Editing Heterojunction

{{Short description|Interface between two layers or regions of dissimilar semiconductors}}
A '''heterojunction''' is an interface between two [[Layer (electronics)|layer]]s or regions of dissimilar [[semiconductor]]s. These semiconducting materials have unequal [[band gap]]s as opposed to a [[homojunction]]. It is often advantageous to engineer the electronic energy bands in many solid-state device applications, including semiconductor lasers, [[solar cell]]s and transistors. The combination of multiple heterojunctions together in a device is called a '''heterostructure''', although the two terms are commonly used interchangeably. The requirement that each material be a semiconductor with unequal band gaps is somewhat loose, especially on small length scales, where electronic properties depend on spatial properties. A more modern definition of heterojunction is the interface between any two solid-state materials, including crystalline and amorphous structures of metallic, insulating, [[fast ion conductor]] and semiconducting materials.

== Manufacture and applications ==

Heterojunction manufacturing generally requires the use of [[molecular beam epitaxy]] (MBE)<ref name=":0">Smith, C.G (1996). "Low-dimensional quantum devices". Rep. Prog. Phys. 59 (1996) 235282, pg 244.</ref> or [[chemical vapor deposition]] (CVD) technologies in order to precisely control the deposition thickness and create a cleanly lattice-matched abrupt interface. A recent alternative under research is the mechanical stacking of layered materials into [[van der Waals heterostructures]].<ref name="GeimGrigorieva2013">{{cite journal|last1=Geim|first1=A. K.|last2=Grigorieva|first2=I. V.|title=Van der Waals heterostructures|journal=Nature|volume=499|issue=7459|year=2013|pages=419–425|issn=0028-0836|doi=10.1038/nature12385|pmid=23887427|arxiv=1307.6718|s2cid=205234832}}</ref>

