# Conduction & Valence Band Energies under Biasing (PN & PIN Junctions)

Previously, we discussed the effect of doping concentrations on the energy band gap. The conclusion of this process was that the doping concentration alone does not alter the band gap. The band gap is the difference between the conduction band and valence bands. Under biasing, the conduction and valence bands are in fact affected by doping concentration.

One method to explain how the doping level will influence the conduction band and valence band under bias is by demonstrating the difference between the energy bands of a PN Junction versus that of a PIN Junction. Simulations of both are presented below. The intermediate section found between the p-doped and n-doped regions of the PIN junction diode offer a more gradual transition between the two levels. A PN junction offers a sharper transition at the conduction and valence band levels simulatenously. A heterostructure, which is made of more than one material (which will have different band gaps) may produce even greater discontinuities. Depending on the application, a discontinuity may be sought (think, Quantum well), while in other situations, it may be necessary to smooth the transition between band levels for a desired result.

The conduction and valence bands are of great importance for determining the carrier concentrations and carrier mobilities in a semiconductor structure. These will be discussed soon.

PN Junction under biasing (conduction and valence band energies): Code Used (PN Junction):

#TOP TO BOTTOM – Structure Specification
region num=1 bottom thick = 0.5 material = GaAs NY = 20 acceptor = 1e18
region num=2 bottom thick = 0.5 material = GaAs NY = 20 donor = 1e18

PIN Junction Biased: PIN Junction Unbiased: Code Used (PIN Junction):

#TOP TO BOTTOM – Structure Specification
region num=1 bottom thick = 0.5 material = GaAs NY = 20 acceptor = 1e18
region num=3 bottom thick = 0.2 material = GaAs NY = 10
region num=2 bottom thick = 0.5 material = GaAs NY = 20 donor = 1e18

Here, the carrier concentrations are plotted: # Energy Bandgaps

Previously, a PN Junction Simulator in ATLAS program was posted. Now, we will use and modify this program to explore more theory in respect to semiconductor materials, high speed electronics and optoelectronics.

The bandgap, as mentioned previously is the difference between the conduction band energy and valence band energy. The materials GaAs, InP, AlGaAs, InGaAs and InGaAsP are simulated and the bandgap values for each are estimated (just don’t use these values for anything important).

• GaAs: ~ 1.2 eV
• InP: ~ 1.35 eV
• AlGaAs: ~ 1.8 eV
• InGaAs: ~0.75 eV
• InGaAsP: 1.1 eV Here the conduction band and valence band are shown. The structure used in the PN Junction Simulator is found below:

#TOP TO BOTTOM – Structure Specification
region num=1 bottom thick = 0.5 material = GaAs NY = 20 acceptor = 1e17
region num=3 bottom thick = 0.001 material = InP NY = 10
region num=4 bottom thick = 0.001 material = GaAs NY = 10
region num=5 bottom thick = 0.001 material = AlGaAs NY = 10 x.composition=0.3 grad.3=0.002
region num=6 bottom thick = 0.001 material = GaAs NY = 10
region num=7 bottom thick = 0.001 material = InGaAs NY = 10 x.comp=0.468
region num=8 bottom thick = 0.001 material = GaAs NY = 10
region num=9 bottom thick = 0.001 material = InGaAsP NY = 10 x.comp=0.145 y.comp = 0.317
region num=2 bottom thick = 0.5 material = GaAs NY = 20 donor = 1e17

### Is the bandgap affected by doping the concentration level?

A quick simulation (below) will tell us that the answer is no. What might influence the bandgap however? And what could the concentration level change? This (above) is a simulation of GaAs with layers at different doping concentration levels. The top is a contour of the bandgap, which is constant, as expected. The top right is a cross section of this GaAs structure (technically still a pn junction diode); the bandgap is still constant. The bottom two images are the donor and acceptor concentrations.

The bandgap energy E_g is the amount of energy needed for a valence electron to move to the conduction band. The short answer to the question of how the bandgap may be altered is that the bandgap energy is mostly fixed for a single material. In praxis however, Bandgap Engineering employs thin epitaxial layers, quantum dots and blends of materials to form a different bandgap. Bandgap smoothing is employed, as are concentrations of specific elements in ternary and quarternary compounds. However, the bandgap cannot be altered by changing the doping level of the material.

