Dynamics of graded-composition and graded-doping semiconductor nanowires under local carrier modulation

Wenjuan Deng; Jijun Zou; Xincun Peng; Jianbing Zhang; Weilu Wang; Yijun Zhang; Daoli Zhang

doi:10.1364/OE.24.024347

1. Introduction

Semiconductor nanowires (NWs) have attracted tremendous attention due to their scientific significance and potential applications including solar cells [1, 2], optical sensors [3–5], photodetectors [6, 7], and memory devices [8, 9]. Internal electric fields often exist in NWs and are caused by local defects, charge transfer, electrode contacts, surface states, or band-gap offset [10]. Unintentional internal junctions arising from variations in doping or composition can similarly affect the internal electrostatic fields [11]. These fields may strongly influence device performance. Scanning photocurrent microscopy (SPCM) combines electrical measurement and local illuminations with a focused laser, and is a powerful tool for providing information on critical local transport processes such as carrier generation, recombination and subsequent diffusion and drift without perturbing the device. SPCM provides valuable analysis of local band bending and carrier diffusion lengths [12]. This technique has recently been used to characterize contacts in nanowire and carbon nanotube devices [13–15], and two-dimensional field effect transistors [16], identify the active region in photodetectors [17], probe local photovoltaic quantum efficiency and map electronic band bending in NWs [18–21].

In these applications, diffusion force drives free charge carriers to move by the carrier density gradient [11], and drift force drives them to move by built-in and/or induced fields [22]. However, drift and diffusion currents are always present, even in the absence of initial electric fields. These currents exist internally at equilibrium, but cancel each other out. The large electron and hole gradients may cause diffusion currents and the disparity in mobilities between electrons and holes causes the accumulation of local net charges, which induce built-in fields and give rise to drift currents [10]. Non-uniform doping [11] and graded composition [23] materials can all induce more complicated built-in fields in the device. Although there have been many investigations of nanowires and their device properties, a comprehensive analysis of such carrier dynamics in graded-doping and graded-composition NWs using local carrier modulation is lacking. Therefore, a fundamental understanding of carrier dynamics in such NWs is still elusive. In this work, by applying Cogenda TCAD genius software based on a finite volume algorithm, a carrier dynamic model was established. We also performed comprehensive simulations and gained a better understanding of graded-composition and graded-doping NWs in the SPCM configurations.

2. SPCM models

In a typical SPCM setup, as illustrated in Fig. 1(a), a NW is placed on top of a substrate, which is contacted by two metal electrodes. The NW is locally excited with a focused laser beam. For the scanning photocurrent measurements, two electrodes of the NW are shorted or electrically biased, when scanning the laser from one electrode to another electrode. The photocurrent density is calculated as a function of laser position. For photon energy above the band gap, the diameter of the NW is smaller than the optical absorption depth, and the NW is assumed to be isotropic and homogeneous, the device can therefore be approximated with a one-dimensional model [10]. According to this approximation, we designed an AlGaAs nanowire with a diameter of 100 nm. The wavelength of the laser was 532 nm. The device in Fig. 1(a) can be approximated using a one-dimensional model along the axial direction. The electric potential and current density are calculated by solving Poisson's and the current continuity equations. When temperature effects are neglected, Poisson's equation is given by,

ε \frac{d^{2} φ (x)}{d x^{2}} = - q [p (x) - n (x) + N_{d} (x) - N_{a} (x)]

where ε is the dielectric constant, φ(x) is the electrostatic potential, q is the electron charge, N_d(x) and N_a(x) are the donor and acceptor concentrations, respectively, which are supposed to be fully ionized at room temperature, and n(x) and p(x) are the electron and hole concentrations, respectively. Charge carriers, generated by local laser excitation, drift and diffuse along the axial direction under the effects of the electric field and concentration gradient, respectively. In the steady state, the total current density is the sum of hole drift, hole diffusion, electron drift, and electron diffusion, and is generally given by,

{\begin{matrix} J_{n} (x) = q n (x) μ_{n} (x) E_{n} (x) + q D_{n} (x) \frac{d n (x)}{d x} \\ J_{p} (x) = q p (x) μ_{p} (x) E_{p} (x) - q D_{p} (x) \frac{d p (x)}{d x} \\ J = J_{n} (x) + J_{p} (x) \end{matrix}

where J_n(x) and J_p(x) are the electron and hole currents, respectively, D_n(x) and D_p(x) are the electron and hole diffusion coefficients, respectively, μ_n(x) and μ_p(x) are the electron and hole mobilities, respectively, and E_n(x) and E_p(x) are the intensities of the electric field accelerating the electrons and holes, respectively.

