Terahertz gap is defined loosely as the gap between the electronic (≥300um) and optical (≤30um) electromagnetic spectrum, see Fig1. (0.3THz-10THz).(Borak 2005) It is the most underdeveloped part of the spectrum due to the lack of a convenient radiation source. Therefore terahertz generation is mainly produced from upward conversion of electronic sources or downward converting from optical sources. (Ferguson and Zhang 2002) Both methods are not ideal as they each have their own limitations; pulsed operation, cryogenically cooled, limited by size, complexity and too expensive.(Williams 2007)
As there exists an extensive range of applications in the THz region varying from biomedical to industrial and security imaging, production monitoring, astronomy and chemical analysis. To meet the needs of these applications requires a compact, coherent, continuous-wave (cw) solid state source operating near room temperature. The first quantum cascade laser (QCL) operating in the terahertz region at 4.4 THz was demonstrated in 2002 and fabricated on GaAs/AlGaAs.(Kohler, Tredicucci et al. 2002). The QCL represents terrific promise in meeting the key criteria outlined above. This project is on the development and fabrication of a Si/SiGe QCL.
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One of the main reasons why this topic is important is for the realisation of electrically pumped silicon laser which so far to date has not been achieved. If this could be achieved then it could allow monolithic integration with CMOS/BICMOS devices and the realisation of a single integrated chip. The benefits from this would be cheaper manufacture costs as there would be less components required to produce a fully working system and also a performance improvement from removing the bottleneck of interconnects between devices.(Paul 2005)
Another motivation for the
One of the main reasons why this topic is important is that a SiGe QCL will have inherent advantages over a (group 35) QCL (Sorel 1996). Some of these advantages are the lower rates of electron-phonon or hole-phonon scattering between subbands. Due to the covalent bonding of Si and Ge, the group IV nonpolar phonon scattering is weaker than the polar phonon scattering found in ionic III-V semiconductors. Since laser gain is proportional to the lifetime between subband states this means that group 4 should have higher gain. Also the lack of polar optical phonon scattering below the optical phonon energy of around 62meV in group 4 compared to that of a group 5 which has the phonon scattering which results in a non radiative lifetime between laser subband states having a strong temperature dependence(Paul 2005). By working on this project it is hoped to play a role in the fabrication of the first ever electrically pumped silicon based laser.
Intro needs serious redrafting!!
Fig 1: Electromagnetic spectrum showing THz gap between electronic and optical spectrum
Fig2: Monolithic integration of CMOS/ BICMOS with silicon devices
Semiconductor Laser Diode Basics
A homojunction laser diode (LD) is very similar in terms of design with a standard light emitting diode (LED). For a standard LED, radiation occurs under forward bias of a pn junction (see fig3). For a direct bandgap material where electrons are injected from the n to the p and holes are injected from the p to the n there is an excess of minority carries in the depletion region also known as the active region. When the carriers recombine they emit a photon in random directions and hence this process is known as spontaneous emission.
For spontaneous emission to occur a short carrier lifetime and diffusion length are required. This is the case for direct bandgap materials like GaAs where no change in crystal momentum is required for the recombination process, so there is a high probability of spontaneous emission. An indirect band gap material would require at least one phonon involved in the recombination process and so there is a low probability of spontaneous emission to occur. (Add equations from lecture notes i.e. internal quantum efficiency)(Wood 1994)
Fig3: PN junction under forward bias showing electron hole recombination. E-K diagrams of direct/indirect bandgap materials
Stimulated emission (Equations from optoelectronics book)
A laser diode differs from an LED in that it relies upon a process known as stimulated emission (light amplification by stimulated emission). This process occurs when a photon interacts with a conduction band electron which recombines with a hole in the valence band that produces another photon. Therefore one photon has stimulated the emission of another photon and these two can stimulate further photons (see fig4). (Zeghbroeck 2007) The photons produced all have the same phase, direction, polarization and frequency of the incoming photon. To ensure that a photon interacts with a conduction band electron and not with an electron in the valence band which results in absorption, have to engineer a population inversion. In a semiconductor laser population inversion is achieved by having a larger population of electrons in the lower part of the conduction band than the electrons in the higher part of the valence band (see fig5).
