Temperature-dependent internal photoemission probe for band parameters

Yan-Feng Lao and A. G. Unil Perera

Phys. Rev. B 86, 195315 – Published 26 November 2012

Abstract

The temperature-dependent characteristic of band offsets at the heterojunction interface was studied by an internal photoemission (IPE) method. In contrast to the traditional Fowler method independent of the temperature ( $T$ ), this method takes into account carrier thermalization and carrier/dopant-induced band-renormalization and band-tailing effects, and thus measures the band-offset parameter at different temperatures. Despite intensive studies in the past few decades, the $T$ dependence of this key band parameter is still not well understood. Re-examining a $p$ -type doped GaAs emitter/undoped Al $_{x}$ Ga $_{1 - x}$ As barrier heterojunction system disclosed its previously ignored $T$ dependency in the valence-band offset, with a variation up to $\sim - 10^{- 4}$ eV/K in order to accommodate the difference in the $T$ -dependent band gaps between GaAs and AlGaAs. Through determining the Fermi energy level ( $E_{f}$ ), IPE is able to distinguish the impurity (IB) and valence bands (VB) of extrinsic semiconductors. One important example is to determine $E_{f}$ of dilute magnetic semiconductors such as GaMnAs, and to understand whether it is in the IB or VB.

Received 14 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.195315

Authors & Affiliations

Yan-Feng Lao and A. G. Unil Perera^*

Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA

^*uperera@gsu.edu

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Vol. 86, Iss. 19 — 15 November 2012

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Figure 1
(a) The VB diagram of a $p$ -emitter/ $i$ -barrier IPE system. $ρ (ε, - E_{f}) f (ε)$ is the multiplication of the hole energy distribution ( $ρ$ ) and the FD function ( $f$ ). Shown are the (i) nondegenerate and (ii) degenerate doped emitter. Typical IPE processes are labeled as (1) and (2), consisting of optical transitions in the emitter and the escaping of holes from the VB of the emitter to the VB of the barrier. (b) Schematic DOS as a function of energy. By including a band tail, hole states are extended into the forbidden gap (atop the VB). The DOS tail contributes a higher photoemission yield at $h ν > E_{f} + Δ$ compared to that without the DOS tail.Reuse & Permissions
Figure 2
(a) TDIPS fittings to the quantum yield spectra of samples S12a and S12b the emitters of which are nondegenerate and degenerate doped, respectively. The higher yield of S12b at the low-energy end than S12a results from the thermionic emission. Their Fermi level difference was obtained to be $E_{f_{b}} - E_{f_{a}} = 24.5$ meV. The corresponding band pictures with $E_{f}$ lying in the band gap (S12a) and in the VB (S12b) are shown in the insets. The different sharpnesses of barriers close to the heterointerface are due to the MIF barrier lowerings. (b) TDIPS fitting (solid line) to the IPE data (scattered data points) of the $n$ -type GaAs/Al $_{x}$ Ga $_{1 - x}$ As heterojunction adopted from Coluzza et al.,[3] along with the comparison with their Fowler fitting[14] (dashed line).Reuse & Permissions
Figure 3
(a)–(d) are typical experimental quantum yield spectra (scattered data) of GaAs/Al $_{x}$ Ga $_{1 - x}$ As heterojunctions (see Table for sample structures) at different bias voltages and temperatures. Solid lines are the TDIPS fitting curves based on Eq. (4) with $Y_{0}$ , $C_{0}$ and $Δ$ as the fitting parameters. The thermionic emission yield ( $Y_{0}$ ) increases with increasing biases and temperatures. Insets plot the yield spectra in a larger energy range to show the IVB transitions where arrows indicate the $s o$ - $h h$ onsets. The rectangle frames indicate the regions where fittings were made.Reuse & Permissions
Figure 4
(a) Typical plots of $Δ$ against (Electric Field) $^{1 / 2}$ . Solid lines are the least-square fits according to the relationship between the MIF barrier lowering and the electric field. Extrapolated $Δ$ values at zero field were used to obtain band offsets. (b) The average VB offsets [ $Δ E_{v {av}}$ ] over various temperatures, in order to compare with previously reported $T$ -independent data.[2, 7] The composition dependent $Δ E_{v {av}}$ was obtained by a linear fit. Also shown are $Δ E_{v}$ data adopted from Refs. 2 and 7.Reuse & Permissions
Figure 5
(a) Temperature-dependent VB offsets (scattered data) for different GaAs/Al $_{x}$ Ga $_{1 - x}$ As samples. Shown are the temperature coefficients of $Δ E_{v}$ obtained by linear fittings (dashed lines) and taking into account the data of Yi et al.[2] at 4.2 K. The $T$ -dependent $Δ E_{v}$ as a function of $x$ was also obtained to be $Δ E_{v} = (0.570 - 1.39 \times 10^{- 4} T) x$ (eV). (b) Calculated $[Δ E_{g}^{T} / Δ E_{g}^{0K} - 1]$ as a function of temperature by using reported band-gap parameters:[6, 7, 13, 53, 54] i) GaAs/Si, ii) InP/GaAs, iii) InAs/GaSb, iv) GaAs/Al $_{x}$ Ga $_{1 - x}$ As, and v) HgTe/Hg $_{1 - x}$ Cd $_{x}$ Te. The scattered data points are calculations using TDIPS determined $Δ E_{v}^{T}$ and the $Δ E_{c}$ data of O’Shea et al..[2] The shaded areas correspond to heterojunctions with varied alloy fractions. The larger $T$ dependence of band gaps implies more prominent $T$ dependence in band offsets.Reuse & Permissions
Figure 6
Schematics of DOS and VB structures of extrinsic semiconductors showing IB (a) separated from the VB and (b) merged with the VB. The VB of (b) is upward shifted rigidly by $Δ_{BGR}$ . $h h$ , $l h$ , and $s o$ denote the heavy-hole, light-hole, and spin-orbit split-off bands, respectively. $Δ$ is defined as the energy difference between $E_{f}$ and the potential barrier. (c) Calculated $[Δ - Δ E_{v}]$ as a function of hole density for $p$ -type (Ga,Mn)As/Al $_{x}$ Ga $_{1 - x}$ As and GaAs/Al $_{x}$ Ga $_{1 - x}$ As junctions. The $Δ$ value of (Ga,Mn)As/Al $_{x}$ Ga $_{1 - x}$ As is calculated by taking $E_{f}$ data from Ohya et al.[19] and the Mn binding energy of 0.112 eV.[18] Indicated (dashed vertical line) corresponds to the IMT critical density.[18] The merged-band picture of (Ga,Mn)As should lead to a similar $Δ$ variation to $p$ -type GaAs.Reuse & Permissions

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