Resonant tunneling diodes (RTDs) have come full-circle in the past 10 years after their demonstration in the early 1990s
as the fastest room-temperature semiconductor oscillator, displaying experimental results up to 712 GHz and fmax values
exceeding 1.0 THz [1]. Now the RTD is once again the preeminent electronic oscillator above 1.0 THz and is being
implemented as a coherent source [2] and a self-oscillating mixer [3], amongst other applications. This paper concerns
RTD electroluminescence – an effect that has been studied very little in the past 30+ years of RTD development, and not
at room temperature. We present experiments and modeling of an n-type In0.53Ga0.47As/AlAs double-barrier RTD
operating as a cross-gap light emitter at ~300K. The MBE-growth stack is shown in Fig. 1(a). A 15-μm-diam-mesa
device was defined by standard planar processing including a top annular ohmic contact with a 5-μm-diam pinhole in the
center to couple out enough of the internal emission for accurate free-space power measurements [4]. The emission spectra
have the behavior displayed in Fig. 1(b), parameterized by bias voltage (VB). The long wavelength emission edge is at
= 1684 nm - close to the In0.53Ga0.47As bandgap energy of Ug ≈ 0.75 eV at 300 K. The spectral peaks for VB = 2.8 and
3.0 V both occur around = 1550 nm (h = 0.75 eV), so blue-shifted relative to the peak of the “ideal”, bulk InGaAs
emission spectrum shown in Fig. 1(b) [5]. These results are consistent with the model displayed in Fig. 1(c), whereby
the broad emission peak is attributed to the radiative recombination between electrons accumulated on the emitter side,
and holes generated on the emitter side by interband tunneling with current density Jinter. The blue-shifted main peak is
attributed to the quantum-size effect on the emitter side, which creates a radiative recombination rate RN,2 comparable to
the band-edge cross-gap rate RN,1. Further support for this model is provided by the shorter wavelength and weaker
emission peak shown in Fig. 1(b) around = 1148 nm. Our quantum mechanical calculations attribute this to radiative
recombination RR,3 in the RTD quantum well between the electron ground-state level E1,e, and the hole level E1,h.
To further test the model and estimate quantum efficiencies, we conducted optical power measurements using a
large-area Ge photodiode located ≈3 mm away from the RTD pinhole, and having spectral response between 800 and
1800 nm with a peak responsivity of ≈0.85 A/W at =1550 nm. Simultaneous I-V and L-V plots were obtained and
are plotted in Fig. 2(a) with positive bias on the top contact (emitter on the bottom). The I-V curve displays a pronounced
NDR region having a current peak-to-valley current ratio of 10.7 (typical for In0.53Ga0.47As RTDs). The external quantum
efficiency (EQE) was calculated from EQE = e∙IP/(∙IE∙h) where IP is the photodiode dc current and IE the RTD current.
The plot of EQE is shown in Fig. 2(b) where we see a very rapid rise with VB, but a maximum value (at VB= 3.0 V) of
only ≈2×10-5. To extract the internal quantum efficiency (IQE), we use the expression EQE= c ∙i ∙r ≡ c∙IQE where
ci, and r are the optical-coupling, electrical-injection, and radiative recombination efficiencies, respectively [6]. Our
separate optical calculations yield c≈3.4×10-4 (limited primarily by the small pinhole) from which we obtain the curve
of IQE plotted in Fig. 2(b) (right-hand scale). The maximum value of IQE (again at VB = 3.0 V) is 6.0%. From the implicit
definition of IQE in terms of i and r given above, and the fact that the recombination efficiency in In0.53Ga0.47As is
likely limited by Auger scattering, this result for IQE suggests that i might be significantly high.
