n-Type phosphorous-doped SiNWs were grown by chemical vapor deposition through the gold-catalyzed VLS method as described in 15 16 , on n-type silicon substrates (3-5 mΩ cm). The SiNW growth temperature was in the range of 500-650°C, and the n-type doping was achieved by adding PH₃ to SiH₄, with PH₃/SiH₄ ratios which can vary from 0 to 2 × 10^-2. Subsequent to the growth, the catalyst was removed, and in some cases, a rapid thermal annealing at 750°C for 5 min was done to activate dopant impurities. SiNWs were then embedded into spin-on-glass matrix in order to be planarized by chemical-mechanical polishing 16 .

Table 1 describes the samples that were electrically analyzed by CP-AFM. The samples were grown at the same temperature (500°C), and they differentiate themselves on the nominal doping concentration. Figure 1b illustrates a sample of vertical SiNWs on n-type Si wafer with diameters in the range of 50-100 nm. The length of wires after planarization was estimated around 1 μm.

Local electrical measurements were performed using a Digital Instruments Nanoscope IIIa Multimode AFM associated with the home-made conducting probe extension called "Resiscope" 12 . This setup allows us to apply a stable DC bias voltage (from -10 to +10 V with 0.01 V resolution) to the device and to measure the resulting current flowing through the tip as the sample surface is scanned in contact mode. Local resistance values can be measured in the range of 10²-10¹² Ω, which allows investigations on a variety of materials 17 18 and devices 19 20 . Measurement accuracy based on calibrations is below 3% in the range of 10²-10¹¹ Ω, and it can reach 10% for higher resistance values.

Reliable and understandable electrical measurements through CP-AFM setup require a well-characterized conductive tip. Depending on the experimental conditions, the AFM conductive tip should be the most suitable in terms of serial resistance that must be taken into account in the electrical analysis of SiNWs. B-doped diamond- and PtIr-coated Si cantilevers, with an intermediate spring constant of about 2 N/m, prove to be suitable for our experimental conditions, since measured resistance values are mostly greater than their intrinsic resistances that are estimated at 5-10 and 0.3-1 kΩ, respectively.

The CP-AFM details and more specifically the sample configuration and biasing are displayed in Figure 2. In case of horizontal SiNWs, the DC bias voltage was applied to the ITO pad, while for vertical SiNWs it was applied through the doped silicon wafer.

Figure 3 shows a large AFM scan illustrating the topography and electrical image properties of the sample structure based on an ITO pad (bottom of the image) from the border of which in-plane nanowires are distinguishable. In addition, the topography allows it to point out long channels that were dug during the growth of SiNWs. Nevertheless, these long channels are empty and indeed they are not electrically discernable from the insulating a-Si:H layer that surrounds the wires. On the contrary, SiNWs show electrical conductivity when the wires are not broken or disconnected from the ITO pad.

In Figure 4, a 20 × 20 μm² surface scan which displays the topography and the electrical properties of a micrometer-wide horizontal silicon oval shaped wire (1 μm wide and 300 nm thick) is presented. The topography points out an inhomogeneous surface morphology that is clearly confirmed by the local mapping of resistance. Indeed, conductive paths along the wire are put in evidence and linked to the topographic features of the wire envelope. The accuracy of these features depends essentially on convolution effects associated to the AFM tip shape. It seems reasonable that several SiNWs have been produced and have partially contributed to the growth of this long and wide silicon wire 10 explaining the electrical and surface microstructure.

In the same figure, the empty growth channel resulting from the unexpected cut of the wire with the AFM probe can also be noticed. Broken pieces of silicon remaining in the channel reveal a slight electrical conduction (10¹¹ Ω) although they are electrically isolated through the undoped a-Si:H layer (10¹² Ω). Possible explanations are that the whole surface of the remaining piece of silicon in contact with the a-Si:H layer fully contributes to decrease the electrical contact resistance or that the friction of the AFM tip induces charging effects which are electrically observable.

Horizontal SiNWs have also been characterized under different applied voltages. As illustrated in Figure 5, the local resistance maps were measured in the same region at 2, 6, and 10 V, respectively. The analysis of the electrical images points out a local resistance that decreases in function of the applied voltage. More specifically, the local resistance of SiNWs measured at 2 V decreases one order of magnitude at 6 V and two orders of magnitude at 10 V. Such behavior was also observed for negative applied biases. An interesting observation comes from the high bias regime (V > 2 V) which underlines the increase of local resistance of the wire versus its length. However, high bias regime can also broaden the electrical images of wires.

