Constant Final State Yield Spectroscopy

• CFS-YS is a photoelectron spectroscopy technique that fixes the detected electron kinetic energy and varies the photon energy to directly probe the initial-state density of states.
• It minimizes the assumptions required in conventional photoelectron yield methods by effectively excluding parasitic channels like biphotonic electron emission.
• Experimental demonstrations in C60 and Alq3 highlight its efficacy in resolving occupied states, revealing exciton-induced artifacts and surface-anion effects in organic semiconductors.

Searching arXiv for the cited CFS-YS and related selective final-state spectroscopy papers. Constant Final State Yield Spectroscopy (CFS-YS) is a photoelectron spectroscopy mode in which the detected photoelectron kinetic energy $E_\mathrm{k}$ is held fixed while the photon energy $h\nu$ is scanned, so that the measured signal is the partial yield at a constant final state rather than the total emitted-electron yield. In the context of low-energy photoemission from organic semiconductors, CFS-YS is presented as the reliable route for determining the density of occupied in-gap states, provided that the chosen final-state condition excludes parasitic emission channels such as biphotonic electron emission (BEE). Under that condition, the CFS-YS spectrum $Y_\mathrm{CFS}/h\nu$ tracks the initial-state density of states (DOS) much more faithfully than conventional photoelectron yield spectroscopy (PYS) or its derivatives (Nakazawa et al., 1 Oct 2025).

1. Measurement principle and formal structure

CFS-YS is defined operationally by fixing the detected photoelectron kinetic energy and scanning the photon energy. In the reported implementation, the method used the same $h\nu$-dependent high-sensitivity ultraviolet photoelectron spectroscopy setup as the energy-distribution measurements: monochromated photons from 1.5 to 8.4 eV, a hemispherical analyzer, and a fixed analyzer pass condition selecting a chosen $E_\mathrm{k}$ (Nakazawa et al., 1 Oct 2025). The measurement therefore samples a selected final state rather than integrating over all accessible final kinetic energies.

The underlying angle-integrated photoemission expression is

$$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$

where $D_\mathrm{i}$ is the initial-state DOS, $D_\mathrm{f}$ the final-state DOS, $\lvert M_{\mathrm{fi}}\rvert^2$ the transition matrix element, $X(E_\mathrm{k})$ the transport probability to the surface, and $h\nu$0 the surface transmittance probability. At fixed $h\nu$1, the factors $h\nu$2, $h\nu$3, and $h\nu$4 are constant in principle, so the CFS yield becomes

$h\nu$5

Accordingly,

$h\nu$6

and if the $h\nu$7-dependence of $h\nu$8 is small, the plotted CFS-YS spectrum directly tracks the initial-state DOS.

The central conceptual advantage follows directly from this fixed-final-state geometry. Scanning $h\nu$9 varies the sampled initial binding energy $Y_\mathrm{CFS}/h\nu$0 while keeping the final-state factors fixed. This reduces the number of assumptions required to interpret the signal as a DOS, especially relative to total-yield methods that necessarily integrate over a continuum of final kinetic energies.

2. Relation to conventional PYS and derivative-based DOS reconstruction

In conventional PYS, the measured total yield is

$Y_\mathrm{CFS}/h\nu$1

Explicitly,

$Y_\mathrm{CFS}/h\nu$2

If one assumes $Y_\mathrm{CFS}/h\nu$3, $Y_\mathrm{CFS}/h\nu$4, $Y_\mathrm{CFS}/h\nu$5, and $Y_\mathrm{CFS}/h\nu$6 to be constant, this reduces to

$Y_\mathrm{CFS}/h\nu$7

Under that approximation, the derivative

$Y_\mathrm{CFS}/h\nu$8

is taken to represent $Y_\mathrm{CFS}/h\nu$9. With the further assumption $h\nu$0, Tadano-type analysis gives

$h\nu$1

so the DOS is approximated by

$h\nu$2

The distinction is methodological rather than merely notational. PYS interprets a total yield integrated over final kinetic energies, whereas CFS-YS measures a selected final state. This is why CFS-YS is described as requiring fewer assumptions. The derivative-PYS and second-derivative-PYS procedures are only valid if the detected yield is truly due to the single-quantum external photoelectron effect (SQEPE) from occupied states. The paper’s central argument is that this condition often fails in organic semiconductors under low-energy illumination (Nakazawa et al., 1 Oct 2025).