Fig. 1 (a) SPCM measurement scheme. (b) Dark current-voltage characteristic of the AlGaAs NW device. (c) Band diagrams and photocurrent generation mechanisms for different structured AlGaAs NW devices: i-ii, uniformly-doping AlGaAs NW devices at 0 and 1 V drain-source bias, respectively, iii, the graded-doping AlGaAs NW device at no bias, iv, the graded-composition AlGaAs NW device at no bias.

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The charge carrier concentrations in Poisson's equation satisfy the current continuity equations,

{\begin{matrix} \frac{1}{q} \frac{d J_{n} (x)}{d x} - U (x) + G (x) = 0 \\ - \frac{1}{q} \frac{d J_{p} (x)}{d x} - U (x) + G (x) = 0 \end{matrix}

The photoelectron generation function is given by,

G (x) = α (x) I_{0} [1 - R (x)] [1 - \exp (- α (x) T_{n}]

where U(x) is the carrier recombination rate, G(x) is the carrier generation rate, R(x) is the reflectivity of the photocathode, α(x) is the absorption coefficient of the photocathode material, T_n is the thickness (diameter) of the nanowire, and I₀ is the incident light intensity.

The non-equilibrium electrons and holes are generated only in the laser illumination area with a rate of G(x), whereas they are recombined throughout the entire NW with a rate of U(x) [24, 25]. We consider three basic recombination mechanisms: Shockley-Read-Hall (SRH), direct (or radiative), and Auger recombination. The total recombination is considered as the sum of all:

U (x) = U_{S R H} (x) + U_{d i r} (x) + U_{A u g e r} (x)

where U_SRH(x), U_dir(x) and U_Auger(x) are SRH, direct and Auger recombination, respectively. These mechanisms can be determined by the following equations:

{\begin{matrix} U_{d i r} (x) = B [n (x) p (x) - n_{i e}^{2}] \\ U_{S R H} (x) = \frac{n (x) p (x) - n_{i e}^{2}}{τ_{p S R H} [n (x) + n_{i e} \exp (\frac{E_{t r a n}}{k T_{L}}) + τ_{n S R H} [p (x) + n_{i e} \exp (\frac{E_{t r a n}}{k T_{L}})]} \\ U_{A u g e r} (x) = C_{augn} [p (x) {n (x)}^{2} - n (x) n_{i e}^{2}] + C_{augp} [n (x) {p (x)}^{2} - p (x) n_{i e}^{2}] \end{matrix}

where B is the direct recombination coefficient, C_augn and C_augp are the Auger coefficients for electrons and holes, respectively, τ_nSRH and τ_pSRH are the lifetimes for electrons and holes, respectively, and E_tran is the parameter of the trap level. The electron and hole lifetimes are determined by:

{\begin{matrix} τ_{nSRH} = \frac{τ_{n 0}}{1 + N_{total} / N_{S R H N}} \\ τ_{pSRH} = \frac{τ_{p 0}}{1 + N_{total} / N_{S R H P}} \end{matrix}

where N_SRHN and N_SRHP are the critical concentrations of n and p type impurities, respectively, N_total is the total dopant concentration, and τ_n0 and τ_p0 are the intrinsic electron and hole lifetimes, respectively.

The total carrier lifetime τ_n is defined by the following:

\frac{1}{τ_{n}} = \frac{1}{τ_{S R H}} + \frac{1}{τ_{d i r}} + \frac{1}{τ_{A u g e r}}

In this work, ideal ohmic-ohmic electrical contacts are assumed at the two NW terminals, which are the most frequently used in SPCM experiments. For the simulated system, the recombination of electrons and holes at the NW surface can be normalized into the bulk through an effective recombination lifetime [26]. At the electrode-semiconductor interface of a NW device with an ohmic contact, the electron quasi-Fermi level is equal to the hole quasi-Fermi level. Finally, the coupled Poisson's and continuity equations are solved numerically using a finite volume method with uniform meshing. To exemplify the simulation, we consider eleven AlGaAs NW devices with different structures, as listed in Table 1. The material parameters, such as the carrier mobility and optical absorption coefficient, are listed in Table 2, which were obtained from the literature [10, 27–31]. All simulations were performed at room temperature unless specified otherwise.

