Biphotonic Electron Emission in Organic Semiconductors

• Biphotonic electron emission (BEE) is a multiphoton process in organic semiconductors where electron emission results from exciton fusion rather than traditional single-quantum photoemission.
• It operates via exciton–exciton and exciton–anion fusion channels, producing fixed onset kinetic energies independent of photon energy and demonstrating superlinear photon-flux dependence.
• Understanding BEE is crucial as it affects the interpretation of photoelectron spectroscopy data and impacts the performance of devices like OLEDs and organic solar cells.

Biphotonic electron emission (BEE), in the usage established for organic semiconductors, denotes a low-photon-energy photoelectron-emission channel in which the emitted electron ultimately derives from the energy of two photo-induced excitations rather than from ordinary single-quantum external photoelectron effect (SQEPE) out of a pre-existing occupied state. In thin-film organic semiconductors, BEE is treated as an effective biphotonic process mediated by exciton fusion—specifically exciton–exciton fusion or exciton–anion fusion—and it is consequential both as a genuine microscopic process and as a spectroscopic pitfall, because it can dominate low-energy photoelectron yield and be mistaken for the density of occupied in-gap states (Nakazawa et al., 1 Oct 2025).

1. Definition and conceptual scope

In this formulation, BEE is not described as ordinary one-step SQEPE, and it is also not described primarily as a textbook coherent two-photon photoemission event. Rather, the defining idea is that low-energy photons first generate excited states and/or anions in the material, and interactions between these photo-generated species then produce a superexcited state that ejects an electron into vacuum. The term therefore refers to photoelectron emission via exciton fusion, i.e. a nonlinear, multi-particle process enabled by photo-generated excitons and/or anions (Nakazawa et al., 1 Oct 2025).

The mechanism is explicitly divided into two channels. In exciton–exciton fusion, two excitons interact and one partner is promoted to a superexcited state. In exciton–anion fusion, a relaxed exciton interacts with an anion whose occupied state is the singly occupied molecular orbital (SOMO), again producing a superexcited state that emits an electron. This usage follows earlier organic-crystal work and is applied to thin-film organic semiconductors in the recent study.

A central consequence of this definition is that BEE is distinct from any interpretation in which low-energy photoelectron yield is assumed to be the integral of the occupied density of states (DOS). In the BEE channel, the detected electron is not a direct readout of a pre-existing occupied in-gap state. That distinction underlies the methodological critique of derivative photoelectron yield spectroscopy (DPYS).

2. Microscopic mechanism and energetic structure

For exciton–anion fusion, the mechanistic sequence is written as

$$\mathrm{M} + h\nu \rightarrow \mathrm{M}^{**} \rightarrow \mathrm{M}^{*},$$

followed by

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$

Here $\mathrm{M}$ is the neutral molecule, $\mathrm{M}^{*}$ the relaxed exciton, $\mathrm{M}^{**}$ the superexcited state, $\mathrm{M}^{-}$ the anion, and $e^{-}$ the emitted electron (Nakazawa et al., 1 Oct 2025).

For exciton–exciton fusion, the process is written as

$$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$

The relevant energetic reference points are the HOMO, occupied in-gap states, the neutral-molecule LUMO, the SOMO of anion states, the vacuum level, the neutral ionization energy $I$, the anion ionization energy $I_{\mathrm{anion}}$, and exciton energies such as $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$0 and $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$1. For conventional SQEPE, the onset kinetic energy tracks photon energy linearly:

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$2

for HOMO emission,

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$3

for occupied in-gap states, and

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$4

for SQEPE from anion SOMO states.

BEE differs at the level of onset energetics. For exciton–anion fusion,

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$5

and for exciton–exciton fusion,

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$6

The onset kinetic energy is therefore independent of $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$7, because emission is controlled by internal excitation energies rather than directly by the photon energy of the detected event. This $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$8-independent onset is one of the strongest signatures of BEE.

3. Separation from competing low-energy photoemission channels

The low-energy photoelectron response of organic semiconductors is separated into three pathways: SQEPE from occupied in-gap states, SQEPE from the SOMO of anions, and BEE via exciton fusion (Nakazawa et al., 1 Oct 2025).

