1. G. M. Penello, A. P. Ravikumar, D. L. Sivco and C. Gmachl
Asymmetric Multi-Quantum Well Infrared Photodetector with a Bound State in the Continuum
Hello, my name is Germano Maioli Penello and I am presenting our work on Asymmetric Multi-Quantum Well Infrared Photodetector with a Bound State in the Continuum . This work was done in collaboration with Arvind Ravikumar, Deborah Sivco and under supervision of prof. Claire Gmachl.
G. M. Penello, A. P. Ravikumar, D. L. Sivco and C. Gmachl

2. Outline Quantum well infrared photodetector – QWIP
Continuum-localized state
Asymmetric heterostructure
Simulation of the heterostructure
Growth and characterization of the designed sample
Conclusion and future steps
I will start the presentation giving an simple overview of the three different configurations used for QWIPs. After that, I will explain, by using an optical analogy, how to confine the electron above the barrier in a continuum localized state. This explanation will give us a physical idea of the confinement and also will allow to create interesting photodetectors. For our sample in this presentation, we will use an asymmetric heterostructure where the confined state in the continuum is “leaky” and we will discuss what to expect in this heterostructure.
The calculation of the energy levels was made using the transfer matrix method and a nonparabolic approximation was used. I will briefly discuss the growth and processing of the sample, and then we will show characterization in more details. After the conclusion, I will also present the future steps we are taking with the confined state configuration and the samples shown here.

3. Quantum Well Infrared Photodetector
QWIP
Quantum Well Infrared Photodetector
Continuum
Continuum
Continuum
Bound to continuum
Bound to bound
Bound to quasibound
When designing a quantum well infrared photodetector, three different configurations are mainly used; bound to continuum, bound to bound and bound to quasibound. Each one has its own advantage and drawbacks, namely: The bound to continuum configuration has an easy carrier extraction and is tunable for a fixed bandoffset, but its photocurrent has a broader peak due to transitions from the localized state to extended states in the continuum.
The bound to bound configuration has a high selectivity resulting from the transitions from two localized states, is also tunable for a fixed bandoffset but its photocurrent suffers from a poor carrier extraction; an extra energy is needed to generate photocurrent.
The most used configuration for a QWIP is a bound to quasibound where one can achieve a narrow absorption peak and an easy carrier extraction. The main drawback of this configuration is that the transition energy is not very tunable. For a fixed bandoffset, there is an ideal quantum well thickness to match the bound to quasibound configuration.
In a close look on the states involved in the transitions, we identify two states on the QWIPs, an extended state (also called the continuum) and an confined state. The confined states are always below the barrier (inside the quantum well) and the extended states are above the barrier (gray region on the figures).
Easy carrier extraction
Tunable for a fixed bandoffset
Lower selectivity (broad absorption peak)
High selectivity (narrow absorption peak)
Tunable for a fixed bandoffset
Poor carrier extraction
Good selectivity (narrow absorption peak)
Easy carrier extraction
Limited tunability for a fixed bandoffset

4. Refraction and reflection
Bragg mirror
How to confine an electron in the continuum?
Refraction and reflection
Bragg mirror for electrons
The first question we want to answer is “How to confine an electron in the continuum?”.
To explain the confined state in the continuum, we will use an analogy to what is known from wave optics. To confine a state inside a quantum well, we use barriers to “reflect” the electron wavefunction. If we “reflect” the electron back and forth in between two barriers we create a region where the electron is confined.
If we take a close look on the extended states in the continuum, the electron wavefunction suffers a refraction when crossing from one layer to the other. This is where we use the analogy known from optics to create a Bragg mirror for electrons, reflecting the electron with a particular energy by analyzing the wave interference of the wavefunction as it crosses an layered material.
The figure in the right shows an energy state around 600 meV where we can observe the destructive interference of an electron state on the heterostructure.
reflection on
the interface
Confined states below the barrier
refraction on
the interface
Extended states above the barrier
reflection on
a layered material
Confined states above the barrier

