# Integrated High Resolution Digital Color Light Sensor in 130 nm CMOS Technology

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## Abstract

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^{2}of silicon area (including three photodiodes and the analog part of the ADC). The DSP is currently implemented on FPGA.

## 1. Introduction

## 2. Principles of Operation

## 3. Color Sensor Design and Measurements

#### 3.1. Proposed Photo Sensor Principles

#### 3.1.1. “Red” Spectral Response Sensor

**Figure 2.**(

**a**) Illustration of carrier generation and lateral carrier diffusion for short (light grey carriers) and long light wavelengths (dark grey carriers); (

**b**) Effect of lateral carrier diffusion on photodiodes responsivities.

#### 3.1.2. “Blue” Spectral Response Sensor

**Figure 3.**(

**a**) A retrograde p-well can be used to shield substrate carriers; (

**b**) The responsivity of the shielded pn-junction NPPW is sensitive to short (blue) light wavelengths.

#### 3.2. Proposed Color Sensor Implementation

**Figure 4.**Cross-section of the proposed color sensor structure with three-sensor output signals NPL, NWD, and NPPW with different spectral responsivities.

#### 3.2.1. Color Sensor Simulations

**Figure 5.**(

**a**) Simulated electron current density of the color sensor structure; (

**b**) Simulation results of the responsivity of uncovered NPL and NWD photodiodes without the influence of the oxide/dielectric stack.

## 4. High Resolution Light to Digital Conversion

#### 4.1. Photocurrent to Digital Converter

_{LF_chp}$\cong 2\text{kHz}$. A 24-bit decimator output signal is digitally mixed with signal $C\left(n\right)=LF\_CHP$; it translates the main spectral line to the DC, while the remaining offset voltage of the complete modulator is up-converted to the spectral line at frequency f

_{LF_chp}; the MA filter removes this spectral component. In this way, a special kind of nested chopper technique is implemented, which offers the best results regarding the offset and the 1/f noise. The residuals of the LF chopping spectra are removed in a first order moving average filter (MA_filter in Figure 6 that calculates the average of the two consecutive results of the decimation filter output according to Equation (2), where ${y}_{n}=k\cdot {I}_{photo}+{V}_{off}$ and ${y}_{n-1}=-k\cdot {I}_{photo}+{V}_{off}$:

**Figure 7.**A simplified circuit diagram of a hybrid, 3rd order $\mathrm{\Sigma}\mathrm{\Delta}$ modulator with multi-bit FIR-DAC and a corresponding compensation circuit IntEz. It also includes a multiplexer where three pairs of photo-diodes are connected in addition to an input for testing purposes.

**Figure 8.**FIR-DAC filter implementation. The weights are implemented by current sources with different ratios. The reference current is possible to adjust to compensate inaccuracy due to matching.

**Figure 9.**S-C implementation of compensation filter $K\left(z\right)$ with a switched capacitor circuit.

#### 4.2. Modelling and Simulations

**Figure 10.**Spectra of the bit-stream for a sine-wave input light with an amplitude of 24 k Lux. The frequency is 1kHz and produces a 300 nA amplitude: (

**a**) the spectrum of the bit-stream with chopping off; the most important non-ideal effects are included; (

**b**) the spectrum at the moving average filter output with word-length reduced to 22 bits; the input signal is the same as for (

**a**), but in this case LF chopping is on.

#### 4.3. Circuit Design

**Figure 11.**Simplified circuit diagram of the amplifier of the first CT integrator with HF chopper switches included.

#### 4.4. System and Circuit Simulation Results

**Figure 12.**Circuit simulation result: SnR as a function of input light intensity with LF and HF choppers switched on.

## 5. Color Signal Processing

_{X}, T

_{Y}, T

_{Z}) is generated, as shown in Figure 13.

_{X}, T

_{Y}, and T

_{Z}can be expressed as integration over wavelength λ, where S(λ) is the received spectral power distribution of an illuminant. As S(λ) is usually measured at discrete intervals, the tristimulus values can be rewritten as the sum suggested in Equations (4)–(6):

_{X}, T’

_{Y}, T’

_{Z}) when applied to the responsivity of the three photodiodes of the color sensor, as shown in Figure 13b. T’

_{X}, T’

_{Y}, T’

_{Z}can be obtained by the same method:

**Figure 14.**Use of training patterns to generate a transformation matrix suitable for different light spectra.

_{1}(λ) … S

_{n}(λ), are used as training stimuli to create a set of outputs with the X,Y,Z color matching function (Figure 14a) and a set of outputs defined by the color sensor responsivities (Figure 14b). A transformation matrix M with a minimum dimension of 3 × 3 can be used to transform T’

_{X}, T’

_{Y}, T’

_{Z}into T

_{X}, T

_{Y}, T

_{Z}according to Equation (8):

_{X}, T’

_{Y}, T’

_{Z}to the approximated X, Y, Z values T’

_{X,T}, T’

_{Y,T}, T’

_{Z,T}using Equation (9). The transformed values T’

_{X,T}, T’

_{Y,T}, T’

_{Z,T}have a relative error in relation to the ideal X, Y, Z tristimulus values to T

_{X}, T

_{Y}, T

_{Z}:

_{X,T}, T’

_{Y,T}, T’

_{Z,T}and the reference tristimulus values T

_{X}, T

_{Y}, T

_{Z}, a non-linear combination of the three sensor output values T’ like T’

_{X}× T’

_{Y}, T’

_{Y}× T’

_{Z}, or T’

_{X}× T’

_{Z}can be used to extend the sensor output information. The transformation matrix therefore needs to be extended to 6 × 3. However, since T

_{Y}, which is the luminance, is usually normalized to one, the transformation matrix M can be reduced to 4 × 3. The non-linear extension of the transformation matrix significantly decreases the relative error for the 15 light sources from 40% to below 10%. On the other hand, the increase of the transformation matrix also results in an increase of hardware for the mathematical operations from nine multipliers and six adders up to 12 multipliers and nine adders.

