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.[3] The heterojunction is used to separate charge carriers in a similar way to a p–n junction. The Heterojunction with Intrinsic Thin-Layer (HIT) solar cell structure was first developed in 1983[4] 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%.[1][5][6]
Lasers: Using heterojunctions in
compound semiconductors
to form lasing heterostructures.
Bipolar transistors: When a heterojunction is used as the base-emitter junction of a
The behaviour of a semiconductor junction depends crucially on the alignment of the
energy bands
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.[8] 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
conduction band
offsets.
Tersoff
AlGaAs
.
The 60:40 rule is a heuristic for the specific case of junctions between the semiconductor GaAs and the alloy semiconductor AlxGa1−xAs. As the x in the AlxGa1−xAs side is varied from 0 to 1, the ratio tends to maintain the value 60/40. For comparison, Anderson's rule predicts for a GaAs/AlAs junction (x=1).[11][12]
The typical method for measuring band offsets is by calculating them from measuring exciton energies in the luminescence spectra.[12]
Effective mass mismatch
When a heterojunction is formed by two different
band structure. In order to calculate the static energy levels within the achieved quantum well, understanding variation or mismatch of the 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 . In addition, in 1966, Conley et al.
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 and are both continuous in interface regions.
Mathematical details worked out for quantum well example.
Using the Schrödinger equation for a finite well with width of and center at 0, the equation for the achieved quantum well can be written as:
Solution for above equations are well-known, only with different(modified) k and [15]
.
At the z = even-parity solution can be gained from
.
By taking derivative of (5) and multiplying both sides by
.
Dividing (6) by (5), even-parity solution function can be obtained,
.
Similarly, for odd-parity solution,
.
For
numerical solution
, taking derivatives of (7) and (8) gives
even parity:
odd parity:
where .
The difference in effective mass between materials results in a larger difference in ground state energies.
Nanoscale heterojunctions
In
anisotropic
structures such as the one seen in the image on the right.
It has been shown
conduction bands in these structures is the conduction band offset. By decreasing the size of CdSe nanocrystals grown on TiO2, Robel et al.[17] found that electrons transferred faster from the higher CdSe conduction band into TiO2. 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 holes may be on one side of the junction whereas the lowest energy for electrons is on the opposite side. It has been suggested[17] that anisotropic staggered gap (type II) nanoscale heterojunctions may be used for photocatalysis, specifically for water splitting