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Photodiodes

　Photodiodes are semiconductive optical sensor, which if boradly defined, may enen include solar battleries. However, here we consider only the information aspect of these devices rather than the power conversion. In a simple way, the operation of a photodiode can be described as follows. If a pn-junction is forward bised (positive side of a battery is connected to the p side.) and is exposed to light of proper freqency, the current increase will be very small with respect to a dark current. If the junction is reverse bised (Fig.13.3), the current will increase quite noticeably. Impinging photons create electron-hole pairs on both sides of the junction. When electrons enter the conduction band they start flowing toward the positive side of the battery. Correspondingly, the created holes flow to the negative terminal, meaning that photocurrent "ip" flows in the network. Under dark conditions, leakage current "i0" is independent of applied voltage and mainly is the result of thermal generation of charge carriers. Thus, a reverse-biased photodiode electrical equivalent circuit (Fig.13.4A) contains two current sources and a RC network.
　The process of optical detection involves the conversion of optical energy (in the form of photons) into an electrical signal (in the form of electrons). If the probability that a photon of energy "hv" will produce an electron in a detection is "n", then the average rate of production of electrons < r > for an incident beam of optical power P is given by [2]:

　　　　　　　　　　　　　　　　　　　　　　　< r > = nP/hv　　　　　　　　　　(13.6)

　The production of electrons due to the incident photons at constant rate < r > is randomly distributed in time and obeys Poisson statistics, so that the probablility of the production of m electrons in some measurement interval τ is given by

　　　　　　　　　　　　　　　　　　　p ( m ,τ) = ( < r >τ)^m 1/m! e^(-τ)　　　(13.7)

　The statistics involved with optical detection are very important in the determination of minimum detectable signal levels and hence the ultimate sensitivity of the sensors. At this point, however, we just note that the electrical current is proportional to the optical power incident on the detector.

　　　　　　　　　　　　　　　　　　　　　　　i = < r > e = neP/hv　　　　　　　　(13.8)

　where e is the charge of an electron. A charge in input power ΔP (due to intensity modulation in a sensor, for instance) results in the output curent Δi. Since power is proportional to squared current, the detector's electrical power output varies quadratically with input optical power, making it a "square-law" detrctor.
　The voltage-to-current response of a typical photodiode is shown in fig.13.4B. If we attach a high input impedance voltmeter to the diode (corresponds to the case when i=0), we will observe that will increasing optical power, the voltage changes in a quite nonlinear fashion. In fact, variations are logarithmic. For the short circuit conditions ( V = 0 ), that is when the diode is connected to a current-to-voltage conventer ( Fig.4.10B ), current varies linearly with the optical power. The current-to-voltage response of the photodiode is given by [3]

　　　　　　　　　　　　　　　　　　　　　　　i = i0(e^eV/kbT -1 )-is　　　　　　(13.9)

　where i-0 is a reverse "dark current" which is attributed to the thermal generation of electron-hole pairs, i-s is the current due to the detected optical signal, kb is Boltzmann constant, and T is absolute temperature. Combining Eqs.(13.8) and (13.9) yields

　　　　　　　　　　　　　　　　　　　　　　　i = i0(e^eV/kbT -1 )-neP/hv　　　(13.10)

　which is the overall chericteristic of a photodiode. An efficiency of the direct conversion of optical power into electric power is quite low. Typically, it is in the range of 5% ~ 10%, however, in 1992 it was reported that some experimental photocell were able to reach an effciency as high as 25%. In the sensor technologies, however, the photocell are generally not use. Instead, an additional high resistivity intrinsic layer is present between "p" and "n" type of the material, which is called a PIN photodiode (Fig.13.5). The depth to which a photon can penetrate a photodiode is a function of its wavelength which is reflected in a spectral response of a sensor (fig 13.2).
　Besides very popular PIN diodes, several other types of photodiodes are used for sensing ligtht. In general, depending on the function and construction, all photodiodes may be classified as follows:

　1. The PN photodiodes may include a SiO2 layer on the outer surface (fig.13.6A). This yields a low level dark current. To fabricatea high-speed version of the diode, a depletion layer is increased thus reducing the junction capacitance (fig.13.6B). To make the diode more sensitive to UV, a p layer can be made extra thin. A version of the planar diffusion type is pnn+ diode (fig.13.6C) which has a lower sensitivity to infrared and higher sensitivity at shorter wavelength . This is due primarily to a thick layer of a low-resistance n+ silicon to bring the nn+ boundary closer to depletion layer.
　2. The PIN photodiodes (Fig.13.6D) are an improved verson of low-capacitance planar diffusion diodes. The diode uses an extra high-resistance I layer between the p and n layers to improve the response time. These devices work even better with reversed bias, therefore, they are designed to have low leakage current and high breakdown voltage.
　3. The Schottky photodiode (Fig.13.6E) have a thin gold coating sputtered onto the n layer to form a Schotty pn-junction. Since the distance from the outer surface to the junction is small, UV sensitivity is high.
　4. The avalanche photodiodes (Fig.13.6F) are named so because if a reverse bias is applied to pn-junction and a high intensity field is formed with the depletion layer, photon carriers will be accelerated by the field and collide with the atoms producing the secondary carriers. In turn, the new carriers are accelerated again resulting in the extremely fast avalanche-type increase in current.

