During the past few years, much attention has been paid to silicon nanowire transistors which are considered key to future scaling beyond the 10 nm technology node due to their excellent electrostatic control and simple process.^[1–4] Moreover, with the shrinking of the device scales, one-dimensional (1D) transport can be clearly observed in silicon nanowire transistors even at room temperature.^[5,6] Meanwhile, the influence of dopant atoms is increasingly remarkable on the characteristics of devices in such a small dimension of sub-10 nm. Dopant distribution and fluctuations can cause a device-to-device fluctuation in threshold voltage^[7] and on/off current.^[8,9] Some work gained a remarkable insight into the transport of electrons in different dopant environments at low or room temperature, such as single dopant atom^[10,11] or a few dopant-induced quantum dots.^[12–14] Furthermore, when the channel size approaches several tens of nanometers, the electron transport through a dopant-atom array can be observed.^[12] The arrangement and position of the dopant atoms have a more significant influence on the transport property in nanowire devices with diameters less than 1 nm.^[15,16] It is essential in understanding the influence of the ionized dopant on the electronic characteristic. Here, we explore the transport spectroscopy from Hubbard bands in a dopant atom array to 1D conduction band in n-doped silicon junctionless nanowire transistor (JNT) by varying the temperature from 6 K–250 K. In particular, we study the effect of dopant ionization at critical temperatures on the shifted current-off voltage, the minimum electron mobility, and the transition of electron transport mechanics.

The device fabrication started from a (100)-oriented silicon-on-insulator (SOI) wafer with a top silicon thickness of 55 nm and buried oxide of 145 nm. After growing a 20-nm thermal oxidation layer, the SOI wafer was uniformly implanted by phosphorus ions with a doping fluence of 1×10¹³ cm⁻² at an energy of 33 keV. A uniform phosphorus doping concentration of N_D ≈ 2×10¹⁸ cm⁻³ could be achieved after annealing at 1000 °C in N₂ for 15 s. Silicon nanowire was defined along the ⟨110⟩ direction by electron beam lithography (EBL) and inductively coupled plasma (ICP) etching. The sacrificial oxidation was introduced to reduce the etching damages. After being rinsed in the 5% HF, the nanowire was oxidized in dry oxygen at 900 °C for 1 h to form a 22-nm gate dielectric and to further reduce the cross-sectional area of the nanowire channel. Finally, a silicon nanowire channel with a width of 18 nm and height of 30 nm was achieved. After depositing a 200-nm-thick polysilicon layer to wrap the nanowires, EBL and ICP etching were used to obtain a polycrystalline silicon gate with a gate length of 280 nm. The top view scanning electron microscopy (SEM) image of our device is shown in Fig. 1(a). After depositing 200-nm SiO₂ for passivation, 20-nm Ni and 300-nm Al were evaporated to form Ni/Si ohmic contact and final metallization with the help of conventional optical lithography. Figure 1(b) shows the schematic structure of our JNT. The single n-channel JNTs were measured in a vacuum chamber at temperatures ranging from 6 K–250 K with the Lakeshore-340 temperature controller and Agilent B1500 semiconductor parameter analyzer.

Fig. 1.

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	Fig. 1. (color online) (a) Top view SEM image of our device after gate formation. The cross section of channel is 18 nm × 30 nm and the gate length is 280 nm. (b) Three-dimensional schematic of JNT after Al pad formation.

Temperature-dependent transfer characteristics in both linear and log scales are shown in Fig. 2(a) for the JNT at the bias V_ds = 10 mV within a temperature range from 6 K–100 K. Current steps can be observed clearly below 50 K but gradually smear with the increase of the temperature, and eventually disappear beyond 75 K. The I_ds–V_g curves show a current minimum at 20 K for a fixed drain voltage. Moreover, the curves increasing with the temperature rising have a positive shift below a temperature of 20 K and a negative shift above a temperature of 20 K. To show more clearly, the transconductance g_m curves are presented in Fig. 2(b) as a function of gate voltage V_g at V_ds = 10 mV for various temperatures. The g_m–V_g curve has a maximum positive shift in gate voltage at 20 K, if we set the gate voltage at 6 K as a reference. Each current step in Fig. 2(a) corresponds to the population of an individual 1D sub-band.^[17–19] The experimental subband energy spacing can be estimated according to gate voltage spacing ΔV_g from^[12,20]

Fig. 2.

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	Fig. 2. (color online) (a) Drain current Ids and (b) transconductance gm (gm = ∂Ids/∂Vgs) versus gate voltage Vg of a single channel JNT at Vds = 10 mV at different temperatures. The curves in panel (b) are shifted for clarity.

