Escape-Energy Parameters for Metals and Semiconductors

In any metallic element or alloy, and thus 0 = — p is a materials constant. This is not true, however, in a nonhomogeneous or nonmetallic substance because the Fermi position is not a unique constant of the material. For example, in a semiconductor such as GaP, Ep can be made to vary 1-2 eV by doping , as described below. 

The Fermi level (and work function) variation results from the band structure of semiconductors, where uppermost electron levels (those above the tightly bound core states) break into two well-defined nonoverlapping allowed-energy regions separated by a large energy gap of size Q( 2eV in GaP) the Fermi level can fall anywhere within this gap depending on minute quantities of impurities present, and p can vary spatially within the semiconductor if it is placed in contact with other substances. 

The variation of the work function and the Fermi level in metals and semiconductors is illustrated in Fig. 5.2. In the metal (Fig. 5.2a), the Fermi level is fixed at the energy where the N lowest-lying electron states are filled with the N electrons in the (uppermost) band of valence electrons. There are many additional empty electron states above p, but these remain empty regardless of the presence of small amounts of foreign contaminants. The position of p and the value of (j) in metals are thus rigorous materials constants. 

In the semiconductor (Fig. 5.2b) the Fermi level is located within the forbidden energy bandgap between Ey and E. The N states in the valence band ( below y) are essentially filled with N valence electrons and the remaining electron states (above Eq) are nearly empty. p can be varied from one extreme position to another (from p y to p c) without severely upsetting this balance of filled and empty electron states the valence band remains essentially filled with the requisite N electrons and the conduction band remains essentially empty unless p comes within a few hundredth of an electron volt of either Ey or 

In practice, p is adjusted by adding trace quantities of selected impurities— the process of doping to obtain p-type or n- type conduction. The impurities add a very low density of allowed states within the forbidden region of the crystal, and the position of p must adjust between (, and Ey Ep to Ep ) to maintain a total of N filled electron states. (For the present discussion the substance remains the same generic semiconductor with and without this 0.01 % doping.) Because the work function is defined as / = j, - p, its value 

Fermi level can fall anywhere within this gap depending on minute quantities of impurities present, and Ep can vary spatially within the semiconductor if it is placed in contact with other substances. 

---