Despite their expense, heterojunctions have found use in a variety of specialized applications where their unique characteristics are critical:
* ''Solar cells'': Heterojunctions are formed through the interface of a [[crystalline silicon]] substrate (band gap 1.1 eV) and [[amorphous silicon]] thin film (band gap 1.7 eV) in some solar cell architectures.<ref>{{Citation |last=Leu |first=Sylvère |title=Crystalline Silicon Solar Cells: Heterojunction Cells |date=2020 |url=http://link.springer.com/10.1007/978-3-030-46487-5_7 |work=Solar Cells and Modules |volume=301 |pages=163–195 |editor-last=Shah |editor-first=Arvind |access-date=2023-04-18 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-030-46487-5_7 |isbn=978-3-030-46485-1 |last2=Sontag |first2=Detlef|url-access=subscription }}</ref> The heterojunction is used to separate charge carriers in a similar way to a [[p–n junction]]. The [[Heterojunction solar cell|Heterojunction with Intrinsic Thin-Layer]] (HIT) solar cell structure was first developed in 1983<ref>{{cite journal|doi=10.1143/JJAP.22.L605|title=Amorphous Si/Polycrystalline Si Stacked Solar Cell Having More Than 12% Conversion Efficiency|year=1983|last1=Okuda|first1=Koji|last2=Okamoto|first2=Hiroaki|last3=Hamakawa|first3=Yoshihiro|journal=Japanese Journal of Applied Physics|volume=22|number=9 |pages=L605–L607|bibcode=1983JaJAP..22L.605O |s2cid=121569675 }}</ref> and commercialised by [[Sanyo]]/[[Panasonic]]. HIT solar cells now hold the record for the most efficient single-junction silicon solar cell, with a conversion efficiency of 26.7%.<ref name=":0" /><ref>{{cite journal|doi=10.7567/JJAP.57.08RB20|title=High-efficiency heterojunction crystalline Si solar cells|year=2018|last1=Yamamoto|first1=Kenji|last2=Yoshikawa|first2=Kunta|last3=Uzu|first3=Hisashi|last4=Adachi|first4=Daisuke|journal=Japanese Journal of Applied Physics|volume=57|number=8S3 |pages=08RB20|bibcode=2018JaJAP..57hRB20Y |s2cid=125265042 }}</ref><ref>{{Cite web |title=HJT - Heterojunction Solar Cells |url=https://www.solarpowerpanels.net.au/hjt-heterojunction-solar-cells/ |access-date=2022-03-25 |website=Solar Power Panels |language=en-AU}}</ref>
* ''Lasers'': Using heterojunctions in [[laser]]s was first proposed<ref>{{cite journal|doi=10.1109/PROC.1963.2706|title=A proposed class of hetero-junction injection lasers|year=1963|last1=Kroemer|first1=H.|journal=Proceedings of the IEEE|volume=51|issue=12|pages=1782–1783 }}</ref> in 1963 when [[Herbert Kroemer]], a prominent scientist in this field, suggested that [[population inversion]] could be greatly enhanced by heterostructures. By incorporating a smaller [[direct band gap]] material like [[GaAs]] between two larger band gap layers like [[AlAs]], [[charge carriers in semiconductors|carriers]] can be confined so that [[lasing]] can occur at [[room temperature]] with low threshold currents. It took many years for the [[material science]] of heterostructure fabrication to catch up with Kroemer's ideas but now it is the industry standard. It was later discovered that the band gap could be controlled by taking advantage of the [[quantum size effects]] in [[quantum well]] heterostructures. Furthermore, heterostructures can be used as [[waveguide]]s to the [[step-index profile|index step]] which occurs at the interface, another major advantage to their use in semiconductor lasers. Semiconductor [[diode laser]]s used in [[CD]] and [[DVD]] players and [[fiber optic]] [[transceiver]]s are manufactured using alternating layers of various [[Semiconductor materials|III-V]] and [[Semiconductor materials|II-VI]] [[compound semiconductor]]s to form lasing heterostructures.
* ''Bipolar transistors'': When a heterojunction is used as the base-emitter junction of a [[bipolar junction transistor]], extremely high forward [[Gain (electronics)|gain]] and low reverse gain result. This translates into very good high frequency operation (values in tens to hundreds of GHz) and low [[leakage current]]s. This device is called a [[heterojunction bipolar transistor]] (HBT).
* ''Field effect transistors'': Heterojunctions are used in [[HEMT|high electron mobility transistors]] (HEMT) which can operate at significantly higher frequencies (over 500&nbsp;GHz). The proper [[doping (semiconductors)|doping]] profile and band alignment gives rise to extremely high [[electron mobility|electron mobilities]] by creating a [[2DEG|two dimensional electron gas]] within a [[intrinsic semiconductor|dopant free region]] where very little [[scattering]] can occur.
* ''Catalysis'': Using heterojuntions as photocatalyst has demonstrated that they exhibit better performance in CO<sub>2</sub> photoreduction, H<sub>2</sub> production and photodegradation of pollutants in water than single metal oxides.<ref>{{cite journal |last1=Ortiz-Quiñonez |first1=Jose-Luis |last2=Pal |first2=Umapada |title=Interface engineered metal oxide heterojunction nanostructures in photocatalytic CO2 reduction: Progress and prospects |journal=Coordination Chemistry Reviews |date=October 2024 |volume=516 |pages=215967 |doi=10.1016/j.ccr.2024.215967|doi-access=free }}</ref> The performance of the heterojunction can be further improved by incorporation of oxygen vacancies, crystal facet engineering or incorporation of carbonaceous materials.

== Energy band alignment ==

[[Image:Heterojunction types.png|430px|thumb|right|The three types of semiconductor heterojunctions organized by band alignment.]]
[[File:Straddling gap heterojunction band diagram.svg|thumb|[[Band diagram]] for straddling gap, ''n''-''n'' semiconductor heterojunction at equilibrium.]]

The behaviour of a semiconductor junction depends crucially on the alignment of the [[energy band]]s at the interface.
Semiconductor interfaces can be organized into three types of heterojunctions: straddling gap (type I), staggered gap (type II) or broken gap (type III) as seen in the figure.<ref>{{Cite book|title=Semiconductor Nanostructures Quantum States and Electronic Transport|url=https://archive.org/details/semiconductornan00ihnt|url-access=limited|last=Ihn|first=Thomas|publisher=Oxford University Press|year=2010|isbn=9780199534432|location=United States of America|pages=[https://archive.org/details/semiconductornan00ihnt/page/n82 66]|chapter=ch. 5.1 Band engineering}}</ref> Away from the junction, the [[band bending]] can be computed based on the usual procedure of solving [[Poisson's equation]].

