VCSELs for Cesium-Based Miniaturized Atomic Clocks

"Whoever treads a path seeking knowledge,

Allah will make easy for him the path to Paradise",

The Prophet Muhammad (PBUH).

Acknowledgement

This dissertation would not have been possible without the help of many people. Firstly. I would like to express my sincere gratitude to my supervisor apl. Prof. Dr.-Ing. Rainer Michalzik, who gave me this great opportunity to do this work and to participate in a European collaborative research project involving several academic partners, international research institutes and many industrial enterprises with the target to realize the first European miniaturized atomic clock demonstrators. He was always a source of support and new ideas that have had a profound effect on this dissertation.

Special thanks go to all people at the Institute of Optoelectronics which I have gladly worked with during this dissertation, particularly, Wolfgang Schwarz who taught me how to process VCSELs, and always supported me with his vast expertise in microwave measurements, Dietmar Wahl who put much effort in growing many VCSEL wafers where reaching the Cs D1 wavelength was always challenging, my friend and office-mate Alexander Kern for his valuable advices to improve measurement setups, helping with SEM pictures and of course the very enjoyable time we spent together during our PhDs, Rudolf Rösch for his continuous support in dry etching, contact metallization and substrate thinning, Susanne Menzel for her great help in dealing with different chemicals in the cleanroom, Dr.-Ing. Jürgen Mähnß for reading and correcting the first draft of this dissertation, Alexander Hein for assistance with lifetime measurements and Anna Bergmann for her kind help with contact metallization.

I also thank very much all students who worked with me during the years of this PhD work and contributed strongly with their diploma, master and bachelor theses to the success of the atomic clock VCSELs. Namely, my thanks go to Simeon Renz, Andreas Strodl, Md. Jarez Miah and Mustafa Kazu. I would also like to thank Md. Tanvir Haidar, Sujoy Paul and Niazul Islam Khan for their great help in characterizing atomic clock VCSELs through their student jobs at the Institute of Optoelectronics.

I am very grateful to all people at the Institute of Electron Devices and Circuits at Ulm University for their support and assistance, particularly, Yakiv Men for performing the electron-beam lithography steps for all the grating VCSEL wafers and Tatyana Purtova and Gang Liu for their continuous assistance with microwave reflection measurements.

Many thanks go to all the project partners of MAC-TFC, especially Dr. Christoph Affolderbach from UniNE-LTF and Dr. Vincent Giordano from FEMTO-ST, who answered all the questions on the physics of miniaturized atomic clocks, enhancing greatly my understanding of the subject and Dr. Rahel Strässle and Dr. Yves Pétremand from SAMLAB at EPFL for providing me with microfabricated Cs vapor cells for the measurement of the absorption spectra presented in App. G.

I am very grateful to Dr.-Ing. Dieter Wiedenmann from Philips U-L-M Photonics and his team for their support especially with mounting VCSEL chips in TO cans. Acknowledgements also go to Dr. Pierluigi Debernardi from IEIIT-CNR Torino for performing simulations of grating VCSELs using his excellent model, Dr.-Ing. Marwan Bou Sanayeh from Notre Dame University who helped very much by processing VCSELs during his frequent visits as a guest scientist at the Institute of Optoelectronics.

My gratitude is also extended to the members of the PhD commission, apl. Prof. Dr.-Ing. Rainer Michalzik, Prof. Dr. Martin Hofmann from Ruhr-Universität Bochum, Prof. Dr. Ulrich Herr and Prof. Dr.-Ing. Albrecht Rothermel for all the efforts they exerted.

Finally, special thanks and appreciation to my beloved parents, my dear brother Samer and my dear sister Soha for their unconditional support and encouragement despite the long distance.

This dissertation was first published by Ulm University, Ulm in 2014.

