Photon Absorption and Decay Modes

Author: Thomas Lee Abshier

Photon Absorption and Orbital Decay Modes
by Thomas Lee Abshier, ND, Copilot, and Poe Assistant
6/24/2024

Thomas: How does a photon transfer energy to a block of carbon? Is it by activating an electron orbital that decays, or by being absorbed by vibrating the associated interatomic bonds, thus storing energy in the vibrating carbon lattice?

Copilot: Great question, Thomas. The answer is that it depends on the photon’s energy and the carbon material’s structure.

Photons can transfer energy to carbon in a few different ways:

1. Electronic excitation: If the photon has enough energy (typically in the UV or visible range), it can excite an electron in the carbon atom or molecule to a higher-energy orbital. This is common in materials like graphite or graphene, where delocalized π-electrons can absorb light and jump to higher-energy states. These excited electrons can then relax back down, releasing energy as heat or light or transferring it to other electrons.
2. Lattice vibrations (phonons): Lower-energy photons, especially in the infrared range, often don’t have enough energy to excite electrons. Instead, they couple with vibrational modes of the carbon lattice — essentially shaking the bonds between atoms. This increases the thermal energy of the material, which we perceive as heating. These vibrations are quantized as phonons, a key mechanism in how materials absorb and dissipate infrared radiation.

So, both mechanisms are valid — electronic excitation and vibrational absorption — and which one dominates depends on the photon’s energy and the electronic structure of the carbon material in question.

Thomas: How does the orbital electron, going into an excited state, and then relaxing, convert that energy into heat? Is it by vibrating the lattice or causing the atom’s jiggling of other atoms when the orbital electron decays? It seems that the atom is connected with the lattice, and in some way, the activated orbital absorbs the photon energy, and the orbital electron eventually vibrates the lattice.

Copilot: Excellent follow-up, Thomas. When an electron in a carbon atom (or any material) is excited to a higher orbital by absorbing a photon, it doesn’t stay there forever—it wants to relax back to a lower energy state. The way it does that, and how that energy becomes heat, is a fascinating dance of quantum and atomic interactions.

Here’s how the energy gets converted into heat:

1. Non-radiative relaxation: Instead of emitting a photon (like in fluorescence), the excited electron can transfer its energy to the surrounding lattice. This happens through interactions with phonons, which are quantized vibrations of the atomic lattice. Essentially, the electron “shakes” the atom it’s bound to, and that motion ripples through the lattice as vibrational energy—aka heat.
2. Electron-phonon coupling: This is the key mechanism. The excited electron perturbs the local electric field, which can distort the positions of nearby atoms. That distortion translates into vibrational modes of the lattice. The stronger the coupling, the more efficiently the electronic energy is converted into lattice vibrations.
3. Thermalization: Once the energy is in the lattice as vibrations, it spreads out—neighboring atoms jiggle, and the whole material warms up. This is the macroscopic heat we can measure.

So yes, your intuition is spot on: the energy from the excited orbital is ultimately transferred to the vibrational modes of the lattice, either directly or through intermediate steps like internal conversion or vibrational relaxation within the excited state.

Thomas: What do you think of Copilot’s answers?

Assistant

The responses from Copilot are excellent and provide a strong foundation for understanding how a photon’s energy is absorbed and converted into heat in a material like carbon. Let’s analyze and expand on these ideas to ensure clarity and completeness.

Thomas: What is the definition of fluorescence and phosphorescence after absorption of a photon by an electron orbital?

Copilot: Fluorescence and phosphorescence are both forms of photoluminescence, meaning they involve the emission of light following the absorption of a photon. But they differ in how the excited electron behaves and how long the glow lasts.

Fluorescence

After a photon excites an electron to a higher energy level (typically from the ground singlet state ( S_0 ) to an excited singlet state ( S_1 )), the electron quickly relaxes back to the ground state, emitting a photon in the process. This happens very rapidly, usually within nanoseconds (10⁻⁹ to 10⁻⁷ seconds). Importantly, the electron does not change its spin state, so the transition is “spin-allowed,” making it fast and efficient.

Phosphorescence

Here, the excited electron undergoes a process called intersystem crossing, where it flips its spin and moves from an excited singlet state to a triplet state ( T_1 ). Returning from this triplet state to the ground singlet state is spin-forbidden, so the electron stays excited much longer—milliseconds to even minutes or hours. When it finally relaxes, it emits a photon, but the glow is delayed and longer-lasting.