Table 1. Structural parameters for different NW devices.

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Table 2. Physical parameters used in the simulations.

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The dark current-voltage curve is shown in Fig. 1(b), which has current versus voltage characteristics and indicates that the contacts to the GaAs NWs are surely ohmic [33]. This is similar to the Fig. 6 in reference 33. As mentioned above, built-in electric fields exist in the NW devices, induced by the graded doping and graded composition structure, drastically affect the charge flow and collection in the NW devices, resulting in distinct SPCM behavior. As a result, in the following section, we will discuss and analyze these two types of NW device, and compare with the uniform doping NW device. Their band diagrams are schematically illustrated in Fig. 1(c). Illuminating the device by photons may cause the uniform nanowire band bending near the contacts, and result in minority carrier drift and diffusion currents, even there is no external bias (Fig. 1(c-i)), but they are faint under low photo-injection levels. Due to the band bending induced by the electric field established by the external bias (Fig. 1(c-ii)), the drift of excess carriers forms the photocurrent. The band bending regions of graded doping and compositions are shown in Figs. 1(c-iii) and 1(c-iv), in which there is a built-in electric field that facilitates the movement of photoelectrons and produces a current.

3. Simulations and discussion

3.1. Uniform-doping AlGaAs NW device

Figure 2 shows the simulated zero-bias SPCM profiles of S1 with relatively low photo-injection levels (Fig. 2(a-ii), laser intensity is 100 Wcm⁻²). When the Al composition is zero (Fig. 2(a-i)), the device is a GaAs NW. A conduction band bending (Fig. 2(a-iii)) can be induced along the NW axis due to the faster mobility of electrons than holes away from the photo-injection area [35], it can inform the built-in electric field, which prompts the electron and hole reversed drift. But the built-in electric field is too weak the diffusion will dominate over the drift under photo-excitation, which accumulates net negative charges (electron concentration), as shown in Fig. 2(a-iv). The electron current density (J_n) is nearly equal to the hole current density (J_p), and their direction is reversed, so the total current density (J_tot) is minute, as shown in Fig. 2(b). When the laser position is away from the contacts, the distance between laser position and contacts increases, which causes difficulty for the photo-carriers to reach the contact and then the currents (Fig. 2(c)) decrease linearly. This is not surprising, when the laser position is far away from the contacts, the excited carriers are difficult to collect, so the total current density decreases linearly from the two contacts and reaches its minimum at the middle of the NW. The result can also be seen from Fig. 2(b), the values of J_n and J_p are not equal at the anode contact when the laser position is x_laser = 3 μm, but they are equal when the laser position is x_laser = 8 μm. The maximum value of current density decreases with increasing NW length, because the carriers have to diffuse a longer distance before being collected by the electrodes. The total photocurrent density is less than 120 pA/cm² in this structure, which is limited by the diffusion length of minority carriers.

Fig. 2 (a) Mole fraction distribution (i), incident laser intensity and position (ii), band diagram (E_Fn, E_Fp) (iii), and distribution of majority (dashed lines) and minority carriers (solid lines) profiles (iv) when the laser is focused at x_laser = 8 μm in AlGaAs NW devices, where the value of minority carriers, electrons, is magnified 10³ times. (b) Total photocurrent (J_tot), electron (J_n) and hole (J_p) photocurrent density distribution profiles of NW devices when the laser is focused at x_laser = 3, 8 μm, as indicated by the vertical yellow line (from left to right). (c) Total current density profiles of NW devices with different NW lengths. (d) Simulations of the effect of recombination on total current density with local laser illumination, where τ_n0 is the parameter for SRH recombination, B is the parameter of direct recombination coefficient, simulating the effect of the τ_n0 parameter when fixing the B parameter value, and the same as the other parameter.