　Thereforem these diodes work as amplifiers making them useful for detecting extremely small levels of light.
　There are two general operating modes for a photodiode: the photoconductive (PC) and the photovoltaic (PV). No bias voltage is applied for the photovoltaic mode. The result is that there is no dark current, so there is only thermal noise present. This allows must better sensitivities at low light levels. However, the speed response is worse due to an increase in Cj and response to longer wavelengths is also reduced.
　Figure13.7A shows a photodiode connected in a PV mode. In this connection, the diode operates as a current generating device which is represented in the equivalent circuit by a current source ip (Fig.13.7B). The load resistor Rb determines the voltage developed at the input of the amplifer and the slope of the load characteristic is proportional to that resistor.

　when using a photodiode in a photovoltaic mode, its large capacitance Cj may limit the speed response of the circuit. During the operation with a direct resistive load, as in Fig.13.7A, a photodiode exhibits a bandwidth limited mainly by its internal capacitance Cj. Figure.13.7B model such a band width limit. The photodiode acts primarily as a current source. The capacitence ranges from 2 to 20000 pF depending for the most part on the diode area. In parallel with the shunt is the amplifier's input capacitance (not shown) which results in a combined input capacitance C. The diode resistance usually can be ignored as it is much smaller than the load resistance Rb. The net input network determines the input circuit response rolloff. The resulting input circuit response has a break frequency f1 = 1/2 πRLC, and the response is [4]

　　　　　　　　　　　　　　　　　　　　　　　　Vout = -Rlip / (1+j f/f1)　　　(13.11)

　For a single-pole response, the circuit's 3-dB bandwidth equals the pole frequency. The expression reflects a typical gain-vs-bandwidth compromise. Increasing Rb gives a greater gain but reduces f1. From a circuit perspective, this compromise results from impressing the signal voltage on the circuit capacitances.
　The signal voltage appears across the input capacitiance C = Cj + C_OPEM. To avoid the compromise, it is desirable to dvelop input voltage across the resistor and prevent it from charging the capactiances. This can be achieved by employing a current-to-voltage amplifier ( I / V ) as shown in fig.13.8A. The amplifier and its feedback resistor RL translate the diode current into a buffered output voltage with excellent linearity. Added to the figure is a feedback capactior CL that prodies a phase compensation. An ideal amplifier holds its two inputs at the same voltage ( ground in the figure ), thus the inverting input is called a virtual ground. The photodiode operates at zero voltage across its terminals which improves the response linearity and prevent charging the diode capactiance. This is illustrated in Fig.13.7C where the load line virtually coincides with the current axis, because the line's slope is inversely proportional to the amplifier's open loop gain A.
　In practice, the amplifier's high, but finite open-loop gain limits the performance by developing small, albeit non-zero voltage across the diode. Then, the break frequency is defined as

　　　　　　　　　　　　　　　　　　　　　　fp=A/2gpRLC = Af1　　　　　(13.12)

　where A is the open-loop gain of the amplifier. Therefore, the break frequency is increased by a factor A as comoared with f1. It should be noted that when frequency increases, gain, A, declines, and the virtual load attached to the photodiode appears to be inductive. This results from the phase shift of gain A. Over most of the amplifier's useful frequency range, A has a phase lag of 90`. The 180` phase inversion by the amplifier converts this to a 90` phase lead which is specific for the inductive impedance. This inductive load resonates with the capacitance of the input circuit at a frequency equal to fp (fig.13.8B) and may result in an oscillating reponse (Fig.13.9) or the circuit instability. To restore stability, a compensating capacitor CL is placed across the feedback resistor. Value of the capacitor can be found from:

　　　　　　　　　　　　　　　　　　　CL = 1/(2πRLfp) = ( C C c )^0.5　　(13.13)

　where Cc = 1/(2πRLfc), and fc is the unity-gain crossover frequency of the operational amplifier. The capacitor bottosts the signal at the inverting input by shunting RL at higher frequnecies.
　When using photodiodes for the detection of ow-level light, noise floor should be seriously considered. There are two main components of noise in a photodiode: shot noise and Johnson noise (see Sec4.9). Besides the sensor, amplifier's and auxiliary component noise also should be accounted for [Eq.(4.90)].
　For the phtoconductive operating mode (PC), a reverse bias voltage is applied to the photodiode. The result is a wider depletion region, lower junction capaticance Cj, lower series resistance, shorter rise time, and linear response in photocurrent over a wider range of light intensities. however, as the reverse bias is increased, shot noise increase as well due to increase in a dark current. The PC mode circuit diagram is shown in Fig.1310A and the diode's load characteristic is in fig.13.10B. The reverse bias moves the load line into the third quadrant where the response linearity is better than that for the PV mode ( The second quadrant ). The load lines crosses the voltage axis at the point corresponding to the bias voltage E, while the slope is inversely proportional to the amplifier's open-loop gain A. The PC mode offer bandwidths to hunders of MHz, providing an accompanying increase in the signal-to-noise ratio.

機動戦士ガンダム MS IGLOO 第603技術試験隊中間報告書

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