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REVIEW 3 major objections 6 minor 26 references

Photon emission gain in Er doped Si light emitting diodes by impact excitation

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Er-doped silicon LEDs can emit multiple photons per injected electron.

desk verdict Useful device engineering and a clean empirical model, but the 'photon emission gain' claim is a differential-slope artifact that does not survive contact with the paper's own equations. read the letter →

arxiv 2505.18438 v1 pith:SR35AOIY submitted 2025-05-24 physics.optics cond-mat.mes-hall

Huayou Liu , Jiayuan Zhao , Jing Zhang , Huan Liu , Jiajing He , Ulrich Kentsch , Shengqiang Zhou , Manfred Helm
show 1 more author
Yaping Dan
This is my paper · ORCID
classification physics.opticscond-mat.mes-hall PACS 78.60.Fi85.60.Jb
keywords erbium-dopedsiliconimpactexcitationphotonemissiongaininternalquantumefficiencyreverse-biasedLEDelectroluminescencephotonics1.54µm
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a single hot electron traversing the depletion region of a reverse-biased Er-doped silicon diode can excite several Er ions, so the diode emits multiple photons per injected electron. The authors model this photon emission gain as $G = L_{\mathrm{ex}}/\ell$, the ratio of the electroluminescence region width to the electron mean free path, and report that the measured gain matches this ratio from 300 K down to 78 K. They also report an internal quantum efficiency (photons created per injected electron) of 1.84% at 78 K, about twenty times the room-temperature value. If the claim holds, silicon photonics gains a more efficient, electrically pumped route to communication-band light near 1.54 µm.

What carries the argument

The load-bearing object is the impact-excitation rate $W_{\mathrm{ex}} \simeq W_{\mathrm{ex}0}\, n \sqrt{qE\ell - \Delta}$, which sets how many Er ions are excited per unit volume per second when electrons with mean free path $\ell$ are accelerated by electric field $E$. Combined with the steady-state balance $W_{\mathrm{ex}}(N_{tt}-N_{Er}) = W_d N_{Er}$ and the width $L_{\mathrm{ex}}$ of the region where $qE\ell \geq \Delta$, this yields the internal quantum efficiency expression used to fit the data. The central identity $G = L_{\mathrm{ex}}/\ell$ counts how many mean-free-path segments fit inside the emission region, each segment being one opportunity for a re-accelerated electron to excite another Er ion; the paper tests this identity against the measured superlinear slope of photon flux versus electron flux.

What would settle it

Measure the low-flux differential slope $d\Phi/dI$ on a diode whose electroluminescence width is independently imaged to be shorter than the electron mean free path; the claimed relation $G = L_{\mathrm{ex}}/\ell$ predicts a slope below one, whereas an interpretation artifact from the exponential reverse-current fit could still produce a slope above one near threshold.

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Extended reading notes

Core claim

The central discovery claimed is that reverse-biased Er/O/B co-doped Si PN junctions exhibit photon emission gain: the photon flux rises superlinearly with injected electron flux, and the low-flux slope exceeds one. The authors attribute this to multiple impact excitations: an electron accelerated by the depletion-region field loses energy to one Er ion, is re-accelerated, and collides again, so a single electron can excite several Er ions when the electroluminescence region is longer than the mean free path. Quantitatively, the gain is claimed to equal $G = L_{\mathrm{ex}}/\ell$; the measured gain and this ratio agree at all temperatures studied, and the same relation reproduces a gain of about 2.8 in the authors' earlier narrower-junction device with $L_{\mathrm{ex}}/\ell = 10\,\mathrm{nm}/4\,\mathrm{nm}$. The paper further claims an internal quantum efficiency of 1.84% at 78 K, obtained after correcting for the 2.3% escape probability of photons from bulk silicon.

Load-bearing premise

The gain claim rests on interpreting the measured slope of photon flux versus reverse current as photons per electron that actually undergo impact excitation, which assumes the reverse current is dominated by exactly those electrons.

