Photovoltaic Detectors
Photovoltaic (PV) photocurrent generation is based on the separation of electrical carriers by a built-in electric field at a p-n junction or Schottky barrier [top of Fig. 6.1(b)]. By diffusion, the electrons and holes generated within a diffusion length of the junction reach the space-charge region. The generated photocurrent shifts the current-voltage characteristics as is shown in the bottom of Fig. 6.1(b).
The graphene p-n junctions can be feasibly obtained since the Fermi level can be easily tuned because of the limited density of states and ease of formation of p-type or n-type doping. The electrical and optical properties of graphene p-n junctions are different from traditional silicon p-n junctions in terms of the response speed and physical mechanisms involved in photoconversion. Figure 6.4 illustrates the creation of a junction between positively (p-type) and negatively (n-type) doped regions of graphene. The same effect can be reached by applying a source-drain bias, producing an external electric field. Since graphene is a semimetal, generating
FIGURE 6.4 Schematic of photo-induced extraction of electron-hole pairs and its separation at the graphene p-n junction.
a large dark current, that last approach is usually avoided. The built-in field can be introduced in different ways, either by local chemical doping and electrostatically using split gates, or by exploiting the work-function difference between graphene and the contacts. Typically, p-type doping is reached for metals with a work function higher than that of intrinsic graphene (4.45 eV), whereas the graphene channel can be adjusted to the p- or n- state by the gate.
Photodiodes are usually operated at zero bias (photovoltaic mode) or at reverse bias (photoconductive mode). The absolute response of the photodiode is usually smaller than that of a photodetector working with the photoconducting or photogating mechanisms, since there is no internal gain. Under the reverse-bias operation, the junction capacity is reduced, increasing the speed of the photodiode. Strong reverse bias can initiate impact ionization multiplication of carriers, or avalanching (avalanche photodiode). The large internal gain results in detection of an extremely low signal power. Electron-electron scattering in graphene can lead to the conversion of one high electron-hole pair (e-h) energy into multiple e-h pairs of lower energy, potentially enhancing the photodetection efficiency [6].
Figure 6.5 shows graphene phototransistor architecture, accompanied by the short-circuit photocurrent induced by light. Phototransistors basically have the same three-terminal configuration as field-effect transistors (FETs). In the operational mode of a normal FET, the amount of current
FIGURE 6.5 Graphene phototransistor: (a) structure of transistor and (b) a schematic view of photocurrent generation.
flowing (the drain current, Id) in the accumulated channel is controlled by the magnitude of the gate voltage (V^) at a given source-to-drain bias (Vrfs), for phototransistors; the control of channel conductance can additionally be induced by the absorption of light. If there is no bias applied between the source and the drain, minimal photocurrent is collected when the light spot is focused on the middle of the graphene channel. Significant photocurrent is observed when the light is incident on the metal graphene interface area, which is attributed to the conventional PV effect. The built- in electric field in graphene (due to different work functions of the graphene and metal contacts) separates e-h pairs, creating a photocurrent in the external circuit. In the middle of the channel, there is no built-in electric field and, as a result, no photocurrent is observed. The built-in electric field can be further adjusted by a gate bias influencing the photocurrent.
Photo-thermoelectric Detectors
The most recent approach (the Seebeck effect) also employs the photo- thermoelectric (PTE) effect to create an electric field, due to electron diffusion into metal contacts. This effect is based on the thermoelectric effect caused by non-uniform light illumination. It can be also created by strong differences in the absorption of distinct parts of the device under uniform illumination. Figure 6.6 illustrates the light-induced heating effect in a semiconductor channel (e.g., in a field-effect transistor), which leads to a temperature gradient.
The internal voltage responsible for current flow is directly proportional to the temperature gradient difference
FIGURE 6.6 Photo-thermoelectric effect: (a) in a semiconductor channel and (b) current-voltage characteristics
where as is the Seebeck coefficient, commonly expressed in pV/K. The Seebeck coefficient is usually expressed in terms of the conductivity, o, of the material [7]
where к is the Boltzmann constant, and the derivative of the electrical conductivity, a, with respect to energy, E, must be evaluated at the Fermi energy [E=Ep=hv[kF, with h the reduced Planck constant, vF the Fermi velocity (in graphene about 106 m/s), and kF the Fermi wavevector]. In the semiconductor, the sign of the Seebeck coefficient is determined by the majority charge polarity.
The coefficient as is the effective or relative Seebeck coefficient of the device, composed of two dissimilar conductors “a" and “b”, by electrically joining one set of their ends. Consequently, a thermovoltage is equal to:
where aa and ab are the absolute Seebeck coefficients of the materials, a and b. In the example shown in Fig. 6.6(a), with two junctions between the contact metal and the semiconductor, the voltage difference across them is
In the last equation, the term asmetai is neglected because the Seebeck coefficients of pure metals are in the order 1-//V/K, much smaller than typical values for semiconductors.
The magnitude of AVPTE is small and typically ranges from tens of pV to tens of mV (Fig. 6.7). In order to drive current through the device, the ohmic contacts to the semiconductors are required. The weak thermal gradient can be achieved in the case of illumination of a uniform semiconductor, when no current flows in the device, since no external bias is applied. It should be noted that both relative and absolute Seebeck coefficients are temperature dependent and the proportionality between the potential difference generated and the temperature gradient is valid only within the limit of a small temperature difference.
Figure 6.6(b) shows typical current-voltage characteristics of a device with a photoresponse dominated by the photo-thermoelectric effect. Linear dependence of I-V curve indicates that the Schottky barriers are small (ohmic contacts). The photothermoelectric effect generates a current at zero bias without changing the resistance.
Here, differences between the photothermoelectric effect and the bolo- metric effect will be highlighted. In the bolometric effect, the homogeneous temperature change affects the resistivity of a material, and the
FIGURE 6.7 The Seebeck coefficients as a function of resistivity for various materials (after Ref. [8]) bolometric effect cannot drive a current in a device, only modify the magnitude of the current under external bias and illumination. For a bolometer, the sign of the photocurrent is related to the change in the material conductivity with temperature. In the case of PTE, the sign of the photocurrent is related to the difference in Seebeck coefficients between the components of the junction.
The PTE plays an important role in photocurrent generation [3,9]. For example, in graphene, due to the fact that the optical phonon energy is large (~ 200 meV), hot carriers created by the induced light remain at a temperature higher than that of the lattice for many picoseconds. Equilibrium between the hot electrons and the lattice is reached via the slower scattering mechanism between charge carriers (although the charge carriers are substantially speeded-up due to disorder-assisted collisions) and acoustic phonons (nanosecond range). The carrier heat capacity is much smaller than the lattice heat capacity, which leads to a larger temperature gradient in the channel, enhancing the PTE effect. The spot of incident radiation induces carrier temperature variations, and hot carriers generated by photons diffuse due to the temperature gradient, leading to photocurrent generation as was presented in Fig. 6.8, with the carrier and lattice exhibiting different temperatures. The photocurrent direction, due to the PV and PTE effects, is the same, making experimental determination of their relative contributions extremely difficult.
