Fig. 1.16 – 1x1µm2 AFM picture of GaN surface grown at 930˚C.
at the dislocation core where an atom at the surface is missing. We see easily in the AFM picture in figure 1.16 that lines of several surface depressions at the surface can be formed on some steps without affecting their form.
1.4 | III-Nitrides polarization
This section will be dedicated to an important phenomenon which is the polarization in III-N materials. It is actually a combination of two components : the spontaneous polarization and the piezoelectric one. The polarization in III-N materials is a lot stronger than in other semiconductors, and this opened the power and high frequency field for devices application. This polarisation directly allows us to make high electron mobility transistors without any doping in contrast to most of III-V materials.
1.4.1 | Spontaneous polarization
The bonds between metal and nitrogen atoms are covalent and partially ionic. Indeed nitrogen atoms are more electronegative than that of gallium, aluminum or indium. Thus a dipole moment is created, directed towards the metal atom along the bond. In a perfect tetrahedron, the four dipole moments present on the four bonds framing each atom would be nullified. However, the hexagonal crystal structure induces a deformation of the tetrahedron. This simply involves the fact that the barycentre of positive charge does not coincide with that of negative charges. This therefore results in a so-called spontaneous polarization PSP independent of the stress state of the material. Bonds and global polarization of III-N materials are shown in figure 1.17.
Values are subject to debate, but it is nevertheless accepted that for GaN, AlN and InN binary, spontaneous polarizations have respective values : -0.034 C/m2, -0.090 C/m2and -0.042 C/m2.[35]
Direction of polarization is defined from N to Ga (charge - to charge +). Thus, when we are in gallium face we can easily see that the spontaneous polarization is negative because at the opposite direction
Fig. 1.17 – Dipolar moment and spontaneous polarization of III-N materials.
of growth direction. On the other hand the polarization is positive in nitrogen face.
1.4.2 | Piezoelectric polarization
There is another component to the total polarization of III-N materials, which is the piezoelectric polarization PPE. It starts when the layer deposited on the substrate is strained, that is to say in tension or compression. If the layer is under tension (case of an AlGaN on thick relaxed GaN, for instance), then the piezoelectric polarization has the same sign as the spontaneous polarization when growing in the c-direction with gallium face. The two polarization components are added together. By contrast, they have opposite signs if it is in the case of a compression layer on GaN, and of course one subtracts from the other. So we define in both cases the total polarizationPT OT =PSP +PP E which is the algebraic sum of the spontaneous and the piezoelectric polarization. Along the z axis (parallel and oriented in the same direction as the growth) and considering that the III-N layer is subjected to an isotropic biaxial stress in the plane (0001), the expression of the piezoelectric polarization is as following.[36]
PP E =e33.z+e31·(x+y) (1.7) x=y = a−aa 0
0 corresponds to deformations in the plane. eij are elements of the piezoelectric tensor in C/m2 unity. a, c are the two lattice parameters of the materials epitaxied and a0 and c0 are the lattice parameter of the same material when it is relaxed.
In the case where the stresses are isotropic in the planes of the epitaxial layers, we can connect the deformation in z with the x and y ones.[36]
z =−2C13
C33
·x (1.8)
C13 and C33 are the elastic constants of the material for which we are studying the deformation. From (1.7) and (1.8) we can deduce : [36]
1.4. III-NITRIDES POLARIZATION 21
Fig. 1.18 – Total polarization orientation in AlGaN/GaN heterostructure.
PP E = 2a−a0
1.4.3 | Two-dimensional electron gas generation in III-nitrides
The principle of operation of an HEMT is based on the presence of a 2D electron gas in the GaN confined at the interface between a GaN pseudosubstrate for example and the barrier layer made of a ternary alloy which is typically AlGaN or InAlN (cf. figure 1.18. This gas is characterized by a high electron density of about 1013 cm-2 for an AlGaN/GaN structure, which is two to five times higher compared to a material such as GaAs. The electron mobilities are at 300K around 2000 cm2/V.s for AlGaN/GaN.
The electron mobility of the bulk GaN is about 900 cm2/V.s. If it increases at the interface with the barrier layer, this is because there are fewer interactions of the electrons with the crystal network thanks to the confinement of the latter within the 2D gas.
The two-dimensional electron gas is formed in the following manner. For example the polarization is determined at the interface of AlGaN/GaN stack by the following equation : [36]
∆P =Pint=PSP,AlGaN +PP E,AlGaN −PSP,GaN −PP E,GaN (1.10) This resultant polarization is nothing other than a virtual surface charge density fixed at the interface of the stack. Note that if this is the the case of a relaxed thick GaN pseudosubstrate :PP E,GaN = 0.
These positive fixed charges in the case of an AlGaN / GaN heterostructure, will then attract electrons from GaN bulk and surface. We can calculate the concentration with the following equation : [36]
Ns = −∆P
e (1.11)
e is the charge of an electron (1,602.1019C). These electrons are mainly derived from the material surface states.
On the other hand the contacting of the two semiconductors causes a discontinuity in their valence and conduction bands. Furthermore, the fact that an electric field is resulting from the polarization of the
Fig. 1.19 – Valence and conduction band versus the depth of the material. Highlighting of the potential well.[37]
Fig. 1.20 – III-N HEMT heterostructure
layers, the potential well formed by the contact between the AlGaN and GaN tends to have a triangular shape in which the quantized energy levels take different values from that a classical potential well having a rectangular shape. The electrons attracted to the interface are thus trapped and confined in the potential well, thus the GaN layer. The quantum well formed at the interface is illustrated in figure 1.19.