In order to get more precise information about the variation of the local resistance in function of the applied bias, CP-AFM was locally used for investigating the I-V characteristics on individual SiNWs. Figure 6 displays a log-log plot of the I-V characteristics where two identifiable slopes are put in evidence. Indeed, the analysis of the slopes following a power-law dependence (I ∝ V ⁿ ) allows us to estimate two transport regimes with a transition around 1 V. The slope n = 1.6 (V < 1 V) points out charge injection which is a characteristic of a space-charge limited current (SCLC) 21 . The slope n = 3 (V > 1 V) indicates a trap-limited SCLC, that can be analyzed in the frame of a trap distribution with an increasing density of states toward the band edge. Interface and surface states in low-dimensional semiconductors such as nanowires are expected to be the most common defects, which greatly influence the electrical transport properties 22 . We also should keep in mind that SiNWs were here obtained thanks to an a-Si:H layer that is known to possess a quite large density of states in the gap, with exponential band tails.

Figure 7 depicts a 10 × 10 μm² surface map that illustrates, from left to right, the topography and the electrical properties of undoped SiNWs (CD-08-001). The brightest spots (highest features) in the topography image represent the SiNWs which are generally well correlated with the conductive blue spots in the electrical image. However, the zoom (4.2 × 4.2 μm²) allows it to point out several examples of SiNWs which are not electrically conductive (dot-line circle) as distinct from those showing conductive properties (full-line circle). The oxide formation and the AFM tip loading force are possible reasons that could explain that SiNWs appear insulating in native.

The three samples were carefully imaged, and a statistic was made in a few tenths of SiNWs. An example of cross-sectional profiles involving SiNWs is illustrated in Figure 8. The conducting wires are easily put in evidence with a decrease of the local resistance by several orders of magnitude with respect to the background signal. For the most highly doped sample, the local resistance of the SiNW drops by more than six orders of magnitude, whereas the intermediate doped and undoped samples show a decrease of four and three orders of magnitude, respectively. These measurements clearly point out that the SiNWs conductivity can be controlled by the incorporation of phosphorus impurities. However, the phosphorus doping efficiency and activation cannot be directly discussed through such measurements. Resistivity measurements are indeed required.

As illustrated in Figure 9, local I-V measurements were performed for each sample on top of the SiNW using a PtIr AFM tip. All the three samples show a linear behavior with inverse slopes of 1.9-2.3 × 10⁸, 5.3-6.7 × 10⁶, and 4.5-10 × 10⁴ Ω, respectively, for the undoped, 1 × 10¹⁸ and 1 × 10²⁰ for the doped samples. These values illustrate the total measured resistance R _tot which can be decomposed as follows:

R tot ≈ R AFMtip + R tip/SiNW + R SiNW + R back ,

where R _AFMtip is the intrinsic resistance of the AFM tip, R _tip/SiNW refers to the contact resistance involving the AFM tip and the SiNW, R _SiNW designates the intrinsic resistance of the SiNW, and R _back the back contact resistance between the highly doped silicon wafer and the SiNW. The intrinsic resistance of the SiNW (R _SiNW) is given by ρl/S where ρ, l, and S are the resistivity, the length of the wire, and the wire sectional area, respectively.

The presence of contact resistance often implies the presence of a barrier which gives rise to diode-like behavior or sigmoidal I-V characteristics. In some cases, a linear dependence on applied bias can be measured indicating that the barrier resistance involved in the contact resistance can be neglected. The contact resistance only consists then in a geometrical resistance which depends on the electrical radius 23 . In order to estimate the geometrical resistance, the Wexler resistance model 24 25 was used, which describes the transition between the diffusive and ballistic transport regimes in constricted contacts.

Wexler formula is described as

R W = 4 ρ 3 π a K + ρ 2 a Γ ( K ) ,

where K = λ/a is the ratio of the carrier mean free path, l, to the electrical radius, a, and Γ(K) is a monotonous function that takes the value 1 at K = 0 and decreases slowly reaching the limit of 0.694.

For the estimation of R _tip/SiNW, the electrical radius was chosen equal to 10 nm, and the electron mean free path in the range 1-80 nm assuming bulk silicon values. From these calculations, the resistivity values were estimated to be in the range of 20-40 Ω cm for the undoped sample, 0.1-1.2 Ω cm for the intermediate doped sample, and 0.008-0.016 Ω cm for the highly doped sample. In terms of electrically active phosphorus, it corresponds to 1-2 × 10¹⁴, 0.5-7 × 10¹⁶, and 2-6 × 10¹⁸ cm^-3, respectively. These values, extracted from bulk silicon values, indicate that the phosphorus incorporation is not fully activated despite the thermal anneal activation at 750°C. Recent results of CP-AFM show that phosphorus activation in SiNWs is enhanced at higher temperatures growth (T > 500°C) without the need of post-annealing treatment.

From the point of view of the CP-AFM measurements more accurate resistivity measurements could be achieved in the future making a pre-calibration of the technique using standard doped silicon wafers 26 .