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Room-temperature miconductor heterostructure refrigeration
K. A. Chao, Magnus Larsson, and A. G. Mal’shukov
Citation: Applied Physics Letters 87, 022103 (2005); doi: 10.1063/1.1992651
View online: dx.doi/10.1063/1.1992651
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Room-temperature miconductor heterostructure refrigeration
K.A.Chao a ͒and Magnus Larsson
Division of Solid State Theory,Department of Physics,Lund University,S-22362Lund,Sweden
A.G.Mal’shukov
Institute of Spectroscopy,Russian Academy of Sciences,142092Troitsk,Moscow Region,Russia
͑Received 28February 2005;accepted 25May 2005;published online 8July 2005͒
With the proper design of miconductor tunneling barrier structures,we can inject low-energy electrons via resonant tunneling,and take out high-energy electrons via a thermionic process.This is the operation principle of our miconductor heterostructure refrigerator ͑SHR ͒without the need of applying a temperature gradient across the device.Even for the bad thermoelectric material AlGaAs,our calculation shows that at room temperature,the SHR can easily lower the temperature by 5–7K.Such devices can be fabricated with the prent miconductor technology.Besides its u as a kitchen refrigerator,the SHR can efficiently cool microelectronic devices.©2005American Institute of Physics .͓DOI:10.1063/1.1992651͔
Thomas Seebeck discovered in 1822that a temperature difference between the two ends of a sample produces a volt-age drop,and realized that such a system can be ud as a thermoelectric power generator.In 1838,Heinrich Lenz ob-rved the freezing of a water drop into ice on a bismuth-antimony junction when an electric current pass through the junction in one direction,and the melti
ng of the ice into water when the current was reverd.Conquently,a ther-moelectric power generator also works as a refrigerator.
miss什么意思
The figure of merit Z =S 2/,determines the thermo-electric efficiency of a material:is the electric conductiv-ity,S is the Seebeck coefficient,and is the thermal conduc-tivity.Around 1950,Ioffe concluded from his calculation of figure of merit that miconductors are among the best ther-moelectric materials,suitable for making solid state refrig-erators.Since then,extensive rearch effort has discovered many thermoelectric materials with ZT Ӎ1,where T is the temperature measured in Kelvin.Various types of thermo-electric coolers have been propod and/or tested.1However,materials with ZT Ӎ1are still not good enough for commer-cial power generators and/or refrigerators.
In the thermoelectric process,electron motion is continu-ously interrupted by scattering,and such a diffusive charge carrier transport cannot produce the required high for a large value of the figure of merit.To further improve the device efficiency,new mechanisms and new structures are then required.From the definition of the figure of merit Z =S 2/,it is desired to reduce the thermal conductivity ,which is not an easy task.2By manipulating the energy quan-tization in low-dimensional systems to modify the thermo-electric process,theoretical studies 3,4have suggested an
in-crea of the figure of merit of one-dimensional conductors.However,it is difficult to confine phonons in one dimension.
On the other hand,in the thermionic process that was first noticed by Thomas Edison in 1883,electron motion is ballistic and can in principle yield a high value of the figure of merit.A conventional thermionic device has two parallel metal plates parated by a small distance.The two plates can be identical or different,with one hot and the other one cold.Electrons are thermally excited from one metal to the
other,over the potential barrier in between.The first thermi-onic power generator was made in 1958,and was called the thermo electron engine .5The energy distributions for thermi-onic emission and the relevant resonance tunneling were dis-cusd in an early review by Gadzuk and Plummer.6Several cooling devices bad on thermionic emission have since been investigated.7–10The efficiency of a thermionic device depends on the height of the potential barrier between the two metal plates.It was originally thought that this height is determined by the work functions of the two metal plates,and if the work function of the anode is lower than 0.35eV,the efficiency at room-temperature operation will meet the commercial requirement.However,this is a wrong conclu-sion.As pointed out by Mahan,11the actual potential barrier height is determined by the space charge betwe
quiksilveren the metal plates,which is about 0.7eV at room temperature,indepen-dent of the work functions of the metal plates.To reduce the amount of space charge,metal-miconductor multilayer structures for thermionic devices were propod,12in which the space charge region is replaced by a miconductor.It was later found that the figure of merit of such a thermionic device was not as high as expected,and could even be com-parable to a corresponding thermoelectric device.13–15A re-cent suggestion to improve the ZT is to u nonconrvation of lateral momentum.16
The problem of thermal conductivity can be largely sim-plified in a cooling device without externally impod tem-perature gradient.There have been ideas to u the Fowler-Nordheim emission process.17,18So far the working devices have a double tunnel-junction structure.The mechanism of cooling is to have low-energy ͑cold ͒electrons tunnel through one junction into the active region.The cold electrons ab-sorb heat from the lattice and become hot,with sufficiently high energy to tunnel out of the active region through an-other junction.The temperature of the system is then lowered.19For a normal metal/insulator/superconductor junc-tion system,20starting from 300mK,the temperature of the system was lowered to 100mK,and for a system of two different superconductors,21the temperature drops from 1.02T c 2to 0.7T c 2,where T c 2=0.51K.The microrefrigera-tors cannot operate above the superconducting transition temperature,and therefore can be ud only for special pur-
a ͒
Electronic mail:chao@teorfys.lu.
