Heterojunctions

Modulation-doped heterojunctions• They are the interfaces between two

semiconductors of different gaps, and are one of the most versatile building blocks of electronic devices, especially those based on III-V compounds

• Most studied heterostructure is n-type AlxGa1−xAs and almost intrinsic or lightly doped p-type GaAs hetrojunction.

• Similar to the MOS structure, an inversion layer of electrons is formed in the GaAs close to the GaAs–AlGaAs interface.

• Therefore the principle be very similar to MOS structure

• Mainly used in higher frequencies than Si devices due to the high mobility of electrons in GaAs.

• Most important device applications are based on a Schottky structure of the type metal–AlGaAs–GaAs

• The band diagram of the AlxGa1−xAs–GaAs heterojunction

• We have an AlGaAs–GaAs heterojunction, where the left material is GaAs doped with Al and the right one is near-intrinsic GaAs. This structure is called a modulation-doped heterojunction and the method to produce it is known as modulation doping

• Before the two semiconductors enter in contact, the Fermi-level in n-type AlGaAs is close to the conduction band, and for lightly p-doped GaAs is located close to the middle of the gap

• The bands are flat because the materials are electrically neutral and have uniform doping

• The barrier between the material in the conduction band, ∆Ec, can be approximately found following Anderson’s rule.

• According to this rule, when we join two materials, the vacuum levels should line up. If χA and χB are the electron affinities of the AlGaAs and GaAs, respectively, we should have ∆Ec ≡ χA − χB

• Since the electron affinity of a semiconductor is defined as the energy required for an electron located at the bottom Ec of the conduction band, to get out of the solid, i.e. χ = Evac– Ec.

• According to this rule, one gets a value of ∆Ec of 0.35 eV for a doping x in AlxGa1−xAs around 0.3.

• When both materials in contact, some of the electrons from the donors of the n-material will cross the interface reaching the undoped GaAs.

• Similar to the p–n junction, an internal electric field will be created and directed from the non-neutralized donors in the AlGaAs to the additional electronic charges in the GaAs.

• This field causes the band bending

• At equilibrium, the two Fermi levels line up, the bands are bent like in the case of the p–n junction, with the only difference that the barrier ∆Ec is created.

• Far from the interface, the bottom Ec of the conduction bands is flat and at the same distance from the Fermi level EF

• The quantum well for the electrons produced at the AlGaAs–GaAs interface has a shape close to a triangle similar to MOS structure

• If we call z the direction perpendicular to the interface, the electrons forming the 2D inversion layer are free to move along the (x, y) plane, but their energy for the motion along z is quantized as in a potential well.

• An important aspect of this heterojunction is that the charge carriers are located in a region (mainly in the GaAs), spatially separated from the AlGaAs semiconductor which originates the free electrons

• For understanding, solution by Poisson’s equation for the potential and Schrödinger’s equation for the electron wave functions, but they are complicated.

• So the problem has been solved, usually taking some approximations, such as assuming that the potential well is perfectly triangular in shape

• The wells cannot be assumed to be of infinite height, since Ec ≈ 0.3 eV. Detailed calculations also allow calculation of the average width of the well (40–80Å), the electron concentration per unit area, ns ≈ 1012cm−2, and the energy ε1 of the first level ≈ 0.04 eV

SiGe strained heterostructures• At first SiGe heterojunctions did not attract

too much attention, because of the large lattice constant difference between Si and Ge which amounts to about 4% (≈ 0.2 Å)

• This means that a critical thickness should not be surpassed otherwise the structure breaks off.

• Also the energy gaps of silicon (Eg = 1.12 eV) and germanium (Eg = 0.66 eV) are fairly small, then the height of the barriers which appear at the interface should always be small.

• But SiGe heterostructures are used in several fields such as high frequency transistors and IR photodetectors. Since SiGe are strained, the degeneracy of the heavy and light hole bands is lifted and the band structures show similar features to those shown below

• Two typical examples of SiGe heterostructures

• First case, the substrate is <001> Si (Eg = 1.17 eV) and the strained active layer Si0.7Ge0.3 (Eg = 0.78 eV).

• In this case the conduction band offset is smaller comparing to the valence band offset. This situation allows the formation of a 2D hole gas in the SiGe alloy, with electron mobilities around 2m2V−1s−1. It is about half of that of a typical MOSFET

• In second case, the situation is reversed and the strained layer is Si. Here the discontinuity in the conduction band is fairly large and the electrons form a 2D gas, with free motion in the plane of the interface.

• The silicon effective mass corresponding to this motion is the low transversal one (mT ≈ 0.19m∗ 0), therefore yielding a high mobility of around 20m2V−1s−1, which is several times higher than that of the MOSFET.

• SiGe heterostructures have also found an important application in the field of bipolar silicon transistors

• One way to improve the efficiency of a bipolar transistor is to use a narrow-bandgap material for the base region, which improves the efficiency of the Si emitter region.

• This can be achieved by reducing values of the SiGe bandgap alloys, in comparison to silicon.

• The strain that appears in the heterojunction also contributes to the decrease of the bandgap. The large bandgap offset allows the fabrication of a highly doped, low resistivity, base material, which extends the performance of silicon transistors to much higher frequencies.