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Fig4: Stimulated emission process
Fig5: Difference in electron population between the conduction and valence band
This can be done by using a pn junction like the one used for the LED except that that each side is heavily doped. By applying a large bias voltage (eV > Eg) the Fermi level of the n side is moved level or greater than the p conduction band (vice versa). Then the built in potential is removed and so the active region can fill up quickly with electrons and holes and will give rise to spontaneous emission where the photons produced will stimulate further emission.
Further considerations of making a successful laser apart from optical gain (population inversion) is the need of optical confinement. This is especially true in the case of the homojunction LD where the active region is extremely small compared to the overall size of the device. Any photon that escapes the active region into the bulk material is likely to be absorbed and wont further any stimulated emission. Optical confinement can be achieved by having a lower refractive index than the core (Needs serious fixing!) With a large optical confinement the gain can then be greatly increased by optical feedback by way of an optical cavity. An optical feedback can be made by placing reflective mirrors at the ends of the cavity which ensures photons will travel multiple times along the cavity, therefore increasing the optical gain. Such a cavity is called a Fabroy-Perot optical resonator and can be produced by cleaving the ends of the semiconductor. Travelling waves inside the cavity must form standing waves placing restrictions on the wavelengths that can resonate.
(Equations regarding cavity modes)
2 QCL Fundamentals
The Quantum cascade laser is a unipolar device in that there is only one carrier (electrons or holes) as opposed to the LD and LED which produce photons through the interband recombination of electrons with holes.(Harrison 2005) As already seen for the LD the emitted photon has wavelength governed by the bandgap of the bulk material and so there is no suitable semiconductor material to emit terahertz radiation using standard LD design as a bandgap of less than 60meV would be required. This is even true of the quantum well LD shown in fig6. The QCL on the other hand emits photons based on the energy difference between electronic transitions between subband states in quantum wells. (fig6b). (Equation) Therefore the QCL is unique in that it is not bound by the bandgap of the host material but can be specifically engineered(Capasso, Tredicucci et al. 1999) to operate over a large range of frequencies. Thus it can be tailored for the terahertz gap.
Fig6: Interband recombination and intersubband transition
Engineering subband states for intersubband (intrasubband) transition requires some knowledge about quantum wells. A quantum well is formed when a thin layer of a semiconductor material with a narrow bandgap is sandwiched between two layers of a wider bandgap. This creates a heterostructure and if the layer of the narrow bandgap is thin enough (≤ 10nm) then it is susceptible to quantization effects which produce distinct subband states. An example of these subband states can be seen from the textbook example of the infinitely deep square well (fig7). This is a purely idealised example where the barriers have potential infinite in height and are infinite in length. Outside the well the wave function must be zero and inside the well the time independent Schrödinger equation is equal to
A solution to equation must form bound states and a non degenerate energy spectrum therefore choose
Using continuous boundary conditions the wave function vanishes at the walls of the well therefore
Thus the energy of each state is found from equation 2, where n is the quantum number and labels the states. The normalized wave function describing each state is equation 3. From fig7b it is clear that by confining a particle to a region of space it produces discrete energy levels which are known as the subbands.