The first pathway is the conventional interpretation used in PYS and DPYS DOS analysis. One photon ejects one electron from a pre-existing occupied state in the gap, and the onset shifts with slope $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$9 as a function of $\mathrm{M}$0. Under the usual assumptions, this channel reflects the occupied DOS.

The second pathway is still single-quantum photoemission, but from a photo-generated charged state rather than from the neutral occupied DOS. The sequence is

$\mathrm{M}$1

$\mathrm{M}$2

An electron can then be emitted from the anion SOMO, again with onset slope $\mathrm{M}$3 versus $\mathrm{M}$4.

The third pathway, BEE, is fundamentally different. The emitted electron is produced only after interaction of two excited species. Spectroscopically, this yields a fixed onset kinetic energy rather than an onset that tracks $\mathrm{M}$5. It can therefore produce electrons even when the photon energy is below the effective work function for ordinary SQEPE.

Photon-flux dependence provides an additional discriminator. SQEPE is approximately linear in photon flux. BEE is superlinear because it depends on populations of two interacting photo-generated species. For anion–singlet fusion the key proportionality is

$\mathrm{M}$6

Because $\mathrm{M}$7 scales linearly with photon flux but $\mathrm{M}$8 can scale between $\mathrm{M}$9 and $\mathrm{M}^{*}$0, the BEE signal can scale between $\mathrm{M}^{*}$1 and $\mathrm{M}^{*}$2. For pure exciton–exciton fusion, the simplest expectation is approximately quadratic scaling with photon flux. The analysis therefore does not assign a universal exact exponent of $\mathrm{M}^{*}$3 to all BEE signals.

4. Experimental realization in Alq$\mathrm{M}^{*}$4

Tris(8-hydroxyquinoline) aluminum, Alq$\mathrm{M}^{*}$5, is the principal case study in which BEE is resolved experimentally through PYS, $\mathrm{M}^{*}$6-dependent high-sensitivity ultraviolet photoelectron spectroscopy (HS-UPS), CFS-YS, and photon-flux dependence (Nakazawa et al., 1 Oct 2025).

In PYS, Alq$\mathrm{M}^{*}$7 shows an ionization energy of about $\mathrm{M}^{*}$8 together with notable peaks at $\mathrm{M}^{*}$9, $\mathrm{M}^{**}$0, and $\mathrm{M}^{**}$1. If PYS were simply the integral of occupied DOS, the yield should increase monotonically with photon energy, so these peaks already imply additional physics. HS-UPS then determines the effective work function from the secondary-electron cutoff to be $\mathrm{M}^{**}$2, yet photoelectron yield is observed at $\mathrm{M}^{**}$3. Because SQEPE from occupied states requires photon energies at least equal to the effective work function, this sub-work-function yield cannot originate from ordinary occupied-state photoemission.

The decisive evidence comes from $\mathrm{M}^{**}$4-dependent HS-UPS. For $\mathrm{M}^{**}$5–$\mathrm{M}^{**}$6, HOMO emission shows an onset with slope $\mathrm{M}^{**}$7, consistent with $\mathrm{M}^{**}$8. For $\mathrm{M}^{**}$9, a weak onset also shifts with slope $\mathrm{M}^{-}$0 and is assigned to SQEPE from anion SOMO states, with fitted $\mathrm{M}^{-}$1. At the same time, a strong low-$\mathrm{M}^{-}$2 feature near the secondary-electron cutoff exhibits nearly identical lineshapes across photon energies, and its onset remains fixed at about $\mathrm{M}^{-}$3 independent of $\mathrm{M}^{-}$4. That fixed onset is the direct identification of BEE.

The energetic consistency check narrows the microscopic channel. Using $\mathrm{M}^{-}$5, $\mathrm{M}^{-}$6, neutral ionization energy $\mathrm{M}^{-}$7, and $\mathrm{M}^{-}$8, the calculated BEE kinetic energies are negative for singlet–singlet, triplet–triplet, singlet–triplet, and anion–triplet channels, whereas anion–singlet fusion gives

$\mathrm{M}^{-}$9

close to the observed onset near $e^{-}$0. The Alq$e^{-}$1 BEE channel is therefore assigned specifically to singlet–anion fusion.

