# Germanium Single Crystals for Photonics
## 8 The Effect of Photonic Drag of Current Carriers in Germanium
Emerging EMF is proportional to the power of the incident radiation. Germanium is a direct-gap semiconductor, in which the maximum energy of the valence band is located at the center of the Brillouin zone, where two valence bands merge, and below is a third valence band, split off from the first two due to spin-orbit interaction [72]. The upper zone corresponds to heavy holes, the next zone to light ones. In this case, the ratio of the masses of heavy holes to light ones is \(\sim\)8. There are no holes in the third, lower, zone. Photodetectors based on p-type germanium use direct intraband transitions since the CO\({}_{2}\) laser radiation quantum hv = 0.117 eV is absorbed in the crystal mainly due to the intraband transition between the sub-bands of holes with heavy and light masses. The resulting photoEMF is used to register the radiation parameters with \(\lambda\) = 10.6 \(\upmu\)m. The sensitivity range is limited from below by equipment noise, and from above by the bleaching effect associated with the impossibility of transitions due to the presence of filled states and due to the competition of hole transition rates caused by the action of radiation and interhole collisions. In this case, the hole perceives not only the energy, but also the momentum of the photon. The movement of holes relative to the crystal lattice in the direction of radiation propagation occurs due to the need to fulfill the laws of conservation of energy and momentum. In this case, a potential difference arises between the ends of the crystal rod--the photon drag EMF (\(V\)). The main advantages of such a photodetector are as follows: time resolution up to 10\({}^{-10}\) s, large dynamic range (10-10\({}^{7}\) W/cm\({}^{2}\)), operation at room temperature, and sensitivity of the order of 0.1-1.0 V/MW. The time constant (\(\tau\)) of the device is described by a simple Formula (4):  
\[\tau=\text{nc}/\text{L}, \tag{4}\]  
where L is the length of the working crystal of the photodetector; n is the refractive index; c is the speed of light. The laws of conservation of energy and momentum force holes to move in the crystal lattice in the direction of radiation propagation. This initiates the appearance of a potential difference between the ends of the crystal rod--the photon drag EMF (\(V\)) (5):  
\[V=\frac{CW_{pl}\rho(1-R)}{\text{Sh}w}, \tag{5}\]  
where \(C=\text{e}(-\tau_{\text{h}}\text{v}_{\text{h}}+\tau_{\text{L}}\text{v}_{\text {L}})\) is the constant of the crystalline sample, in which \(\text{v}_{\text{h}}\) and \(\text{v}_{\text{L}}\) are the group velocities of heavy and light holes, respectively, \(\tau_{\text{h}}\) and \(\tau_{\text{L}}\) are the relaxation times of pulses in two-hole systems, e is the electron charge; \(W_{pl}\) is the peak power of the laser pulse; \(\rho\) is the specific electrical resistance of the material; \(S\) is the area of the receiving zone; \(R\) is the reflection coefficient from the input plane of the receiver (for Ge \(R\) = 0.36); \(\hbar=\text{h}/2\pi\) is [PERSON]'s constant; \(\omega\) is the angular frequency of laser radiation. To obtain the maximum signal, it is necessary to optimize the sample by the following parameters: \(\rho\), S, L. The maximum value of the measured EMF is observed at the greatest crystal length. However, it is impossible to significantly increase the length due to noticeable absorption of radiation in p-type Ge. In addition, the time resolution decreases. Therefore, when it is necessary to measure subnanosecond pulses, it is necessary to reduce the sensitivity by decreasing the time constant due to shortening the crystal. When measuring the radiation of lasers with relatively \"long\" pulses, it is more advantageous to use a photodetector with the maximum possible length of the crystal rod. The paper [40] reports a technical solution that made it possible to combine measurements of subnanosecond and comparatively \"long\" pulses using a single device.