Semiconductor physics: pièce de resistance?

Semiconductor physics

Semiconductors underpin solar panels, electric vehicles and electronics. Hence this 20-page note aims to explain semiconductor physics from first principles: their conductivity and resistance, their use in devices, plus implications for materials value chains and the energy transition itself?

Semiconductors: conductivity calculations?

Semiconductor conductivity

This datafile calculates the semiconductor conductivity and semiconductor resistivity from first principles, based on their bandgap, doping, electron and hole mobility, temperature, the Fermi-Dirac distribution and the Effective Density of States. Put in any inputs you like to compute the resistance of silicon, germanium or GaAs.


The purpose of this data-file is to break down the conductivity of semiconductors, in spreadsheet format, from first principles, as a useful reference file for our broader modelling of semiconductors, from solar panels to electric vehicles.

The basic formula for conductivity in metals is that S=neμ, where n is the number of charge carriers (usually an integer multiple of the number of atoms), e is the fundamental energy of an electron (1.6 x 10^-19 Joules per electron) and μ is the mobility of the electrons in the material (maybe around 40cm2/V-s as a good ballpark for copper). Resistivity in Ohm-cm is simply 1 ÷ conductivity in Siemens per centimeter.

The formula for conductivity in semiconductors is more complex than metals, because the charge carriers may be conduction band electrons, valence band holes, donor electrons from pentavalent dopants or acceptor holes from trivalent dopants. But generally semiconductor conductivity: σ = ne e μe + np e μp, and these values are in the data-file.

For intrinsic semiconductors, the number of conduction band electrons must be computed as a function of the bandgap, Boltzmann’s constant, temperature and the Effective Density of States (Nc). That final term, in turn, is calculated by multiplying the Fermi-Dirac distribution by the Density of States function and then using calculus to find the ‘area under the curve’. It is all in the data-file.

Semiconductor physics
How semiconductors work. Fermi-Dirac x Density of States yields Effective Density of States and number of Charge Carriers

Undoped silicon (aka intrinsic silicon) will likely have an intrinsic resistivity of around 250,000Ω-cm at room temperature, of which 90% comes from the conductivity of conduction band electrons (rather than holes). There might be 5 x 10^22 silicon atoms per cm3, yielding 1.6 x 10^10 conduction band electrons per cm3, with an average mobility of 1,425 cm2/V-S. These numbers can all be flexed in the data-file.

Doping makes semiconductors an order of magnitude more conductive, and enables their assembly into devices such as light emitting diodes, transistors and solar cells. Moderately doped silicon might contain 1 impurity per 10^7 silicon atoms yielding 5 x 10^14 charge carriers per cm3 (table below). Each 10x increase in doping concentration generally improves conductivity by 10x.

Semiconductor conductivity
Doping of semiconductors in terms of impurities per silicon atom and per cm3

Although even a heavily doped semiconductor will still be about 500-5,000x more resistive than a conductive metal such as copper. Please download the data-file to stress test semiconductor conductivity and resistivity. More of the theory is explained in our overview of semiconductors.

Mitsui Chemicals: solar encapsulants?

Mitsui Chemicals solar encapsulants

Solar encapsulants are 300-500μm thick films, protecting solar cells from moisture, dirt and degradation; electrically insulating them at 4 x 10^15 Ωcm resistivity; and yet allowing 90% light transmittance. The industry is moving away from commoditized EVA towards specialized blends of co-polymers and additives. Is there a growing moat around Mitsui Chemicals’ solar encapsulants?


Mitsui Chemicals traces its origins back to 1912, employs 19,000 people globally, and is listed in Tokyo. The company has featured in our work before, as 15-20% of revenues are derived from polyurethanes, where we think the rise of electric vehicles could free up cheap feedstocks and raise polyurethane margins.

Another view in our recent research is that new energies are entering an age of materials, where there is less running room to achieve deflation via ‘scaling up to mass manufacturing’. Materials are increasingly important. Solar and battery manufacturers will increasingly be willing to pay premia for advanced materials that improve efficiency.

Consistent with this thesis, Mitsui Chemicals is restructuring its films business in 2023-24, spinning out a packaging films business, and concentrating upon films and industrial films, combined into a new, wholly owned subsidiary called Mitsui Chemicals ICT Materials Inc, which is envisaged to become a “third pillar of earnings” across the company.

Solar encapsulants. The role of 300-500μm thick encapsulant layers is to encase solar cells, protect them from humidity, dirt/dust, damaging UV, electrically insulate them and ‘cushion’ them from damage or vibration against the rigid overlying glass and rigid underlying back-sheet. However, typical encapsulants only transmit 90% of the light through the solar module, and they are prone to degradation and delamination.