Photon-flux dependence is consistent with that assignment. At $e^{-}$2 and $e^{-}$3, where the low-energy feature is assigned to BEE, the peak intensity scales approximately as $e^{-}$4 and $e^{-}$5, respectively. By contrast, at $e^{-}$6, where the signal is assigned to SQEPE from anions and excitons or anions are not formed because the photon energy is below the optical bandgap, the intensity is linear in photon flux.

High-$e^{-}$7 CFS-YS then recovers the actual DOS. At $e^{-}$8, the DOS of in-gap states follows

$e^{-}$9

with $$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$0, and a Gaussian peak at $$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$1 is assigned to the SOMO DOS of the anion. The SOMO onset is reported as $$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$2 in the main text and $$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$3 in the summary. The study further states that CFS-YS revealed the DOS of in-gap states and SOMO over six orders of magnitude, and that direct determination of the stabilized SOMO clarifies the role of Alq$$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$4 as an electron injection layer in organic light-emitting diodes.

5. Consequences for PYS, DPYS, and CFS-YS

The methodological problem posed by BEE is rooted in the assumptions behind DOS extraction from photoelectron-yield measurements. The standard three-step photoemission expression is written as

$$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$5

and the total PYS yield is

$$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$6

Under the usual simplifying assumptions that $$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$7, $$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$8, $$\mathrm{M}_1^* + \mathrm{M}_2^* \rightarrow \mathrm{M}_1 + \mathrm{M}_2^{**} \rightarrow \mathrm{M}_1 + \mathrm{M}_2^+ + e^{-}.$$9, and $I$0 are effectively constant with $I$1,

$I$2

so that

$I$3

If $I$4 near low kinetic energies, then

$I$5

and the second derivative can approximate $I$6 (Nakazawa et al., 1 Oct 2025).

For CFS-YS, because $I$7 is held fixed,

$I$8

so that $I$9 can be regarded as proportional to $I_{\mathrm{anion}}$0, assuming weak $I_{\mathrm{anion}}$1-dependence of $I_{\mathrm{anion}}$2.

These DOS relations all assume that the detected electrons arise from SQEPE of occupied states. Once BEE contributes, that assumption fails. BEE is not described by the same initial-state DOS integral, and therefore DPYS or low-$I_{\mathrm{anion}}$3 CFS-YS can no longer be interpreted as faithful DOS estimators. The practical manifestation is severe because “the BEE signal masks the DOS.”

Several consequences follow. First, PYS is no longer monotonic with photon energy, so the integrated-DOS picture breaks down directly. Second, sub-work-function emission demonstrates that part of the yield is energetically inaccessible to ordinary occupied-state SQEPE. Third, derivative operations amplify non-DOS structure. In C$I_{\mathrm{anion}}$4, where only SQEPE from HOMO and in-gap states is present, DPYS still introduces artifacts, including a $I_{\mathrm{anion}}$5 peak absent in CFS-YS and a threshold shifted too low due to smoothing and broadening. In Alq$I_{\mathrm{anion}}$6, where BEE is present, DPYS shows oscillations near $I_{\mathrm{anion}}$7, $I_{\mathrm{anion}}$8, and $I_{\mathrm{anion}}$9 and even negative values in some regions. Not every discrepancy is therefore necessarily BEE, but BEE makes the failure substantially worse.

Conventional low-$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$00 CFS-YS is likewise vulnerable. In Alq$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$01, CFS-YS measured at the secondary-electron cutoff peak ($$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$02) shows peaks around $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$03, $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$04, and $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$05 similar to DPYS, but HS-UPS demonstrates that electrons with $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$06 are BEE-dominated. When CFS-YS is instead measured at $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$07, above the BEE-dominated region, the BEE peaks disappear and the remaining spectrum can be assigned to real occupied states.