Editorial extensions

If this is right

  • A single electron can produce more than one 1.54 µm photon when the emission region is wider than the electron mean free path, so reverse-biased Er:Si LEDs need not be limited to one photon per electron.
  • The gain is set by the ratio of electroluminescence width to mean free path, so widening the depletion region and lowering carrier concentration directly increase photons per electron.
  • Cooling from room temperature to 78 K suppresses nonradiative Er relaxation and raises the internal quantum efficiency by about a factor of twenty.
  • The extracted design parameters — optically active Er concentration near $10^{20}\,\mathrm{cm}^{-3}$ and mean free path rising from about 115 nm to 185 nm as temperature falls — give concrete targets for future device engineering.
  • Because the emission is electrically pumped and at the communication band, the authors argue the mechanism is a foundation for silicon-based on-chip lasers and quantum light sources.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If $G = L_{\mathrm{ex}}/\ell$ holds across devices, the photon-number statistics of this LED should show a random number of photons per injected electron; a superconducting-nanowire single-photon detector paired with a low-noise current source could test that directly.
  • The inverse analogy to photoconductive gain suggests a timing trade-off: more gain means later photons, so pulse-to-pulse jitter may grow with $L_{\mathrm{ex}}$, which would matter for clocked quantum communication.
  • A continuous test would be to grade the doping so that $L_{\mathrm{ex}}$ changes monotonically within one device; the predicted gain-versus-voltage curve could then be checked without fabricating many samples.
  • The claim that the optically active Er concentration is temperature-independent at about $10^{20}\,\mathrm{cm}^{-3}$ could be cross-checked by independent absorption or pump-probe measurements on the same diodes.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript reports photon emission gain in Er-doped silicon LEDs operated under reverse bias, defined as the emission of multiple photons per injected electron. The authors measure the reverse-bias current-voltage characteristic and the absolute near-infrared photon flux at several temperatures, fit their impact-excitation model [Eq. (3)] to the internal quantum efficiency, extract parameters including the electron mean free path ℓ, and compare a low-bias differential slope G = dΦ/d(I_R/q) with L_ex/ℓ. They report an internal quantum efficiency of 1.84% at 78 K and claim that this validates the gain mechanism G = L_ex/ℓ, with an additional check on a previously published device.

Significance. If the gain claim were established, it would be of clear interest for silicon photonics, because it would imply that a single hot electron can excite multiple Er ions in a wide depletion region and thereby increase the efficiency of communication-band silicon light sources. The paper contains useful experimental ingredients: calibrated absolute power measurement, KPFM characterization of the junction, temperature-dependent electroluminescence data, and parameter extraction that is compared with literature values. However, the central claim is not supported by the presented analysis. The differential-slope gain is confounded by the voltage sweep, and the comparison with L_ex/ℓ is partly circular because ℓ is extracted from the same IQE fits. These are load-bearing problems with the main conclusion, not presentation issues.

