## 2 Dynamic Nuclear Polarization in Semiconductor Nano-and Microstructures
### Optically Induced DNP in Semiconductors
#### 2.1.3 Fundamentals of the Optically Induced DNP
The nuclear spin relaxation time due to the hyperfine interaction is \(T^{\prime}_{n}\) (ii) Every electron is subjected, next to the applied magnetic fields, to the total magnetic field of all polarized nuclei. These two magnetic fields are comparable because electrons at low energy levels interact with a large number of nuclei. The electron spin relaxation time due to the hyperfine interaction is \(T^{\prime}_{1}\). As a consequence, there occurs a _feedback_, which leads to a steady-state polarization of both electron and nuclear spins. There has been a renewed interest in the hole-nuclei hyperfine interaction in semiconductor quantum dots [22]. The main effect arises from the coupling of the nuclear spin with the hole wavefunction within the same unit cell, that is, the short-range part of the dipole-dipole interaction [12]. The potential effect of large inhomogeneous elastic strain in nanostructures (like quantum dots) on the microscopic Bloch hole wave function is considered as a possible route to _engineer the hyperfine coupling_. Similar to the electron spins, the difference in numbers of nuclei (with spin \(I\)=1/2, like \({}^{29}\)Si) possessing spins up and down \(=M_{\uparrow}-M_{\downarrow}\) is selected as a measure of the nuclear spin magnetization \(I_{z}\equiv\Delta/2\). At arbitrary value of the nuclear spin \(I\), \(\Delta\) denotes the difference between the populations of the adjacent nuclear spin states. The total number of nuclear spins is supposed to be equal to \(N~{}=~{}M_{\uparrow}+M_{\downarrow}\). (or the sum of all available spin eigenvalues at arbitrary \(I\)). The thermal equilibrium value of the difference \(\Delta\) at\(I\) is the fo the nuclear spin value following: [23]  
\[\Delta_{0}~{}=~{}\frac{N\mu_{Bn}\beta_{0}}{I(2I+1)k_{B}T}~{}. \tag{9}\]  
The corresponding steady-state magnetization on nuclei with spin \(I\) = 1/2 is \(I_{0}~{}=~{}\Delta_{0}/2\). In terms of the gyromagnetic ratios, that is, \(\gamma_{e}~{}=~{}-\frac{\mu_{Bn}}{1/2}\), \(\gamma_{n}~{}=~{}\frac{\mu_{Bn}}{I}\), the relative magnetization of nuclei takes on the form (see Section IX.3 in Reference [12]):  
\[\frac{\langle I_{z}\rangle}{I_{0}}~{}=~{}1-s\frac{\left|\gamma_{e}\right|}{ \gamma_{n}}. \tag{10}\]  
In analogue to the Overhauser effect [16], the steady-state nuclear polarization is _enhanced_ as if the nuclear gyromagnetic ratio \(\gamma_{n}\) would be increased by \(s\left|\gamma_{e}\right|\). Near the saturation, when \(s\) is close to 1, this increase theoretically may be as large as \(\left|\gamma_{e}\right|\)/\(\gamma_{n}\) = 3310 in \({}^{29}\)Si [17], (p. 489). The experimentally observed nuclear spin polarization enhancement extrapolated to an infinite time of continuous irradiation by an  
\[\frac{dD}{dt}~{}=~{}-\frac{D-D_{0}}{T_{1}}-\frac{D}{\tau}. \tag{4}\]0 Feedback coupling of the electron spin system (ESS) and the nuclear spin system (NSS) in a semiconductor. Optically oriented electrons polarize the nuclei (arrow _polarization_) Because of the polarization, an _effective magnetic field_ arises, which, in its turn, affects the electron orientation and hence the luminescence polarization. (Reprinted from Reference [21], © (1984), with permission from Elsevier). unpolarized light constitutes \(\langle I_{2}\rangle/I_{0}=-5.6\)[14]. According to Equation (10), this implies the saturation parameter \(s\)\(-\)\(2\times 10^{-3}\). The nuclear magnetization (Figure 2a) produced by optical pumping in a field of 1G (extrapolated to infinite time of continuous irradiation) corresponded to the equilibrium polarization in a field of 28 kG at 77 K and constituted \(\langle I_{2}\rangle=3.7\times 10^{-6}\). Thus, the enhanced nuclear polarization as high as \(2.8\times 10^{4}\) due to the optical pumping was experimentally demonstrated [14]. Polarized electronic spins are produced by optical pumping with _circularly polarized_ light. Both spin directions are created in the conduction band.