Optical absorption in a semiconductor material is the key-effect to convert optical power into an electrical current. This conversion is done by a photodiode which is the first stage in any optical receiver. Discrete photodiodes can be connected to transimpedance amplifier (TIA)chip in multi-chip packages by wire bonding or in heterogeneous integrated circuits. The discrete solution performance can be optimized separately by using photodiode and TIA from different technologies. The high costs due to a complex production and assembly process and potential noise sources and bandwidth reduction due to bonding pads and package pins are the main drawbacks.

An alternative low-cost solution in the visible spectral range is the integration of photodiodes with the TIA and post amplifiers in standard CMOS and BiCMOS technologies. The maturity and performance of standard CMOS technologies make the optoelectronics integrated circuits (OEIC) a competitive solution for many low-cost consumer and sensor applications. OEIC give a better performance than discrete solutions because there are no bonding pads, no bond wires and no package pin parasitics between photodiode and amplifier input [1].

Figure 1 PIN Photodiode structure

# Integrated Photodiode

The integrated photodiode is the main component and the first stage in the integrated optical receiver. The photodiode converts the optical power into an electrical current. The photodiode should convert photons into charge carrier pairs with maximum efficiency and to transport them to the electrodes as fast as possible. Also the capacitance of the photodiode must be as low as possible to keep the high frequency loss of the photocurrent low to reach highest possible sensitivity. These demands are partially conflicting. So a trade-off is necessary, especially due to the wavelength dependence of the penetration depth. More details about the theory of integrated photodiodes can be found in [2,3].

Depending on the specific application, the thickness of the intrinsic zone of the photodiode must be optimized; Figure 1 shows the structure of a PIN photodiode. For a good trade-off, the main parameters that must be known are the maximum data rate, the operating wavelength, type of photodiode and the maximum voltage available for the photodiode. A main characteristic of integrated optical receivers is the achievable sensitivity, which depends strongly on the responsivity of the photodiode and also the capacitance, so minimum capacitance and maximum responsivity lead to maximum sensitivity. This could be achieved by increasing the thickness of the intrinsic layer. But this contradicts to speed, since increasing the intrinsic layer thickness without increasing the reverse voltage would lead to a double penalty (quadratic dependence) since the electric field decreases and so the speed of the charge carriers decreases. Additionally the distance the charge carriers have to drift increases and so the whole transition time of the charge carriers increases dramatically. To solve this problem partially the voltage across the diode has to be increased according to the increase of the thickness of the intrinsic layer. The main goal is that the electric field is at a high constant level where the charge carriers travel with saturation drift velocity. In practice, however, the saturation velocity is not achieved in most cases due to limited available supply voltage.

Often a certain data rate is given, so the photodiode has to achieve a certain rise- and fall-time. In a first order approximation the necessary 10%-90% rise- and fall-time of the photodiode can be calculated from the formula (1) with td as the drift time through the intrinsic zone.

When rise- and fall-time are nearly equal, then the formula (1) simplifies to formula (2) and gives approximately the drift-time of the charge carriers through the drift zone. In both cases the factor 3 indicates a conservative approximation and for an aggressive approximation the factor can be two.

The cut-off frequency of the PIN-photodiode can be estimated by:

Under the assumption that the drift velocity reaches saturation(v_{s}=10^{7} cm/s) the maximum allowable thickness of the intrinsic layer can easily be calculated by:

The necessary voltage for the PIN-diode can now also be calculated with the electric field where saturation occurs.

# Transimpedance Amplifier

Photodiodes do not use any amplification effect and have responsivity (ratio of output current to input light intensity) that is for example ≤ 0.5A/W for a silicon photodiode at a light wavelength of 650nm. Therefore a combination of a photodiode with an amplifier is necessary in all practical applications. In optical receivers current-to-voltage converters are necessary in order to convert the photocurrent delivered by the photodiode into an output voltage which is proportional to the input current. The transimpedance amplifier is the most suitable preamplifier configuration used in optoelectronic receivers. For most optical receiver applications these amplifiers need a high and also variable gain, high bandwidth, low noise and low input impedance. The main characteristics of transimpedance amplifiers are discussed in [3].