Mitsui Chemicals solar encapsulants
Encapsulant likely allows 90 percent transmittance of light in the visible spectrum to underlying solar cells, or less if degraded

Ethylene vinyl acetate has historically dominated the solar encapsulant market, and retains a >50% market share in 2023. However, polyolefin encapsulants (POE) and mixed EVA-POE-EVA encapsulants (EPE) have been gaining share, as they protect better against degradation. Reasons are explained in the data-file.

Based on the patent library, Mitsui Chemicals’ solar encapsulant offering is clearly focused on alpha-olefin co-polymer encapsulants, plus additives to improve their processibility, longevity and ultimately the performance of solar modules.

Please download the data-file for our conclusions into Mitsui Chemicals solar encapsulants (and the market more broadly), based on reviewing relevant patents, to assess whether the company has a growing moat in this space, as well as more broadly, in the new age of materials.

Global polysilicon production capacity?

Global polysilicon production

Polysilicon is a highly pure, crystalline silicon material, used predominantly for photovoltaic solar, and also for ‘chips’ in the electronics industry. Global polysilicon capacity is estimated to reach 1.65MTpa in 2023, and global polysilicon production surpasses 1MTpa in 2023. China now dominates the industry, approaching 90% of all global capacity.


Polysilicon is a highly pure form of silicon material (over 99.999%), often formed via the Siemens process, converting 98-99% pure metallurgical grade silicon into silane gases, then vapor depositing pure silicon crystals out of the silane gas, at 10-20nm per minute, at 600-1,100◦C temperatures, for 80-110 hours. Polysilicon is then further purified and crystallized into mono-crystalline polysilicon via the Czochralski method, for use in photovoltaic solar and other semiconductor chips (over here, model here).

Global polysilicon production capacity likely reaches 1.65MTpa in 2023 and global polysilicon production reaches 1MTpa. For context, production of the key input material, silicon metal, is around 8.5MTpa (per the USGS), and production of the key raw material, silica, is around 350 MTpa (per our silica screen).

This data-file aggregates polysilicon production by facility, by company, by region, by country and over time. China now controls almost 90% of the world’s polysilicon production capacity, with six large Chinese companies comprising over 80% of capacity.

Global polysilicon production
China has ramped up and now controls almost 90 percent of all global polysilicon production

Aggregating polysilicon production data is opaque. Some large Chinese producers publish surprisingly little data. Others have mysteriously deconsolidated production facilities, especially in Xinjiang, after international groups criticized their use of Uyghur labor. Another issue is that some facilities have appeared to operate well above nameplate capacity, raising questions about what their ‘capacity’ really is.

Global polysilicon production by company is estimated in one tab of this data-file, simply taking the best public data-points we can find, triangulating between different sources, and settling on the most sensible estimates that we can find.

Global polysilicon production
Global polysilicon production capacity by company x

Although gross solar additions have risen by 65x in the past 15-years, growing at a CAGR over 30% per annum, surpassing +200GW YoY in 2022, this has not been entirely propitious for polysilicon incumbents. The materials balance of a solar module has seen thinner wafers reducing polysilicon intensity by two-thirds since 2005 (chart below-left), while rapid capacity expansion in China has seen utilization fall from around 85% on average around 2010 to 60% in 2022-23 (chart below-right). This may be an important lesson for other value chains with large growth ahead in the energy transition.

Global polysilicon production
Global polysilicon capcaity utilization has been falling due to lower polysilicon intensity and intense Chinese capacity expansion

New energies: the age of materials?

new energies costs

Over the past decade, costs have deflated by 85% for lithium ion batteries, 75% for solar and 25% for onshore wind. Now new energies are entering a new era. Future costs are mainly determined by materials. Bottlenecks matter. Deflation is slower. Even higher-grade materials are needed to raise efficiency. This 14-page note explores the new age of materials, how much new energies deflation is left, and who benefits?

Solar costs: a breakdown over time?

Solar costs have deflated by 75% in the past decade to around $1,000/kW. 60% has been the scale-up to mass manufacturing, and 40% has been rising efficiency of solar modules. Materials costs now look likely to dominate future costs and their trajectory. And advanced materials can help double efficiency again from here? Who benefits?


Solar costs have deflated from $4,000/kW to $1,000/kW in the decade from 2012 to 2022, as measured at utility scale solar projects, using our solar bill of materials, and global commodity price databases.

60% of solar cost deflation in the past decade has come from the scale-up to mass manufacturing: as solar installations scaled up by 7x to well over 200GW per year, manufacturing fell from 50% to 18% of the total installed costs of a utility-scale project.