5. Continuum-localized states
“Defect” on the superlattice. E
The approach we are interested in this work is one that uses a “defect” on the superlattice to create a bound state inside the quantum well and also on the otherwise continuum. The “defect” on the superlattice creates a localized state in the continuum that can be analyzed exactly as commented on the previous slide – electrons with a certain wavelength cannot propagate on the two bragg mirrors surrounding the “defect”.
This approach has the advantages of increase the transition energy if compared to the other configurations commented on the first slide, it has a high selectivity (the transitions are between boundd-to-bound states), it has an easy carrier extraction (similar to a bound to quasibound transition) and it has a good tunability (depending on the defect and on the superlattice, one can select the energy of the transition). Another property explored in this presentation is the low thermal excitation expected for this photodetector since we reduce the density of extended states in the continuum.
Bragg mirror
“defect”
Bragg mirror z
Increase transition energy
High selectivity
Easy carrier extraction
Tunability not limited by bandoffset
Low thermal excitation

6. Asymmetric QWIP E z
Asymmetric structure to explore a photovoltaic QWIP and a bias dependence of the photocurrent.
The heterostructure we will present today explore the ideas mentioned in the previous slides with a different touch. Instead of creating two bragg mirrors and completely confine the electron in a central quantum well, we will create a leaky wavefunction - the electron wavefunction is not completely confined. This design will be used to explore a new way of creating a photovoltaic QWIP and also to explore the bias dependence of the photocurrent.
With this structure we expect to obtain a high selective QWIP, because the main transition is between states with a high spatial overlap. Since the excited state is not fully localized and the heterostructure is asymmetric, we expect this sample to have an easy carrier extraction in a preferential direction. This asymmetry on the heterostructure is vital to develop a photoconductive QWIP. We also expect the QWIP to have a low thermal excitation, since the superlattice decrease the density of the extended states in the continuum.
High selectivity
Easier carrier extraction in one direction
Low thermal excitation

7. (confined state in the continuum)
Simulation
Asymmetric sample
Reference sample 9 7 9 7 7 7 7 7
Bound to continuum QWIP
Bound to bound QWIP
(confined state in the continuum)
InGaAs / InAlAs lattice matched to InP
Monolayer = nm
LQW = 7 monolayers ~
DQW = 9 monolayers ~
Barriers = 24 monolayers ~
Absorption cross section
Transfer matrix method
FWHM = 30 meV Dl/l ~ 0.1
(Typical in bound to bound transition)
To analyze our heterostructure, we simulate two different samples. One is the asymmetric sample discussed before and the other is a sample based on a single quantum well in a bound to continuum configuration. The reference sample will be used to understand the effects of the surrounding quantum wells in the asymmetric sample. The graphs on the top shows the localized energy levels of the heterostructure. To simplify the view, we are not showing the miniband states created by the lateral quantum wells.
In the samples, we will use InGaAs and InAlAs lattice matched to InP.
The simulation was made considering the number of monolayers on each layer of the heterostructure. The “defect” quantum well have 9 monolayers (aprox. 2.6nm), the lateral quantum wells have 7 monolayers (aprox. 2.1nm) and the barriers have 24 monolayers.
By using the transfer matrix method, we calculate the energy levels and we estimate the absorption cross section based on the calculation of the dipole moments of the transitions from the ground state. Typical bound to bound transitions in QWIPs show a delta lambda over lambda of 10%. Since the transition involved in our QWIP is on 300 meV, we used a full width at half maximum of 30 meV.
The graph in the bottom right shows the calculation of the absorption for the reference sample and the asymmetric sample. Here we can see that the asymmetric sample is expected to have a narrower transition if compared to the reference sample.
2.1 nm
2.6 nm
7.0 nm

8. Samples MBE Processing InGaAs / InAlAs lattice matched to InP
n-doped (2x1018 cm-3)
Active layers repeated 20x
separated by 30 nm InAlAs
InGaAs contact layers n-doped
(2x1018 cm-3)
Processing
Wet etch
Ti/Au metallization
45o lapping
Au wire bond
Reference sample
n-doped
Asymmetric sample
The sampes were grown by molecular beam epitaxy and, as commented before, are composed of InGaAs and InAlAs lattice matched to InP. In the asymmetric sample, only the “defect” quantum well was doped to populate the ground state of the heterostructure. The active layers were repeated 20x to increase absorption and a thick 30 nm barrier of InAlAs was used to uncouple the subsequent active layer. The active region was embedded in InGaAs n-doped contact layers doped at the same level.
The samples were processed as rectangular mesas by regular wet etching followed by Titanium gold metallization to allow ohmic contacts. To couple the light in the QWIPs, a 45 degree lapping was performed followed by mounting the sample on a chip carrier and gold wire bond.
QWIP mesa