The preamplifier is used to convert the incoming photocurrent into an output voltage, which is amplified by the following stages. The simplest way to do this conversion is a resistor between the PD output and the supply voltage as shown in Figure 2. The preamplifier is one of the determining parts concerning the sensitivity and bandwidth of an optical receiver. The sensitivity mainly depends on the responsivity of the *PD* and the input referred noise current of the circuit. Due to the fact that the output current of the *PD* is the smallest signal in the circuit, this point is the most sensitive concerning noise. The signal-to-noise ratio is most critical at the input node of the preamplifier. Therefore, the noise of the preamplifier is the dominating part of the input referred noise current. Again the noise of the resistor Rand the first amplifying stage are the deciding factors.

Figure 2 Simplest possibility of the preamplifier

The most interesting characteristics of the preamplifier, therefore, are the bandwidth and the input referred noise of the circuit. For the simple receiver shown in Figure 2 the bandwidth is indirectly related to the capacitance of the input node and the resistor R. In this simple model, the capacitance of the input node consists of the capacitance of the PD, and the input capacitance of the amplifier. To achieve a high bandwidth therefore the resistance Rhas to be small, as well as the capacitance of the input node.

The noise of the circuit shown in Figure 2 depends also on the resistor R, the capacitance of the input node and the first amplifier stage of the following amplifier. To achieve high bandwidths the resistor R must be small and therefore its noise current dominates the sensitivity of the optical receiver. With a more complicated circuit, for example a *TIA*, a better performance can be achieved.

# Shunt-Shunt Feedback TIA

Figure 3 shows the basic circuit of a shunt feedback *TIA* as a preamplifier. In the *TIA* circuit C_{T} consists of the capacitance of the *PD* and the input capacitance of the *TIA*.

Figure 3 Basic circuit of a *TIA* as preamplifier

Let us compare the small-signal transfer functions of the two structures in Figure 2and Figure 3, which is the transimpedance gain v_{o}/i_{in} .

From Figure 2

From Figure 3

The DC transimpedance gain for the simple *TIA* in Figure 2 is the transimpedance resistor value R_{fb}. For high amplifier gains A_{o} this is also the case for Figure 3. Comparing the frequency behavior, the dominant pole which defines the small-signal bandwidth for the two circuits are defined by:

From Figure 2

From Figure 3

Equation (8) shows, that the bandwidth of the simple resistor *TIA* is completely defined by a given transimpedance and photodiode capacitance. Equation (9) shows, that the shunt-shunt feedback *TIA* has an approximately A_{o} times higher bandwidth compared to a simple resistor TIA. The amplifier gain A_{o} is design dependent and higher than 1 for frequencies up to the amplifiers transit frequency f_{t}. Therefore the increased bandwidth for the same transimpedance value is one of the most important advantages of a shunt-shunt feedback *TIA* compared to a simple resistor solution.

The advantage of a shunt-shunt feedback *TIA* compared to the simple circuit described before is the fact that the bandwidth is indirectly related to the resistor *R*_{fb} divided by the open-loop gain A_{0 }of the TIA(R_{fb}/A_{0}). Therefore the noise can be decreased for a given bandwidth, because of a large resistor RF. The smaller C_{T}

and the larger R_{fb}, the higher the sensitivity is for a given responsivity (more discussion will be presented in the next sections). For a high bandwidth it is important to have small C_{T} and small*
*R

_{fb}. C

_{T}is dominated by the PD capacitance, a tradeoff between sensitivity and bandwidth has to be found for the feedback resistor.

[1] M. Atef and H. Zimmermann, “10Gbit/s 2mW Inductorless Transimpedance Amplifier “, IEEE International Symposium on Circuits and Systems (ISCAS),2012.

[2]H. Zimmermann, Integrated Silicon Optoelectronics, Springer, 2000.

[3]H. Zimmermann and K. Schneider, Highly Sensitive Optical Receivers, Springer, 2006.