# PN Junction Simulator in ATLAS

This post will outline a program for ATLAS that can simulate a pn junction. The mesh definition and structure between the anode and cathode will be defined by the user. The simulator plots both an unbiased and biased pn junction.

go atlas

Title PN JUNCTION SIMULATOR

#Define the mesh

mesh auto
x.m l = -2 Spac=0.1
x.m l = -1 Spac=0.05
x.m l = 1 Spac=0.05
x.m l = 2 Spac =0.1

#TOP TO BOTTOM – Structure Specification
region num=1 bottom thick = 0.5 material = GaAs NY = 20 acceptor = 1e17
region num=2 bottom thick = 0.5 material = GaAs NY = 20 donor = 1e17

#Electrode specification
elec num=1 name=anode x.min=-1.0 x.max=1.0 top
elec num=2 name=cathode x.min=-1.0 x.max=1.0 bottom
#Gate Metal Work Function
contact num=2 work=4.77
models region=1 print conmob fldmob srh optr
models region=2 srh optr
material region=2

#SOLVE AND PLOT
solve init outf=diode_mb1.str master
output con.band val.band
tonyplot diode_mb1.str

method newton autonr trap maxtrap=6 climit=1e-6
solve vanode = 2.5 name=anode
save outfile=diode_mb2.str
tonyplot diode_mb2.str
quit

This program may also be useful for understanding how different materials interact between a PN junction. This simulation below is for a simple GaAs pn junction.

The first image shows four contour plots for the pn junction with an applied 2.5 volts. With an applied voltage of 2.5, the recombination rate is high at the PN junction, while there is low recombination throughout the unbiased pn junction. The hole and electron currents are plotted on the bottom left and right respectively. Here is the pn junction with no biasing. The beam profile can also be obtained:  # AlGaAs/GaAs Strip Laser

This project features a heterostructure semiconductor strip laser, comprised of a GaAs layer sandwiched between p-doped and n-doped AlGaAs. The model parameters are outlined below. The structure is presented, followed by output optical power as a function of injection current. Thereafter, contour plots are made of the laser to depict the electron and hole densities, recombination rate, light intensity and the conduction and valence band energies.        # HEMT – High Electron Mobility Transistor

One of the main limitations of the MESFET is that although this device extends well into the mmWave range (30 to 300 GHz or the upper part of the microwave spectrum), it suffers from low field mobility due to the fact that free charge carriers and ionized dopants share the same space.

To demonstrate the need for HEMT transistors, let us first consider the mobility of GaAs compound semiconductor. As shown in the picture, with decreasing temperature, Coloumb scattering becomes prevalent as opposed to phonon lattice vibrations. For an n-channel MESFET, the main electrostatic Coloumb force is between positively ionized donor elements (Phosphorous) and electrons. As shown, the mobility is heavily dependent on doping concentration. Coloumb Scattering effectively limits mobility. In addition, decreasing the length of the gate in a MESFET will increase Coloumb scattering due to the need for a higher doping concentration in the channel. The means that for an effective device, the separation of free and fixed charge is needed. A heterojunction consisting of n+ AlGaAs and p- GaAs material is used to combat this effect. A spacer layer of undoped AlGaAs is placed in between the materials. In a heterojunction, materials with different bandgaps are placed together (as opposed to a homojunction where they are the same). This formation leads to the confinement of electrons from the n- layer in quantum wells which reduces Coloumb scattering. An important distinction between the HEMT and the MESFET is that the MESFET (like all FETs) modulates the channel thickness whereas with an HEMT, the density of charge carriers in the channel is changed but not the thickness. So in other words, applying a voltage to the gate of an HEMT will change the density of free electrons will increase (positive voltage) or decrease (negative voltage). The channel is composed of a 2D electron gas (2DEG). The electrons in the gas move freely without any obsctruction, leading to high electron mobility.

HEMTs are generally packed into MMIC chips and can be used for RADAR applications, amplifiers (small signal and PAs), oscillators and mixers. They offer low noise performance for high frequency applications.

The pHEMT (pseudomorphic) is an enhancement to the HEMT which feature structures with different lattice constants (HEMTs feature roughly the same lattice constant for both materials). This leads to materials with wider bandgap differences and generally better performance.