Energy current density

According to Planck, blackbody radiation implies a universal dependence of the energy density per photon energy interval d(huj). This results in an energy current density djV,bb per photon energy interval d(fuj) given by... 

Fig. 4.1. Energy current densities per photon energy of AMO (dotted line) and AM 1.5 (solid line, [1]) solar radiation. The thin solid line is the spectrum of a 5 800 K blackbody emitted into the solid angle 6.8 x 10-5...

Even more important for quantum energy converters, e.g., solar cells, than the energy current density is the photon current density, because it determines the rate at which electrons are excited. Neglecting impact ionisation effects, the excitation of one electron requires at least one absorbed photon. 

The generation rate AG is calculated from (4.2) for a blackbody spectrum of 5 800 K incident from a solid angle 6.8 x 10—5, as subtended by the sun. As can be seen from Fig. 4.1, this blackbody spectrum is very close to the AMO spectrum and gives a total energy current density of 1.39 kW/m2, compared with 1.35 kW/m2 for AMO. The temperature of the solar cell and its surroundings is 300 K, which determines a reverse current of only 3x 10-16 A/m2 due to the absorption of blackbody radiation from the surroundings. 

Figure 4.7 gives the current-voltage characteristic for a 2-band system with a band gap of 1.30 eV. The efficiency r is shown in Fig. 4.8. With increasing band gap q> the short-circuit current decreases and the open-circuit voltage increases. The efficiency r), taken as the maximum power for each band gap divided by the incident energy current density of 1.39 kW/m2, has a maximum value of 29.9% for a band gap of 1.30 eV.

Fig. 4.8. Efficiency rj, open-circuit voltage Voc, and short-circuit current density jsc as a function of the band gap a of a 2-band system illuminated by blackbody radiation at 5 800 K with an incident energy current density of 1.39 kW/m2...

The particle and energy current densities j(z, t) and j z, t) possess a z component only because of the rotational symmetry of the velocity distribution F U, vjv,z, t) around the direction of S,. This is an immediate consequence of the assumption that the field action occurs only parallel to this direction. 

Fig. 19. Solution region of the relaxation problem (left) and spatial relaxation of density and energy current density in neon (right).

The spatial evolution of the density n(z)/n(oo) and the energy current density jezi )ljezi )< normalized on their respective values in the established uniform state at large z, is shown in Fig. 19 (right) for a neon plasma at the field E = -5 V/cm. 

The figure clearly illustrates that the boundary value f i,U) for the anisotropic distribution initiates a weakly damped, spatially periodic relaxation of the density and energy current density of the electrons, and that the corresponding relaxation length becomes very large and takes about 100 cm at this field. This periodic relaxation behavior is in substantial contrast to the largely monotone evolution of all important electron kinetic quantities in the temporal relaxation process shown above. 

Because of the cylindrical symmetry of the total electric field in the column plasma, in two-term approximation the expansion of the velocity distribution can be represented by the expression f U,v/v,r) = 2n) mg/2f [fQ(U,r)+f U,r)v /v+f.(U,r)v,/v]. This expansion includes, in addition to the isotropic distribution fo(U, r), a radial component fr(U, r) and an axial component f (U,r) of the vectorial anisotropic part of the velocity distribution. In particular, this radial distribution component allows the particle and energy current density of the electrons in the radial direction to be described and thus reveals significant aspects of the electron confinement by the radial... 

The International System of Units (SI units) has been used. Its merits are unquestionable it removes the use of conversion factors, especially in energy measurement it does away with the use of mixed units, such as amperes per cm (amperes belongs to the mks system, and cm to the cgs system) it does not use arbitrary units such as the calorie. The disadvantage of using this system is that the familiar numbers, such as bond energies, current densities etc., look different. While this difficulty is real, it can be readily overcome by a few comparison exercises. 

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