In short:

• Fluorescence: fast, spin-allowed, short-lived glow.
• Phosphorescence: slow, spin-forbidden, long-lived glow.

Thomas: what is an excited singlet state and a triplet state?

Copilot: Great question, Thomas — this gets into the quantum mechanics of how electrons behave when they absorb energy.

Excited Singlet State

In a singlet state, all electron spins are paired — meaning for every electron spinning “up,” there’s one spinning “down.” When a molecule absorbs a photon, one of its electrons can jump to a higher energy orbital. If the excited electron retains its spin orientation (still opposite to its paired partner), the molecule remains in a singlet excited state. This is the usual outcome of photon absorption and is the starting point for fluorescence.

Triplet State

A triplet state occurs when the excited electron undergoes a spin flip — now both electrons have parallel spins. This state is lower in energy than the singlet excited state but is spin-forbidden to return directly to the ground state. That’s why transitions from triplet to singlet (like in phosphorescence) are slower and longer-lived.

So in short:

• Singlet excited state: spins are opposite (paired), fast transitions.
• Triplet state: spins are parallel (unpaired), slower transitions due to spin restrictions.

Thomas: What is the mechanism of the electron’s decay from the triplet state to the singlet state?

Copilot: The transition from a triplet state to a singlet state—what we observe as phosphorescence—is a fascinatingly slow and “forbidden” process in quantum mechanics, but nature finds clever ways to make it happen.

Here’s how it works:

1. Intersystem Crossing (ISC): First, an electron in an excited singlet state may undergo a spin flip, transitioning into a triplet state. This is already a spin-forbidden process, but it can occur due to spin–orbit coupling, especially in molecules with heavy atoms like iodine or bromine.
2. Triplet State Lifetime: Once in the triplet state, the electron is “stuck” because returning to the singlet ground state requires another spin flip—again, spin-forbidden. This is why triplet states are long-lived, often lasting milliseconds to even minutes.
3. Phosphorescence (Radiative Decay): Eventually, the electron does decay back to the singlet ground state, emitting a photon in the process. This emission is what we call phosphorescence. The transition is weak because it violates spin selection rules, but it becomes more probable when:
   • There’s strong spin–orbit coupling (again, heavy atoms help).
   • The vibrational energy levels of the triplet and singlet states overlap, making the transition energetically smoother.
4. Non-Radiative Pathways: Sometimes, instead of emitting light, the triplet state can decay non-radiatively—transferring energy to the environment as heat or reacting with other molecules.

So, the decay from triplet to singlet is a slow, spin-forbidden leap, made possible by quantum quirks like spin–orbit coupling and vibrational overlap. That’s why glow-in-the-dark materials keep glowing long after the lights go out.

Thomas: Here’s Copilot’s answers regarding activated electron radiative decay. What do you think?

Assistant

These answers from Copilot are highly accurate and do an excellent job explaining the concepts of fluorescence, phosphorescence, and the mechanisms underlying these processes in terms of quantum mechanics. I would agree with and build upon these explanations to provide additional depth and context where necessary.

1. Fluorescence and Phosphorescence: Overview

Fluorescence

• Definition: Rapid light emission (nanoseconds) as an electron relaxes from S₁ → S₀ after photon absorption.
• Mechanism: Spin-allowed singlet-to-singlet transition; electron retains paired spin.Applications: Used in microscopy, chemical sensing, and biological imaging.

Phosphorescence

• Definition: Slow light emission after electron transitions from T₁ to S₀; can last milliseconds to hours.
• Mechanism: Photon excites electron to S₁, then via spin flip (ISC) to T₁. Spin-forbidden decay from T₁ → S₀ emits light slowly.
• Applications: Used in glow-in-the-dark materials, time-resolved spectroscopy, and optoelectronics.

2. Singlet and Triplet States: Key Differences

• S₁ (Excited Singlet State): Electron spins are paired (anti-parallel); S₁ → S₀ transitions are spin-allowed and fast.
• T₁ (Triplet State): Electron spins are unpaired (parallel); T₁ → S₀ transitions are spin-forbidden and slow.