9. Photocurrent
Asymmetric sample
Reference sample
80K
-5V
80K 0V
Dl/l=0.23
Dl/l=0.10
The most important characterization on our samples is the measurement of the photocurrent spectrum. The measurement is performed by shining IR radiation on the polished surface of the sample and collecting the electrical signal with the aid of an FTIR.
The black line on the graph on the left show the photocurrent spectrum of the reference sample at 80K and -5V. Since this sample is a regular QWIP in a bound to continuum transition, the photocurrent measurement is performed under applied bias. The red line is the simulated absorption cross section. The broad photocurrent peak is expected for a bound to continuum transition.
The figure in the right shows the photocurrent spectrum of the asymmetric sample with a confined state in the continuum. One more time, there is an excellent agreement between the simulated absorption and the photocurrent. As expected, the peak is narrower than the reference sample (the delta lambda over lambda is 0.10, typical value for a bound to bound transition). It is also important to notice that since this sample is asymmetric, no bias is needed to generate photocurrent. This is also an expected feature of this heterostructure and this result shows that our QWIP can be used as a photovoltaic QWIP.
Excellent agreement between theoretical and experimental results.
Photocurrent observed without applied bias on the asymmetric sample
“Four zone” photovoltaic QWIP

10. Photocurrent “Leaky” localized state More extended states to couple
An interesting result is observed in the asymmetric sample under applied bias voltage. Under positive bias, the asymmetric QWIP has a similar photocurrent shape if compared to the reference sample. Under negative bias, the two samples have a very different behavior. We explain this situation by analyzing the direction of the photocurrent over the heterostructure. Under positive bias, the localized state in the continuum is leaky, facilitating the extraction of the electron and also, since there is only one lateral quantum well, there are more extended states to couple broadening the photocurrent. This explains why the photocurrent of the asymmetric sample resembles the photocurrent of the reference sample.
Under negative bias, the direction of the electron extraction is directed to the bragg mirror region with les extended states to couple. The state is localized and thus generates a narrower photocurrent when compared to the reference sample.
“Leaky” localized state
More extended states to couple
Broad photocurrent peak
Similar to the reference sample
Localized state
Less extended states to couple
Narrow photocurrent peak

11. Dark current Asymmetric vs. reference sample Reference sample
Asymmetric sample
300K
300K
80K
80K
Asymmetric vs. reference sample
Similar dark current at low temperature (equivalent tunneling current – same spacer between active layers)
lower dark current at temperatures above 150K (lower thermal excitation – less extended states available)
We also compared the dark current of both samples in order to understand the thermionic current. The samples were kept in a cryostat inside a closed heat shield to avoid any external radiation to generate photocurrent. The temperature was controlled in steps of 20K, from 80K to room temperature. The graph in the top left shows the dark current for the reference sample and the one at top right shows the dark current for the asymmetric sample. The dashed vertical line shows the voltage value used in the bottom right graph. In this graph we compare the currents for all the temperatures at a fixed bias. Here we show that the dark current of the asymmetric sample is lower for all the temperatures at -2.5 V.
At low temperature, the asymmetric sample has a slightly lower but similar dark current if compared to the reference sample. The dark current is similar in this regime because the current is dominated by the tunneling between subsequent active layers. Since the spacer is the same on both samples, we already expected the dark current to be similar. At higher temperatures (to the left on the horizontal scale), the dark current of the asymmetric sample is lower than the reference sample by around one order of magnitude. This result is explained by the lower thermal excitation due to the less available extended states above the barrier of the quantum well. One more time, the bragg mirrors act as a filter, reducing the available extended states to propagate in the sample and thus reducing the thermal excitation.

