GaAs Ga has a valency of III and As has V. When Ga and As atoms are brought together to form the GaAs crystal, as depicted in Figure 5.54, the three valence electrons in each Ga and the five valence electrons in each As are all shared to form four covalent bonds per atom. In the GaAs crystal with some 1023 or so equal numbers of Ga and As atoms, we have an average of four valence electrons per atom, whether Ga or As, so we would expect the bonding to be similar to that in the Si crystal: four bonds per atom. The crystal structure, however, is not that of diamond but rather that of zinc blende (Chapter 1).
a. What is the average number of valence electrons per atom for a pair of Ga and As atoms and in the GaAs crystal?
b. What will happen if Se or Te, from Group VI, are substituted for an As atom in the GaAs crystal?
c. What will happen if Zn or Cd, from Group II, are substituted for a Ga atom in the GaAs crystal?
d. What will happen ifSi, from Group IV, is substituted for an As atom in the GaAs crystal?
e. What will happen if Si, from Group IV, is substituted for a Ga atom in the GaAs crystal? What do you think amphoteric dopant means?
f. Based on the discussion of GaAs, what do you think the crystal structures of the III-V compound semiconductors AlAs, GaP, InAs, InP, and InSb will be?
The Correct Answer and Explanation is :
Let’s tackle your questions one by one:
a. Average Number of Valence Electrons per Atom:
In GaAs, Gallium (Ga) atoms have 3 valence electrons, and Arsenic (As) atoms have 5 valence electrons. In a pair of one Ga and one As atom, the total number of valence electrons is (3 (Ga) + 5 (As) = 8) electrons. Since there are two atoms in this pair, the average number of valence electrons per atom is ( \frac{8}{2} = 4 ) electrons per atom. This is similar to the average in silicon, where each atom also effectively shares four electrons through covalent bonds.
b. Substituting Se or Te for As:
Selenium (Se) and Tellurium (Te) belong to Group VI and have 6 valence electrons each, which is one more than As. Substituting either Se or Te for As in GaAs would result in an extra valence electron, potentially creating a free electron (n-type doping). This additional electron would make the semiconductor more conductive due to the increase in charge carriers.
c. Substituting Zn or Cd for Ga:
Zinc (Zn) and Cadmium (Cd) are Group II elements, each with 2 valence electrons, one fewer than Ga. Substituting Zn or Cd for Ga would result in a deficit of one valence electron (p-type doping), which effectively creates a “hole” or a positive charge carrier. This increases the conductivity by enabling more charge carriers in the form of holes.
d. Substituting Si for As:
Silicon (Si) has 4 valence electrons, one fewer than As. Substituting Si for As would also result in p-type doping by creating holes due to the lack of one electron that As would normally contribute. This makes the crystal more conducive through the mechanism of hole mobility.
e. Substituting Si for Ga and Amphoteric Dopant:
Silicon substituted for Ga (both have 4 valence electrons) maintains the balance of electrons, so ideally, it wouldn’t change the electrical properties significantly. However, Si can act as an amphoteric dopant; it can either donate an electron or accept an electron depending on the local environment in the crystal lattice, which allows it to function either as an n-type or p-type dopant.
f. Crystal Structures of III-V Compound Semiconductors:
III-V compound semiconductors like AlAs, GaP, InAs, InP, and InSb generally crystallize in similar structures as GaAs, predominantly in the zinc blende structure. This structure is characterized by each atom being tetrahedrally bonded to four atoms of the other type, providing a symmetric and closely packed crystalline formation that is conducive to semiconductor properties. These materials can also potentially adopt the wurtzite structure under certain growth conditions.
These responses should address the theoretical considerations and possible implications of substituting different elements in the GaAs crystal, including how these changes impact electrical properties and crystal structure.