Covalent bonds in p-type semiconductor

[introspect84]

Hi,

I am from an engineering background and I am in the process of learning about semiconductor physics to get a more generalized picture on the operation of the devices rather than just the operating characteristics. To start with I am studying about the p-type and n-type semiconductors. Visualizing the way a n-type semiconductor is doped appears straightforward to me on the outside. I started with an example of doping Si by P. P has 5 valence electrons of which one is fred as a free electron. This makes it with 15 protons and 14 electrons, of which 4 are in valence shell. The 4 valence electrons of 'P ion' can make covalent bonds with 4 neighboring Si atoms. The P atom ends up with a + ve charge owing to the loss of electron. The crystal lattice is formed with "P ion" substituted for a Si atom in an intrinsic crystal.
Next, I tried to see how the p-type semiconductor works. Another example, doping Si with B. B has 3 electrons on valence shell. So, it must either lose 3 electrons or gain 5 electrons or share electrons such that it attains octet stability. With Si having 4 electrons on valence shell, I don't see anyway B can attain octet stability. The book (Electronic principles, by Malvino) shows p-type with a bond and an electron missing which is termed as a hole. In my opinion, there must be no bond possible as B just has 3 electron which are shared with 3 Si atoms. From where did the 4 electron could come to make this covalent bonding possible ? I am sure that the book is right but I am not able to find it convincing at the level at which it is presented. One way I thought of it was B atom takes an electron to form B- ion which involves in the covalent bonding. If that is the case, how does the hole is formed after the bond is formed (i.e.) how is the bond broken ? Where did the electron come for the ionization to occur? Are there any general rules/theory that can be applied to see why this happens. Making B as an ion fits the picture but then why not Ca or Li ion.

Any opinions or deeper thoughts on this would be helpful and appreciated.

Best Regards,
JR

 

[DrDu]

Boron can form a fourth two-electron bond at the expense of a bond between two silicon atoms losing one electron, hence becoming a one electron bond. This can happen between any two neighbouring silicon atoms which is the same as saying that the whole is delocalized.

 

[introspect84]

Hi DrDu, Thank you for your explanation. I understand from you that one of the 2 electron bond of Si is made a one electron bond and the extra electron is used in the bonding of B. It seem to make sense now. B seem to pull the electron from the Si atoms to attain its octet stability. More the B atoms in a pure Si crystal, more electrons pulled from Si atoms leaving more one electron covalent bonds and hence more holes.

 

[asitiaf]

Why the electrons of bonds between two Si atoms will go for B and Si bonding.

Are the bond energy between two Si atoms less than that required between a B and Si atom.

Moreover,
The book (Electronic principles, by Malvino) shows p-type with a bond and an electron missing which is termed as a hole.
Means the book shows one electron bond between B and Si.

Can there exist a bond of just only one electron.


Please explain.

 

[DrDu]

Question marks exist!

 

[Darwin123]

Why the electrons of bonds between two Si atoms will go for B and Si bonding.

Are the bond energy between two Si atoms less than that required between a B and Si atom?

The difference in bond energy is insignificant for a "simple-acceptor". By "simple-impurity", I mean one where the electrostatic interaction dominates the potential of the carrier (i.e., conduction-electron for donor or valence-hole for acceptor.).

There is a difference in bond energy of deep-level impurities. However, boron in silicon is not a deep-impurity.

Moreover,
The book (Electronic principles, by Malvino) shows p-type with a bond and an electron missing which is termed as a hole.
Means the book shows one electron bond between B and Si.

Can there exist a bond of just only one electron?

No. That is probably the point of the diagram. When the hole is located in a specific-orbital at the acceptor-atom, then the bond associated with that specific-orbital doesn't exist. However, holes are mobile. Therefore, the hole doesn't stay in that specific-orbital.

The hole "migrates" from that specific-orbital when the orbital takes an electron from another orbital. When the hole migrates from that orbital, the covalent bond associated with that specific-orbital can reform.

The total result of this migration is that the hole acts as though it were a positively-particle. This approximation is sufficient form most engineering problems. There are multiple reasons for this migration, but engineering-oriented courses rightfully disregard the detailed mechanisms. The mechanisms for migration of both conduction electrons and holes are of more interest to physicists and physical-chemists. I will list a few heuristic explanations for the migration.

The electrons in the specific-orbital can always tunnel to orbitals of the same energy. "Tunneling" is a quantum-mechanical process that has several names. It is sometimes called hybridization, or state-mixing. For example, the specific-orbital can steal an electron from orbitals in the same electronic-shell as the specific orbital. The hole can hop around the shell in the atom. Thus, the weakening in bond-strength can be "shared" within the same atom. So the bond in the specific-orbital isn't completely destroyed. The hole hops around the electronic-shell so fast that the bonds don't have enough time to disappear. This would occur even at absolute zero temperature.

At finite temperatures, the atoms in the crystal are vibration. The atoms all have vibrational-energy, which is also called phonon-energy. Energy in a nearby vibrating-atom can be absorbed by an electron in the valence-band of that nearby atoms, so that the electron hops from the nearby atom to the specific-orbital of the impurity atom. This is referred to as "thermal ionization of the hole." The born atom becomes ionized (i.e., negatively-charged) by stealing an electron from the nearby silicon atom.

Basically, the vibrating nucleus "knocks" the electron from a nearby silicon atom to the boron atom. The hole then migrates from the boron atom to the nearby silicon atom. Of course, the same process can occur in the nearby silicon atom. That silicon atom can steal an electron from another silicon atom. So the "hole" can travel from silicon atom to silicon atom as though it were a particle itself. Since a positive charge is associated with the hole, the hole acts as though it were a positively charged particle.

Of course, the hole merely represents a missing electron in an entire electronic-shell of atoms. This is why the hole is sometimes called a "quasiparticle". The same goes for conduction-electrons. Actually, the electron in the conduction-band isn't the result of one electron-traveling. There is a reshuffling of electrons in the atomic-shells associated with the conduction-band. So the conduction-electron merely "acts" like one negatively charged particle. Thus, the conduction-electron is also a "quasiparticle".

The over-all approximations work fairly well under most circumstances. The conduction-electron acts like a negatively charged-particle and the valence-hole acts like a positively charged particle. However, the extra layer of complexity makes one difference that may be important even to an engineer. The effective-masses of the conduction-electron and the valence-hole are different from the mass of an isolated electron.

I went through the extra detail in anticipation of a possible next question. Why do the effective-masses of conduction-electron and valence-hole differ from the mass of a real electron?

The interactions caused by tunneling cause the electrons in the atoms to behave differently from an electron in a vacuum. Therefore, the effective-mass of a conduction-electron is generally less than the mass of a true electron. The effective-mass of a valence-hole is generally more than the effective-mass of a true electron.

The change in effective-masses of electron and hole determine the mobility of the electron and hole. So return to this post when you get to the discussions about mobility!