major comments (3)
  1. [Fig. 3(b) and the paragraph beginning 'Finally, let us revisit Figure 3(b)'] The gain is defined as the differential slope dΦ/d(I_R/q) of a voltage-swept measurement. Under the paper's own model, Φ(V) = IQE(V)·I_R(V)/q, with IQE given by Eq. (3), W_ex ∝ n·sqrt(qEℓ − Δ), and I_R fitted as I_R = I_0(exp(V/V_0) − b). Differentiating gives dΦ/d(I_R/q) = IQE(V) + (I_R/q)·(dIQE/dV)/(d(I_R/q)/dV). Near the impact-excitation threshold, dIQE/dV is positive and steep while the denominator is finite, so the second term can exceed unity even when IQE(V) is everywhere below unity. The paper's reported peak IQE is 1.84% (Fig. 3(c)), i.e., 0.0184 photons per injected electron; a differential slope greater than one is therefore fully compatible with every electron emitting far less than one photon on average. The superlinear initial rise in Fig. 3(b) only shows that the additional electrons injected at higher reverse bias arrive when the per-electron excitation probability is larger; it does not demonstrate multiple photons per injected electron.
  2. [Eq. (3) and Fig. 3(h)] The comparison G ≈ L_ex/ℓ is not an independent validation. The electron mean free path ℓ is obtained by fitting Eq. (3) to the IQE(V) data shown in Fig. 3(c), and the same fits and fitted ℓ are used to construct the photon-flux curve whose low-bias slope defines G; L_ex is obtained from Eq. (1) using V_min also extracted from the same data set. The agreement in Fig. 3(h) is therefore a consistency test between a measured slope and a ratio of fitted parameters from the same data, not a prediction that could falsify the model. The previous-device check based on ref. [15] is less circular, but it again relies on a mean free path extracted from the same impact-excitation theory and does not remove the voltage-sweep confound described above.
  3. [Eq. (3) and the treatment of reverse current] The analysis assumes that the total reverse current I_R consists of electrons that traverse the electroluminescence region and contribute to impact excitation, with the injection electron rate taken as I_R/q. In a reverse-biased Si pn junction at these temperatures, the reverse current is generation current arising throughout the depletion region, so carriers are generated at different positions; an electron generated near the n-side will not traverse the entire high-field region, and holes also contribute to the measured current. This assumption can bias both the extracted ℓ and the low-bias slope assigned to per-electron gain. The manuscript should either justify this identification quantitatively from the device geometry and generation profile, or model the position-dependent contribution of the current to impact excitation.
minor comments (6)
  1. [Throughout the manuscript] There are unresolved 'Error! Reference source not found.' placeholders in the captions and body text, including after 'Figure 1(a)' and 'Figure 2(e)'; these must be repaired before any resubmission.
  2. [Fig. 3(c) and abstract] The claim that the IQE of 1.84% is a 'record' is not supported by a systematic comparison with prior reverse-bias Er-doped Si LEDs at the same wavelength and temperature; the word 'record' should be removed or substantiated with a literature table.
  3. [Eq. (1) and surrounding text] The notation for the electroluminescence width is inconsistent: L_ex, L_exp, and L_expn appear in the same passage; each subscript should be defined and used consistently.
  4. [Eqs. (2) and (3)] Eq. (2) is referred to as 'eq. (2)' but is not shown with an equation number; number it explicitly, and define every symbol in Eq. (3), including the cross-sectional area A_c and the conversion factor used to go from photon power to photon flux.
  5. [Fig. 3(a) and the reverse-current fit] The empirical fit I_R = I_0(exp(V/V_0) − b) is introduced without reporting the fitted parameters I_0, V_0, and b or their uncertainties; these values are needed to evaluate the derivative argument in the gain analysis.
  6. [Fig. 3(f) and the extracted mean free path] The extracted mean free path of 185 nm at 78 K is about two orders of magnitude larger than the ~4 nm value quoted from ref. [15] for a highly doped device; the manuscript should discuss whether this difference is consistent with the doping and temperature dependence of electron transport in Si.

Circularity Check

3 steps flagged · score 6.0 of 10

The claimed gain G=Lex/ell is a differential slope of a voltage-swept curve compared with a mean free path fitted from the same IQE data; the cross-device 'validation' reuses the same fitted theory.

  1. fitted input called prediction [Figure 3(c)-(h); eq.(3) and paragraph 'From the fittings... Finally, let us revisit Figure 3(b)...']
    "From the fittings, we extracted the relaxation rate Wd, the term αNtt, the mean free path ℓ and the minimum voltage for impact excitation Vmin. ... Finally, let us revisit Figure 3(b) ... the derivative of the photon emission flux with respect to the electron flux at low end is significantly larger than 1. It implies that every additional electron injected into the diode excites multiple photons. ... Logically, the emission gain should be approximately equal to Lex/ℓ, i.e. G = Lex/ℓ. ... The gain and the ratio are indeed comparable over the entire temperature range."