A common misconception is that any low-energy yield spectrum, once differentiated, is a DOS. The reported analysis rejects that equivalence. In this treatment, derivative-based PYS is a model-dependent inference that breaks down when additional photoelectron-generation channels contribute to the measured yield.

3. Competing photoelectron-generation channels and the failure mode of low-energy PYS

The reported difficulty in determining in-gap DOS arises because low-energy photons in organic semiconductors can generate excitons and anions, and those excited species can themselves produce photoelectrons. The low-energy signal is therefore not necessarily an integrated occupied DOS. Three distinct mechanisms are identified (Nakazawa et al., 1 Oct 2025).

SQEPE from occupied in-gap states is the desired channel. Its threshold obeys

$h\nu$3

with slope 1 in $h\nu$4 versus $h\nu$5.

SQEPE from the SOMO of anions occurs because low-energy illumination can create photocarriers and trapped negative carriers near the surface:

$h\nu$6

$h\nu$7

Photoemission from the anion SOMO follows

$h\nu$8

which also gives an onset line with slope near 1. Without channel discrimination, this signal can be mistaken for in-gap DOS.

Biphotonic electron emission via exciton fusion is the principal pitfall. In exciton–anion fusion,

$h\nu$9

followed by

$E_\mathrm{k}$0

with onset

$E_\mathrm{k}$1

In exciton–exciton fusion,

$E_\mathrm{k}$2

and

$E_\mathrm{k}$3

In both BEE routes, the onset kinetic energy is approximately independent of $E_\mathrm{k}$4, because it is set by relaxed exciton energies and ionization or detachment energies rather than by direct one-photon photoemission from occupied states.

This fixed-onset behavior is the diagnostic contrast with SQEPE. The paper further notes that for exciton–anion fusion,

$E_\mathrm{k}$5

so the emitted-electron signal can scale as

$E_\mathrm{k}$6

whereas a pure one-photon SQEPE signal should be linear in photon flux. This implies that photon-flux dependence is not a secondary experimental detail but a direct test of whether the measured yield remains interpretable as DOS.

Once BEE contributes, the derivative-PYS premise fails in two ways. The yield no longer reflects a simple integral over occupied states, and the low-kinetic-energy region used to infer in-gap DOS is dominated by electrons whose thresholds are determined by exciton energetics. This is why the paper states that “the BEE signal masks the DOS.”

4. Experimental demonstrations in C$E_\mathrm{k}$7 and Alq$E_\mathrm{k}$8

The clean reference case is C$E_\mathrm{k}$9. In $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$0-dependent HS-UPS, two onset lines were observed: HOMO emission for $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$1–6.6 eV following $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$2 with $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$3 eV, and occupied in-gap emission for $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$4–6.4 eV following $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$5 with $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$6 eV (Nakazawa et al., 1 Oct 2025). In this case the conventional SQEPE interpretation is validated, which explains why CFS-YS works well.

Alq$$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$7 is the central demonstration because it exhibits precisely the failure mode that motivates CFS-YS. PYS showed an ionization energy $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$8 eV, but also peaks at $$N(E_\mathrm{k}, h\nu)_\mathrm{PES} \propto (h\nu)\lvert M_{\mathrm{fi}}\rvert^{2} D_\mathrm{i}(E_\mathrm{k} - h\nu) D_\mathrm{f}(E_\mathrm{k}) X(E_\mathrm{k}) T(E_\mathrm{k}),$$9, 3.7, and 3.2 eV, together with photoelectron yield below the effective work function of 3.7 eV. Those features are incompatible with a monotonically increasing integrated DOS signal. The derivative PYS data were correspondingly distorted, with oscillations near 4.6, 3.5, and 3.1 eV and negative values between 5.5–5.2 eV and 3.8–4.0 eV.

