaInN under biaxial compression the band gap is defined by the Γ 7 c - Γ 9 v A transition with an experimental deformation potential for biaxial compression of E g (A)/ ε zz = 15.4 ev (T = 10 K, 67 ) resulting in b = 3.8 ev for the band gap in relaxed GaInN. Together we find the following relations: E g = 3.42 ev (1 - x) ev x ev x (1 - x) 0 x 0.2, (12) for GaInN pseudomorphic to GaN along the c-axis and E g = 3.42 ev (1 - x) ev x ev x (1 - x) 0 x 0.2 (13) for relaxed GaInN. Similar experimental results within a smaller composition range have been reported by absorption measurements. 69 Previous results supporting values of the bowing parameter of b = 1 ev 70,71,10 can be shown to coincide with our experimental data under the inappropriate interpretation of InN fractions from the c-lattice constant neglecting strain. Early absorption data 72 can be described by b = 2-3 ev when considering the range 0 x 0.2 while for 0 x 0.7 they propose b = 1 ev. Significantly higher values b = ev have been reported recently in a small number of unstrained GaInN films in luminescence (0.07 < x < 0.17) 73 in reasonable agreement with our data. For a further discussion of the composition dependence of the bowing parameter refer to Ref Derivation of Electric Field Strength From an interpretation of the Franz-Keldysh oscillation behavior the magnitude of the electric field can be derived. Within a commonly used approximation a plot of 4/(3 π) (E(C i ) - E(C 0 )) 3/2 versus the indices of the extrema i is interpreted in Fig. 8 (according to Eq. 9). Up to six and in some cases eight extrema can be resolved. For each sample points can be approximated by straight lines the slope of which corresponds to (hθ) 3/2, and to the electric field through Eq. 10. Herein µ = 0.2 m e is the joint effective DOS mass. Due to the lack of better data we assume it to be constant at the GaN electron value µ = 0.2 m This is a valid approximation since µ enters only as a square root. The model in Eq. 9 makes use of the band gap energy E g. This point should therefore be the origin of the linear interpolation in Fig. 8. In our data, however, E g is only assigned to the dominant minimum and therefore, just as the other points, subject to error bars. Again comparing to the case of GaAs where excitonic contributions distort the description of the first extrema a good linear fit of all extrema is found here in Fig. 8 including index 1 and, in extrapolation to E g, also index 0. 11

12 F is not affected by a variation of the photo excitation power by a factor of 10 and together with the very high value of F we conclude that this field is not induced by the PR mechanism itself. Instead we deduce that F is a constant field across the ternary layer and we attribute it to the polarization field induced by the biaxial stress conditions and/or the alloy discontinuity by means of Eq. 10. This experiment is not conclusive about the causes of the polarization. By help of the first principles theory results, however, predicting similar equilibrium polarization in InN and GaN the above effect must be attributed to piezoelectricity Piezoelectric Field by Pseudomorphic Strain Analyzing all samples in the above scheme we derive the dependence of the net electric field F present in the ternary layer as a function of the c-lattice constant (Fig. 9). 34 Scales for the derived ε zz strain and the x are given. F increases with ε zz corresponding to a piezoelectric constant P/ ε zz = 0.46 C/m 2 (slope indicated by dashed line). The typical maximum field observed is 0.6 MV/cm. In one case a field of 1.1 MV/cm is found. The large field value must be attributed to the net static piezoelectric field in the structure. The piezoelectric field extrapolates to zero field for finite strain (ε zz = ) and a residual polarization P eq = 3.9 mc/m 2, (P eq P/ ε zz < 0) when extrapolating to the epitaxial GaN underneath the ternary layer. While the presence of a residual polarization can be associated with variations in the strain or polarization status of the epilayers the considerable scatter of data might be a consequence of any polarization relaxing mechanism effectively reducing the electric field such as structural defects and inversion domains. Furthermore the derived values are net fields as they may in part be screened by mobile carriers Luminescence in Polarized Thin Films A direct consequence of the internal fields is the effective band gap shrinking by the Franz-Keldysh effect (photon assisted tunneling). 65 The field-induced tilting of the bands in real space creates a triangular tunnel barrier for spatially indirect transitions below the gap. This can be expressed by an exponentially decaying effective DOS with a slope parameter determined by hθ and therefore by the electric field (Eq. 10). Room temperature PL together with PR is shown in Fig. 10. PL is found to exhibit a significant redshift with respect to the above defined band gap E g from PR. Similar observations in thin GaInN layers have been reported by Chichibu et al.. 40 Several models have been proposed to explain the origin including the formation of Inrich regions and clusters. 