    ℓ is a free parameter used in eq.(3) to fit the same IQE(V) vs reverse-voltage data whose photon-flux/electron-flux differential slope is then called the gain. Lex is also derived from fits (eq.(1) to the FWHM data). Therefore the agreement G ≈ Lex/ℓ is not an independent prediction: it compares a differential form of the fitted curve with a ratio of fit-determined quantities. Consistent fits to eq.(3) essentially guarantee that the fitted model's d(Phi)/d(IR/q) and fitted (Lex, ℓ) are mutually compatible, so the agreement in Fig. 3(h) is a consistency check, not a test.

  2. self definitional [Paragraph beginning 'Finally, let us revisit Figure 3(b)...'; Figure 3(b)-(g)]
    "the derivative of the photon emission flux with respect to the electron flux at low end is significantly larger than 1. It implies that every additional electron injected into the diode excites multiple photons."

    Both axes in Fig. 3(b) are functions of the same reverse voltage V. With the paper's own eq.(3), Phi(V) = IQE(V) * IR(V)/q, so d(Phi)/d(IR/q) = IQE(V) + (IR/q) dIQE/dV / (d(IR/q)/dV). Near the impact-excitation threshold, W_ex ~ sqrt(qEℓ - Δ) makes dIQE/dV steeply positive while IR is exponential in V, so this differential expression can exceed 1 even though the paper's own maximum average IQE is 1.84%. The superlinear slope is therefore an artifact of sweeping V (raising current, excitation probability, and emission width simultaneously), not a measurement of multiple photons per injected electron; calling it 'emission gain' loads the conclusion into the definition.

1 more flagged steps
  1. self citation load bearing [Final validation paragraph before Conclusion; ref. [15]]
    "More interestingly, in our previous publication[15], the Er doped Si LED has a much higher carrier concentration in the p and n region. The electroluminescence region is as narrow as 10 nm and the mean-free path extracted from the theoretical fitting is ~ 4 nm. Consistently, we observed an experimental photon emission gain ~ 2.8 by impact excitation, very close to the ratio of the electroluminescence region width to the mean-free path (10 / 4 = 2.5)."

    This is presented as an independent cross-device validation, but the mean free path (~4 nm) comes from 'the theoretical fitting' of the same impact-excitation theory developed in the authors' prior PRL [15], and Lex=10 nm is inferred from the same model. The ratio 2.5 is thus not an external measurement; it is another output of the same fitted theory. The gain ~2.8 is again a differential slope of a voltage-swept photon vs current curve. Agreement between a slope and a theory-inferred ratio, both produced by the same self-cited framework, does not provide independent support for G = Lex/ℓ.

full rationale

The paper reports a real empirical feature: at low reverse bias the photon flux rises faster than linearly with reverse current, and the IQE(V) curves are well fit by the proposed rate-equation model. However, the central claim that this slope is a per-electron photon-emission gain G = Lex/ℓ is not independently established. The gain is defined as dPhi/d(IR/q) along a voltage sweep; under the paper's own equations this differential equals IQE(V) plus a positive voltage-dependent term and can exceed unity while IQE is only 1.84%, so the slope does not by itself imply multiple photons per electron. Moreover, the mean free path ℓ used to form Lex/ℓ is a parameter fitted with eq.(3) to the very same IQE data, and Lex is fitted from eq.(1); the Fig. 3(h) agreement is therefore an internal consistency relation, not a prediction. The cross-device check in ref. [15] is weakened because the cited prior work is by the same group and supplies the mean free path from the same theoretical fitting. Some independent support exists (FWHM-derived Na agrees with resistivity, Wd parameters agree with literature), but those do not validate the gain mechanism. The burden of the central claim therefore rests on a self-consistent fit plus a differential-slope reinterpretation, warranting a partial circularity score of 6.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The gain claim rests on several fitted parameters, most importantly ell and Vmin, and on a same-group impact-excitation model carried over from PRL 132, 246901. No independent single-electron-counting experiment is provided.