6. Diagnostic criteria and practical protocol

The practical protocol proposed for low-energy photon measurements is explicit and begins with screening for BEE (Nakazawa et al., 1 Oct 2025).

The first diagnostic is photon-flux dependence. If spectral shape and intensity are linear and stable with photon flux, the signal likely reflects SQEPE and DOS. If the spectrum changes with photon flux or shows superlinear intensity, BEE is likely involved.

The second diagnostic is energetic feasibility. Expected BEE kinetic energies are calculated from

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$08

for exciton–exciton fusion and

$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$09

for exciton–anion fusion. If all such $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$10 values are negative, BEE should not be observed in principle; if positive, BEE may appear.

The third diagnostic is $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$11-dependent HS-UPS. A slope-$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$12 onset versus $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$13 indicates SQEPE. A fixed onset kinetic energy indicates BEE. This step identifies the kinetic-energy window contaminated by exciton-fusion emission.

Once BEE is established, the recommended response is not to trust DPYS or low-$$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$14 CFS-YS. Instead, CFS-YS should be performed at a fixed kinetic energy above the BEE-dominated region. The advocated workflow is therefore: screen for BEE by energetics and photon-flux dependence, verify the channel by $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$15-dependent UPS, move the CFS-YS detection energy above the BEE window, and only then extract DOS.

The authors also note several caveats. Exciton energy is approximated by the optical bandgap in the broader materials survey as a first-order estimate of singlet energy. Observed BEE depends on whether the emitted electron has sufficient kinetic energy to escape. Photon-flux exponents are not universal for exciton–anion fusion. Broader material classifications that rely on simplified criteria such as $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$16 are useful as screening rules rather than full microscopic proof.

7. Device relevance and relation to adjacent multiparticle-emission phenomena

BEE is presented not merely as a spectroscopy artifact but also as an intrinsic process with consequences for organic optoelectronic devices (Nakazawa et al., 1 Oct 2025). In OLEDs, BEE via exciton–exciton or exciton–anion fusion can quench excitons non-radiatively, reduce luminescence efficiency, generate hot electrons and cations, promote bond dissociation and degradation, and disturb carrier balance under bias. For exciton–exciton fusion in the emissive layer, one exciton deactivates by transferring energy to another, which becomes superexcited and produces a hot electron plus cation. For singlet–anion fusion under bias, where anions accumulate at heterointerfaces, the process can explain loss of photoluminescence efficiency above turn-on because singlets are quenched by anions. In organic solar cells, the same process may also be viewed as a carrier-generation pathway because exciton fusion can create a hot electron and a cation.

Two neighboring literatures help delimit what BEE is not. Work on overbias photon emission in monolayer transition-metal-dichalcogenide tunneling LEDs analyzes a different higher-order nonequilibrium process: two-electron coherent tunneling generates one excitonic optical excitation, yielding overbias light emission with threshold near half the exciton energy. That process is conceptually related through the combination of multiple elementary excitations into a single higher-energy final state, but it is not BEE in the photoemission sense, because the driving field is tunneling electrons and the output is a photon via exciton recombination rather than an emitted electron (Shan et al., 2023).

Likewise, studies of electron pair emission from surfaces address coincidence detection of two emitted electrons and the experimental separation of true and random coincidences. Those methods are relevant if BEE were operationally recast as a coincidence problem, but they do not discuss biphotonic electron emission in the nonlinear two-photon-absorption sense explicitly. Their importance is methodological rather than definitional: they provide a framework for rate scaling, accidental-background subtraction, and instrument tradeoffs in correlated two-electron measurements (Kamrla et al., 2021).

Taken together, these distinctions place BEE within a broader class of multiparticle, nonthermal emission phenomena while preserving its specific meaning in organic-semiconductor photoemission: a photoelectron-emission channel generated by exciton fusion, identifiable by an $$\mathrm{M}^{*} + \mathrm{M}^{-} \rightarrow \mathrm{M} + \mathrm{M}^{**} \rightarrow 2\mathrm{M} + e^{-}.$$17-independent onset kinetic energy and superlinear photon-flux dependence, and decisive for the correct interpretation of low-energy photoelectron-yield data.