In order to clarify the effect of temperature on the shift of the curve, the temperature-dependent tendencies of the current-off voltage V_gp and the gate voltage V_gm at the maximum g_m peak are shown in Fig. 3(a). The current-off voltage V_gp is shifted positively from 6 K–20 K and negatively from 20 K–250 K. The gate voltage V_gm has a similar temperature-dependent tendency, confirming that the curves varying with temperature have shifted as a whole. To give a clear insight into the inner physics, the temperature dependencies of the effective mobility and electron concentration are drawn in Figs. 3(b) and 3(c), respectively. The effective mobility can be extracted from^[21]μ_eff = g_{m max}/C_ox(W_eff/L)V_ds, where g_{m max} is the maximum of transconductance peaks, L is the gate length, and W_eff is the effective width and defined as twice the nanowire height plus the nanowire width. A prominent feature shown in Fig. 3(b) is the effective mobility minimum at 20 K. The mobility minimum at 20 K comes from the interplay between impurity scattering and thermal activation at low temperature.^[22] As the ionized dopant atoms increase with the temperature rising from 6 K–20 K, more positive scattering centers are induced, resulting in the decrease of the mobility. At higher temperature, the ionized impurity scattering is gradually reduced by the shorter interaction time due to the thermal activation, causing the effective mobility to increase at temperature from 20 K–100 K. Figure 3(c) shows a quantitative result about the electron concentration. The electron concentration from 6 K–250 K can be expressed as^[23]

Fig. 3.

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	Fig. 3. (color online) (a) The current-off voltage Vgp and the gate voltage Vgm at the maximum gm peak versus temperature. The Vgp and Vgm are marked by dots and asterisks in Fig. 2(b). The current-off voltages are set to be the gate voltage at which the current is 10−12 A. (b) Effective mobility dependence on temperature. (c) Electron concentration dependence on temperature.

Figure 4 shows the temperature-dependent evolution of the electron transport spectroscopy from Hubbard bands in a dopant atom array to 1D conduction band. At the initial stage of the conductance below the temperature of 50 K, additional current oscillations before the first current step of 1D transport can be observed at V_ds = 10 mV as shown in Fig. 4(a). The corresponding transconductance g_m curve is drawn in Fig. 4(b) to clarify the temperature effect of the additional current oscillations. The fine g_m peaks are sensitive to temperature and smear quickly with increasing temperature. At very low temperature, the ionized dopant atoms are isolated and form discrete quantum dots.^[28] The three fine g_m peaks at 6 K can be attributed to the transport through three discrete dopant-induced quantum dots.^[29] The discrete ionized dopants in an array for the initial channel are coupling with each other to form the Hubbard band due to the repulsion of electrons with the same spin.^[30] Two clear g_m envelopes instead of three fine g_m peaks can be observed in Fig. 4(b) from 10 K to 30 K, which validates the formation of the Hubbard band. The two transconductance envelopes are separated by an average gate-voltage spacing ΔV_g = 0.464 V at the temperature range from 10 K to 30 K, corresponding to an energy spacing of 2.85 meV according to Eq. (1). The average energy spacing of 2.85 meV corresponds to the energy gap between two Hubbard bands, which accords well with the value given in Ref. [23] in a similar device. The thermal energy k_BT of electrons at 30 K is about 2.6 meV, which is closer to the calculated energy gap of 2.85 meV. As a result, the merging of two Hubbard bands can be observed at the temperature of 50 K, in which the thermal energy is higher than the Hubbard band gap.

Fig. 4.

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	Fig. 4. (color online) (a) Conductance curves G–Vg (a) and (b) transconductance curves gm–Vg at Vds = 10 mV for different temperatures. The curves at each temperature are systematically shifted for the clarity of the fine current steps. The values of gate voltage spacing of two transconductance peaks are 0.464 V at 10 K, 15 K, 30 K and 0.4 V at 20 K, respectively.

To clarify the electron transport mechanisms at different temperatures, Arrhenius plots of conductance curve at three g_m valleys and the corresponding maximum positions are drawn in Fig. 5(a). The conductances remain stable within the temperature range from 6 K–30 K. The activation energy can be estimated to be 0.14 meV, 0.09 meV, 0.06 meV, and 0.17 meV for the curves at V_g1, V_gm, V_g2, and V_g3, respectively, according to the slope of the curve in Fig. 5(a), in which the curve is described by

Fig. 5.

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	Fig. 5. (color online) (a) Arrhenius plots of conductance at various gate voltages, which correspond to maximum peaks at Vgm and three valleys Vg1, Vg2, Vg3 in the transconductance curves of Fig. 2(b). (b) Activation energies versus the gate voltage in different temperature regions.

In this research, we demonstrate the transport spectroscopy of dopant atom array in heavily n-doped silicon JNT from 6 K–100 K. The clear current steps for 1D subband transport are maintained below the temperature of 75 K. With the temperature increasing form 6 K–20 K, the ionization of the dopant atoms results in the suppression of the effective mobility and the positive shift of the current-off voltage. The transition of the electron transport from the Hubbard band to 1D conduction band is identified below the temperature of 50 K by the temperature-dependent evolution of g_m peaks at the initial stage of the transfer characteristics. Arrhenius plots of conductance curves indicate the transition of electron transport mechanism at the temperature of 30 K from relatively temperature-independent region to linearly dependent region. Our study reveals that the ionized dopant atoms play an important role in the performance of silicon JNT. The in-depth understanding of dopant-induced QDs is highly desirable at giving better control for further scaling of transistors.