4.2.1 Verification of the Interface State Density Distribution Uniformity

The uniformity of the initial interface trap distribution can be verified using the dependence of the maximum value of the charge pumping current (I_cp,max) versus the nominal gate electrode length (L_g). A linear relationship between I_cp,max and L_g would suggest an absence of disparity between the interface state density near the source-drain region and the center of the channel. In this case the assumption that the pre-stressed N_it profiles are uniform along the channel is adequate [175]. Extrapolation to I_cp,max = 0 reveals the difference (ΔL) between the nominal (L_g) and effective (L_eff) channel lengths, which contributes to the CP current [173]

A limited number of works devoted to N_it(x) extraction techniques from the CP current, where this dependence has been verified, is available [175,177,164]. However, from the physical viewpoint, it is difficult to evaluate the legitimacy of the obtained findings in the last two papers. In fact, in [177] only two gate lengths are used with a limited L_g spread, while a suspiciously linear behavior is presented in [164].This suggests that this issue demands a more detailed analysis.

**Figure 4.5:** Local threshold V_th(x) and flatband V_fb(x) voltage profiles of a pre-stressed device calculated using different approaches.

To determine the effective length L_eff, a careful calculation of local flatband V_fb(x) and threshold V_th(x) voltage distributions as crucial quantities controlling the matter is performed. Due to the symmetry of the source and drain for the fresh device, results only for the drain half of the device are presented, confirmed in [178]. For an unstressed transistor V_th(x) and V_fb(x) can be obtained with the method described in Section 4.1 employing the device simulator MiniMOS-NT. The carrier distribution required for the local threshold and flatband voltage calculation was estimated to be 2× 0¹³cm^-3 and 8×10¹⁴cm^-3 for the simulation. The validity of the obtained curves has been verified using the Monte-Carlo device simulator MONJU. Figure 4.5 shows a good agreement between the results. Note that in the low voltage region the agreement degrades due to the stochastic nature of the Monte-Carlo approach which can not provide enough precision in this area. As stated in [173,175], the effective channel length for a constant base-level charge pumping technique is defined as L_eff = 2|l - L_c| for V_gh ⩾ V_th(L_c), where l is the solution of the equation V_fb(l) = V_gl and L_c is the center point of the channel specified by the device geometry.

**Figure 4.6:** (a) Maximum value of the charge pumping current for different gate electrode lengths of the fresh 5V n-type MOSFET. (b) Charge pumping current of an undamaged device. Interface and border trap components are revealed.
(a) (b)

The simulation yields an effective channel length of 0.504um while V_gl was held at -5V for the fresh device. Figure 4.6a depicts I_cp,max plotted vs. L_g and a simple linear extrapolation of CP data gives L_eff = 0.67um, i.e. the position is practically on the drain contact. Such an experimental value of the effective channel length is extremely dubious and supports the idea of a non-uniform N_it profile. Let us emphasize that in the case of a homogeneous N_it distribution one may obtain a V_th(x) profile directly from the charge pumping current I_cp(V_gh) for the undamaged device employing the method proposed in [175,178]. According to this approach

A comparison between this "experimental" and the simulated threshold voltage profiles V_th(x) can confirm the interface state density non-uniformity and is shown in Figure 4.5. However, such a wide discrepancy in the results can not be induced by the difference in initial N_it because the V_th shift corresponds to an interface trap density of ~10¹²cm^-2, i.e. for a heavily stressed device. This anomalous offset has a simple explanation: the method based on (4.5) does not work properly due to the border trap contribution to the CP current (see Section 1.3). As it was explained in detail in [181], a presence of trapped border charges Q_bt requires special attention to distinguish between contributions to I_cp induced by border (I_cp,bt(V_gh)) and interface states I_cp,it(V_gh))

The presence of I_cp,bt(V_gh) results in a spurious determination of I_cp,max and L_eff and, as a consequence, to an erroneous value for the uniform N_it profile. Thus, an additional separation procedure of CP current components must be performed. This separation of I_cp,bt(V_gh) from the total CP current relies on the following features of the employed charge pumping technique: at V_gh ⩾ V_th(L_c) the interface state density can not increase I_cp because the active measurement area has already reached L_eff. That is, I_cp,it(V_th(L_c)) = const. An explicitly revealed plateau (see Figure 4.6b) corresponds to the saturation of an interface trap induced dose of the charge pumping current and the absence of the Q_bt contribution. This means, for V_gh⩾ V_th(L_c) the border trap contribution to the CP signal is

This finding is supported by the interface state dynamics based on the Shockley-Read-Hall theory [182] (see Figure 4.6b). The experimental data in Figure 4.6a was processed according to the described scheme.

Unfortunately, the method suggested above is not appropriate for the varying base-level technique because a continuous increase of the active measurement area occurs, when this method is implemented. Moreover, in the case of CP measurements with a lower gate pulse frequency (a few kHz [181]) it is not possible to expose the saturation plateau and a more complicated extraction scheme of border trap contributions (as proposed in [34]) must be employed.