Efficiency gains drove the other 40% of the deflation, as the average solar panel in 2022 produces 2.5x more power than in 2012, with efficiency rising from 15% to 23% and module size rising from 1.7m2 to 2.7m2.

Solar costs over time
Solar module size in m2, module efficiency in percent and module output in Watts over time

Efficiency gains are the best form of deflation, because they lower the per kW costs of all fixed cost line items, from permitting to installation. Including materials costs. When a similar amount of material per module — sometimes even more material per module — delivers more kW of power, this reduces the cost of materials in $/kW terms.

Solar costs over time
Materials use over time in solar modules

Our analysis into changing solar cells suggests that higher grade materials and manufacturing processes can potentially double solar efficiency again from here, and we wonder if this creates large opportunities for advanced materials and manufacturing technologies (research note here).

The data-file also aggregates similar breakdowns of materials, manufacturing and installation costs for other new energies, such as wind and batteries, in order to draw some useful comparisons and contrasts.

new energies costs
New Energies materials and manufacturing as percent of total cost

Solar costs over time are also disaggregated across 45 lines in the data-file, including input variables that can be flexed, to stress-test different scenarios for future solar costs.

HJT solar: Indium summer?

Indium in HJT solar

HJT solar modules are accelerating, as they are highly efficient, and easier to manufacture. But HJT could also be a kingmaker for Indium metal, which is used in transparent and conductive thin films (ITO). Our forecasts see primary Indium use rising 4x by 2050. Indium is 100x rarer than Rare Earth metals. It could be a bottleneck. This 16-page note expores the costs and benefits of using ITO in HJTs, and who benefits as solar cells evolve?

Vacuum pumps: company screen?

The global market for vacuum pumps is worth $15bn per year, with growing importance for making semiconductors, solar panels and AI chips. This data-file reviews ten leading companies in vacuum pumps, including one European-listed capital goods leader, a European pure-play and a Japanese-listed pure-play.


The vacuum pump market is worth $15bn per year, and some sources imply that over half of the market now comprises semiconductor applications, such as the vacuum chambers used for vapor deposition and sputtering, when manufacturing AI chips and solar cells.

Other applications, back in the traditional industrial landscape, use vacuum pumps. Ranging from the food manufacturing industry (one company website that we reviewed comprehensively lists how their technology is used in making cheese), through to gas separations via swing adsorption, membranes or petrochemicals.

Many processes in the semiconductors are remarkable because they use vacuum chambers to prevent contamination from, and reaction with, atmospheric air, when depositing thin film layers of 5-250 nm. If normal pressure is 1 bar, some of these processes can occur at 0.001 mBar, i.e., 1 millionth of an atmosphere.

Evacuating a vacuum chamber down to 0.1-0.001 mBar can take 90+ minutes, while the pump continues working, pumping out ever smaller quantities of air, which equates to an exponentially rising energy consumption per unit of sm3 of air that is pumped. As a rule of thumb, we think that reaching 0.1-0.01 mBar will require 0.3-0.5 kWh of electricity per m3 of volume in the vacuum chamber (charts below).

Leading companies in vacuum pumps
Energy demands of vacuum pumps rise linearly as pressure decreases exponentially. Expect 0.3 kWh per sm3 at 0.1 mBar.

Atlas Copco is the industry leader in vacuum pumps. Its market share, and recent acquisitions are explored in the data-file. But total group operating margins were 21% in 2022 and ROCE was 29%. Vacuum pumps comprise 28% of the company’s revenues. In its vacuum pump business, Atlas Copco’s 2022 orders were 65% electronics and semiconductors, 21% chemicals/process industries including the food packaging industry and 12% general manufacturing. More via the Atlas Copco website. But this is interesting, as Atlas Copco has screened well in other areas of TSE research, such as in compressors, increasingly important for industrial gases and CCS value chains.

Other leading companies in vacuum pumps? Listed pure-plays in both Germany and Japan also feature in the data-file. Plus industrial conglomerates in the US, Europe and Japan, with varying concentration.

There are some interesting data-points in the commentary about who leads in supplying vacuum pumps to the semiconductor industry.

Renewables: how much time to connect to the grid?

time to connect to the grid

Is the power grid becoming a bottleneck for the continued acceleration of renewables? The median approval time to connect to the grid for a new US power project has climbed by 30-days/year since 2001; and has doubled since 2015, to over 1,000 days (almost 3-years) in 2021. Wind and solar projects are now taking longest to inter-connect, due to their prevalence, lower power quality and remoteness. This data-file evaluates the data, looks for de-bottlenecking opportunities, and wonders about changing terms of trade in power markets.