40,75 From the spatially resolved PL we find no evidence for significant variation of the effective PL band gap. The observed distribution, however, of 28 mev (x = 0.187) cannot account for a redshift as large as mev. On the other hand in our data the discrepancy closely (i.e., ± 20 mev) corresponds to one half-period of the PR oscillation and the maximum of PL lies very close to the maximum labeled i = - 1 (Fig. 10). Within all the PR spectra extrema i = -1 and i = +1 are found symmetrically around i = 0 and we propose that i = -1 be the tail state's equivalent of i = ,43 The apparent localization in i = -1, E -1 - E g, therefore corresponds to E +1 - E 0 = (3 π/4) 2/3 hθ. 12

13 Assuming a constant electric field across this energy the effective DOS has decayed to e -π = 4 % and for the given high field values the base of the tunnel barrier closely corresponds to an effective Bohr radius a r = 3 nm. This limited model furthermore suggests that the maximum in i = -1 is the extension of the oscillations into the evanescent tail states. It therefore corresponds to a transition involving the electric field induced tail states (Franz-Keldysh effect). In a simplified model the redshift between the PL gap and PR gap can be well approximated by the band gap tilting across the dimension of the excited particle, i.e., the electron-hole pair: E = F e a r = mev, where a r is the effective reduced Bohr radius. Within the range of our samples (0 < x < 0.2) our model can well explain the observed redshift in the material studied. Again it is the large magnitude of the field that emphasizes this well-known effect Electric Field and Bandedges The presence of such a large internal field has severe consequences for mobile carriers. A schematic of the band structure neglecting band bending is given in Fig. 11. At the heteroepitaxial interface the step in strain induces large fixed piezoelectric charges and a band tilting. Photocarriers will be separated in the field and drift along in opposite directions. The charge separation is limited by the built-up of a diffusion field between the accumulated carriers that will compensate the piezoelectric driving force. In the limit of thick films inversion layers of both carrier types should be expected. This should be of high relevance for electronic transport devices such as HEMTs and HBTs. The separation of carriers should lead to long recombination lifetimes and possibly is the origin of long non-exponential decay behavior observed in time resolved experiments The accumulation of high mobility carrier gases is could behave as a bi-stable switch. Recombination or re-trapping of the carriers is strongly suppressed by the large spatial separation of the carriers. 76. The process might be suitable for a variety of devices including memory cells for electrical or optical pulses. Performing the transfer to binary GaN we expect identical effects to occur leading to fields of 50 kv/cm in typically strained GaN/sapphire heterostructures. This field could provide sufficient charge separation to explain observed effects of persistent photoconductivity 76,79,80 and other remanence effects, e.g., in the PL of GaN. 81. Metastability in GaInN/InN structures and strained GaN layers therefore might be associated with wurtzite inherent piezoelectricity while other mechanisms such as structural defects also need to be considered. Concerning our GaInN material we find that strain, piezoelectric effects, and its associated huge electric fields are the dominant parameter determining the electronic and its associated absorption and luminescence properties. We propose that the translation invariance induced by the field is the major contribution in the apparent band gap tailing. This case of Franz-Keldysh effect in our highly homogeneous material dominates effects of other broadening mechanisms such as alloying disorder and composition fluctuations. Within electric fields of this strength the conventional concept of excitons is not applicable. Consequently the piezoelectric field gains a high priority in the description of the band and defect structure. We furthermore do not find evidence for discrete energy levels possibly associated with In-rich clusters. 13