Various models exist to predict the band alignment.
* The simplest (and least accurate) model is [[Anderson's rule]], which predicts the band alignment based on the properties of vacuum-semiconductor interfaces (in particular the vacuum [[electron affinity]]). The main limitation is its neglect of chemical bonding.
* A ''common anion rule'' was proposed which guesses that since the valence band is related to anionic states, materials with the same anions should have very small valence band offsets. This however did not explain the data but is related to the trend that two materials with different anions tend to have larger [[valence band]] offsets than [[conduction band]] offsets. 
* Tersoff<ref>{{cite journal|author=J. Tersoff|doi=10.1103/PhysRevB.30.4874|title=Theory of semiconductor heterojunctions: The role of quantum dipoles|year=1984|journal=Physical Review B|volume=30|issue=8|pages=4874–4877|bibcode = 1984PhRvB..30.4874T }}</ref> proposed a ''gap state'' model based on more familiar [[metal–semiconductor junction]]s where the conduction band offset is given by the difference in [[Schottky barrier]] height. This model includes a [[dipole]] layer at the interface between the two semiconductors which arises from [[electron tunneling]] from the conduction band of one material into the gap of the other (analogous to [[metal-induced gap states]]). This model agrees well with systems where both materials are closely lattice matched<ref name="pallab">Pallab, Bhattacharya (1997), Semiconductor Optoelectronic Devices, Prentice Hall, {{ISBN|0-13-495656-7}}</ref> such as [[GaAs]]/[[AlGaAs]].
* The ''60:40 rule'' is a heuristic for the specific case of junctions between the semiconductor GaAs and the alloy semiconductor Al<sub>''x''</sub>Ga<sub>1−''x''</sub>As. As the ''x'' in the Al<sub>''x''</sub>Ga<sub>1−''x''</sub>As side is varied from 0 to 1, the ratio <math>\Delta E_C/\Delta E_V</math> tends to maintain the value 60/40. For comparison, Anderson's rule predicts <math>\Delta E_C / \Delta E_V = 0.73/0.27</math> for a GaAs/AlAs junction (''x''=1).<ref>{{cite book|isbn=9780852965580|url=https://books.google.com/books?id=s7icD_5b67oC|title=Properties of Aluminium Gallium Arsenide|last1=Adachi|first1=Sadao|date=1993-01-01}}</ref><ref name="Debbar">{{cite journal|doi=10.1103/PhysRevB.40.1058|title=Conduction-band offsets in pseudomorphic InxGa1-xAs/Al0.2Ga0.8As quantum wells (0.07≤x≤0.18) measured by deep-level transient spectroscopy|year=1989|last1=Debbar|first1=N.|last2=Biswas|first2=Dipankar|last3=Bhattacharya|first3=Pallab|journal=Physical Review B|volume=40|issue=2|pages=1058–1063|pmid=9991928|bibcode = 1989PhRvB..40.1058D }}</ref>

The typical method for measuring band offsets is by calculating them from measuring [[exciton]] energies in the [[luminescence]] spectra.<ref name="Debbar" />

== Effective mass mismatch  ==

When a heterojunction is formed by two different [[semiconductor]]s, a [[quantum well]] can be fabricated due to difference in [[band structure]]. In order to calculate the static [[energy level]]s within the achieved quantum well, understanding variation or mismatch of the [[Effective mass (solid-state physics)|effective mass]] across the heterojunction becomes substantial. The quantum well defined in the heterojunction can be treated as a finite well potential with width of <math> l_w</math>. In addition, in 1966, Conley et al.<ref>{{cite journal|doi=10.1103/PhysRev.150.466|title=Electron Tunneling in Metal–Semiconductor Barriers|year=1966|last1=Conley|first1=J.|last2=Duke|first2=C.|last3=Mahan|first3=G.|last4=Tiemann|first4=J.|journal=Physical Review|volume=150|issue=2|pages=466|bibcode = 1966PhRv..150..466C }}</ref> and BenDaniel and Duke<ref>{{cite journal|doi=10.1103/PhysRev.152.683|title=Space-Charge Effects on Electron Tunneling|year=1966|last1=Bendaniel|first1=D.|last2=Duke|first2=C.|journal=Physical Review|volume=152|issue=2|pages=683|bibcode = 1966PhRv..152..683B }}</ref> reported a [[boundary condition]] for the [[Envelope (mathematics)|envelope function]] in a quantum well, known as BenDaniel–Duke boundary condition. According to them, the envelope function in a fabricated quantum well must satisfy a boundary condition which states that <math> \psi (z) </math> and <math> {\frac {1} {m^*} }{\partial \over {\partial z}} \psi (z) \,</math> are both continuous in interface regions.

