Research of shot noise based on realistic nano-MOSFETs Open Access

With the device scaling down, the driving capability and switching speed is increased, and the noise is also increased.^1–3 As the channel length decreased, the noise model is no longer applicable in long channel MOSFET, and the dominant noise changes from thermal noise to shot noise. The experimental and simulation results have proved the existence of shot noise in nano-MOSFET,^4–7 and the noise were suppressed by Fermi and Coulomb.^8–11 

Shot noise is the non-equilibrium noise of charge quantization. At low frequencies, the noise power spectrum can be expressed as S=γ2qI, Where I is the dc current, q is the electron charge, and γ is the so-called shot noise suppression factor. If there is no interaction between carriers, the noise is poisson, then γ=1. On the contrary, the presence of repulsive or attractive correlations yields γ < 1 or γ > 1, which correspond to suppressed or enhanced shot noise, respectively.¹² 

Shot noise is suppressed in nano-MOSFET, and the noise is closely associated with the structure parameters and working parameters of the device. At present, there is no in-depth study on the shot noise suppression of nano MOSFET. Although the research mentioned the theory and studied about shot noise suppression with mesoscopic conductor in nano-MOSFET, but it neither do in-depth research, nor give shot noise expression;⁶ Although the literature¹ gave an expression, but it did not consider the suppression of Fermi and Coulomb. There are also research give basic conclusions only through experiment or simulation.^5,8 Excess noise limits the low-power and low-voltage of device, it should be controlled. Shot noise is the main component of excess noise in nano-MOSFET, suppression of shot noise can effectively reduce the excess noise due to the reduction of the size of MOSFET. This requires a clear relationship between the shot noise and dispersion parameters of device.

In this paper, firstly, shot noise test system was established, and the experimental results shown that the shot noise were suppressed by the Fermi and Coulomb interaction in nano MOSFET. Then, shot noise model were established. At the same time, the variation of shot noise under different suppression were discussed, while the shot noise were varied under different suppression (mainly the bias voltage, temperature and the doping concentration). Finally, noise characteristics were compared with experimental results.

Shot noise test system must meet the following requirements:

1. Low temperatures. Thermal noise has a great influence on the shot noise test, thus it is necessary to use cryogenic devices in order to suppress the device thermal noise.

2. Test system with high gain and low background noise. Shot noise is a weak signal, in order to capture the shot noise signals better, the test system must have a large enough gain and a very low background noise, therefore requires a high magnification amplification system.

3. Effective removal of low frequency noise. For MOSFET devices, 1/f noise is the main component in low frequencies. In shot noise test, it is important to remove the influence of low-frequency 1/f noise on shot noise.

According to the conditions for the test system of shot noise, a low temperature test system was established, being composed chiefly of low-temperature device, double shielding structure, bias device, a low noise amplifier, data acquisition, analysis software and hardware, and so on. Shot noise test flow diagram is designed as shown in Figure 1.

Select 90nm single-gate MOSFET device, its threshold voltage is 0.7V. Measure the shot noise power spectrum(S_I) of device at low temperatures. First, the device is set to work in the sub threshold region, means that the gate voltage(V_GS) is 0.25V. The variation of shot noise power spectrum with source-drain current was shown in Table I (S_F in Table I is full shot noise power spectral density). Then, the gate voltage V_GS is set to 1.2V, and the device is work in the linear region and saturation region. As shown in Table II, the shot noise power spectrum changed with source-drain current. The test bandwidth of the system is 1Hz-300KHz. Test sampling rate is 1MHz. Since the power spectrum data will be affected by 1/f noise in the low frequency range, the selected frequency range would be 250KHz to 300KHz. The calculated average of noise power spectrum within the frequency range make the test result more accurate.

As seen from experimental values in the table, when the source-drain voltage is small, there are no consistent increase trend in the shot noise power spectral density with the current; when the source-drain voltage increases, we can see shot noise clearly, but lower than full shot noise, which means shot noise were suppressed by Fermi and Coulomb.

The transport processes in nano-MOSFET are dominated by quasi-ballistic or ballistic transports. Its noise is mainly shot noise. The expression for shot noise is:

Where S_B is the ballistic noise without considering the effect of Fermi and Coulomb interaction on shot noise. For the source and drain doped shot noise in ballistic nano-MOSFET, the degeneration of carrier cause significant suppression to shot noise, so a shot noise suppression factor γ was introduced in ballistic transport nanometer MOSFET.¹⁰ 

Where v is the velocity in carrier transport direction; f_S is the Fermi Dirac occupation factors; Gate capacitance(C_G) is $𝐶𝑄𝑆=𝑞2⟨⟨∂𝑓𝑆/∂𝐸𝐹𝑆⟩⟩,$$⟨⟨h⟩⟩=2∫0∞dE⋅N3Dh$⁠, h is function of kinetic energy in trasnsport direction E.¹⁰ 

