Figure 1 Shows the cross-sectional view of an AlGaN/ GaN HEMT. The layer sequence is, from top to bottom, metal/n-AlGaN/undoped-AlGaN/undoped-GaN with a 2- DEG formed at the unintentionally doped (UID)-AlGaN/ GaN interface.

As established above, the AlGaN/GaN HEMTs simulated shows only the first two subbands occupied at T = 300 K. Thus, the total density of the 2-DEG accumulated in the channel can be approximately expressed as: (Equation (1), see the bottom of this page) where K_B, ħ, and E_F are the Boltzmann constant, Planck constant and the Fermi energy constant respectively.

Under total depletion approximation, the density of charge depleted in the AlGaN layer is obtained using the assumption of total depletion by solving Poisson’s equation [11,12]:

where q is the electron charge, ε and d = d_d + d_i are the permittivity and the total thickness of the AlGaN layer, respectively, E_F is the Fermi level with respect to the bottom of the conduction band in the GaN layer, and V_th is the threshold voltage of the HEMT given by:

where is the effective barrier height of the Schottky gate, ∆E_c is the discontinuity of the conduction band at the interface between the UID-AlGaN and the GaN layers. is the doping concentration in n-AlGaN layer, and σ is the polarization induced charge density at the interface. Equations (1) and (2) have to be solved simultaneously and the interfacial sheet electron concentration in the strong inversion regime is given by [11]:

where E₁ and E₂ are the subband energies.

Calculations were carried out in order to study the impact of gate voltage on the 2-DEG density. We wanted to show the influence of different Al composition and the barrier thickness on the characteristic N_s = f(V_gs). Figure 2 shows the variation of 2-DEG sheet density versus the gate voltage V_gs calculated for different AlGaN layer thickness and reveals that: 1) when the thickness d_d of the AlGaN donor layer increase, the concentration of 2-DEG increases with V_gs. 2) The threshold voltage of the transistor shifts toward increasingly in absolute value with increased d_d. 3) the increase of the electron density is due to the increased effect of the piezoelectric and spontaneous polarization. 4) the slope of the N_s-V_gs plots corresponds to the gate capacitance of the structure, which is linked directly to the separation between the gate and 2-DEG, more precisely to the thickness d_d, the latter is growing more capacities decreases and beyond the threshold voltage decreases it induces the reduction in the gate capacity, this is demonstrated for d_d = 20 nm, the slope is 2.1 × 10¹² cm⁻²∙V⁻¹, while that for d_d = 26 nm, the slope is 1.4 × 10¹² cm⁻²∙V⁻¹. This shows that high values of the barrier width are favorable to achieving significant electronic density and to obtain low gate capacitance values. The calculations were carried out by using the parameters: a composition of aluminum equal

to 0.23, doping density order to 10¹⁸ cm⁻³, and a spacer width 30 Å.

Figure 3 shows the variation of 2-DEG density Ns versus the gate voltage V_gs calculated for different Al composition and reveals that: 1) when the Al mole fractions in AlGaN/GaN HEMTs increase the electron density increases as well for the threshold voltage which exhibits shifts toward increasingly in absolute value as a function Al composition. 2) The variation in the Al mole fractions shown will also vary considerably the threshold voltage (−4 to −6 V), however, this variation does not influence on the slope of the N_s-V_gs characteristics.

The Current-Voltage is related to the density variation for the 2DEG density under the influence of a gatesource voltage applied of the component. In fact, any action on the gate voltage V_gs has the effect to modify the electronic population of the channel which varies the electrons density n_s. Several authors have developed models in order to account for the I_ds-V_ds characteristics electrical behavior of HEMTs [13,14]. First, we started to introduce conventional expression of the drain-source current I_ds according to the voltage drain-source V_ds in order to determine ideal characteristics I_ds-V_ds for different values of V_gs. The current I_ds is proportional to the density of electrons in the channel n_s which is expressed as follows [11,12]:

where Z is the channel width and µ is the mobility of carriers. In deriving I_ds, we have neglected the diffusion current and the dependence of μ as a function of the built-in electric field. The drain-source current is obtained by integrating I_ds along the channel. The boundary conditions are: V(x = 0) = R_s∙I_ds and V(x = L) = V_ds − (R_s + R_d)∙I_ds where R_s and R_d are the source and drain contact resistances and V_ds is the bias voltage applied to the drain with respect to the source. In the linear regime, the voltage drops across source and drain resistance accesses can be neglected. Therefore, the drain-source current is expressed according to [12]:

In saturation regime, the channel current tends to saturate and ceases to increase with the drain-source voltage. It is straight forward to establish at the drain gate (x = L):

Here, F_s represents the critical electric field for velocity saturation. According to Equations (4) and (5), V_dsat as well as I_dsat are given by:

and

We simulate the I_ds-V_ds characteristics by a Matlab program using the above relations for several values of V_gs. Figure 4" target="_self"> Figure 4 shows the Current-Voltage characteristics for different gate voltage V_gs ranging from −4 V to 0 V. These characteristics correspond to an ideal HEMT structure, i.e. without considering the anomalies may be present in this type of component. It appears clearly that the saturated drain current increases when increasing gate voltage.

However, the drain current increase is influenced by gate lengeth. An example is given to 300 K for the V_gs = 0 V are shown in Figure 5. As can be seen the variation of saturated drain-current as a function of drain voltage at different gate lengths. The plots reveal enhanced drain current in decreasing gate lengths. It should be, however, noted that the use of short gate lengths seem to be an appropriate way to achieve improved electron transport in AlGaN-related HEMTs.

Experimental studies have been reported on the gate length effect in output characteristics I-V [15]. These studies demonstrated that reducing the gate length resulting in a higher drain current. This is coherent because the drain current of HEMTs is directly proportional to the drift velocity. When the gate length decreases the effects of excess speed are more pronounced induced an increase of the drift velocity in order to optimize the output current in the kind of transistors.

Kink effect is a detrimental phenomenon for the FET performance. It leads to an output-conductance increase, a transconductance decrease, a drain current drop and a dispersion between DC and RF characteristics. Many studies of the kink effect have been reported [16,17], but due to its complex behaviour, the origin of this effect is still a subject of controversy. Theoretically, the kink effect was coarsely described in various kind of FETs, like Si MOSFETs, GaAs MESFETs and AlGaN/GaN high electron mobility transistors (HEMT’s) [18,19]. Many research experiences are directed toward understanding and eliminating these parasitic effects and minimizing the trapping effects [20,21]. In this part, we will report the parasitic effects, observed in output characteristics I_ds-V_ds namely kink effect of GaN-based HEMT. Some authors have performed two-dimensional (2-D) numerical simulations. However, there are only few analytical study which explained the origin of this effect. Consequently, for further improvement of AlGaN/GaN HEMTs it is crucial to investigate the impact of the kink effect on transport properties of the AlGaN/GaN HEMT’s. Many studies have correlated kink effect with defects on AlGaN/GaN transistors [22]. For this reason we developed an analytical current-voltage model for AlGaN/GaN power HEMT that incorporates the expression of concentration. Assuming that only a single deep trap is present in the host lattice with a concentration N_T and based on the balance equilibrium, the proportion of ionized traps is expressed as:

where N_D represents the density of residual donor impurities, (E_c − E_T) is the binding energy of the trap, N_c is the density of states in the conduction-band and T is the local lattice temperature. By taking into account the ionized electron traps, the electron sheet concentration in the channel will be given by the extended relationship:

As a direct consequence, activated electrons from deep traps can participate noticeably to the conductive channel current. For V_ds larger than the pre-kink bias, the drainsource voltage and the drain current should have both the following forms:

and

By introducing the modified term using Equation (9), we achieve the new characteristics I_ds-V_ds (Figure 6) showing the apparition of a kink effect at a certain drain-voltage called kink voltage (V_kink).

This effect appears for high drain-to-source voltage V_ds increasingly in order to pinch off the channel. The results are shown in Figure 6. We can easy notice the variation of the kink current ∆I_kink simulated as a function of defects concentration for different gate-to-source voltages (V_gs).

These results are in a good agreement with this approach which confirms the influence of deep defects, present in AlGaN/GaN HEMT transistors. However, the drain-source current continues to increase even in the saturation region for such V_gs values which tends towards zero and for decreasingly high values of concentration traps.

The result is illustrate in the tridimensional plot in Figure 7, in order to represent ΔI_kink(N_T, V_gs). This last plot represents the value of kink current (ΔI_kink) increases as the gate voltage tends to 0 V and the defects concentration decreases.