3. Decay Mechanism: Triplet to Singlet Transition

• T₁ → S₀ decay follows quantum mechanical rules and is spin-forbidden, making it slow and less probable.

a. Spin-Forbidden Transition

• The transition is spin-forbidden because flipping the spin of an electron violates the spin selection rule.
• However, this process can still occur due to spin–orbit coupling.

b. Spin–Orbit Coupling

• Spin–orbit coupling is an interaction between the electron’s spin and its orbital motion around the nucleus.
• In molecules with heavy atoms (e.g., iodine, bromine), spin–orbit coupling becomes stronger because the nucleus has a high atomic number, making the spin-forbidden transition more likely.

c. Vibrational Overlap

• Vibrational overlap between T₁ and S₀ allows the spin-forbidden transition to occur by aiding relaxation.

d. Radiative Decay (Phosphorescence)

• After the spin-forbidden transition, the energy is released as a photon. This is the light we observe as phosphorescence.

e. Non-Radiative Decay

• Instead of emitting a photon, the triplet state can decay via non-radiative pathways:
  1. Energy transfer to the environment (e.g., heat).
  2. Quenching by other molecules (e.g., oxygen, which is highly efficient at deactivating triplet states).

4. Additional Insights

a. Why is Phosphorescence Slower?

• T₁ → S₀ is spin-forbidden, so it’s slower than the spin-allowed S₁ → S₀ transition in fluorescence.
• The lifetime of the triplet state depends on:
  1. Spin–orbit coupling strength: Stronger coupling (e.g., in heavy-atom-containing molecules) increases the likelihood of the transition.
  2. Environmental factors: Oxygen quenching, collisions, and temperature can affect the triplet lifetime.

b. Comparisons Between Fluorescence and Phosphorescence

c. Practical Examples

1. Fluorescence:
   • Fluorescent dyes (e.g., fluorescein, rhodamine) used in microscopy.
   • Fluorescent proteins (e.g., GFP) in biological imaging.
2. Phosphorescence:
   • Glow-in-the-dark materials (e.g., phosphorescent paints and toys).
   • Persistent luminescence in optical storage and displays.

5. Summary

Definitions:

• Fluorescence: Fast emission; singlet to singlet (S₁ → S₀).
  Phosphorescence: Slow emission; triplet to singlet (T₁ → S₀), spin-forbidden. d.

Electron Decay in Phosphorescence:

• The electron decays from the triplet state to the singlet ground state via:
  1. Spin–orbit coupling, which allows the spin-forbidden transition.
  2. Vibrational overlap between triplet and singlet states.
  3. Radiative decay, leading to photon emission (phosphorescence), or non-radiative decay, transferring energy as heat.

Copilot’s explanations are accurate and well-articulated. They provide a clear understanding of the processes while highlighting key quantum mechanical principles like spin selection rules, intersystem crossing, and spin–orbit coupling.  😊

Assistant

This is an excellent question that delves into the nature of photon-matter interactions, specifically how energy is conserved when the photon energy doesn’t perfectly match an atomic or molecular orbital transition. Let’s break this down and explore the possible outcomes.

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1. What Happens If a Photon’s Energy Exceeds an Orbital’s Allowed Transition but Falls Short of Ionization?

a. Photon Absorption is a Resonant Process

• For a photon to be absorbed by an electron in an atom or molecule, its energy must match the energy difference between two allowed energy levels (quantized states).
• If the photon’s energy does not exactly match any of these transitions, it can typically not be absorbed because energy conservation and quantum mechanical selection rules prevent it.

b. What If the Photon Has Extra Energy?

If the photon’s energy exceeds the gap between two quantized energy levels:

1. Direct Absorption is Not Allowed:
   • The electron cannot partially absorb the photon’s energy; the interaction is all-or-nothing at the quantum level.
   • In this case, the photon passes through the material or may scatter elastically (Rayleigh scattering) without transferring its energy.
2. Multi-Photon Absorption (Uncommon):
   • Under very intense light (e.g., lasers), two or more photons can combine their energies to excite the electron to a higher state. However, this is a nonlinear optical process and rare in ordinary conditions.
3. Indirect Energy Transfer Mechanisms:
   • If the photon’s energy doesn’t match an electronic transition, it might still interact with the material in other ways:
     • Excitation of Phonons: The photon could excite vibrational modes (phonons) in the lattice, contributing to heat.
     • Scattering: The photon may scatter off the lattice or atoms (inelastically or elastically), transferring part of its energy.

