2. Solve and draw empty lattice energy band diagram for fc lattice along
Consider a free electron, empty lattice model with effective mass m* in a simple cubic crystal with direct lattice distance a, and reciprocal lattice vectors of length a. Find the energies at the high symmetry points Г, X, M and R and indicate the zone boundary rsion along TX, TR, Г b. Find the expression for the lowest energy band in the XM direction. Sketch the Energy band diagram along RIXM「 c.
Consider the free electron energy bands of an fcc crystal
lattice in the empty lattice approximation in the reduced zone
scheme in which all k’s are in the first Brillouin zone. Plot in
the [111] direction the energies of all bands up to 6 times the
lowest band energy at the zone boundary at
= (2?/a)( 1/2 , 1/2 , 1/2 ). Let this be the unit of energy. This
problem shows why band edges need not be necessarily at...
4. Label each band diagram below with an appropriate label.(4) Draw the band diagram for a p-type and n-type semiconductor(4). Briefly describe an experiment that you could perform to distinguish between a conductor and a semiconductor (they both look shiny and hard at room temperature).(2) (10 points) (d (rt o :ODH Energy
Draw an equilibrium band diagram for Si p-n junction and find contact potential? if energy between Fermi level and conduction band of n-type 97 meV and energy between Fermi level and valence band of p-type 67 meV ?
or a Silicon sample energy band diagram shown below, assume room temperature and the band gap Eg 1.1 eV 6) F calculate the probability of a state with energy Ec to be filled; calculate the probability ofa state with energy Ev to be empty. a. b. 0.2 eV Ее Ef Ev enn l+
or a Silicon sample energy band diagram shown below, assume room temperature and the band gap Eg 1.1 eV 6) F calculate the probability of a state...
Draw the energy band diagram at equilibrium for the p+ /n/p semiconductor heterostructure (p+ indicates a p-type semiconductor which is heavily doped, i.e., more heavily doped than p). You should indicate Ec (conduction band), Ev (valence band), Ei (intrinsic Fermi level), and Ef (Fermi level) throughout the device structure. show your work (i.e., you should start from the diagram of individual material pieces). State any reason for your drawing.
4. Si MOS capacitor (tox10 nm, 3.9; Nd 1015 cm-3) (a) Draw the energy band diagram if the capacitor is biased to accumulation Label all important parts and energy levels. (b) Redraw the diagram now for the case at minimum capacitance. Derive the expression for the minimum capacitance and then calculate what this value is.
4. Si MOS capacitor (tox10 nm, 3.9; Nd 1015 cm-3) (a) Draw the energy band diagram if the capacitor is biased to accumulation Label all...
Question 1 Calculate the first few energy bands for free electrons in a two-dimensional square lattice, shown in the band structure diagram below (ie. label the energies at the intercepts which are numbered). Some points may be equivalent to others 4 (a) Brillouin zone and (b) energy bands for free electrons in a square lattice. [15]
Question 1 Calculate the first few energy bands for free electrons in a two-dimensional square lattice, shown in the band structure diagram below (ie....
Show that the first three bands in the empty lattice model span the following energy ranges: h2 EL : 0 → 2mea 7212 27212 2mea? mea2 22h2 972h2 mea? 2mea? E2 : E3 :
A1 The primitive lattice vectors of a 2-dimensional lattice where and are unit vectors along the horizontal and vertical, respectively. Sketch this lattice, including on your sketch the lattice points, primitive vectors, and primitive unit cell ax and p2 (a/2)( are p Write down an expression for the conventional lattice vectors, and state the number of lattice points in a conventional unit cell Draw conventional lattice vectors on your sketch 6 Marks A2 m) atoms at each site, the dispersion...