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According to parameters from the literature [28–32], the effect of Auger recombination is found to be very weak in AlGaAs/GaAs materials, so we only consider the effects of direct and SRH recombination. We simulated several SPCM profiles (Fig. 2(d)) as a function of the B and τ_n0 coefficient for a 16 μm long NW device. On the basis of the results, we have the following conclusions: (i) the change of carrier lifetime does not alter the nearly central symmetric nature of SPCM, but it does alter the total current density, (ii) when the carrier lifetimes for direct and SRH recombination are of the same order of magnitude, the effect of any recombination coefficient change on current density is pronounced, (iii) fixing one coefficient and changing the other by one order of magnitude affects the B coefficient more than that the τ_n0 coefficient and (iv) the total current density decreases with the increase of the B coefficient, because of the decrease in electron lifetime and increases with the increase of the τ_n0 due to the electron lifetime increase.

3.2 Graded-doping AlGaAs NW device

To simulate the effect of graded doping on the photocurrent of the NW device, we considered three types of exponentially doping structures, S2-S4. Figure 3(a-iv) shows the distribution of majority and minority carriers profiles when the laser is focused at x_laser = 2 μm in the S2 structure. The hole concentration is nearly invariant (Δp<<p), but the change in electron concentration (Δn>>n) is pronounced with the photo-excitation (low injection lever). Exponentially variation doping structure [36] can induce the built-in electric field (the direction is from left (low doping) to right (high doping)), as shown in Fig. 3(a-iii). This can also be seen from the accumulating net negative charges (electrons concentration) in Fig. 3(a-iv). Figure 3(b) shows the current density profiles including electron current density (J_n), hole current density (J_p) and total current density (J_tot1,J_tot2) when the laser is focused at x_laser = 2 and 8 μm, respectively. In the presence of the electric field, drift dominates over diffusion of the carriers, the photo-excited electron and hole are separated by the electric field and drift toward the opposite sides of the NW device, the excess free carriers drift at a rate, producing current, I. With the movement of local laser position from the contacts to the middle of the NW, carriers diffuse currents decrease and drift currents increase, under the built-in electric field, increasing drift currents are larger than the decreasing diffuse currents, so the total currents increase.

Fig. 3 (a) Mole fraction distribution (i), incident laser intensity and position (ii), band diagram (E_Fn,E_Fp) (iii), and distribution of majority (dashed lines) and minority carriers (solid lines) (iv) when the laser is focused at x_laser = 2 μm in the S2 device, where the value of minority carriers, electrons, is magnified 10³ times. (b) Total photocurrent, electron and hole photocurrent density distribution profiles of S2 device when the laser is focused at x_laser = 2, 8μm as indicated by the vertical yellow line. (c) Total current density profiles of the S1-S4 devices with local laser illumination. When the dopant type of the NW wire is changed, the direction of the photocurrent changed, we reverse the photocurrent sign of the n-type exponentially doping NW wire to compare with the p-type doping structures. The current density are magnified 10³ times and the laser intensity is 100 Wcm⁻² in S1 device. The devices are all simulated at zero bias in this figure. (d) The current density profiles of the effects of random doping fluctuation (S2^’) and the presence of defects (S2*) on the photo-currents in S2 device.

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We simulated the current density of the devices S2-S4 and compared them with that of the device S1 in Fig. 3(c). Some interesting results are found: i) the total current density of exponentially doping NW devices is about six orders of magnitude larger than that for the uniformly doping device. This illustrates that built-in electric field can also accelerate the photo-currents of device exactly the same as an external applied voltage [34]. ii) the total current in the device S2 is about six times larger than that of the S4. This is due to the built-in electric field in the device S2 is larger than that of the device S4 [36], the photo-currents increase with the field increase [34]. iii) unlike the central symmetric nature of the uniformly doping structure, the total currents of the exponential structured NW devices all firstly increase to a maximum value, then decrease with the laser position movement from the middle to both sides. The total current profile is similar to that in reference 34. The current is about 2 nA when the laser position is at about 3.8 μm in reference 34 with bias of 0.1V, and the current is 3.85 nA when the laser position is at 3μm in device S2. iv) the current intensity peaks shift towards the left from the S4 and S2 structures to the S3 structure. Due to the electron mobility is much larger than the hole mobility at E_n(x) = E_p(x), electrons are easily collected, the total density of the S2 (electrons are minority carriers) structure is larger than for S3, and the current density peak of S3 (holes are minority carriers) is closer to the anode contact. Due to the effect of the electric field, induced by the graded doping structure, on carrier transport, the doping structure of NWs, i.e. graded or uniformly doping or p-type or n-type doping, can be determined according to the SPCM profiles.