14 7. Polarization in Quantum Well Structures Our initial discussion has focused on the properties of polarized thin film material. Of high application relevance, however, are quantum well heterostructures with well thicknesses of a few nm only. In such a system a polarization controlled separation of electrons and holes is generally limited to the width of the quantum wells L w and it is this case where the observation of the QCSE has led to the interpretation of large electric fields to act within the wells of GaInN/GaN MQW structures. 29,30 Such an analysis is based on a comparison of luminescence peak energies and calculations of the interband transition energies in dependence of an acting electric field. Several authors have made use of such calculations both within the GaInN/GaN 29,30 and the GaN/AlGaN 35,82 MQW systems. Due to the nature of this elaborate process a series of assumption must be made concerning band structure parameters such as effective DOS masses, band gap energies, and relative bandoffsets in dependence of the actual layer composition. Furthermore, the more complex case of inhomogeneous well material is very difficult to describe at the present status of available material data. Due to these limitations it is highly desirable to obtain independent experimental results for the strength of the acting electric field. Here again modulated reflectivity can provide direct means to probe the joint DOS and to derive accurate readings of F Polarity of Polarization Field in the Barrier ER under variable bias voltage in a doped sample is presented in Fig. 12. An electric field is applied perpendicular to the doped MQW layer by two lateral top contacts. 95 Si doping to cm -3 is limited to the barrier region. One of the contacts is formed by a transparent electrolyte. ER is measured in the area of this contact. Negative bias voltages correspond to a lowering of the electron potential at the layer surface while positive voltages correspond to a electron depletion of the surface and extension of the field across the MQW thickness (see sketches in Fig. 13). Above an energy of ev, strong FKOs appear in most of the spectra extending up to ev (note the capped signal extrema in E i in this presentation). At lower energies, interference fringes appear as is apparent from the comparison with the DC reflection signal. Interpretation of the oscillation period along the approximation of the electro-optical functions results in a rather accurate reading of the electric field as shown by the good linear variation of 4/(3π) (E i - E 0 ) 3/2 vs. the index i of the extrema (inset of Fig. 13). We identify field values (Fig. 14) varying at a rate of F/ U bias = MV/cm/V corresponding to a reasonable effective total depletion length of 220 nm and a significant field value of F 0 = 0.51 MV/cm at zero bias voltage with reference to the C electrode. The sign of the field can be derived to F 0 = + F 0 e z, pointing along the growth direction in this case. This reveals that even in highly Si doped material, significantly large electric fields are active without an external bias. The appearance of FKOs at and above the GaN band gap energy reveals that the associated field must be assigned to the GaN barriers F b = F 0 (also seen in Ref. 62). An origin in the underlying undoped epilayer must be excluded because contact to the sample is made only in the top-most MQW region. Despite the high doping conditions of the sample, the applied bias voltage can vary F within an optical absorption length of 100 nm equivalent to the entire MQW region by an amount of F b = 0.36 MV/cm. Neglecting any contact losses, the geometrical field maximum would be 2 MV/cm. 14

15 7.2. Balanced Polarization Dipoles Considering equilibrium polarization and piezoelectric effect no field should be expected in the strain free GaN well pseudomorphically linked to the thick GaN epilayer underneath. Under the condition of cyclic boundary conditions at both sample surfaces in thermodynamical equilibrium mobile charges are accumulated to balance the polarization cascade on a macroscopic scale. Therefore an electric field in the barriers F b is the direct response to polarization P and fields F w within the wells 36 according to F avg (L w + L b ) = F w L w + F b L b. For thermodynamical equilibrium we add a depolarization field of screening charges with the effect that F avg = 0 and a balancing of the polarization dipoles F w L w = - F b L b. (14) The observed direction of the electric field in the bias dependence therefore is that of the response to the initial polarization field in the well F w = - F w e z. pointing from the growth surface to the substrate in typical MOVPE growth Screening of Polarization Charges Our discussion so far has addressed the direct derivation of electric field strength as a result of polarization. In the presence of doping charges, however, also the effect of screening must be considered. Our approach is the following. Dipole charges such as the piezoelectric polarization across the GaInN well can only be screened by paired charge carriers of both polarities. Such a situation exists in the spatial separation of free carriers from their fixed dopant charges. Consider a large polarization charge of σ = cm -2 for a large field of 1.2 MV/cm expected near x = 0.2. From basic electrostatic considerations it follows that for effective mass-type