Effect of the depletion region in topological insulator heterostructures for ambipolar field-effect transistors

Formation of a depletion region at the vertically stacked topological insulator $p\text{−}n$ heterostructures is one of the effective approaches to minimize residual carrier density in the bulk regions. Here, we report on characterization of field-effect transistor (FET) based on ${\left(\mathrm{B}{\mathrm{i}}_{0.26}\mathrm{S}{\mathrm{b}}_{0.74}\right)}_2\mathrm{S}{\mathrm{e}}_3/\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ topological insulator heterostructures with a vertical $p\text{−}n$ junction configuration. The thicknesses of the top $p\text{−}{\left(\mathrm{B}{\mathrm{i}}_{0.26}\mathrm{S}{\mathrm{b}}_{0.74}\right)}_2\mathrm{S}{\mathrm{e}}_3$ layer vary from $d=8$ to 25 nm with 3-nm constant thickness of the bottom $n\text{−}\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$. Even at zero gate voltage, increasing thickness of the top layer inverts the dominant conducting carrier from $n$-type to $p$-type. With applying gate voltage, the effect of depletion region at the interface is clearly revealed as a voltage shift of charge neutral point in ambipolar FET operation. The systematic shift of charge neutral point in FET operation clearly indicates that the formation of depletion region can be explained with conventional semiconductor $p\text{−}n$ junction model. In the topological insulator $p\text{−}n$ heterostructures, the thickness tuning of both $p$-type and $n$-type layers is quite important to minimize the residual charge density in the whole device region. The band engineering with $p\text{−}n$ junction will be further applicable to extract the electrical properties of surface state.

Figure 1

(a) Schematic of layer geometry of the field-effect transistor (FET) device consisting of ${\left(\mathrm{B}{\mathrm{i}}_{0.26}\mathrm{S}{\mathrm{b}}_{0.74}\right)}_2\mathrm{S}{\mathrm{e}}_3$ ($d$-nm)/$\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ (3-nm) grown on InP (111) substrate. Corresponding band profile at Γ-point is shown in right panel. $E_{\mathrm{F}}$, SS, VB, and CB represent Fermi energy, surface state, valence band, and conduction band, respectively. (b) Top-view photograph of FET device. D, G, and S represents drain, gate, and source electrode, respectively. (c) The sheet resistance ($R_{\mathrm{xx}}$) as a function of temperature (T) for ${\left(\mathrm{B}{\mathrm{i}}_{0.26}\mathrm{S}{\mathrm{b}}_{0.74}\right)}_2\mathrm{S}{\mathrm{e}}_3/\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$-based FET (BSS-FET) with $d=8$ (blue), 12 (green), 17 (yellow), and 25 nm (red) at gate voltage $V_{\mathrm{G}}=0\mathrm{V}$. (d) $R_{\mathrm{xx}}$ as a function of $V_{\mathrm{G}}$ for BSS- FET with different $d$ measured at $T=1.5\mathrm{K}$. Color code is identical to (c). That for 6-nm $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$-based FET is also shown (grey) as a control experiment.

Figure 2

(a)–(h) Sheet ($R_{\mathrm{xx}}$) and Hall ($R_{\mathrm{yx}}$) resistances versus gate voltage ($V_{\mathrm{G}}$) for each BSS-FET with top ${\left(\mathrm{B}{\mathrm{i}}_{0.26}\mathrm{S}{\mathrm{b}}_{0.74}\right)}_2\mathrm{S}{\mathrm{e}}_3$ thickness $d=$ (a, b) 8, (c, d) 12, (e, f) 17, and (g, h) 25 nm under magnetic field $B=0\mathrm{T}$ (black) and 15 T (red). The $V_{\mathrm{CNP}}^{R\mathrm{xx}}$ is defined as the gate voltage where $R_{\mathrm{xx}}$ shows a maximum. $V_{\mathrm{CNP}}^{R\mathrm{yx}}$ is defined as the gate voltage where $R_{\mathrm{yx}}$ under 15 T changes its sign. Both of $V_{\mathrm{CNP}}^{R\mathrm{xx}}$ and $V_{\mathrm{CNP}}^{R\mathrm{yx}}$ are indicated as black arrows in (a, c, e, g) and (b, d, f, h), respectively. All measurements were performed at $T=1.5\mathrm{K}$.

Figure 3

(a–d) $R_{\mathrm{xx}}$ and (e–h) $R_{\mathrm{yx}}$ versus B for each BSS-FET at the representative $V_{\mathrm{G}}$. The $V_{\mathrm{G}}$ values in (a, e), (b, f), (c, g), and (d, h) are indicated as triangles in Figs. 2(a, b), 2(c, d), 2(e, f), and 2(g, h), respectively, with the same color code. All measurements were performed at $T=1.5\mathrm{K}$.

Figure 4

(a) Top ${\left(\mathrm{B}{\mathrm{i}}_{0.26}\mathrm{S}{\mathrm{b}}_{0.74}\right)}_2\mathrm{S}{\mathrm{e}}_3$ layer thickness dependence of $V_{\mathrm{CNP}}^{R\mathrm{xx}}$ (closed circles) and $V_{\mathrm{CNP}}^{R\mathrm{yx}}$ (open circles) obtained from Fig. 2. The dashed line shows $V_{\mathrm{CNP}}^{R\mathrm{xx}}$ ($V_{\mathrm{CNP}}^{R\mathrm{yx}}$) equal to zero. (b, c) Top layer thickness $d$ dependences of (b) the peak value of $R_{\mathrm{xx}}$ under $B=0\mathrm{T}$ (black) and 15 T (red) and (c) minimum electron ($n_{\min .}$) and hole ($p_{\min .}$) densities calculated from Hall measurements (see text).

Figure 5

(a–c) Schematics of band diagram along $z$ direction in $d$-nm ${\left(\mathrm{B}{\mathrm{i}}_{0.26}\mathrm{S}{\mathrm{b}}_{0.74}\right)}_2\mathrm{S}{\mathrm{e}}_3\left(\mathrm{BSS}\right)/3\text{−}\mathrm{nm}\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ (BS) heterostructure with (a) $d\ll$ critical thickness $d_{\mathrm{c}}$, (b) $d\sim d_{\mathrm{c}}$, and (c) $d>d_{\mathrm{c}}$. $E_{\mathrm{C}}$, $E_{\mathrm{V}}$, and $E_{\mathrm{F}}$ represent conduction band minimum, valence band maximum, and Fermi energy, respectively.