Fig7a: Infinite square well b: Subband states (right)
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A major benefit from intersubband transition is that since there is no electron hole recombination, the electron is not annihilated and can be utilized further by cascading the electron through a staircase potential of coupled wells. The electron will emit a photon each time it makes a transition from the active subband states in the quantum well and by quantum mechanical tunnelling, the electron can tunnel from the ground state of a well into an excited state in the neighbouring well and start the whole process over again see fig8. Therefore by cascading coupled quantum wells the optical gain in the QCL can be amplified, which is especially important for terahertz radiation as the power of the laser is directly proportional to the frequency of the emitted radiation. As terahertz radiation is on an order of 103 magnitudes less than visible light by cascading can bring the power back up to roughly the same level. (Kohler, Tredicucci et al. 2002; Paul 2005)
Fig8: Staircase potential with electron cascading emitting multiple photons
Quantum mechanical tunnelling
A particle encountering a barrier that has a potential energy greater than the energy of the particle would expect classically that the particle would be reflected back of the barrier. Quantum mechanically however there is a finite probability that the particle will pass straight through (fig8). This is a purely quantum mechanical effect which is due to the wave nature of particles and is known as quantum mechanical tunnelling. (Zettili 2009)
Fig8: Quantum mechanical tunnelling through a single barrier of potential greater than particle energy
For the single barrier case the probability of transmission can be found as
If E << V0 Then equation 3 can be approximated as
Therefore for a high probability of tunnelling requires a short tunnelling distance L, small potential barrier V0 and light effective mass. Therefore for the QCL to be efficient need to use a material that has a light effective mass.
Double barrier-Resonant tunnelling
An example that is more closely related to the transport of electrons in a QCL by tunnelling is the double barrier case. If a quantum well like the one in fig7 has barriers either side that are thin enough then an electron is no longer truly bound to a subband state but can tunnel out giving rise to a resonant state. This is also the building block of the resonant tunnelling diode.
By choice of layer thickness and applied electric field, lifetimes and tunnelling probabilities of each level are engineered in order to obtain population inversion between two sub-bands
Fig9: resonant tunnelling diode showing NDR
History of QCL First QCL and design, advances in IR to FIR, SiGe designs why p type
History of QCL
The first suggestion of the quantum cascade laser was in 1971 when Kazarinov and Suris proposed the use of intersubband transitions in a superlattice structure, electrically pumped by tunnelling for light amplification.(Kazarino.Rf and Suris 1971) A superlattice structure can be seen as an extension beyond that of the double barrier presented in fig9. By increasing the number of barriers/wells within a semiconductor this creates a periodic potential and the electron (hole) is no longer confined to a discrete subband state in a quantum well but is equally likely to be found in any of the quantum wells resulting in the formation of a miniband. Much like the way the conduction and valence band are formed by the periodic potential of the crystalline structure there can be multiple minibands with minigaps in between. Therefore a superlattice can be used to filter the energy of electrons, allowing only those within the minibands to pass or reflecting those in the minigaps.(Davies 1998))
Due to the invention of molecular beam epitaxy (MBE) in 1969, superlattice structures could be finally realized by the potential to grow monolayers with precise control. (Beere, Fowler et al. 2005) This technology paved the way for producing devices that could exploit quantum mechanical effects. It wasn't until 1988 however that the first intersubband luminescence was witnessed and this was in the FIR region (Helm, Colas et al. 1988).
The first intersubband laser followed later, some 23 years after the first proposal by Kazarinov and Suris in 1994 when Jerome Faist at Bell labs demonstrated the quantum cascade laser. The design is shown in fig10 and is based on a three quantum well active region where the radiative transition is diagonal (intersubband) between subband states 3 and 2. Population inversion is obtained by a fast depopulation of electrons from level 2 to 1 by setting the subband separation between them to the longitudinal optical (LO) phonon resonance energy. By doing this it allows to take advantage of an extremely fast and dominate scattering process, where the non radiative LO phonon scattering time is much quicker than the radiative transition time. Each active region is separated by a doped superlattice injector/collector that collects electrons from the lower states and injects them into the excited radiative state in the next stage and so the process is cascaded.
The first device was grown on InGaAs/AlInAs/InP and operated at 4.2um. Lasing was achieved in pulsed mode producing up to 10mW at cryogenic temperatures.(Faist, Capasso et al. 1994)
Fig10: First working QCL based on a 3QW active region
It was only a year after their invention that QCLs achieved continuous wave (cw) operation(Faist, Capasso et al. 1995) at cryogenic temperatures, and in pulsed mode up to room temperature a year after that (Faist, Capasso et al. 1996). In 2002 came the first cw QCL operating at room temperature.(Beck, Hofstetter et al. 2002) The device lased at 9.1um with up to 17mW of output power. Ever since its creation the QCL has become the dominate source over the MIR region.
