Irreversibility between emission and detection spectra of quantum well diode

We here experimentally demonstrate simultaneous emission-detection phenomenon, and make an analysis on irreversibility of spectral emission-detection overlap, which may answer why the quantum well diode can only detect and modulate higher-energy photon than that emitted by itself.
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Video:  The coexistence of light emission and detection happens when we turn on the quantum well diode and shine extern light on it at the same time.

Monolithic integration of photonic devices with electronics shows a promising approach for realizing high-speed, low-power optoelectronic system on a chip [1]. But this goal should overcome substantial limitation for the integration of photonic functions of light emission, modulation and detection. Multiple-functioning devices are highly needed for uniting electronics and photonics on a single chip. By inserting InGaN quantum well structure into a p-n junction, the III-nitride diode inherently exhibits multiple functionalities of light emission, detection and modulation [2, 3]. Figure 1 illustrates spectral emission-detection overlap for a typical InGaN quantum well diode. As a transmitter, the light emission increases with increasing injection current. As a receiver, the quantum well diode can absorb light photons to liberate electron-hole pairs. The diode can also function as a modulator since its responsivity is greatly influenced by adjusting bias voltage. Spectral emission-detection overlap endows the diode with the capability to detect and modulate the light emitted by the device sharing identical quantum well structure [4].All transmitter, receiver and modulator are key components for monolithic photonic circuit on a single chip, which have been reported using a standard foundry process [5-8]. Park et al. developed ion bombardment approach to create regions of high electrical resistance, producing arrays of InGaN light-emitting diodes with a resolution as high as 8,500 pixels per inch [9]. Zheng et al. reported the monolithic integration of enhancement-mode n-channel and p-channel GaN field-effect transistors to construct a family of elementary GaN CMOS logic gates [10]. These works pave promising routes to monolithically integrate III-nitride photonics with electronics on a tiny chip.

Figure 1 Typical spectral emission-detection overlap of quantum well diode.

Enlarging spectral overlap will enhance the performance of monolithic multicomponent system. However, only shorter-wavelength light photons can be detected and modulated. It means that light emission and detection inside the diode are irreversible processes. We introduce energy diagram theory to unveil its physical mechanism. Figure 2 Schematic energy diagram for a quantum well diode, showing several possible transitions.

Figure 2 illustrates a schematic energy diagram for a quantum well diode in which the energy is plotted vertically and the horizontal lines are for each allowed values of the energy E0, E1, E2, E3. The energy E0 in the valence band is the lowest possible condition, and several possible transitions are demonstrated. When we inject current into the diode, the electrons in one of these conduction bands absorb energy to drop to a lower state and radiates energy in the form of light. According to the conservation of energy, the frequency of the emitted light is determined by the difference in the energy. For example, the frequency of the light which is liberated in a transition from energy E3 to energy E0 is

ω30=(E3-E0)/h       (1)

  The symbol h is the Planck constant that is the proportionality constant relating a photon's energy to its frequency [11]. Other possible transitions would be from energy E3 to energy E2, energy E2 to energy E1 and energy E1 to energy E0. Then, these define spectral emission lines. On the other hand, when we shine light on the diode, the holes absorb photons of right frequencies to go up from the valence band to different conduction bands [12]. In a reversible process, we can obtain

 ω03=ω30=(E3-E0)/h       (2)

As a matter of fact, the reversible process is an idealization. According to second law of thermodynamics, irreversible process occurs in practice and the total entropy of the system always increases. Therefore, the holes need higher energy (it will absorb higher-frequency photons) to climb up a potential hill to get to the conduction bands and remain in these states. Can you see that this implies that

 ω03≥ω30=(E3-E0)/h       (3)

Extending our work to the law of conservation of mass-energy, Einstein proposed a fundamental interchangeability between mass and energy: they are different manifestations of the same thing and thus, the mass of a body is a measure of its energy content [13]. In a given fabric of spacetime, a body emits the energy in the form of radiation when we make the body disappear. The memorable equation is written as:

E=mv2   (4)

The symbol v is the velocity of radiation. If a body is converted completely into energy at the speed c of light, the liberated energy is mc2. It means that a huge energy will be liberated when we convert a tiny amount of matter completely into energy in the form of photon radiation. Also, in an idealized reversible process, we can transcribe photons into a body if we can manipulate an enormous amount of energy at a speed of light. However, the irreversible process often happens. Therefore, in irreversible process, the required energy to convert energy completely into a body can be written as:

E=hω=mc2≤mv2=m*(s/t)2  (5)

Then we can obtain

h/m≤s*v   (6)

The symbols t and s are time and space that force acts through, respectively. In fact, it’s amazing since this equation happens to come out the Heisenberg uncertainty principle. The simple formula that involves the general relations of energy, mass, space and time of a body is a differential manifestation of second law of the thermodynamics.

In summary, quantum well diode exhibits an intriguing physical phenomenon because of its spectral emission-detection overlap. The diode can emit and detect light simultaneously, making it possible to merge identical diodes together to separately function as transmitter, modulator and receiver on a single chip. Based on irreversible process and energy diagram theory, we unveil physical mechanism of the spectral emission-detection overlap and answer why the device can only shorter-wavelength photon than that emitted by itself. We extend our work further and arrive at the view that the Heisenberg uncertainty principle is a differential manifestation of second law of the thermodynamics, which may help us to deeply understand various expressions of the nature.

References

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  13. A. Einstein, “On The Electrodynamics of Moving Bodies,” Jun. 30, 1905, CPAE 2:23

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