Contents

Introduction and Motivation

Clocks and Frequency Standards: Concept, History, Miniaturization, and Applications

2.1 Key Aspects of Clocks

2.1.1 Accuracy

2.1.2 Stability

2.1.3 Quality Factor

2.2 Historical Prospective of Clocks

2.2.1 Mechanical Clocks

2.2.2 Quartz-Based Clocks

2.2.3 Microwave Atomic Clocks

2.3 Miniaturization of Atomic Clocks

2.3.1 Three-Level System and CPT Spectroscopy

2.3.2 Microfabricated Alkali Vapor Cells

2.3.3 Frequency Stability of MACs

2.3.4 Requirements on the Laser Source

2.4 Applications of MACs

Fundamentals of VCSELs

3.1 Device Structure and Properties

3.2 Threshold Conditions

3.3 Operation Characteristics

3.4 Temperature Behavior

3.4.1 Red-Shift Effect

3.4.2 Thermal Resistance

3.5 Dynamic and Noise Behavior

3.5.1 Rate Equations

3.5.2 Small-Signal Modulation Response

3.5.3 Intensity Modulation and Frequency Modulation

3.5.4 RIN

3.5.5 Emission Linewidth

3.6 Polarization Properties

3.7 VCSEL Applications

Design and Fabrication of VCSELs for Miniaturized Atomic Clocks

4.1 Adjustment of Layer Thicknesses

4.2 Design of the Active Region

4.2.1 Bandgap Energy of Bulk AlGaAs and InGaAs

4.2.2 Mechanical Strain Effect

4.2.3 Bandgap Renormalization

4.2.4 Relative Band Offset

4.2.5 Quantum Effect

4.2.6 Experimental Verification

4.3 Single-Mode Emission

4.4 Polarization Control

4.4.1 Concept of Surface Gratings for Polarization Control

4.4.2 Design of Surface Gratings

4.4.3 Simulations of Surface Grating VCSELs

4.5 Layer Structure

4.6 VCSEL Chip Design and Processing

4.6.1 Flip-Chip-Bondable Design

4.6.2 VCSEL Processing

Experimental Characterization of Atomic Clock VCSELs

5.1 Static Characteristics

5.1.1 Operation Characteristics and Emission Spectra

5.1.2 Polarization Control

5.1.3 Far-Field Properties

5.2 Dynamic Characteristics

5.2.1 Small-Signal Modulation Response

5.2.2 Intrinsic Modulation Behavior

Improved and Alternative Atomic Clock VCSELs

6.1 Modification of the Top Bragg Mirrors

6.2 Alternative Surface Grating Approaches

6.2.1 Regular Grating VCSELs

6.2.2 Inverted Grating Relief VCSELs

6.3 Reduction of Processing Complexity

6.4 Reliability Tests

Experimental Cesium-Based Atomic Clock Demonstrator

7.1 VCSEL Description and Packaging

7.1.1 Standard VCSELs

7.1.2 Inverted Grating Relief VCSELs

7.2 Laser Noise and Dynamics

7.2.1 Emission Linewidth

7.2.2 Relative Intensity and Frequency Noise

7.2.3 Modulation Sideband Characteristics

7.3 CPT Resonance Signal Measurement

Conclusion

Cesium Properties

A.1 Fine and Hyperfine Structure

A.2 Zeeman Splitting

MAC-TFC Consortium

Mask Layouts

VCSEL Processing

D.1 Flip-Chip-Bondable VCSELs with Thick Planarization Layers

D.2 Flip-Chip-Bondable VCSELs with Thin Planarization Layer (Simpler Processing)

VCSEL Epitaxial Structure

Experimental Measurement Setups

F.1 Polarization-Resolved Operation Characteristics and Emission Spectra

F.2 Far-Field Measurements

F.3 Small-Signal Modulation Response Measurements

F.4 RIN Measurements

Cesium Absorption Spectra

H List of Acronyms

List of Symbols

I.1 Mathematical Operators, Special Functions and Constants

I.2 Mathematical Symbols

I.3 Greek Symbols

Bibliography

Chapter 1

Introduction and Motivation

Frequency standards or clocks provide time references for a wide range of systems and applications such as synchronization of communication networks, remote sensing and global positioning. Over the last couple of decades, demands on the data rates of many communication systems have substantially increased, imposing more restricted requirements on the stability and accuracy of their timing devices. At the same time applications have become more mobile, increasing the demand for small frequency references with low power consumption.

Atomic clocks have provided the most stable frequency references for more than 50 years [1, 2]. However, the size and power requirements of microwave-cavity-based atomic clocks prohibit them from being portable and battery-operated. Hence, research on miniaturized atomic clocks (MACs) has been carried out by various research groups. The first demonstrations of MACs were done in 2004 separately by two research groups in the United States of America, led by the National Institute of Standards and Technology (NIST) [3] and Symmetricom [4]. A Joint European research project on MACs, funded by the European commission started in 2008 [5, 6]. This dissertation reports on the achievements within the European research project in the design, fabrication and characterization of suitable laser sources for such atomic clocks. MACs use the principle of all-optical coherent population trapping (CPT) excitation which does not require a microwave cavity [7, 8]. Owing to their enhanced stability and low power consumption compared to thermally stabilized quartz-based oscillators, MACs are becoming key elements for the above-stated applications and systems. The CPT excitation is obtained in an extremely compact cesium-based vapor cell of a few cubic millimeters volume which is illuminated by an intensity-modulated laser source at a GHz-range modulation frequency.