FIR QCL challenges
The production of a QCL operating in the FIR region though, has been far more challenging compared to its counterpart in the MIR. This is mainly due to three issues; the energy spacing between the radiative subband states for terahertz radiation is extremely small (10 THz - 1 THz ≈ 40meV- 4meV). Therefore it is harder to selectively inject electrons into the upper excited radiation state and not the lower one. Also to achieve population inversion requires fast depopulation of the lower radiative state but since the energy levels are lower than the LO phonon resonance energy this cannot be used as the main scattering mechanism. Therefore there is difficulty in controlling dominate scattering rates at low energies; electron-electron, electron impurity and interface roughness scattering. Another challenge is the development of a suitable waveguide to confine photons of such long wavelength. In standard LD design as already seen, optical confinement comes from having a dielectric cladding that has a lower refractive index than the core. If this was implemented in a FIR QCL it would require an unpractical and expensive amount of cladding. Free carrier absorption which scales with λ2, heavily affecting the waveguide losses. (Need references)
First FIR QCL
It wasn't until October 2001 that the first QCL with photon energy less than the semiconductor optical phonon was demonstrated at 4.4 THz. The device was grown on GaAs/AlGaAs and had peak powers up to 2mW at 50K. (Kohler, Tredicucci et al. 2002).
From then on, FIR QCLs have been demonstrated over a wide region of the terahertz gap from 5 THz down to 0.85THz. (Needs finishing)
A discussion of the intended approach to the topic. What methods are to be used?
SiGe QCL Fabrication
In order to create a working QCL that can be then tested and characterised requires using device fabrication techniques to make contacts to the device and also pattern the device into the correct feature. This part of the report will describe the standard photolithography techniques (shown below) that will be used in the processing of the SiGe QCL. Photolithography is an optical means for transferring patterns onto a substrate. Patterns are first transferred to a photoresist layer. Photoresist is a liquid film that can be spread out onto a substrate, exposed with a desired pattern, and developed into a selectively placed layer for subsequent processing via etching or metal deposition.
• Surface Preparation
• Coating (Spin Resist)
• Pre-Bake (Soft Bake)
The first stage of any photolithography process is the sample must be cleaned thoroughly. This is required to remove any dust particles from cleaving of the wafer to ensure that there are no contaminants in the photoresist. The standard clean used is a 5 min soak in acetone with ultrasonic agitation followed by a 5 min soak in isopropyl alcohol (IPA) with ultra sonic agitation and then lastly a nitrogen (N2) blow dry.
Coating (Spin Resist)
A requirement of a good photoresist is that it is has to be contaminant free, has good uniformity and adheres well to the surface of the sample. The Shipley Microposit S1800 series meets these requirements and so will be used. For good adhesion ideally want no water on the surface of the sample. Therefore after the surface preparation stage the sample is given a dehydration bake in a convection oven for 10 min at 120C. Then the sample is given an adhesion promoter also known as a surface primer just before the photoresist is applied. The surface primer is applied in the same way as the photoresist as can be seen in fig11. The sample is held on a spinner chuck by vacuum and resist is applied manually by a syringe. For the Shipley Microposit S1818 photoresist a uniform coating is achieved by spinning at 4000rpm for 30 seconds and this corresponds to a resist thickness of approximately 1.8um.
Fig11: Set up for applying the resist.
Pre-Bake (Soft Bake)
After the resist has been spun a soft bake is required to evaporate excess solvent and increase the density of the resist. The Softbake for the S1818 resist is performed on a hot plate set at 85C for 120 seconds.