Since the size of the nanowire is small, we simulated the effects of random doping fluctuations on the photocurrents. A ± 5% random variation of doping density on each point was added. The results for the random doping device (S2^’) are shown in Fig. 3(d). The photocurrent shows no obvious variation. This is because the effects of 5% random doping fluctuations on the built-in electric field induced by graded doping are weak. Whereas, when there is no built-in electric field, such as device S1, the photocurrent randomly varies by over two orders of magnitude. This also illustrates that the models in this work are sensitive to random fluctuations. Figure 3(d) shows the photocurrent profile for simulating the presence of defects (S2* device) in graded-doping AlGaAs NW device S2. The minority carrier lifetime at 3.5 - 4.5 μm was set to be twenty times lower in magnitude than the other positions. As shown in Fig. 3(d), when comparing the line S2 with the uniform carrier lifetime, the photocurrent of line S2* is smaller and there is a shoulder at 3.5 - 4.5μm. Due to the presence of defects, such as dislocations, the recombination of carriers increase, the photocurrents decreases. This profile can help us to determine the presence of defects and their positions in the material.

3.3 Graded-composition AlGaAs NW device

Figure 4 shows the results for the graded composition AlGaAs NW device has been illuminated with a low level intensity laser. The Al composition is made to decrease linearly from right to left (Fig. 4(a-i)). The AlGaAs material is a direct band-gap semiconductor, when the Al composition is less than 0.45. To simplify the analysis and gain a better understanding of carrier dynamics in graded composition materials, we set the maximum Al composition to 0.4 in all simulations. For the Al_xGa_1-xAs material, the band gap, E_g, depends on the Al composition, x, and is given by:

Fig. 4 (a) Mole fraction distribution (i), incident laser intensity and position (ii), band diagram (E_Fn, E_Fp) (iii), and distribution of majority (dashed lines) and minority carriers (solid lines) (iv) at x_laser = 8 μm in device S8, where the value of minority carriers, electrons, is magnified 10⁴ times. (b) Total photocurrent, electron and hole photocurrent density distribution profiles of NW devices when the laser is focused at x_laser = 2, 8 μm as indicated by the vertical yellow line (from left to right). (c) The current density profiles with Al fraction variation for different length NWs when laser position is at the middle of the NW. (d) The total current density profiles for different Al mole fraction devices under local laser illumination. When the dopant type of the NW wire changed, the direction of the photocurrent changed, we reverse the photocurrent sign for the device S9 to compare with devices S5-S8. The current density are magnified 10³ times and the laser intensity is 100 Wcm⁻² in S1 device. The devices are all simulated at zero bias in this figure.

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E_{g} = {\begin{matrix} 1.424 + 1.247 (x), (0 \leq x \leq 0.45) \\ 1.424 + 1.247 x + 1.147 {(x - 0.45)}^{2}, (0.45 \leq x \leq 1.0) \end{matrix}

The graded band gap (ΔE_g) is the sum of the graded conduction (ΔE_c) and valence (ΔE_v) bands. ΔE_c is much greater than ΔE_v in heavily p-type doping AlGaAs NWs [23,37], as shown in Fig. 1(c-iv). Accordingly, E_n(x) is much greater than E_p(x). The built-in electric fields, induced by the graded composition structure in p-type NW devices, are more favorable to the collection of electrons rather than holes.

Figure 4(b) shows the effect of Al composition on the photocurrent density including J_n, J_p, and J_tot1, J_tot2. The built-in electric fields induced (from left to right) by Al composition variation prompt the collection of electrons at the anode contact and the collection of holes at the cathode contact, whereas the collection of electrons and holes at the other contact is suppressed. With the laser position shifting far away from the contact, when the NW length is sufficient, although the diffuse current becomes weak, the drift current becomes distinct, so the total current density at the laser position x_laser = 8μm is larger than that at x_laser = 2 μm as the Al composition linearly varies from 0 to 0.4.