{{hidden begin|border=solid 1px #aaa|title={{center|Mathematical details worked out for [[quantum well]] example.}}}}
Using the [[Schrödinger equation]] for a finite well with width of <math>l_w </math>and center at 0, the equation for the achieved quantum well can be written as:

::<math>-\frac{\hbar^2}{2m_b^*} \frac{\mathrm{d}^2 \psi(z)}{\mathrm{d}z^2} + V \psi(z) = E \psi(z) \quad \quad \text{ for } z < - \frac {l_w}{2} \quad \quad (1)</math>
::<math> \quad \quad -\frac{\hbar^2}{2m_w^*} \frac{\mathrm{d}^2 \psi(z)}{\mathrm{d}z^2} = E \psi(z) \quad \quad \text{ for } - \frac {l_w}{2} < z < + \frac {l_w}{2} \quad \quad (2)</math>
::<math>-\frac{\hbar^2}{2m_b^*} \frac{\mathrm{d}^2 \psi(z)}{\mathrm{d}z^2} + V \psi(z) = E \psi(z) \quad \text{ for } z > + \frac {l_w}{2} \quad \quad (3)</math>

Solution for above equations are well-known, only with different(modified) k and <math>\kappa </math> <ref>Griffiths, David J. (2004). ''Introduction to Quantum Mechanics'' (2nd ed.). Prentice Hall. {{ISBN|0-13-111892-7}}</ref>

::<math> k = \frac {\sqrt{2 m_w E}} {\hbar} \quad \quad \kappa = \frac {\sqrt{2 m_b (V-E)}} {\hbar} \quad \quad (4)</math>.

At the z = <math> + \frac {l_w} {2} </math> even-parity solution can be gained from
::<Math> A\cos(\frac {k l_w} {2}) = B \exp(- \frac {\kappa l_w} {2}) \quad \quad (5)</math>.

By taking derivative of (5) and multiplying both sides by <math> \frac {1} {m^*}</math>

::<Math> -\frac {kA} {m_w^*} \sin(\frac {k l_w} {2}) = -\frac {\kappa B} {m_b^*} \exp(- \frac {\kappa l_w} {2}) \quad \quad (6)</math>.

Dividing (6) by (5), even-parity solution function can be obtained,

::<Math> f(E) = -\frac {k} {m_w^*} \tan(\frac {k l_w} {2}) -\frac {\kappa } {m_b^*} = 0 \quad \quad (7)</math>.

Similarly, for odd-parity solution,

::<Math> f(E) = -\frac {k} {m_w^*} \cot(\frac {k l_w} {2}) +\frac {\kappa } {m_b^*} = 0 \quad \quad (8)</math>.

For [[numerical solution]], taking derivatives of (7) and (8) gives

even parity:
::<math> \frac {df}{dE} = \frac {1}{m_w^*} \frac {dk}{dE} \tan(\frac {k l_w} {2}) + \frac {k} {m_w^*} \sec^2(\frac {k l_w} {2}) \times \frac {l_w} {2} \frac {dk} {dE} - \frac {1}{m_b^*} \frac {d \kappa} {dE} \quad \quad (9-1)</math>
odd parity:
::<math> \frac {df}{dE} = \frac {1}{m_w^*} \frac {dk}{dE} \cot(\frac {k l_w} {2}) - \frac {k} {m_w^*} \csc^2(\frac {k l_w} {2}) \times \frac {l_w} {2} \frac {dk} {dE} + \frac {1}{m_b^*} \frac {d \kappa} {dE} \quad \quad (9-2)</math>

where <math> \frac {dk}{dE} = \frac {\sqrt {2 m_w^*}}{2 \sqrt E \hbar} \quad \quad \quad \frac {d \kappa}{dE} = - \frac {\sqrt {2 m_b^*}}{2 \sqrt {V-E} \hbar}</math>.

The difference in effective mass between materials results in a larger difference in [[ground state]] energies.
{{hidden end}}

