A method used to overcome polarization effects in semi-polar structures of nitride light-emitting diodes emitting green radiation

Seweryn Morawiec Robert P. Sarzaa Wodzimierz Nakwaski Polarization effects are studied within nitride light-emitting diodes (LEDs) manufactured on standard polar and semipolar substrates. A new theoretical approach, somewhat different than standard ones, is proposed to this end. It is well known that when regular polar GaN substrates are used, strong piezoelectric and spontaneous polarizations create built-in electric fields leading to the quantumconfined Stark effects (QCSEs). These effects may be completely avoided in nonpolar crystallographic orientations, but then there are problems with manufacturing InGaN layers of relatively high Indium contents necessary for the green emission. Hence, a procedure leading to partly overcoming these polarization problems in semi-polar LEDs emitting green radiation is proposed. The (1122) crystallographic substrate orientation (inclination angle of 58 to c plane) seems to be the most promising because it is characterized by low Miller-Bravais indices leading to highquality and high Indium content smooth growth planes. Besides, it makes possible an increased Indium incorporation efficiency and it is efficient in suppressing QCSE. The In0.3Ga0.7N/GaN QW LED grown on the semipolar (1122) substrate has been found as currently the optimal LED structure emitting green radiation. - attracted a great interest of research centers due to their possible applications in manufacturing visible and even ultraviolet light emitting diodes (LEDs). These materials, however, differ significantly from most of other IIIV semiconductors, which leads for example to problems with obtaining efficient nitride sources of green radiation (green gap effect) [13]. Their special properties are connected with their wurtzite crystal structure, distinctly different from the zinc blende structure of most of other IIIV semiconductors. In Fig. 1, characteristic planes and axes of this crystallographic structure are shown. Layers of most of nitride devices are usually grown along the c polar axis. Planes parallel to this axis, i.e., perpendicular to the c plane, are electrically neutral (nonpolar), because they contain the same number of both anions and cations, whereas planes between the polar c and any nonpolar orientations are called semipolar ones [5, 6]. Crystallographic plane is usually defined by its inclination angle between the crystallographic direction c and the axis perpendicular to this plane (Fig. 2). In GaN, the c/a ratio is equal to 1.626 [8], whereas its value for the ideal wurtzite structure equals about 1.633 [9], where c and a are the lattice constants in the c and a crystallographic directions, respectively. Therefore, the GaN crystal is compressed in the c direction. It results in some shifting of positive and negative charges, which is always directed along the c axis [10], and is called the spontaneous polarization [9]an intrinsic crystal property. Possible further crystal stresses lead to an additional change of the c/a ratio, which results in the piezoelectric polarization. In quantum wells (QWs), it leads to strong build-in electric fields, and consequently to the quantum-confined Stark effect (QCSE): electrons and holes are shifted in opposite directions (compare peak positions of electron and heavy-hole wave functions determined for the first QW energy levels shown in Fig. 3). Then overlapping of their wave functions Fig. 1 Possible growth planes and crystallographic directions in the hexagonal unit cell (on basis of [4]) Fig. 2 Wurtzite structure in the semi-polar orientation with the local 0xyz and the global 0 x y z co-ordinate systems. inclination angle. The inclination axis is along the <1120> direction. (On the basis of [7]) is strongly decreased, which is discussed in Sect. 5. Moreover, QW barriers are effectively reduced enabling more intense escape currents from QWs, especially at higher temperatures. In most of commercially available substrates, the (0001) c plane is used to manufacture nitride devices, which leads to mostly unprofitable polarization effects. Recently, however, relatively thick c-oriented GaN substrates have been reported (e.g., [11]). Then proper slicing may be used to produce nonpolar or semipolar native GaN substrates [2, 5]. Desired emission of green radiation requires in nitride devices relatively high Indium contents. In nonpolar LEDs, however, an increase in an Indium content results in degraded crystal quality because of required low growth temperatures [2]. Efficiency of some similar semipolar LEDs also decreases for longer wavelengths, but to much less extent. Therefore, the semipolar substrate orientation is considered (e.g., [6]) in our simulation. Quality of layers grown on semipolar substrates has been found to be similar to that of layers grown on nonpolar substrates [7]. However, highquality and high Indium content smooth growth planes may Fig. 3 Band model of the 3-nm In0.3Ga0.7N/GaN QW presenting wave functions of trapped carriers be then obtained with low values of the MillerBravais indices [7]. Besides, also partial reduction of polarization effects may be then obtained. Typical InGaN/GaN LEDs grown on the c-oriented substrate exhibit unprofitable strong polarization effects because both spontaneous and piezoelectric polarizations are increased with an increase in the Indium content in InGaN. They create serious problems especially in highly strained InGaN/GaN QWs with high Indium content designed to emit green radiation [1, 2]. However, it is shown in Sect. 4 that polarization effects are excluded not only for the total polarization reduced to zero, but also for equal polarizations in each layer of LED structure. Anyway, their unprofitable impact on LEDs operation may be at least partly reduced with the aid of a careful technology. 2 Polarization effects in the semi-polar crystal structure A typical nitride LED structure is composed of the following layer sequence: n-type substrate, QW barrier, QW, QW barrier, electron-blocking layer, and p-type layer. Let us consider its manufacturing on a semipolar substrate. The local coordinate 0xyz system is correlated with the substrate crystalline structure (its z axis is directed along the c crystalline axissee Fig. 2), whereas the analogous global 0x y z system has the z axis at the inclination angle with respect to the z axis and x axis along the x axis. The depths of the InGaN/GaN QW within the conduction and valence bands are determined using approach of Sharma and Towe [3] and assuming its ratio (band offset ratio) equal to 1.48. Let us consider the semipolar wurtzite structure shown in Fig. 2. Following the approach reported by Romanov et al. [7], misfit parameters along the x and y axes may be aS aL aScS (aLcS)2 cos2 + (aScL)2 sin2 (aLcS)2 cos2 + (aScL)2 sin2 where aS and cS are hexagonal parameters of the substrate material whereas aL and cL are analogous parameters of the layer material. For the layer thickness below, it (...truncated)