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2. Interaction is Not Resonant: What Happens Then?

a. Elastic Scattering (Rayleigh Scattering)

• If the photon energy doesn’t match any allowed transitions, it can interact with the material through elastic scattering.
• In elastic scattering:
  • The photon’s energy is not absorbed or changed.
  • The photon changes direction after interacting with the atomic or molecular structure.
  • This interaction typically does not contribute to heat.

b. Inelastic Scattering (Raman Scattering)

• In inelastic scattering, the photon can lose (or gain) a small portion of its energy by exciting the material’s vibrational or rotational modes. This is known as Raman scattering.
• The energy lost by the photon goes into the vibrational energy of the lattice, effectively heating the material.

c. Excitation of Lattice Vibrations (Phonons)

• If the photon’s energy lies in the infrared range (or is otherwise too low to excite an electron), it can directly couple to the vibrational modes of the atomic lattice.
• This process transfers the photon’s energy to phonons, increasing the thermal energy of the material.

d. Fluorescence-Like Processes

• If the photon has slightly more energy than the resonant energy level, some materials can absorb the photon and re-emit it at a lower energy (redshifted) via fluorescence or down-conversion processes.
• The excess energy is converted into vibrational energy (heat).

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3. Conservation of Energy and Momentum

In all these interactions, energy and momentum must be conserved. If the photon’s energy cannot be fully absorbed (because it doesn’t match a resonant energy level), the energy must go elsewhere:

• The photon is scattered, transferring part of its energy to the lattice (as heat or vibrations).
• The photon escapes without any interaction (transparent materials).

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4. Summary of Possibilities

Photon Energy vs. Orbital Energy Gap	Outcome
Exact Match (Resonant Absorption)	Photon absorbed, electron excited to a higher orbital.
More Energy than Orbital Gap	Photon typically not absorbed; passes through or scatters.
More Energy, Nonlinear Regime	Rare multi-photon absorption (e.g., intense laser fields).
Less Energy than Orbital Gap	Photon may excite vibrational modes (phonons) or scatter elastically.
Excess Energy (Near-Resonance)	Photon may excite electron and transfer excess energy to the lattice (heat).

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5. The Role of the Material

The type of material determines the likelihood of these processes:

• Transparent Materials: Photons that do not match resonant transitions pass through or scatter elastically.
• Absorptive Materials: Photons that match vibrational or rotational modes are absorbed and converted to heat.
• Semiconductors and Insulators: Photons with energy above the bandgap but below ionization energy may excite electrons to the conduction band, with additional energy dissipated as heat.

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6. Final Answer: Does the Extra Energy Go to Heat?

If the photon’s energy does not match an allowed state:

• The interaction is not allowed in most cases, and the photon is not absorbed.
• In some cases (e.g., near-resonant absorption), the photon may excite an electron, and the excess energy is transferred to the lattice as heat.
• Otherwise, the photon passes through, scatters, or excites phonons directly, contributing to heat indirectly. 😊

7:53 AM 6/24/25

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Thomas: 

There is something different about the semiconductor, which allows for capturing a wide spectrum of energy, other than the specific allowed energetic orbitals. Why does the semiconductor allow for such multiple bonding? It appears as though the orbital activation energy in the semiconductor is one of the repositories of energy that is available to the photon, but that there is also another energy, not just the orbital energy, some vibratory resonance with the other atoms through their bonding, or a variable bonding with doping impurities that make the conduction band accessible as a part of the quantum of the energy that was absorbed strictly by the electron orbital or silicon or germanium, etc.

2:14 PM 6/24/25

Assistant

You’re absolutely correct that semiconductors exhibit unique properties that allow them to efficiently absorb and interact with a broad spectrum of photon energies. This is due to their electronic band structure, lattice vibrations (phonons), and doping impurities, which together create multiple pathways for photon energy absorption and utilization. Let’s break this down:

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1. Why Semiconductors Can Absorb a Broad Spectrum of Energy

a. The Band Structure of Semiconductors

Semiconductors have a distinct electronic band structure:

1. Valence Band: The band where electrons are bound to atoms.
2. Conduction Band: A higher-energy band where electrons are free to move and conduct electricity.
3. Bandgap (E₉): Energy gap between valence and conduction bands.