Vertical-cavity surface-emitting lasers (VCSELs) are compelling light sources for MACs because of their low power consumption, high modulation bandwidth, and favorable beam characteristics. Similar to their use in tunable diode laser absorption spectroscopy (TD-LAS) for regular gas sensing, VCSELs must feature strictly polarization-stable singlemode emission. Additionally, they must provide narrow linewidth emission at a center wavelength of about 894.6nm and be well suited for harmonic modulation at about 4.6GHz in order to employ the CPT effect at the cesium D1 line. VCSELs emitting at 894.6nm have been developed and employed in prototype atomic clocks [9, 10]. Those standard VCSELs with circularly symmetric resonators are often found to be polarizationstable. However, the stability cannot be guaranteed, especially after handling steps like soldering or bonding, which are necessary for microsystem integration and which might cause internal strain. Such unpredictable behavior can considerably reduce the yield of suitable devices from a fabricated wafer. In fact, owing to the cylindrical symmetry of the VCSEL resonator and the isotropic gain and reflectivity provided by the quantum wells and the Bragg mirrors, respectively, the polarization orientation of the emitted light of a standard VCSEL is a priori unknown. In the worst case, the orientation of the polarization can change during operation [11]. Therefore, several attempts have been undertaken in the past to lift the symmetry of the VCSEL structure and the isotropic property of the gain and reflectivity in the device in order to stabilize the polarization in a fixed direction [12]. Among all of these, the incorporation of a linear semiconductor surface grating at the outcoupling facet was found to be the most advantageous. The polarizing effect is induced by the difference in optical losses and thus threshold gains of modes polarized parallel or orthogonal to the grating lines.

The VCSELs for cesium-based MACs, designed and fabricated during the research performed for this dissertation, employ such pure semiconductor–air surface gratings as will be discussed thoroughly in the upcoming chapters. For the purpose of integration with the clock microsystem, flip-chip-bondable VCSEL chip designs are realized and developed. Such chip designs facilitate not only a straightforward mounting but also make the electrical contacts high-frequency compatible. Extensive static and dynamic VCSEL characterization has been performed along with several optimization cycles, supported by numerical simulations of the laser resonator.

The dissertation is organized as follows: first, general key concepts of clocks and frequency standards along with a brief historical overview on their development are introduced. Subsequently, the concept of atomic clocks, their performance, the necessity of their miniaturization, the essentiality of VCSELs as their laser sources and their main applications are discussed. The fundamentals of VCSEL design, operation and applications are presented in Chap. 3. The design of single-mode polarization-stable VCSELs emitting at 894.6nm wavelength suitable for cesium-based MACs is outlined in Chap. 4. The concept of surface gratings for polarization control is presented in the same chapter, where the design of the gratings is based on advanced electromagnetic simulations using a fully-vectorial three-dimensional model [13]. At the end of the chapter, the layer structure of atomic clock VCSELs, the chip design and the fabrication process are discussed. Static and dynamic characteristics of initial generations of atomic clock VCSELs are discussed in Chap. 5, before further improvements and alternatives of such VCSELs are presented in Chap. 6. In the same chapter, preliminary reliability tests of some VCSELs are reported. Investigations on some atomic clock VCSELs, proving their high-level performance and their validity as laser sources for MACs, are discussed in Chap. 7. Such investigations include characterizations of noise and harmonic modulation properties of individual stand-alone VCSELs as well as delineation of the CPT signal of a prototype atomic clock employing such VCSELs. Finally, a conclusion is given in Chap. 8.

Chapter 2

Clocks and Frequency Standards: Concept, History, Miniaturization, and Applications

In this chapter, some key concepts characterizing clock performance are discussed. A brief historical overview on the development of clocks and frequency standards is given. Atomic clocks show best performance in terms of accuracy and stability. However, portable battery-operated applications require miniaturization of the atomic clock to reduce its power and size requirements, as will be explained. Finally, some applications of miniaturized atomic clocks are presented.

