# 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: # 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: # P-I-N Junction Simulation in ATLAS

Introduction to ATLAS

ATLAS by Silvaco is a powerful tool for modeling for simulating a great number of electronic and optoelectronic components, particularly related to semiconductors. Electrical structures are developed using scripts, which are simulated to display a wide range of parameters, including solutions to equations otherwise requiring extensive calculation.

P-I-N Diode

The function of the PN junction diode typically fall off at higher frequencies (~3GHz), where the depletion layer begins to be very small. Beyond that point, an intrinsic semiconductor is typically added between the p-doped and n-doped semiconductors to extend the depletion layer, allowing for a working PN junction structure in the RF domain and to the optical domain. The following file, a P-I-N junction diode is an example provided with ATLAS by Silvaco. The net doping regions are, as expected at either end of the PIN diode. This structure is 10 microns by 10 microns. The code used to create this structure is depicted below. The cutline tool is used through the center of the PIN diode after simulating the code. The Tonyplot tool allows for the plotting of a variety of parameters, such as electric field, electron fermi level, net doping, voltage potential, electron and hole concentration and more.    # Gas Laser and Semiconductor Lasers The Gas Laser

In laboratory settings, gas lasers (shown right) are often used to eveluate waveguides and other interated optical devices. Essentially, an electric charge is pumped through a gas in a tube as shown to produce a laser output. Gasses used will determine the wavelength and efficiency of the laser. Common choices include Helium, Neon, Argon ion, carbon dioxide, carbon monoxide, Excimer, Nitrogen and Hydrogen. The gas laser was first invented in 1960. Although gas lasers are still frequently used in lab setting sfor testing, they are not practical choices to encorperate into optical integrated circuits. The only practical light sources for optical integrated circuits are semiconductor lasers and light-emitting diodes.

The Laser Diode The p-n junction laser diode is a strong choice for optical integrated circuits and in fiber-optic communications due to it’s small size, high reliability nd ease of construction. The laser diode is made of a p-type epitaxial growth layer on an n-type substrate. Parallel end faces may functions as mirrors to provide the system with optical feedback.

The Tunnel-Injection Laser

The tunnel-injection laser enjoys many of the best features of the p-n junction laser in it’s size, simplicity and low voltage supply. The tunnel-injection laser however does not make use of a junction and is instead made in a single crystal of uniformly-doped semiconductor material. The hole-electron pairs instead are injected into the semiconductor by tunneling and diffusion. If a p-type semiconductor is used, electrons are injected through the insulator by tunneling and if the semiconductor is n-type, then holes are tunneled through the insulator.

# The Schottky Diode

The Schottky diode, unlike the PN-junction diode is not made of a n-type and n-type semiconductor junction. Instead, is consists of a highly conductive silicide material or metal compound with an n-type semiconductor silicon material. Different metal compounds will allow for varying forward voltage drops, generally between 0.3 and 0.5 volts. IV curves are often referred to when understanding the function of a diode. One difference that can be inferred from the IV curve comparison is that the Schottky forward current can be much larger, making it useful in applications with higher levels of current. # Diode Voltage Clipping Circuits

We’re already discussed the PN junction in a previous post. Let’s explore some of the applications of the PN diode. It was already discussed that due to the nature of the PN junction, current is only allowed to flow in one direction. This results in two possible scenarios using a diode, depending on the direction it is facing with respect to the source. Diode Clipping Circuits

Diodes in a forward bias allow current to pass, but thereby reducing the voltage level. In a reverse bias, current is stopped but the voltage remains unaffected.

Diode clipping can be done for either the positive or the negative voltage of a sinusoidal (or analog) input voltage. In order to clip both the positive and negative sides of the input voltage, two diodes are needed.

Positive voltage clipping: Negative voltage clipping: Two Diodes: If 0.7 Volts is not the desired output clipping voltage, a bias voltage can be added in each situation above.  # The P-N Junction

A P-N junction is created in a single semiconductor crystal by doping one side as a p-type and one as an n-type. The region where the two types converge is known as the p-n junction.

The extra electrons that were added to the n-type semiconductor move towards the p-type junction side while the holes added through p-type doping are positioned closer to the n-type junction. As electrons leave the n-type region, it becomes positively charged. This process is called diffusion. The depletion region is the area between the p and n-type sides. The state of equilibrium in the p-n junction is the state of the depletion region without any external electrical potential applied. As mentioned before in a previous paper, the Fermi level is the average between the conduction band and the valence band. By altering the levels of electron holes and electrons in the p-type and n-type sections, holes drift toward the the n-type side and electrons move towards the p-type side, which causes both sections to be closer to the Fermi level in their regions of the material. When voltage is applied to the pn junction, electrons and electron holes from either side tend towards equilibrium. If the positive potential is applied to the p-type and it is more positive than the n-type area, holes will travel towards the negative voltage. Through diffusion, electrons or electron holes may jump through the depletion layer. For the reason however that electron holes (positive charge) may only move in the direction of the n-type region and electrons (negative charge) may only move in the opposite direction. The direction of electron flow, due to their negative charge is opposite the conventional direction of current flow. Since electrons are only moving from the n-type region to the p-type region, it can be understood that current will only move in the direction going from the side of the p-type region towards the n-type region. # Negative Resistance

RF/Photonics Lab
November 2019
Jared Alves

Negative Resistance

Arguably the most fundamental equation in electrical engineering is Ohm’s Law (V = I*R) which states that voltage is proportional to the product of current and resistance. From this equation, it is apparent that increasing a voltage across an element will increase the current through that element assuming the resistance is fixed. With a resistor, electrical energy is dissipated in the form of thermal energy (heat) due to the voltage drop between the terminals of the device. This is in direct contrast to the concept of negative resistance, which causes electrical power to be produced instead of dissipated.

Generally, negative resistance refers to negative differential resistance, as negative static resistance is not typically used.  Static resistance is the standard V/I ratio while differential resistance takes the derivative dV/dI. The following image shows an I-V curve with several slopes. The inverse of B yields a static resistance, and the inverse of line C is differential resistance (both evaluated at the point A). If the differential curve has a negative slope, this indicates negative differential resistance. Even when differential resistance is negative, static resistance remains positive. This is because only the AC component of the current flows in the reverse direction. A device would consume DC power but dissipate AC power. This is because the current decreases as the voltage increases, leading to A tunnel diode is a semiconductor device that exhibits negative resistance due to a quantum mechanical effect called “tunneling”.