APPLIED PHYSICS LETTERS 87,022103͑2005͒
0003-6951/2005/87͑2͒/022103/3/$22.50©2005American Institute of Physics
87,
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pos at extremely low temperatures of less than a few de-grees Kelvin.
In this letter we propo an entirely new room-temperature cooling device using miconductor heterostruc-tures.The system takes advantage of both tunneling ballistic transport and thermionic bal
listic transport.We inject cold electrons into the active region with resonant tunneling through one potential barrier,and remove hot electrons from the active region with thermionic process through one ran-dom alloy that rves as a thermal wall to reduce the heat backflow into the active region.Besides the conventional
cooling purpo,our miconductor heterostructure refrig-erator ͑SHR ͒can easily be integrated into the existing microelectronic technology.In contrast to the micro-refrigerators 19–21that work at extremely low temperature less
than 1K,our SHR works efficiently at room temperature.
It is well known that AlGaAs heterostructures are not
good thermoelectric materials.However,the heterostruc-tures have been thoroughly studied and their material param-eters were determined rather accurately.Hence,using
AlGaAs heterostructures as an example to illustrate our
泰国足球队失踪room-temperature SHR we can prent our results with
quantitatively accuracy.Since room-temperature SHRs can
be made even with the bad thermoelectric material AlGaAs heterostructures,it is optimistic to expect that higher efficiency SHRs can be realized with better thermoelectric materials.The upper part ͑A ͒in Fig.1shows the SHR structure and the corresponding potential profile under a bias voltage V .In the center of the SHR,sandwiched between two thin Al y Ga 1−y As alloys which work as potential barriers,is a n -type GaAs.The materials beyond the potential barriers are thin layers of undoped GaAs,thick Al x Ga 1−x As alloy layers,and n -type GaAs.Each undoped GaAs layer is a quantum well in which there is only one quasibound state with energy .The Al x Ga 1−x As alloy layer is very thick such that when a bias voltage V is applied as shown in Fig.1,the carriers that tunnel from the n -GaAs into the quantum well cannot tunnel through the Al x Ga 1−x As layer.The Al concentration in Al y Ga 1−y As is higher than that in Al x Ga 1−x As ͑y Ͼx ͒.For the
convenience of demonstrating our numerical results,we have assumed a symmetric SHR structure.
Since the structure of the SHR is symmetric with respect to the center n -type GaAs,the physical process in the right half of the system ͑enclod by the dash-lined contour ͒are the same as tho in the left half of the system.Therefore,we only need to illustrate in the lower part ͑B ͒of Fig.1the three carrier transport process in the right half of the device.In the n -doped GaAs,the Fermi energy is marked as f .The overbarrier process has no thermoelectric effect.The single-barrier tunneling proc
ess has a weak refrigeration effect.22,23The third transport process,our propod new cooling pro-cess,is the resonant tunneling from the middle n -GaAs into the quasibound level of the GaAs quantum wells,followed by the thermionic escape over the thick Al x Ga 1−x As barriers.In this process,each carrier removes an amount of thermal energy W from the lattice.Therefore,if the device is sur-rounded by an environment of temperature T ,the tempera-ture of the inner part ͑between the two Al x Ga 1−x As alloy layers ͒will be lowered to T −⌬T .We can increa ⌬T by reducing the heat backflow through the two Al x Ga 1−x As alloy layers.This can be achieved by suppressing the phonon heat conductivity and by increasing the alloy layer thickness L C .However,L C must be less than the carrier mean free path in order to maintain the ballistic transport of the thermionic process.
和氏献璧The amount of heat removed by the electric current J from the inner part to the outer environment has two contri-butions:Q s due to the single-barrier tunneling process and Q rt due to the resonant-tunneling thermionic process.Let Q ph be the heat backflow through the two Al x Ga 1−x As alloy lay-ers due to the phonon heat conduction.The coefficient of performance ͑COP ͒of the SHR is then defined as
K =
Q s +Q rt −Q ph JV .͑1͒To operate the SHR we must have positive K .When K is positive,the inner part of the system will cool down to the temperature T −⌬T when the temperature of the outer envi-ronment is T .To demonstrate the quantitative results,we choo the realistic values for the layer widths shown in the
影视动漫学校
upper part ͑A ͒of Fig.1as L B =23Å,L W =50Å,and L C
=1500Å.The potential barrier height is 260meV for the
Al y Ga 1−y As layers and 100meV for the Al x Ga 1−x As layers.
