# Understanding Effective Mass of Holes in GaAs/AlGaAs Quantum Wells

• qanx
In summary, the conversation discusses the difficulty the junior undergrad is facing in a lab analyzing the reflectance spectra for GaAs/AlGaAs quantum wells. They are given the effective mass of the electrons, but are unsure about the mass of the holes, which are created when electrons move from the valence band to the conduction band. It is explained that a fully filled band cannot contribute to a current, but a band with a hole can, as the electrons can jump into the available state. The movement of these electrons is represented as the movement of charged vacancies through the band, which must be assigned a positive charge and a certain mass to account for the current. The conversation also references a source for further information on the topic.

#### qanx

Hello, I am a junior undergrad taking an advanced senior/1st yr grad lab. I've been having some difficulty with a few points in the lab materials we were given (we are analyzing the reflectance spectra for GaAs/AlGaAs quantum wells). We were given the effective mass of the electrons, heavy and light holes. I understand where the effective mass for the electron comes from, but I am not exactly sure where the holes are given mass. It is my understanding that these holes are simply gaps left when electrons move from one state to another (i.e. from the valence band to the conduction band). Is the mass of the hole in some way related to the energy emitted/absorbed in this process?

A fully filled band can not contribute to a current because there are no available states to excite the electrons to. A hole is nothing but a vacancy created in an otherwise filled band. A band with a hole in it can contribute to a current because there is now an available state that an electron can jump into, in the process, leaving behind another vacancy which another electron may hoop into. The movement of all there electrons into nearby vacancies is mathematically represented as the movement of the charged vacancies through the otherwise inert band. But since in reality, the vacancies move in the opposite direction to the electrons, they must be assigned a positive charge if they are to account for the same current. Furthermore, they must be assigned some kind of mass that would account for the correct drift velocity needed to produce this current when a given field is applied.

More on this here: http://britneyspears.ac/physics/basics/basics.htm