HS-UPS resolved three channels in Alq$D_\mathrm{i}$0: HOMO SQEPE for $D_\mathrm{i}$1–6.3 eV with slope $D_\mathrm{i}$2; a weak low-energy feature below 5.4 eV, also with slope near 1, assigned to anion SOMO SQEPE with $D_\mathrm{i}$3 eV; and an intense low-$D_\mathrm{i}$4 feature with onset fixed at $D_\mathrm{i}$5 eV independent of photon energy, proving a BEE origin. Photon-flux dependence reinforced the assignment: at $D_\mathrm{i}$6 and 3.40 eV, the signal scaled as $D_\mathrm{i}$7 and $D_\mathrm{i}$8, whereas at $D_\mathrm{i}$9 eV it was linear in flux, consistent with SQEPE from anions only.

The energetic assignment of the Alq$D_\mathrm{f}$0 BEE channel used tabulated singlet and triplet energies and the measured detachment and ionization energies: $D_\mathrm{f}$1 eV, $D_\mathrm{f}$2 eV, $D_\mathrm{f}$3 eV, and $D_\mathrm{f}$4 eV. The possible BEE kinetic energies were calculated as singlet–singlet $D_\mathrm{f}$5 eV, triplet–triplet $D_\mathrm{f}$6 eV, singlet–triplet $D_\mathrm{f}$7 eV, anion–singlet $D_\mathrm{f}$8 eV, and anion–triplet $D_\mathrm{f}$9 eV. Only anion–singlet fusion gives positive escape kinetic energy, matching the observed $\lvert M_{\mathrm{fi}}\rvert^2$0 eV feature.

The decisive CFS-YS comparison was between low-$\lvert M_{\mathrm{fi}}\rvert^2$1 and high-$\lvert M_{\mathrm{fi}}\rvert^2$2 operation. At $\lvert M_{\mathrm{fi}}\rvert^2$3 eV, conventional CFS-YS reproduced the same spurious peaks as derivative PYS because it sampled the BEE-dominated region. At $\lvert M_{\mathrm{fi}}\rvert^2$4 eV, high-$\lvert M_{\mathrm{fi}}\rvert^2$5 CFS-YS removed those peaks and revealed the HOMO DOS, an exponential in-gap DOS, and a Gaussian SOMO peak from anions. The in-gap DOS was fitted as

$\lvert M_{\mathrm{fi}}\rvert^2$6

with $\lvert M_{\mathrm{fi}}\rvert^2$7 eV. The SOMO peak appeared at a binding energy of 3.1 eV, with onset around 2.5–2.6 eV; the paper gives 2.5 eV in the discussion and 2.6 eV in the summary. In the abstract, the reported dynamic range is more than six orders of magnitude.

The Alq$\lvert M_{\mathrm{fi}}\rvert^2$8 results are also used to interpret device function. The direct determination of the SOMO DOS implies that the electron-occupied state near surfaces and interfaces is substantially deeper than the neutral-molecule LUMO measured by LEIPS. The paper interprets this as evidence that positive polarization charges from spontaneous molecular orientation stabilize surface anions and reduce the effective electron-injection barrier. Using

$\lvert M_{\mathrm{fi}}\rvert^2$9

the surface reorganization energy is estimated as roughly $X(E_\mathrm{k})$0, larger than the bulk or gas-phase value of $X(E_\mathrm{k})$1.

5. Operating criteria, diagnostics, and limitations

The practical rule established for CFS-YS is that the chosen $X(E_\mathrm{k})$2 must lie above the BEE-dominated kinetic-energy range. This is the specific meaning of a valid final-state condition in the reported work: the fixed final kinetic energy must select the desired SQEPE channel while excluding unwanted channels. The paper explicitly warns that conventional CFS-YS performed at the secondary-electron cutoff peak for maximum signal-to-noise can fail in organic semiconductors, because the cutoff region is exactly where BEE electrons appear (Nakazawa et al., 1 Oct 2025).