## 6. Experiments, Measurement Results, and Discussion

#### 6.1. Color Sensor Measurements

**Figure 15.**Photograph of the color-sensor test structure including indication of one sensor stripe and cut-line for cross-section.

Pn-Junction | Bias Voltage | ||
---|---|---|---|

2 V | 1.5 V | 0 V | |

P-substrate/N+ lighted | 3.9 pF | 4.2 pF | 6 pF |

P-substrate/N-well dark | 5.5 pF | 6 pF | 8 pF |

P-well/N+ | 18 pF | 19.2 pF | 28 pF |

#### 6.2. X,Y,Z Color Transformation

_{X,Y,Z}is calculated based on measured sensor responsivities. Also, the ideal tristimulus response T

_{X, Y, Z}based on the CIE CMFs are obtained and a 4 × 3 transformation matrix M is generated. After a quantization of the transformation matrix M and the sensor outputs T’

_{X,Y,Z}to 18-bit and 14-bit, respectively, the transformation was performed to calculate the normalized sensor tristimulus values T’

_{XT,YT,ZT}. The relative error between T

_{X,Y,Z}and T’

_{XT,YT,ZT}is presented in the histograms of Figure 17.

_{YT}) and “red” or X-values (T’

_{XT}). The “blue” or Z-value (T’

_{ZT}) can achieve a very high relative high error, up to 150%. One reason for the high “blue” error is that the relative variation of the three sensor responsivities at low wavelengths is very low, which makes the pseudo-inverse matrix operation, and so the average error of the transformation matrix elements high. An improvement of the sensor responsivity at low wavelengths could, for example, be realized by stripe-shaped photodiodes as reported in [9]. For the presented sensor, a resolution of at least 14-bit of the three sensor signals is necessary. An improved sensor with more than three output signals can be realized [27], where the signal quantization has a significantly higher influence on the measurement error. Therefore, a high-resolution sensor data is mandatory, which explains why we built a 22-bit ADC.

#### 6.3. Measurements of the Photocurrent-to-Digital Converter

^{20}samples of the BS and 2

^{8}outputs of the MA filter were stored to the PC for each amplitude and the FFT analysis at different amplitudes were performed; the signal-to-noise ratio for each amplitude was calculated, and at the end the dynamic range was determined. The results of the measurements of the photo-current-to-digital converter are: $SnR\left({I}_{in}=300\text{nA}\right)\cong 106\text{dB}$ and $DR\cong 117\text{dB}$ (compared to the results in Figure 12 the measurements are a bit worse).

#### 6.4. Integrated Digital Color Sensor Measurements

^{2}). Figure 18b shows the optical measurement set-up; the chip in the package with integrated photo diodes and the modulator are located under the microscope, while FPGA with DSP can be observed on the left part of the picture together with other supporting instruments, for example power supplies, etc.

**Figure 18.**(

**a**) Photo-micrograph of the chip including four photo-diodes input multiplexer and 3rd order modulator with FIR-DAC and compensation filter. DSP is implemented on the FPGA; (

**b**) Optical measurement setup.

- (a)
- The photo currents of differently sensitive photo-diodes as a function of the wavelength of the incident light. This is the result of a measurement with the integrated detection system.
- (b)
- Power of the incident light as a function of the wavelength (see Figure 19b).
- (c)
- Responsivity calculated with $R={I}_{photo}/P$ (P is the incident light power).
- (d)
- The comparison of responsivity: integrated light detection system (lines with symbols) and the optical lab measurement setup, explained in Section 3.2.2.

**Figure 19.**(

**a**) Measured photocurrents of different photo-diodes; (

**b**) Power of the light on the sensor as a function of the wavelength; (

**c**) Responsivity of the complete detection system for three different photo-diodes; (

**d**) A responsivity comparison between the integrated color detection system of this article and measurements obtained with the optical lab setup.

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Strle, D.; Nahtigal, U.; Batistell, G.; Zhang, V.C.; Ofner, E.; Fant, A.; Sturm, J.
Integrated High Resolution Digital Color Light Sensor in 130 nm CMOS Technology. *Sensors* **2015**, *15*, 17786-17807.
https://doi.org/10.3390/s150717786

**AMA Style**

Strle D, Nahtigal U, Batistell G, Zhang VC, Ofner E, Fant A, Sturm J.
Integrated High Resolution Digital Color Light Sensor in 130 nm CMOS Technology. *Sensors*. 2015; 15(7):17786-17807.
https://doi.org/10.3390/s150717786

**Chicago/Turabian Style**

Strle, Drago, Uroš Nahtigal, Graciele Batistell, Vincent Chi Zhang, Erwin Ofner, Andrea Fant, and Johannes Sturm.
2015. "Integrated High Resolution Digital Color Light Sensor in 130 nm CMOS Technology" *Sensors* 15, no. 7: 17786-17807.
https://doi.org/10.3390/s150717786