donors with a typical dopant concentration of cm -3, a full depletion length of 45 nm is needed for compensation. An associated potential step across the depletion would amount to 3.5 ev (Fig. 15a). Screening by doping of such a concentration can therefore not be achieved in typical quantum wells of 2 to 4 nm width and in the present sample the Si doping should not affect the interpretation by more than 10 %. Screening therefore can act only on the long range across the entire MQW region and compensates the built-up polarization to F avg = 0 for vanishing bias. For p-type doping, typical acceptor concentrations reach values of cm -3 leading to screening lengths of the order of 1 nm which should allow a screening within quantum wells. The large binding energy of acceptors, however, would always result in a minimum potential of E 0.24 ev across the depletion length (Fig. 15b). In combination with spacer layers for remote doping, this step can easily hinder the transfer of holes into shallow wells for small InN fraction. Screening should also be possible by bipolar injection of appropriate densities of free carriers under forward bias, i.e., at the lasing threshold. Carrier density values of cm -3 equivalent to cm -2 are, however, insufficient for complete screening even under the assumption of an electron-hole dipole involving the full well width. This is in agreement with recent self-consistent tight binding band structure calculations

16 Therefore the most likely situation is a balancing of the dipole moments between doping layers and polarized layers along the above scheme. This indicates that polarization effects are important on a length scale typical for interfaces, heterostructures, superlattices, and intrinsic regions but not for general bulk applications. 8. Polarization Controlled Bandstructure So far the effects of electric fields in polarized group-iii nitrides can be described in linear and continuos perturbation to the field free case. We observe a gradual shift of band gap energies by the Franz-Keldysh effect and a similar shift between well-defined QW states in form of the QCSE. The more interesting question, however, is whether in the range of such unusually large electric fields new quantized states arise similar to discrete Landau levels in the presence of magnetic fields. In fact FKOs directly reflecting the joint DOS resemble such a situation. A very weak modulation depth on the order of , however, reveal the limitations of this comparison. The concept of quantization in an electric field in the form of Stark ladders has been the subject of considerable interest already around It was concluded that discrete states can only be expected once a discrete base level would be defined from where a ladder would start. Such a situation can be given by the interband transition within discrete QWs subjected to a field along the quantized dimension. In this case the superlattice period, i.e., L w + L b defines a dipole moment F e (L w + L b ) which reflects in the step size of discrete subband levels in adjacent wells combined by tunneling through the barriers This concept has successfully been applied in quantum cascade lasers. 91 The discrete field controlled level splitting defines the emission energy of a unipolar FIR laser device. Such perspectives are but one motivation to investigate the role huge polarization fields play in the electronic band structure of group-iii nitride QWs Composition Dependence PR spectra over a selected energy range of a complete composition set (nominally undoped) are presented in Fig. 16. Spectra are arranged in the sequence of the PL peak energy (see labels) 92 which is a measure also for the composition x and the in-plane strain ε xx. 42 Several PR contributions can be identified. At ev (N 0 ) narrow oscillations are seen that closely correspond to the excitonic band gap in the GaN epilayer. PR in GaN epilayers has been shown to reflect the wurtzite structure and its three associated excitons A, B and C. 55 Within the typical strain of epitaxial GaN excitonic level splitting of A and B accounts for up to 8 mev and has been shown to produce a structure very similar to the signal seen here. The higher lying C exciton is usually difficult to detect and not identified in our spectra. Such excitonic features have been described by the superposition of third derivative-like structures. 93 Within the context of this work features of this fine detail are presently not of concern and we jointly assign N 0 to the excitonic band gap E gx some mev below the fundamental GaN band gap. Within a broader energy range around N 0, a strong periodic modulation of the PR signal with several minima and maxima labeled C i, i = 0 4 is seen in all the samples. Comparing the entire sample set, a trend towards wider oscillation period for higher x appears. Extrema C i appear independently of the oscillations in N 0 indicating that 16