== Nanoscale heterojunctions ==
[[Image:Fe3O4-CdS Nano Heterojunction.JPG|400px|thumb|right|Image of a nanoscale heterojunction between iron oxide (Fe<sub>3</sub>O<sub>4</sub>&nbsp;— sphere) and cadmium sulfide (CdS&nbsp;— rod) taken with a [[Transmission electron microscopy|TEM]]. This staggered gap (type II) offset junction was synthesized by Hunter McDaniel and Dr. Moonsub Shim at the University of Illinois in Urbana-Champaign in 2007.]] 
In [[quantum dot]]s the band energies are dependent on crystal size due to the [[quantum size effects]]. This enables band offset engineering in nanoscale heterostructures. It is possible<ref>{{cite journal|doi=10.1021/ja068351m|title=Type-II Core/Shell CdS/ZnSe Nanocrystals: Synthesis, Electronic Structures, and Spectroscopic Properties|year=2007|last1=Ivanov|first1=Sergei A.|last2=Piryatinski|first2=Andrei|last3=Nanda|first3=Jagjit|last4=Tretiak|first4=Sergei|last5=Zavadil|first5=Kevin R.|last6=Wallace|first6=William O.|last7=Werder|first7=Don|last8=Klimov|first8=Victor I.|journal=Journal of the American Chemical Society|volume=129|issue=38|pages=11708–19|pmid=17727285}}</ref> to use the same materials but change the type of junction, say from straddling (type I) to staggered (type II), by changing the size or thickness of the crystals involved. The most common nanoscale heterostructure system is [[ZnS]] on [[CdSe]] (CdSe@ZnS) which has a straddling gap (type I) offset. In this system the much larger [[band gap]] ZnS [[Passivation (chemistry)|passivates]] the surface of the [[fluorescent]] CdSe core thereby increasing the [[quantum efficiency]] of the [[luminescence]]. There is an added bonus of increased [[thermal stability]] due to the stronger [[chemical bond|bonds]] in the ZnS shell as suggested by its larger band gap. Since CdSe and ZnS both grow in the [[zincblende (crystal structure)|zincblende]] crystal phase and are closely lattice matched, core shell growth is preferred. In other systems or under different growth conditions it may be possible to grow [[anisotropic]] structures such as the one seen in the image on the right.

The driving force for [[Intervalence charge transfer|charge transfer]] between [[conduction band]]s in these structures is the conduction band offset.<ref name="Robel">{{cite journal|doi=10.1021/ja070099a|title=Size-Dependent Electron Injection from Excited CdSe Quantum Dots into TiO2Nanoparticles|year=2007|last1=Robel|first1=István|last2=Kuno|first2=Masaru|last3=Kamat|first3=Prashant V.|journal=Journal of the American Chemical Society|volume=129|issue=14|pages=4136–7|pmid=17373799}}</ref> By decreasing the size of CdSe nanocrystals grown on [[Titanium dioxide|TiO<sub>2</sub>]], Robel et al.<ref name="Robel" /> found that electrons transferred faster from the higher CdSe conduction band into TiO<sub>2</sub>. In CdSe the quantum size effect is much more pronounced in the conduction band due to the smaller effective mass than in the valence band, and this is the case with most semiconductors. Consequently, engineering the conduction band offset is typically much easier with nanoscale heterojunctions. For staggered (type II) offset nanoscale heterojunctions, [[photoinduced charge separation]] can occur since there the lowest energy state for [[electron hole|holes]] may be on one side of the junction whereas the lowest energy for electrons is on the opposite side. It has been suggested<ref name="Robel" /> that anisotropic staggered gap (type II) nanoscale heterojunctions may be used for [[photocatalysis]], specifically for [[water splitting]] with solar energy.

== See also ==
* [[Homojunction]], [[p–n junction]]—a junction involving two types of the same semiconductor.
* [[Metal–semiconductor junction]]—a junction of a metal to a semiconductor.

== References ==
{{reflist|35em}}

==Further reading==
{{refbegin}}
* {{cite book|title=Wave Mechanics Applied to Semiconductor Heterostructures|last=Bastard|first=Gérald|author-link=Gérald Bastard|year=1991|isbn=978-0-470-21708-5|publisher=[[Wiley-Interscience]]}}
* {{Cite book
 | surname1 = Feucht
 | given1 = D. Lion
 | surname2 = Milnes
 | given2 = A.G.
 | title = Heterojunctions and metal–semiconductor junctions
 | publisher = [[Academic Press]]
 | place = [[New York City]] and [[London]]
 | year = 1970}}, {{ISBN|0-12-498050-3}}. A somewhat dated reference respect to applications, but always a good introduction to basic principles of heterojunction devices.
*{{cite journal|title=New insights in the physics of resonant tunneling|author1=R. Tsu|author2=F. Zypman|journal=[[Surface Science]]|volume=228|number=1–3|year=1990|page=418|bibcode=1990SurSc.228..418T|doi=10.1016/0039-6028(90)90341-5}}
*{{cite book |doi=10.1063/1.5047992|bibcode=2018AIPC.1992d0027K |chapter=Thermal annealing improves electrical properties of hetero-junction diode |series=AIP Conference Proceedings |date=2018 |last1=Kurhekar |first1=Anil Sudhakar |title=International Conference on Renewable Energy Research and Education (Rere-2018) |volume=1992 |issue=1 |page=040027 }}
{{refend}}

==External links==
*{{Commonscatinline|Heterojunction band diagrams}}

{{Authority control}}

[[Category:Semiconductor structures]]