Non-degenerate conditions, ballistic transport current is:¹³ 

Where Q_B= BQ(0) is the charge density per unit area at the top of barrier of ballistic transport in nano-MOSFET, Q(0) = C_ox(V_GS−V_th) is the charge density in the inversion layer at the top of barrier, C_ox is oxide capacitance per unit area, V_th is threshold voltage, υ_inj is the injection velocity of contact terminal,^13–17 the intrinsic ballisticity is:

Where ε_D = (kT/q)/L_K is the average electrical field of kT-layer. L_K = L[kT/(qV_DS)]^2/3; r is the backscattering coefficient; μ_n is $μ0(1+θ(VGS−Vth))(1+μ0vSεD)$⁠, the saturated velocity v_S = 1×10⁵m/s, the low field mobility $μ0=120cm2/V⋅S,θ$ is a fitting parameter, to describe the effect of strong electric field perpendicular to the channel on mobility.^13–17 

Deduced from the above formula, the shot noise of realistic nano-MOSFET is

Where f_S(1−f_S) = f_S−$f2S$ is the role of Fermi. When f_S << 1, the small amount of high-end can be ignored. Thus formula (5) is mainly expressed the shot noise under the action of Coulomb effect, which can be expressed as:

Where $(1−v¯SCQSυ(CG+CQS))2$ is the role of Coulomb. When $(1−v¯SCQSυ(CG+CQS))2=1$⁠, the noise under the Fermi interaction can be expressed as:

Under the interaction of the Fermi, the Coulomb and the combination of the both co-existence, the change of shot noise in actual nano-MOSFET with bias voltage, temperature and doping concentration are studied separately. The channel length of the single-gate MOSFET chosen in this paper was 90nm.

The change of noise in actual nano-MOSFET with bias voltage were researched under the interaction of the Fermi function, the Coulomb interaction and the both co-existence, as shown in Figure 2. Shot noise increases with voltage. With the source-drain voltage increases, the channel carriers which suffered inelastic scattering was reduced, and then the role of Coulomb decreased, the Coulomb suppression factor increased. Meanwhile, with the source-drain voltage increase, the height of the barrier reduce, and the reduction of barrier height will diminish the role of Fermi, Fermi suppression factor increases.^18–21 Therefore, Shot noise value(S_S) is smaller than the noise value of Fermi (S_F) and Coulomb(S_C) effects separately.

Experimental results showed that shot noise increases with gate voltage in actual nano- MOSFET,⁸ and we got the same conclusion, as shown in Figure 3. Each shot noise increases with the gate voltage in figure, and S_S is smaller than S_F and S_C separately. This is because the barrier height decreases with gate voltage increased, the number of the channel carriers increase, so that the number of carriers suffered inelastic scattering increased, so as to enhance the Coulomb interaction, leading shot noise suppression, while improving the carrier degeneracy, and then enhance Fermi suppression of shot noise.^18,22,23

For low-doped devices, there is less ionized impurities in the channel, thus scattering mode is mainly based on acoustic wave scattering. As the temperature decreases, the acoustic wave scattering reduce, so there is mainly shot noise in device, and shot noise suppression will be enhanced with temperature being increased, that is the shot noise will decrease with temperature increases, this feature is confirmed in this article. The variation of shot noise with temperature in actual nano-MOSFET is shown in Figure 4. As shown in Figure 4, the shot noise decreases with temperature increases, which is consistent with the simulate conclusions.⁵ As the temperature increases, the average number of phonons increases, the number of inelastic scattering increases, and shot noise suppression enhances.¹⁸ Therefore, S_S is smaller than S_F and S_C separately.

The variation of shot noise in actual nano-MOSFET with doping concentration was shown in Figure 5. With the source and drain doping concentration decreases, each shot noise increases, and S_S is smaller than S_F and S_C separately. The higher the concentration of the source region, the stronger the shot noise suppression. Improve the doping concentration may increase the carrier degeneracy, thereby increasing the Pauli exclusion principle which will suppress shot noise, while shorting the Debye length, enhancing the space charge effect, and increasing the Coulomb interaction suppression also increased.^22–24 

In this paper, shot noise test system was established, and the experimental results confirmed that shot noise were suppressed by Fermi and Coulomb in nano MOSFET. The expressions of shot noise in realistic nano-MOSFETs while considering Fermi effect, Coulomb interaction and the both co-existence, respectively, and analyze the relationship between shot noise and device structure parameters and working parameters. The results we obtained are consistent with those from those given experiments and the theoretically explains. The results showed that shot noise increases with the increase of bias voltage, and decreases with the increase of temperature and the doping concentration of the source and drain. This paper established shot noise test system suitable for traditional nanoscale electronic components (eg. short channel MOS, avalanche diode, etc.); and shot noise model, which plays an active role in revealing the essence of electronic transport, extracting transport parameters, lowing noise etc.

This study was supported by Fundamental Research Funds for the Central Universities (Grant No. K50511050007), National Natural Science Foundation of China (Grant No. 61106062), the Scientific Research Fund of Shaanxi Provincial Education Department (Grant No. 16JK1016, 16JK1015) and the project of Anakang University (Grant No. 2015AYPYZR05).