12. Activation energy 253 meV Ef 262 meV Ef Calculated Ef [1]:
Another analysis made by using the dark current measurements is the determination of the activation energy of the samples. The activation energy is defined as the energy difference from the Fermi level to the beginning of the continuum at zero bias. The figure in the top left shows the values obtained for both samples at several bias voltages. As expected (find reference!), the activation energy has a linear relation with the applied electric field. The activation energy obtained for the reference sample is of 253 meV and for the asymmetric sample is of 262 meV.
Using the model of Levine for a single quantum well, the calculated activation energy for the reference sample is of 242 meV. To calculate this result, we used the nominal value of doping from the growth of the samples. By recalculating with a slightly different doping of 1.7x10^18, we obtain a better comparison between the calculated and measured activation energy.
The approximations used in the model doesn’t apply for the asymmetric sample. But since we are using the coupled QWs to reduce the extended states in the continuum, we expected the activation energy of the asymmetric sample to be slight higher than the reference sample. In other words, the thermal excitation is reduced in the asymmetric sample, as shown on the dark currents measured before.
This can be seen in the calculated transmission by using the transfer matrix method on the graph in the bottom right. Here we calculate the transmission of an electron over one active region of the heterostructure. The vertical dashed line indicates the energy of above the bandoffset. Here we can see that in the reference sample, the transmission right above the barrier is several orders of magnitude higher than in the asymmetric quantum well. This is an explanation why the activation energy of the asymmmetric sample is higher; the electron needs an extra energy above the barrier to be thermally excited and generate dark current.
Calculated Ef [1]:
Nominal value: n-doped to 2x1018
Ef = 242 meV.
Recalculating: n-doped to 1.7x1018
Ef = 254 meV.
[1] B. F. Levine, J. Appl. Phys., 74, 8, R1 (1993)

13. BLIP temperature Background limited infrared performance
Below BLIP temperature, the dominant current is caused by the background radiation (maximal sensitivity of the QWIP).
Reference sample
Asymmetric sample
The background limited infrared performance temperature was measured for both detectors. Below the BLIP temperature, the dominant current is caused by the background radiation. Above the BLIP temperature, the thermionic current is dominant. In other words, the BLIP temperature is obtained when the dark current is equal to the photocurrent generated by the background. The determination of the BLIP temperature is important to guarantee a maximal sensitivity of the photodetector. Results obtained here are consistent with theoretical values obtained in the literature [1] for 4um photoconductive QWIPs.
BLIP temperature ~ 200 K
BLIP temperature ~ 180 K
[*] Quantum Well Infrared Photodetectors-Physics and Applications, Liu, H. C. And Schneider, H., (2007) pag. 71 Fig. 4.16

14. Conclusion and future steps
Asymmetric heterostructure with a confined state in the continuum was designed
Photocurrent measurements confirmed the confined state in the continuum
Photocurrent signal at 0V - photovoltaic QWIP
Bias dependent photocurrent was explained by the asymmetry of the sample
Dark current and activation energy were explained
BLIP temperature agrees with the values reported on the literature
Figures of merit to be measured (responsivity and detectivity)
“Four zone” photovoltaic QWIP to be optimized in our structure
New heterostructures using the confined states in the continuum to be explored
To conclude this presentation, we have shown a design, growth and characterization of a QWIP with a confined state in the continuum in an asymmetric heterostructure. The comparison between a reference sample and our sample confirms the existence of a confined state in the continuum.
The photocurrent signal at 0 V shows that the asymmetric structure can be used as a photovoltaic detector.
The asymmetric structure also shows a bias dependent photocurrent, where the behavior of the photocurrent is explained by the asymmetry of the sample.
The comparison of the dark current and the activation energy is shown and also explained.
The BLIP temperature was measured and agrees well with values reported in the literature.
As a future work, we will measure the figures of merit of both detectors (responsivity and detectivity)
We are designing a new sample tp explore and optimize the structure on a photovoltaic QWIP.
Another ideas of photodetectors with confined states in the continuum are under development.

15. Acnowledges Thank you! Qcllab
Capes Foundation, Ministry of Education of Brazil.
MIRTHE (NSF-ERC)
Thank you!
I would like to acknowledge all the people around me that contributed to this work; my lab friends and my supervisor Claire Gmachl.
I am very grateful for the Brazilian funding agency CAPES and also for the Mirthe Center.
Thank you very much.