Influence of Outer Oxide Charges on the Electrostatics of Metal-Insulator-Semiconductor Tunnel Diode
Authors: Chen Kung-Chu , Lin Kuan-Wun , Hwu Jenn-Gwo 
Published: September 2023

Metal-Insulator-Semiconductor Tunnel Diode (MISTD) has an ultra-thin oxide with thickness less than 3.5 nm. When a MISTD is biased higher than a critical voltage V
C, the device will be driven into the deep depletion region [1]. In this biasing condition, the electrostatics of the device will deviate from the behavior of traditional metal-oxide-semiconductor capacitors with thick oxide [1]. Thus, finding out the critical voltage V
C is important to predict the electrostatics of a MISTD. In this work, we found that there is a systematic deviation of V
C between the theoretical and the experimental values. A model considering the oxide-charge-induced lateral coupling (OCILC) is suggested as a possible mechanism leading to the deviation. With adding effective positive oxide charges of Q
eff/q = 2.4-2.6×1011 cm-2, the calculated V
C can fit well with the experimental observations.

Figs. 1(a) and (b) are the band diagrams of MISTD biased at V
TD < V
C and V
TD > V
C, respectively, where V
TD is the positive voltage applied on the metal. When V
TD < V
C, the generated electrons flow -J
gen,bulk are able to follow the increase in the inversion charges and leakage current -J
tunnel. In this situation, most of the applied V
TD drops on the oxide, and the surface band bending of the silicon ψ
s keeps around its initial value ψ
0, as shown in Fig. 1(a). In contrast, at V
TD > V
C, the generated electrons in original depletion region cannot follow the increase of the tunneling current. To keep the balancing of -J
tunnel = -J
gen,bulk, a large portion of V
TD drops on the silicon and leads to an intense increase in ψ
s, as shown in Fig. 1(b). The MISTD will operate under a significant non-equilibrium region under this bias condition. The balancing of -J
tunnel = -J
gen,bulk is finely discussed in [1].

Ten MISTDs with distinct oxide thicknesses ranging from 23.7 to 34.4 Å were fabricated to extract V
C. The device structure is shown in Fig. 2(a). The shape of the device is a circle with a diameter of 170 µm. From the measured high-frequency capacitance-voltage (HFCV) relations shown in Fig. 2(a), one can observe a flat region before a critical voltage and a quick decrease after the critical voltage. One can further extract surface band bending ψ
s by HFCV [2]. The extracted q∆ψ/kT = q(ψ
s-ψ
0)/kT is plotted in Fig. 2(b), where ∆ψ is the difference between ψ
s and ψ
0. As the definition in [1], we extract V
C at q∆ψ/kT = 3. The extract V
C v.s. t
ox is shown in Fig. 3 as solid symbols. At the same time, theoretical V
C from the modeling proposed in [1] is also attached as a solid line. From Fig. 3, we observed a significant difference in V
C between the modeling and the experimental.

It is suggested that the OCILC causes the deviation of V
C. The mechanism of OCILC is plotted in Fig. 4(a). The positive oxide charges outside the electrode will attract electrons at the silicon surface and form a lateral coupling channel. The potential applied on the electrode will laterally transport through the channel and collect the generated electrons from the lateral region. Finally, the balancing of electrons will become -J
tunnel = -J
gen,bulk-J
gen,lateral, as shown in Fig. 4(b). Because of the extra supplement of electrons (-J
gen,lateral), the MISTD can hold the quasi-equilibrium status to a higher voltage, and the V
C increase. An improved model considering the effect of OCILC is proposed. The calculated result is plotted in Fig. 5. One can observe V
C increase with Q
eff. When positive Q
eff/q is around 2.4-2.6×1011 cm-2, the calculated V
C is close to the V
C extract from the experimental.

In conclusion, we suggested that the oxide charges outside the electrode play an important role in the electrostatics of MISTD. The mechanism of OCILC is proposed to explain the impact. A model considering OCILC is developed to calculate V
C and the results fit well with the experimental results.

This work was supported by the Ministry of Science and Technology of Taiwan, ROC, under Contract No. MOST 111-2221-E-192-MY3 and the National Science and Technology Council of Taiwan, ROC, under Contract No. NSTC 111-2622-8-002-001.

[1] K. W. Lin, K. C. Chen and J. G. Hwu, An Analytical Model for the Electrostatics of Reverse-Biased Al/SiO₂/Si(p) MOS Capacitors With Tunneling Oxide, IEEE Trans. Electron Devices,
69, 1972, (2022)

[2] E. H. Nicollian and J. R. Brews, MOS (Metal Oxide Semiconductor)
Physics and Technology (Wiley, Hoboken) (1982)

Figure 1