From Table 2 we know that electron lifetime increases slowly with increasing Al composition, but whole lifetime decreases rapidly with increasing Al composition. At the beginning, the current densities increase slowly under the built-in electric field. Whereas, with the laser shifting far away from the contact, the increased drift current gradually cannot supplement the decreased diffuse current with the increase of Al composition, so we can see that the photocurrent densities then decrease slowly in 4 and 8 μm NW, as shown in Fig. 4(c). Nevertheless, with the increase of NW length, the effect of diffuse current becomes weak, the photocurrent densities do not decrease but weakly increase when the NW length reach to 16 μm. Figure 4(c) also shows that the photocurrent densities of NW devices with identical Al compositions decrease with increasing NW length. It is well known that these photo-carriers suffer from a higher chance of recombination in a longer NW device.

Figure 4(d) shows the simulated SPCM profiles of NW devices with different linearly graded Al composition structures under illumination with low level injection. As discussed above (Fig. 4(a-iii)), a built-in electric field can be induced along the NW axis due to the variation of the band gap, which is larger at higher Al compositions, as shown in Fig. 4(d). The current densities of the NW wire increase with increasing Al composition. However, the drift of electrons and the diffusion of holes dominate the carrier transport process in p-type graded-composition AlGaAs NW devices due to ΔE_c>>ΔE_v. The distance that the electrons transport is much further than that of the holes, so the peaks of the current intensity in p-type graded-composition AlGaAs NW devices locate close to the cathode contact, which is closer to the cathode contact with the higher Al composition. Comparing to the p-type AlGaAs material, we simulate the current intensity of the n-type AlGaAs structure. We find the peak of the current densities in the n-type graded-composition structure does not locate close to the anode (left) contact (the built-in electric field is from cathode to anode), but locate close to the center position of the NW. This is attributed to the fact that the drift of holes and the diffusion of electrons dominate the carrier transport process in n-type graded-composition structure; however, the mobility of holes is much less than electrons. So, the nature of the graded-composition structure of the NW, in terms of doping type, or whether it is a graded or uniform composition or has a rough composition profile, can be determined according to the SPCM profiles. In this work, the total current profile shape is roughly similar to that in references 34 and 38. A field along the NWs significantly changes the magnitude of the photocurrents, which is an external field in references 34 and 38, whereas a built-in electric field is induced by graded Al composition in this work. Due to this difference, the variation of photocurrent peak value when the external field changed from 1 to 3V in reference 34 is larger than that in this work when the Al composition changed from 0 to 0.4. As discussed above, the reason is that the built-in electric field in p-type graded composition AlGaAs NW device mainly acted on the electron drift, but the external field acted on electrons and holes drift. Due to the difference in NW materials (PbS in reference 38) and device structures (core-shell structure in reference 34), no direct data comparison is available. The model and simulation method established in this work can provide theoretical guidance to SPCM experiments of graded-composition device.

3.4 Graded-doping and graded-composition AlGaAs NW device

Considered the common case with both graded doping and graded composition AlGaAs NW device, the scanning photocurrent profiles were simulated, and some interesting phenomenon were found, as shown in Fig. 5. The devices, S10 and S11, are exponentially graded-doping and linearly graded-composition. The composition increased from left to right, but doping increased from left to right in device S10 and decreased from left to right in device S11. This means that the electric field induced by graded-doping and that induced by graded-composition have the same orientation in device S10, but they are the opposite in device S11. The profile of device S10 is different from the other three and there are two peaks. This is because the parameters, such as carrier mobilities, lifetimes and recombination coefficients, are mainly affected by doping when the Al composition is small (less than 0.1). With increasing doping and Al composition, the effect of doping decreased and that of composition increased on these parameters, and the former is pronounced, so the photocurrent then decreased. However, with the shift of the laser, the collection of carriers increased due to the graded composition structure, so the second peak appeared. Overall, the profile of device S11 is like that of device S8, the photocurrent of device S11 is less than that of device S8 attributed to lesser build-in electric field at the left side of NW. Whereas with decreasing doping, the carrier mobilities increased and recombination decreased, the photocurrent of device S11 is larger than that of S8 at the right side of NW. From the orientation of the photocurrent in device S11, we can also conclude that the build-in electric field induced by graded composition is larger than that of graded doping.

Fig. 5 Current density profiles of the graded-doping and graded-composition NW devices (S10 and S11), compared with the only graded-doping NW device (S2) and only graded-composition NW device (S8).