To estimate i, we have used the experimental total current of Fig. 2(a), the Kane two-band model of interband
tunneling [7] computed in conjunction with a solution to Poisson’s equation across the entire structure, and a rate-equation
model of Auger recombination on the emitter side [6] assuming a free-electron density of 2×1018 cm3. We focus on the
high-bias regime above VB = 2.5 V of Fig. 2(a) where most of the interband tunneling should occur in the depletion region
on the collector side [Jinter,2 in Fig. 1(c)]. And because of the high-quality of the InGaAs/AlAs heterostructure (very few
traps or deep levels), most of the holes should reach the emitter side by some combination of drift, diffusion, and tunneling
through the valence-band double barriers (Type-I offset) between InGaAs and AlAs. The computed interband current
density Jinter is shown in Fig. 3(a) along with the total current density Jtot. At the maximum Jinter (at VB=3.0 V) of 7.4×102
A/cm2, we get i = Jinter/Jtot = 0.18, which is surprisingly high considering there is no p-type doping in the device. When
combined with the Auger-limited r of 0.41 and c ≈ 3.4×10-4, we find a model value of IQE = 7.4% in good agreement
with experiment. This leads to the model values for EQE plotted in Fig. 2(b) - also in good agreement with experiment.
Finally, we address the high Jinter and consider a possible universal nature of the light-emission mechanism. Fig.
3(b) shows the tunneling probability T according to the Kane two-band model in the three materials, In0.53Ga0.47As, GaAs,
and GaN, following our observation of a similar electroluminescence mechanism in GaN/AlN RTDs (due to strong
polarization field of wurtzite structures) [8]. The expression is Tinter = (2/9)∙exp[(-2 ∙Ug
2 ∙me)/(2h∙P∙E)], where Ug is the
bandgap energy, P is the valence-to-conduction-band momentum matrix element, and E is the electric field. Values for
the highest calculated internal E fields for the InGaAs and GaN are also shown, indicating that Tinter in those structures
approaches values of ~10-5. As shown, a GaAs RTD would require an internal field of ~6×105 V/cm, which is rarely
realized in standard GaAs RTDs, perhaps explaining why there have been few if any reports of room-temperature
electroluminescence in the GaAs devices.
[1] E.R. Brown,et al., Appl. Phys. Lett., vol. 58, 2291, 1991. [5] S. Sze, Physics of Semiconductor Devices, 2nd Ed. 12.2.1 (Wiley, 1981).
[2] M. Feiginov et al., Appl. Phys. Lett., 99, 233506, 2011. [6] L. Coldren, Diode Lasers and Photonic Integrated Circuits, (Wiley, 1995).
[3] Y. Nishida et al., Nature Sci. Reports, 9, 18125, 2019. [7] E.O. Kane, J. of Appl. Phy 32, 83 (1961).
[4] P. Fakhimi, et al., 2019 DRC Conference Digest. [8] T. Growden, et al., Nature Light: Science & Applications 7, 17150 (2018).
[5] S. Sze, Physics of Semiconductor Devices, 2nd Ed. 12.2.1 (Wiley, 1981).
[6] L. Coldren, Diode Lasers and Photonic Integrated Circuits, (Wiley, 1995).
[7] E.O. Kane, J. of Appl. Phy 32, 83 (1961).
[8] T. Growden, et al., Nature Light: Science & Applications 7, 17150 (2018).
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Capturing the electron–electron cusp with the coupling-constant averaged exchange–correlation hole: A case study for Hooke’s atoms
In density-functional theory, the exchange–correlation (XC) energy can be defined exactly through the coupling-constant (λ) averaged XC hole n̄xc(r,r′), representing the probability depletion of finding an electron at r′ due to an electron at r. Accurate knowledge of n̄xc(r,r′) has been crucial for developing XC energy density-functional approximations and understanding their performance for molecules and materials. However, there are very few systems for which accurate XC holes have been calculated since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of λ while the electron density remains fixed at the physical (λ = 1) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron–electron cusp using finite basis sets. Focusing on Hooke’s atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the λ-integrated XC hole. Our results indicate that, for Hooke’s atoms, the error introduced by the description of the electron–electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle-, and coupling-constant-averaged XC holes are also calculated and provide a benchmark against which the Perdew–Burke–Ernzerhof and local density approximation XC hole models are assessed.
more » « less- Award ID(s):
- 2042618
- NSF-PAR ID:
- 10498113
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 160
- Issue:
- 1
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 014103
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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