2.1 Key Aspects of Clocks

Clocks or frequency standards are devices which are capable of producing stable and well known frequencies with a given accuracy. They can provide necessary timing references and signals covering a wide range of frequencies which are of a great concern for vast fields in sciences and technologies [2]. A clock consists of two parts, an oscillator which produces stable periodic events and a counter which counts these events and displays the time or frequency. The oscillator itself consists of two components, in particular, a resonator which generates the periodic events and an energy source which provides energy to sustain the stability of the periodic events [14,15]. Commonly, the performance of clocks is evaluated by three figures of merit, namely accuracy, stability and the quality factor of the employed resonator.

2.1.1 Accuracy

Accuracy is the degree of closeness of a measured value to its definition or its ideal value. Conversely, inaccuracy of a measured value is its offset from the ideal value. Practically, the clock accuracy is measured by determining the frequency offset of the periodic events generated by the oscillator from its ideal value known as nominal frequency fnom. The frequency offset can be measured in either the frequency or the time domain. A simple measurement in the frequency domain involves a frequency counter to count and display the frequency output of the clock under test. The relative frequency offset can be given by [15]

where fmeas is the reading from the frequency counter and fis known also as the relative inaccuracy. Frequency offset measurements in the time domain involve phase comparison between the outputs of the clock under test and a reference clock which has to be highly accurate, e.g., the microwave atomic clocks which will be introduced in Sec. 2.2.3. The relative frequency offset in the time domain can be given by [15]

where Δt is the amount of the time deviation and τ .

2.1.2 Stability

Different from accuracy, which indicates how well a clock is set on its nominal frequency, stability indicates how well a clock can produce the same frequency offset over a given interval of time. In practice, clock stability is estimated by measuring frequency offsets over a given interval of time with respect to the mean frequency. In the simplest method, stability can be determined by estimating the standard deviation of a data set of measured frequency offsets. However, frequency offsets are usually a non-stationary data set, since they are time dependent. Thus the mean and the standard deviation often do not converge to particular values. Instead, the mean is alternating each time a new measured data point is added. For these reasons, a non-classical statistic method called Allan deviation is often utilized to estimate the fractional frequency stability as a function of averaging time τ. The Allan deviation [15]

is their number. From (and (2.3) can be thus rewritten as [15]

where ti is the number of data points in the ti set which are equally spaced by τ.

2.1.3 Quality Factor

The quality or Q factor of a resonator is defined as the ratio of the resonance frequency over the linewidth of the resonance. Resonators with high resonance frequency and narrow linewidth exhibit high Q factors. Clock accuracy and stability are closely related to the quality factor of the employed resonator. Today, the unit of second is defined in terms of a particular resonant frequency in the cesium (Cs) atom. Therefore, if a high-Q resonator has a resonance frequency of the Cs atom, then the clock employing such a resonator will accurately generate a second according to its definition. A high-Q resonator has a narrow resonance linewidth which constrains the oscillator to run always at a frequency near its resonance, i.e., higher Q factor leads to better stability. However, a clock with a high-Q resonator would show good stability but poor accuracy, if the resonance frequency of its resonator is not according to the definition of second [14]. Another definition of the Q factor is the ratio of the stored energy in the resonator to the energy loss per each oscillation cycle. Therefore, an ideal resonator with infinity Q factor would run for ever, given a single initial push [14].

2.2 Historical Prospective of Clocks

Sundial clocks or shadow clocks are considered to be the most ancient clocks mankind got to know in the past [14]. Such clocks count and keep the track of the axial spin of the earth around its polar axis and of its rotation around the sun. Both motions were employed as oscillators for this type of clocks. As early as 3500 B.C., ancient Egyptians had built obelisks that could be used to divide the day into several divisions [16]. Obelisks also showed the longest and shortest days of the year when the shadow at noon was the shortest and longest, respectively [16]. In addition to sundial clocks, Egyptians constructed water clocks that in their simplest form consisted of a bowl which is wide at the top and narrow at the bottom, and marked from inside with horizontal hour ticks. The bowl was filled with water that leaks out through a small hole in the bottom [14]. Until the 14th century, Chinese, Greeks and Romans continued to rely on water and even sand clocks [14].

2.2.1 Mechanical Clocks

Water and sand clocks suffered from many problems such as ability