SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

90 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

Problem 2.20In ann-type Si crystal the doping changes abruptly fromND=10^15 to

ND=10^17. Make a qualitative sketch of the band diagram. Calculate

(a) the built-in potential at then+/n−interface, in eV. Also calculate how much of the

band-bending occurs on each side of the junction,

(b) the electric field at then+/n−interface and

(c) the electron concentration at then+/n−interface.

AssumeT= 300K.

Problem 2.21Consider a schottky barrier formed between Al(sφM=4. 1 eV)and

GaAs(qχ=4. 04 eV). Consider that the surface has both acceptor and donor states in equal

concentration, 1.0 eV and 0.6 eV from the conduction band respectively. Assume that the

concentrations are equal (measured incm−^2 ). Assume a thin insulator (δA ̊thick) between

the metal and the semiconductor to help set-up the problem. Calculate the barrier height as

a function of the density of statesDscm−^2. Solve the problem for bothnandptype

semiconductors doped at 1017 cm−^3. Plot.

Note: The problem is solve by balancing charges in the system.

2.15FURTHERREADING

• General bandstructure
  
  
  • H.C. Casey Jr. and M.B. Panish,HeterostructureLasers, Part A, “Fundamental Prin-
    ciples,” Part B, “Materials and Operating Characteristics,” Academic Press, New
    York (1978).
  
  
  • R.E. Hummel,ElectronicPropertiesofMaterials–AnIntroductionforEngineers,
    Springer Verlag, New York (1985).
  
  
  • Landolt-Bornstein,NumericalDateandFunctionalRelationshipinScienceand
    Technology, Vol. 22, Eds. O. Madelung, M. Schulz, and H. Weiss, Springer-Verlog,
    New York (1987).
  
  
  • K. Seeger,SemiconductorPhysics:AnIntroduction, Springer, Berlin (1985).
  
  
  • H.F. Wolf,Semiconductors, Wiley-Interscience, New York (1971).
  
  
  
  


• Bandstructure modification
  
  
  • A.G. Milnes and D.L. Feucht,HeterojunctionsandMetalSemiconductorJunctions,
    Academic Press, New York (1972).
  
  
  • For a simple discussion of electrons in quantum wells any book on basic quantum
    mechanics is adequate. An example is L. Schiff,QuantumMechanics, McGraw-Hill,
    New York (1968).
  
  
  • J. Singh,ElectronicandOptoelectronicPropertiesofSemiconductorStructures, Cam-
    bridge University Press (2003).