The electron direct tunneling from the accumulated poly-silicon surface down to the underlying silicon was measured versus negatively biased gate voltage with the source, drain, and substrate all tied to the ground. It can be seen in Fig. 3.4 that the resulting substrate hole current, which essentially is equal to the electron gate-to-substrate tunneling current, increases with decreasing a. Such dependency reflects the increasing magnitude of lateral compressive stress in the poly-silicon. The confirmative evidence of this origin is that for a given gate-to-STI spacing, the corner stress and channel stress both are comparable, and since the tunnel oxide is rather thin, the lateral compressive stress at the surface of the poly-silicon is reasonably close to that of the underlying silicon. In contrast, the simultaneously measured source/drain or edge direct tunneling (EDT) current decreases with decreasing a, as shown in Fig.
3.5 and Fig. 3.6. To determine the underlying gate-to-source/drain extension overlap length where the EDT prevails, the existing edge direct tunneling models [1], [15], [17] on the basis of the triangular potential approximation [7] (Fig. 3.6) can readily apply with some slight modifications such as incorporating stress dependencies of the subbands in the accumulated poly-silicon surface. First of all, the oxide field Eox at the gate edge is determined through the following expression:
DE
‐ 15 ‐
whereV is the applied gate voltage,DG V the flat band voltage, andFB V the oxide ox potential drop, tox is the gate oxide thickness, and Vpoly and VDE are the potential drops in the n+ poly-silicon and source/drain extension region, respectively. The accumulated electrons mainly populate in the first subband E1 due to the lowest quantized energy dominating. Then, relating the sheet charge density to the number of occupied subband states can establish the charge conservation relationship
1 2
( fn ) md ox ox
q E E η ε E Q
− π = =
h (3.2)
where Efn is the quasi-Fermi level in n+ poly-gate, η is the degeneracy factor, and Q is the available charge for tunnel process. The corresponding stress dependency of the quantized energy is well defined in the literature [9], [15].
( )( ) ( )( ) here. With the aforementioned parameters as input, the lowest subband level with respect to the Fermi level can be quantified. Employing the lowest subband approximation to the accumulated n+ poly-gate and the deep depletion approximation to the source/drain extension region, as drawn in Fig. 3.6, the following expressions can, therefore, be derived:
2
2 2
where NDE is the doping concentration of the source/drain extension. Here, the quantization effective masses mz = 0.98 m0 and md = 0.19m0, and η = 2 were adopted to approximate the band structure for 110 oriented poly-silicon grain [12]. Then, it is a straightforward task to calculate the WKB tunneling probability, taking into account the corrections for reflections from the potential discontinuities [12]. Here, the electron effective mass in the oxide for the Franz-type dispersion relationship was used with mox = 0.53 m0. The SiO2 /Si interface barrier height in the absence of stress is 3.15 eV. Consequently, the edge electron direct tunneling current density can be calculated as a function of the stress σ
( ) ( )
where W is the channel width, and LTN is the gate-to source/drain-extension overlap length. The tunneling lifetime in this equation can be connected with the transmission probability T : τ π1 = h
(
T1( ) ( )
σ E1 σ)
.
Then, with known process parameters and published deformation potential constants [20] as input, the measured EDT was reproduced well, as displayed in Fig.
3.5. Electron tunneling onto the forbidden silicon bandgap occurs in −0.1 V < VG < 0 V; however, an appreciable gate current was measured there. This indicates the existence of the oxide traps or interface states. Only at a more negatively biased gate voltage where the EDT dominates can the effect of the traps be alleviated. In addition, it was found experimentally that the gate edge direct tunneling current is several orders of magnitude larger than the gate-to-substrate current, and hence is dominant
‐ 17 ‐
spans a range of 6.1, 6.0, 5.7, and 5.0 nm for a of 10, 2.4, 0.495, and 0.21 μm, respectively, as demonstrated in Fig. 3.7. The LTN values are found to be comparable with those in the literature [1], [14], [17]. The shift of around 1.1 nm, caused by retarded doping lateral diffusion for stress change from 0 to −320 MPa, is reasonable with respect to the process simulation [6]. In the cited work [6], a device/process-coupled simulation was carried out to produce the lateral doping profile from the source through the channel to the drain, with and without the strain dependencies.
Chapter 4
Gate Induced Drain Leakage Current Simulated under STI-Induced Stress
Section 4.1 Introduction
This drain leakage current is caused by the gate-induced high electric field in the gate-to-drain overlap region. Many researchers have attributed the leakage current to the band-to-band tunneling occurring in the overlap region and named the phenomenon gate-induced drain leakage current (GIDL). The extracted oxide thickness, potential, and doping profiles in the gate-to-drain overlap region are found to play important roles in the GIDL current. The GIDL and its degradation have restricted the scaling of oxide thickness and power supply voltage. In addition, the band-to-band tunneling induced hot-electron injection is proposed to be a programming method for flash memory cells [30] and an erase operation for EEPROM memory cells [31].
Some band-to-band tunneling current models for the GIDL have been proposed [23], [32-35]. These models show well-accepted physical dependence. However, the model in [23] and [32] ignores two physical parameters dependence. The most noticeable parameter is the lateral electrical field near the drain-to-gate overlap region.
The other parameter that should be considered is the dependence of the band bending on the drain doping concentration. The model in [34] considers the built-in lateral field caused by the lateral gradient of the drain doping concentration, but it neglects the contribution of the external drain voltage to the lateral field. The model in [35]
‐ 19 ‐
and lateral field, but the model is a complex integral-form equation. However, the mechanical stress induced by shallow trench isolation (STI) influences the electrical characteristics of the device, including the EDT and GIDL tunneling currents in Fig.
4.1.