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3.5 Effect of temperature and NW diameter to graded doping and composition devices

Figure 6 shows the current density distribution profiles of the graded doping structure (Fig. 6(a)) and graded composition structures (Fig. 6(b)) with temperature variation. As we know, the energy band, intrinsic carrier concentration, dopant concentration, carrier mobility, scattering probability, and absorption coefficient, also vary with a change in temperature [39,40]. At low temperature, impurities are weakly ionized, so the current density is very low in the graded doping structure. With an increase in temperature, more impurities are ionized, the carrier concentration and the built-in electric field increase accordingly, and finally reach a stable value when all impurities are ionized. With further increases in temperature, the intrinsic carrier concentration increases as well. According, the current density increases with increasing temperature, as shown in Fig. 6(a), the effect is more obvious at larger doping variations, which is identical with refs. [41–43], although the carrier mobility decreases with increasing temperature, which is not large enough to offset the effects of other factors. However, for the graded composition structure, the built-in electric field is induced by graded bandgap and does not vary with the change of the temperature, the same as the variation of the intrinsic carrier concentration is also restrained by the larger bandgap when the temperature increases. So as shown in Fig. 6(b), the current densities are larger at low temperature and then slowly decrease due to the carrier mobility obviously decreasing with increasing temperature [40], and the effect is more obvious at larger Al compositions due to the larger built-in electric field.

Fig. 6 (a) Total current density distribution profiles of NW devices with uniform and graded doping structures with temperature variation. (b) Total current density distribution profiles of NW devices with uniform and graded composition structures with temperature variation. The laser is focused at x_laser = 13.5μm.

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Figure 7 is the current density distribution profiles of the graded doping structure (Fig. 7(a)) and graded composition structure (Fig. 7(b)) with NW diameter variation. As seen, with the increase of the NW diameter, the total currents density of all types of structure devices also increase, which is attributed to that more photons are absorbed in the NW with the increase of the NW diameter. The variation are more obvious at less NW diameter and larger built-in electric field, however, the total current densities of all types of structures tend to reach stable values as the NW diameter larger than about 300nm.

Fig. 7 (a) Total current density distribution profiles of NW devices with uniform and graded doping structures with laser diameter variation. (b) Total current density distribution profiles of NW devices with uniform and graded composition structures with NW diameter variation. The laser is focused at x_laser = 13.5μm.

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4. Conclusions

In summary, we have established a carrier dynamics model of graded-doping and graded-composition AlGaAs NW devices under local low level photo-injection. The simulations reveal and predict some important effects that help us to recognize and evaluate the validity of hypotheses that are generally assumed when analyzing SPCM experiments. The main conclusions are: (i) the SPCM profile of uniformly doping GaAs NWs is nearly central symmetric, the current density decreased linearly from the two contacts to the middle of the NW. (ii) The SPCM current of exponentially doping GaAs NWs has a peak value with the laser position movement. (iii) The SPCM peaks of current density in p-type graded-composition structures locate close to the high Al fraction material terminal and this becomes more apparent with increasing Al fraction, but the peak of current density locates at almost the center position in n-type graded-composition structure. (iv) With the increase of the NW diameter, the current density of all types of structure also increase. With the increase of temperature, the current density of the graded doping structure increases, whereas the graded composition structure decreases.

Due to the effects of electric field and mobility difference between electrons and holes on carrier transport behaviors, the nature of graded-composition or graded-doping AlGaAs NWs, such as whether there is graded doping or composition, the graded doping type, if there are defects and their position in material, can also be determined according to the SPCM profiles. The SPCM technique is a powerful tool for providing critical local transport processes and has excellent potential applications in characterization of material properties. The method in this paper can also be referenced to other graded doping or graded composition materials. However, although this work has achieved some promising preliminary results, there are still some scopes for improving the performance of graded doping and graded composition devices, such as considering the surface recombination, quantum confinement effects and graded temperature effects in models, designing Schottky contacts device structure, achieving the suitably theory guide to SPCM experiment.

Funding

This work was supported by the National Natural Science Foundation of China (NSFC) (61261009, 61661002), the Natural Science Foundation of Jiangxi Province, China (20133ACB20005), the Opening Foundation of State Key Laboratory Breeding Base of Nuclear Resources and Environment, East China Institute of Technology, China (NRE1414), and the Foundation of Training Academic and Technical Leaders for Main Majors of Jiangxi Province, China (20142BCB22006).