Several diagnostics are recommended. Photon-flux dependence is the first. If spectral shape is unchanged with photon flux and intensity scales linearly, the signal likely reflects SQEPE and DOS. If intensity is superlinear or the lineshape changes with flux, BEE is likely contributing. A second diagnostic is energetic feasibility: the paper surveys many organics and finds that BEE generally appears when

$X(E_\mathrm{k})$3

and generally does not when

$X(E_\mathrm{k})$4

Alq$X(E_\mathrm{k})$5 is presented as a special case below this line that still shows BEE because anion–singlet fusion is allowed. A third diagnostic is the onset trajectory as $X(E_\mathrm{k})$6 varies: SQEPE gives slope $X(E_\mathrm{k})$7, while BEE gives a photon-energy-independent onset kinetic energy.

The limitations of the DOS interpretation are stated explicitly. CFS-YS still assumes weak $X(E_\mathrm{k})$8-dependence of $X(E_\mathrm{k})$9. By contrast, PYS-to-DOS derivations require stronger assumptions, including constant final-state DOS, transport, and transmittance, and in some analyses the specific form $h\nu$00. The work function or effective vacuum alignment must be known; in the reported experiments it was determined from the secondary-electron cutoff. The setup used a $h\nu$01 V sample bias to ensure the sample vacuum level exceeded the analyzer vacuum level, and the total energy resolution was about 0.17 eV at $h\nu$02 eV. Derivative-PYS analysis required Gaussian smoothing of 0.2 eV FWHM, which itself broadened thresholds and contributed to artifacts.

A further implication is methodological: CFS-YS is reliable not by default, but conditionally. The method becomes trustworthy when the kinetic-energy window has been verified to exclude BEE and related excited-state-induced channels.

6. Broader significance and relation to other final-state-selective spectroscopies

Within organic optoelectronics, the significance of CFS-YS extends beyond DOS metrology. The same analysis that identifies BEE as a spectroscopy artifact also identifies it as a physically relevant process in devices. In OLEDs, exciton–exciton and exciton–anion fusion can quench luminescence nonradiatively, create hot electrons, generate cations that act as degradation species, disturb carrier balance, and increase power consumption if hot electrons are injected into neighboring layers. In solar cells, the same process can be viewed as carrier generation because exciton fusion creates a cation and a hot electron. This suggests that $h\nu$03-dependent HS-UPS combined with selective CFS-YS functions both as a DOS probe and as a probe of exciton–exciton and exciton–anion interactions (Nakazawa et al., 1 Oct 2025).

A distinct but closely analogous use of selective final-state spectroscopy appears in ultracold atoms. The numerical study of two-component disordered Bose gases proposes a scheme in which atoms are transferred from a homogeneous $h\nu$04 condensate into eigenstates of a disordered $h\nu$05 component, with final-state energy selected by

$h\nu$06

That work uses frequency-selected final-state spectroscopy, pulse-shaped narrow-band excitation, spatial filtering, and state-resolved imaging to isolate eigenstates in a narrow energy window close to the mobility edge, and it defines a final-state spectral yield

$h\nu$07

It is therefore strongly analogous to CFS-YS in spirit, but it does not implement a constant-final-state-yield scan protocol; its emphasis is the preparation and imaging of selected final states in a disordered manifold rather than keeping the yield into a chosen final state constant while sweeping another parameter (Werner et al., 2017).

Taken together, these two lines of work define a broader final-state-selective logic. In organic photoemission, CFS-YS isolates a final kinetic energy so that $h\nu$08 can represent the occupied DOS. In ultracold-atom spectroscopy, selective final-state preparation isolates disordered eigenstates so that their spatial structure can be imaged. The shared principle is that final-state selection can convert an otherwise integrated and potentially misleading signal into a spectroscopically interpretable one, but the specific operational meaning of “constant final state” is method-dependent.