Alignment and Exposure
After the softbake the sample is ready for photolithography. The desired layers that are to be transferred to the sample are done by using a photo mask and a mask aligner. By using a CAD tool such as L-edit all layers required for processing are drawn together then separated by software to ensure that they accurately match up. Once the layers have been separated a master copy of the mask is written using electron beam lithography. The mask is made of a quartz substrate coated with chromium where the pattern is etched into the chromium. The mask aligner is then used to align the first layer to the sample. Subsequent layers are aligned to by using 3 degrees of control between mask and the sample(x, y, ÆŸ). To ensure an accurate alignment between layers, alignment marks with a vernier scale are used as can be seen in fig12. Once alignment has been carried out the sample is ready for UV exposure. A number of contact methods between the mask and sample are available; soft contact, hard contact and vacuum contact. For S1818 an exposure time of 5 seconds is required.
Fig12: Alignment marks with vernier scale
This is the stage that removes the exposed resist so that subsequent processing can take place. S1800 series is a positive photo resist therefore after exposure to ultra violet light the photoresist removal rate in the developer greatly increases. The development of S1818 is a 1:1 ratio of Microposit MF developer with RO water agitated for 75 seconds followed by a rinse in RO water.
Post-Bake (Hard Bake)
A Post bake is only required if the subsequent processing step is dry or wet etching, where a 30 minute bake at 120C in a convection oven will stabilize and harden the resist. A typical step that will require the hard bake in the SiGe QCL processing will be etching square or ridge mesas using reactive ion etching (RIE) to form the laser structure. This is a subtractive process where photoresist is used as a mask and any areas without photoresist are etched away.
If however the next stage in processing is making contacts to the QCL by metallization then a soft resist is required and no hard bake is applied. Metallization will be accomplished using a process known as lift off as seen in fig13. The first step is to expose the areas where contacts will be made at the photolithography stage. After the development an oxygen plasma is applied using a barrel Asher to remove photoresist residue which can cause poor metal adhesion. A Hydrofluoric (Hf) acid dip is also used to remove any native oxide to ensure the best possible adhesion. Metal is then deposited either by sputtering or evaporation. Lift off is then achieved by using acetone heated to 50C by a water bath and agitation either by hand or ultra sonic. The last stage of the lift off process is to use the rapid thermal annealer (RTA) to ensure best possible ohmic contacts.
Fig13: Lift off process for metallization
In order to ensure the best possible fabrication process for the SiGe QCLs, test structures will be used to allow characterizing of each processing stage. Therefore some test structures have been designed and a mask plate has been fabricated for standard photolithography processing. The next section will talk about the theory behind the test structures that have so far been designed.
Transfer length method
One such test structure is the Transfer length method (TLM). TLM is a contact measurement technique that gives a complete characterization of the contact by providing the sheet resistance, the contact resistance and the specific contact resistivity of the metal-semiconductor interface. By using this test structure it will allow an accurate estimate of what metals to use for making the best ohmic contacts to the QCL. The design of the TLM consists of four contacts with unequal spacing ranging from 5um to 20um. To prevent current spreading and improve accuracy a mesa etch is performed by RIE. The contacts are made fairly large (150um by 150um) to enable probing by the parametric analyser. A four point probe method (shown in fig11b) is employed to eliminate the parasitic resistance introduced by the probes.
Fig11: TLM with spacing from 5um to 20um b: Four point Probe method
Total resistance RT measured between two contacts is equal to equation 5, where d is spacing between contacts, is sheet resistivity, W is contact width and is metal contact resistance. Rc can be approximated to equation 6, where is the specific contact resistivity and LT is the transfer length found from the intercept at RT = 0.
By measuring the total resistance for each gap from 5 to 20um and plotting RT as a function of d (see Fig 12) can extract the sheet resistance from the gradient of the line, the contact resistance from the intercept at d = 0 and the specific contact resistivity by finding LT and using equation 6.(Schroder 1990)
Fig 12: Plot of RT vs. d
Van der Pauw and Hall bar