free parameters (7)
  • electron mean free path ell = 115 nm (300 K) to 185 nm (78 K)
    Fitted per temperature to IQE versus reverse voltage using eq.(3); directly enters W_ex and the claimed gain G = Lex/ell.
  • minimum impact-excitation voltage Vmin = 1.87 +/- 0.46 V
    Fitted from FWHM of the electroluminescence profile versus reverse bias in Fig. 2(f); used to set Emin and Lex.
  • Er relaxation rate Wd = Arrhenius fit gives Wnr = 6.5e5 s^-1, Ea = 170 meV, Wr = 73 s^-1
    Fitted in eq.(3) at each temperature; controls the saturation shape of IQE versus voltage.
  • radiative fraction alpha = not tabulated; alpha*Ntt fitted and alpha plotted in Fig. 3(e)
    Fitted in eq.(3) at each temperature; used to convert fitted alpha*Ntt into Ntt.
  • optically active Er concentration Ntt = 1.14e20 cm^-3
    Obtained by dividing fitted alpha*Ntt by fitted alpha; not independently measured in this paper.
  • impact excitation coefficient W_ex0 = not given in this paper
    Carried over from prior PRL [15] by the same group; sets the overall scale of W_ex.
  • reverse-current fit parameters I0, V0, b = not reported
    Empirical fit I_R = I0(exp(V/V0)-b) per temperature; used to convert voltage sweeps into electron flux for the gain slope.
assumptions (6)
  • domain assumption Depletion-region field profile is linear in the n and p regions, with Lex determined by qE ell >= Delta.
    Used in eq.(1) and Fig. 2(e) to convert the measured FWHM into an electroluminescence width.
  • domain assumption Impact excitation rate W_ex = W_ex0 n sqrt(qE ell - Delta) from prior PRL [15].
    Central model for the excitation probability; the theory is cited from the same group and not re-derived here.
  • domain assumption Steady-state single-level rate equation W_ex(Ntt - NEr) = Wd NEr.
    Eq.(2) assumes one effective Er excited state and a uniform optically active concentration.
  • domain assumption Wd(T) = Wnr exp(-Ea/kT) + Wr.
    Used to fit Fig. 3(d) and extract Wnr, Ea, and Wr from literature-supported temperature dependence.
  • ad hoc to paper All reverse current I_R consists of electrons traversing the EL region and contributing to impact excitation.
    The paper uses I_R/q as the injection rate without testing whether leakage or non-exciting current contaminates the gain slope.
  • domain assumption Only 2.3% of photons escape from bulk silicon to free space.
    Used to convert external quantum efficiency to internal quantum efficiency, following refs. [15,22].

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Cite this review

Pith. "Pith review of Photon emission gain in Er doped Si light emitting diodes by impact excitation." pith.science (2026). https://pith.science/paper/SR35AOIY

@misc{pith2026250518438,
  author       = {Pith},
  title        = {Pith review of: Photon emission gain in Er doped Si light emitting diodes by impact excitation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SR35AOIY}},
  note         = {Machine review of arXiv:2505.18438}
}
read the original abstract

This work demonstrates photon emission gain, i.e., emission of multiple photons per injected electron, through impact excitation in Er-doped silicon light-emitting diodes (LEDs). Conventional methods for exciting Er ions in silicon suffer from low efficiency due to mismatched energy transfer between exciton recombination and Er excitation. Here, we propose a reverse-biased Si PN junction diode where ballistically accelerated electrons induce inelastic collisions with Er ions, enabling tunable excitation via electric field modulation. Theoretical modeling reveals that photon emission gain arises from multiple impact excitations by a single electron traversing the electroluminescence region, with the gain value approximating the ratio of emission region width to electron mean free path, i.e., G = Lex/l. Experimental results show an internal quantum efficiency (IQE) of 1.84% at 78 K, representing a 20-fold enhancement over room-temperature performance. This work provides a critical foundation for on-chip integration of silicon-based communication-band lasers and quantum light sources.

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