The Fermi energy is =50meV.In our calculation we u
the value 0.05W/cm K for the phonon heat conductivity in
the Al x Ga 1−x As layers,estimated from experiment.24The tunneling current is calculated including the spatial carrier accumulation with a method 25that has explained the ob-rved bistability in asymmetric double-barrier tunneling
structures.26For a given outer environment temperature T ,the calculated temperature drop ⌬T varie
s with the bias volt-age V ,as shown in Fig.2for T =300,280,260,and 240K.It is well known that the resonant tunneling is stopped when the bias voltage becomes sufficiently high.27In this ca,the only cooling process in the device is the single-barrier tunneling.This region in Fig.2is marked by SBT.When this occurs,the curves in Fig.2become innsitive to the applied bias voltage.We e that the resonant-tunneling thermionic process gives a significant contribution to the cooling performance of the SHR.In Fig.2,the region below the curve for a given value of
T has positive COP K Ͼ0.With increasing bias voltage
V FIG.1.The upper part ͑A ͒illustrate the SHR structure and the correspond-ing potential profile under a bias voltage V .The physical process for the operation of this SHR are shown in the lower part ͑B ͒.When a current flows under a bias voltage V ,the temperature in the region between the two thick Al x Ga 1−x As alloy layers is lowered by an amount ⌬T .
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along each curve,the temperature drop ⌬T increas from zero to its largest value and then decreas.K has its maximum value when ⌬T Ӎ0and reduces to zero when ⌬T rais to its maximum value.Taking V =0.25V as an example ͑the dashed line in Fig.2͒,K depends on ⌬T almost linearly and can be well approximated as K ͑T ͒=K 0͑T ͒−␣͑T ͒⌬T .The values of K 0͑T ͒and ␣͑T ͒are ͓K 0͑240͒;␣͑240͔͒=͓0.198;0.066͔,͓K 0͑260͒;␣͑260͔͒
=͓0.17;0.060͔,͓K 0͑280͒;␣͑280͔͒=͓0.236;0.054͔,
and ͓K 0͑300͒;␣͑300͔͒=͓0.255;0.049͔.
The performance of the SHR can be optimized by changing the device structure.For example,if we reduce the width of the Al y Ga 1−y As layers to LB =20Åand the poten-tial barrier height of the Al x Ga 1−x As layers to 200meV,our calculated results are plotted in Fig.3.A full optimization of the device performance is rather tedious and will not be pre-nted here.From the results in Figs.2and 3,we e that for the SHR made with the bad thermoelectric material AlGaAs,one needs a cascade process to cool the system down through a temperature range larger than 10K.However,with a good thermoelectric material,it is possible to have a suffi-ciently large temperature range within which the COP re-mains positive.
There has been a calculation 7to maximize ⌬T using a single-barrier system with a much better thermoelectric ma-terial Hg 1−x Cd x Te.The barrier thickness is 0.6m,which is twice as long as the electron mean free path 0.3m at room temperature.They neglected the phonon heat backflow,and obtained a large value of ⌬T about 20–40K at room tem-perature.In our calculation,we have t L C =0.15m,which is much shorter than the mean free path 0.3m.With this small value of L C we must include the phonon heat backflow,
and becau of this we obtained only 5–7K for ⌬T .If we t L C =0.3m and neglect the phonon heat backflow,our calculated ⌬T can be higher than 20K.
At room temperature,the measured maximum value 27of ⌬T for Al 0.1Ga 0.9As/GaAs single-barrier system is about 1K.In this system the barrier height is 85meV.For the single-barrier tunneling regime in Figs.2and 3,the effective single barrier should be a thin Al y −x Ga 1−y +x As,which is 160meV for Fig.2and 100meV for Fig.3.Our calculated ⌬T is about 2.5K,which is the same order of magnitude as compared to the measured value.
It is important to point out that our calculated value of COP for AlGaAs heterostructure,although small,is at least one order of magnitude larger than the COP of bulk GaAs measured under similar environment.This significant in-crea of COP has a solid theoretical explanation,and is therefore expected to be a general conclusion for other mi-conductor heterostructures.To integrate our SHR into mod-ern electronic devices,we only need to replace half of the SHR by a suitable miconductor electronic device.While we have demonstrated here the fundamental theory of a new type of room-temperature SHR,its technological applica-tions remain to be en.
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.FIG.2.Under an applied bias voltage V ,each curve reprents the tempera-ture drop ⌬T of the inner part of the SHR for a given outer environment temperature T
.
FIG.3.Similar results as in Fig.2but for a different device structure.
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