Acknowledgments

The authors thank Deyi Fu, Ding Gong and Shaotao Jiang for scientific discussions and technical assistance.

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Device No.	1	2	3	S4	5	S6	S7	8	S9	S10	S11
$x_{Al}$	0	0	0	0	-0.1	0-0.2	0-0.3	-0.4	0-0.3	0-0.3	0-0.3
Doping type	p	p	n	p	p	p	p	p	n	p	p
Doping concentration (cm⁻³)	10¹⁸	10¹⁷-10¹⁸		5 × 10¹⁷-10¹⁸	10¹⁸				10¹⁸	10¹⁷-10¹⁸	10¹⁸-10¹⁷

L_NW (μm)	D_NW (nm)	λ_laser (nm)	D_laser (μm)	τ_p0 (ns)	c_augn (cm⁶ s⁻¹)	μ_p (cm² V⁻¹s⁻¹)
1-16	100	532	1	$1 .66+2998 e^{- 36.2 x_{Al}}$	$(10 x_{Al}^{2} - 8 x_{A l} + 1.9) \times 10^{- 31}$	$370 - 970 x_{Al} + 740 x_{A l}^{2}$
B [32] (cm³ s⁻¹)	W_laser (Wcm-2)	N_SRHN (cm-3)	N_SRHP (cm-3)	τ_n0 (ns)	c_augp (cm⁶ s⁻¹)	μ_n (cm² V⁻¹s⁻¹)
1.8 × 10⁻¹⁰	1	5 × 10¹⁷	5 × 10¹⁷	$4.49 + 0.11 e^{13.4 x_{Al}}$	$(55 x_{Al}^{2} - 40.5 x_{A l} + 12) \times 10^{- 31}$	$\frac{8000 - 22000 x_{Al} + 10000 x_{A l}^{2}}{2}$

Device No.	1	2	3	S4	5	S6	S7	8	S9	S10	S11
$x_{Al}$	0	0	0	0	-0.1	0-0.2	0-0.3	-0.4	0-0.3	0-0.3	0-0.3
Doping type	p	p	n	p	p	p	p	p	n	p	p
Doping concentration (cm⁻³)	10¹⁸	10¹⁷-10¹⁸		5 × 10¹⁷-10¹⁸	10¹⁸				10¹⁸	10¹⁷-10¹⁸	10¹⁸-10¹⁷

L_NW (μm)	D_NW (nm)	λ_laser (nm)	D_laser (μm)	τ_p0 (ns)	c_augn (cm⁶ s⁻¹)	μ_p (cm² V⁻¹s⁻¹)
1-16	100	532	1	$1 .66+2998 e^{- 36.2 x_{Al}}$	$(10 x_{Al}^{2} - 8 x_{A l} + 1.9) \times 10^{- 31}$	$370 - 970 x_{Al} + 740 x_{A l}^{2}$
B [32] (cm³ s⁻¹)	W_laser (Wcm-2)	N_SRHN (cm-3)	N_SRHP (cm-3)	τ_n0 (ns)	c_augp (cm⁶ s⁻¹)	μ_n (cm² V⁻¹s⁻¹)
1.8 × 10⁻¹⁰	1	5 × 10¹⁷	5 × 10¹⁷	$4.49 + 0.11 e^{13.4 x_{Al}}$	$(55 x_{Al}^{2} - 40.5 x_{A l} + 12) \times 10^{- 31}$	$\frac{8000 - 22000 x_{Al} + 10000 x_{A l}^{2}}{2}$

Dynamics of graded-composition and graded-doping semiconductor nanowires under local carrier modulation

Abstract

1. Introduction

2. SPCM models

3. Simulations and discussion

3.1. Uniform-doping AlGaAs NW device

3.2 Graded-doping AlGaAs NW device

3.3 Graded-composition AlGaAs NW device

3.4 Graded-doping and graded-composition AlGaAs NW device

3.5 Effect of temperature and NW diameter to graded doping and composition devices

4. Conclusions

Funding

Acknowledgments

References and links

Cited By

Figures (7)

Tables (2)

Equations (9)

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