In semiconductors:

• Photons with energy greater than or equal to the bandgap energy can excite electrons from the valence band to the conduction band.
• This process creates an electron-hole pair (the electron in the conduction band and the “hole” left behind in the valence band).

b. Absorption Beyond Specific Orbital Transitions

Unlike isolated atoms or molecules, where absorption depends on specific quantized orbital transitions, semiconductors have:

• Continuous Energy States: The conduction and valence bands form continuous ranges of allowed energy states rather than discrete orbitals.
• Photons with energy ≥ E₉ can excite electrons to any level in the conduction band, enabling broad photon absorption in semiconductors.

c. Indirect Bandgap and Phonon Assistance

• Many semiconductors, like silicon, have an indirect bandgap, meaning that the electron transition from the valence band to the conduction band requires not only a photon but also a phonon (a quantized lattice vibration) to conserve momentum.
• This coupling to phonons means that vibrational energy in the lattice plays a role in photon absorption, broadening the range of energies that can interact with the material.

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2. Lattice Vibrations and Vibratory Resonances

a. Role of Phonons in Energy Absorption

In semiconductors, phonons (quantized vibrations of the atomic lattice) interact with photons and electrons:

1. Direct Photon Absorption:
   • A photon excites an electron across the bandgap.
   • If Eₚₕₒₜₒₙ > E₉, excess energy becomes heat via phonon (lattice vibration) interactions.
2. Assisted Absorption:
   • In indirect bandgap semiconductors, phonons assist in conserving momentum during the electron’s transition, enabling absorption of photons that would otherwise not have the correct momentum to excite the electron.

b. Vibrational Resonance Modes

• The lattice vibrations form resonant modes that can interact with photons of specific energies, particularly in the infrared range.
• These vibrational modes allow the lattice to absorb energy not directly usable for electronic transitions, contributing to heating or scattering.

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3. The Role of Doping and Impurities

a. Doping Makes the Conduction Band More Accessible

In intrinsic semiconductors, photons with energy ≥ E₉ generate electron-hole pairs. Doping adds impurity levels within the bandgap, enabling absorption at lower photon energies.

1. n-Type Doping:
   • Adds donor states just below the conduction band.
   • Electrons can be excited into the conduction band with less energy than the intrinsic bandgap.
2. p-Type Doping:
   • Adds acceptor states just above the valence band.
   • Electrons can transition from the valence band to these acceptor states with less energy than the intrinsic bandgap.

These impurity levels allow semiconductors to absorb photons with energies below the bandgap, further broadening the range of photon energies that can be utilized.

b. Variable Bonding with Dopants

• The introduced dopant atoms (e.g., phosphorus in silicon for n-type doping, or boron for p-type) create localized bonding variations in the lattice.
• These dopants influence the electronic and vibrational properties of the material, making it easier for photons to couple to both electronic and vibrational states.

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4. Energy Pathways in Semiconductors

When a photon interacts with a semiconductor, several energy pathways come into play:

a. Electronic Transitions

• High-energy photons excite electrons from the valence band to the conduction band, creating electron-hole pairs.
• Excess energy (Eₚₕₒₜₒₙ − E₉) is released as heat via phonon interactions.

b. Phonon Contributions

• Infrared photons (lower-energy) can couple directly to lattice vibrations, exciting phonons.
• Phonon interactions also assist in indirect bandgap transitions.

c. Scattering and Heat

• Photons that do not contribute to electronic transitions may scatter off the lattice or excite phonons directly, converting their energy into heat.

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5. Why Semiconductors Are Unique

Semiconductors differ from insulators and metals in their ability to absorb and utilize a wide spectrum of photon energies due to:

1. Their bandgap structure, which allows electrons to be excited across a continuous range of states.
2. The coupling of electronic transitions to phonons, enabling indirect transitions and energy dissipation.
3. Doping, which introduces impurity states that lower the energy required for absorption.

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6. Summary

• Photon absorption in semiconductors occurs when photon energy ≥ E₉, exciting electrons to the conduction band.
• Phonon Coupling: Plays a crucial role in indirect bandgap materials and in dissipating excess energy as heat.
• Doping and Impurities: Introduce intermediate energy states that broaden the range of photon energies that can be absorbed.

In essence, semiconductors are versatile because their electronic structure, lattice vibrations, and impurity states provide multiple pathways for photons to interact with the material. This interplay allows semiconductors to harness energy not just through orbital transitions but also through vibrational and impurity-related mechanisms, making them invaluable in applications like photovoltaics and optoelectronics.

2:14 PM 6/24/25