Accelerating wind and solar are a crucial part of our roadmap to net zero. But we have also been worrying about bottlenecks, especially in power grids. Project developers are increasingly required to fund new power transmission infrastructure, before they are allowed to interconnect, usually costing $100-300/kW, but sometimes costing as much as the renewables projects themselves (data here). If there is one research note that spells out the upside we see in power grids and electrification, then it is this one. We also see upside in long-distance transmission, HVDCs, STATCOMs, transformers, various batteries.

Other technical papers have also raised the issue of rising interconnection times and power grid bottlenecks for wind and solar. And the US’s Lawrence Berkeley National Laboratory has also started tracking the ‘queue’ of power projects waiting to inter-connect. We have downloaded their database, spent about a day cleaning the data (especially the dates), and aimed to derive some conclusions below.

Methodological notes. The raw LBL database contains a read-out of over 24,000 US power projects that sought to inter-connect to a regional power grid, going back to 1995. However, 13,000 of these applications were withdrawn, 8,000 are still active/pending and 3,500 are classed as operational. 2,500 of the projects have complete data on (a) when they applied for permission to inter-connect to the grid and (b) when they were ultimately granted that permission, allowing us to calculate (c) the approval time (by subtracting (b) from (a)). But be warned, this is not a fully complete data-set. And some States, which have clearly constructed large numbers of utility-scale power projects, seemed not to report any data at all. Nevertheless, we think there are some interesting conclusions.

The median time to receive approval to inter-connect a new US power project to the grid has risen at an average rate of 30-days per year over the past two decades and took over 1,000 days in 2021, which is 2.8 years. This has doubled from a recent trough level of 500 days in 2015 (chart below) and a relatively flat level of 400-days in the mid-2000s.

Renewables projects now take longer to receive approval to connect to the power grid. Wind projects have always taken longer to receive approvals. And recent wind projects continued taking 30% longer than the total sample of approved projects in 2019-21. More interestingly, however, solar projects have gone from taking 50% less time to receive grid connection approvals in the mid-2000s to taking 10% longer than average, especially in 2020 and 2021. Why might this be? We consider five factors…

#1. Project quantity is probably the largest bottleneck. The numbers of different projects receiving permission to connect to the grid are tabulated below. A surge in wind projects in 2005-2012 correlates with the first peak in inter-connection approval times on the chart above. And a more recent peak in utility-scale solar, battery and wind projects correlates with the recent peak of approval times in 2020-21. This suggests a key reason it is taking more time to approve new inter-connections is that grid operators are backlogged. It would be helpful to resolve the backlog. And we wonder if the result might be a change in the terms of trade: favoring grid operators more, favoring capital goods companies more, and requiring project developers to be more accommodating?

#2. Project sizing does not directly explain inter-connection approval times. The average utility-scale solar project has become larger over time (now surpassing 150MW). But wind projects have always been larger than the average power project seeking approval to connect to the grid. And there are many small gas, coal and nuclear projects that take longer to receive connection approval than large ones. So we do not think there is a direct link between power project size and the time needed to approve an inter-connection. However, there may be an indirect link. It is clearly going to take longer to study the impacts of connecting 10 x 100 MW solar projects (in 10x separate locations), than 1 x 1,000 MW nuclear plant, even though both have the same nameplate capacity.

#3. Connection voltage does not explain inter-connection approval times. The median project in the database is connecting into the grid at 130kV. The median wind project is at 145kV. The median gas project is at 135kV. The median solar project is at 110kV. The median battery project is connecting at 140kV. Although we do think that moving power over longer distances is increasingly going to favor higher voltage transmission and also pull on the transformer market.

#4. Power quality seems to explain relative approval times and increasingly so. Another interesting trend is the difference in interconnection approval times between different types of power projects. Wind and solar projects now take 30% and 10% longer than average to receive approvals. Whereas gas, batteries and hydro now take 15%, 50% and 90% less time than average to receive approvals. We think this is linked to power quality. On a standalone basis, wind and solar may tend to reduce the inertia, frequency regulation, reactive power compensation and balancing of power grids. Whereas gas power plants, batteries and hydro typically help with these metrics (each in their own way). We think this adds evidence in support of our power grids thesis.

#5. Remote projects take longer to approve, as they will likely require more incremental transmission lines. The shortest interconnection times across all power projects were in Texas, which already has a very large power grid, arguably the best energy endowment and infrastructure in the world. But other more densely populated states (Michigan, Illinois) tended to have 50% lower times to approve inter-connections than some of the least densely populated states (the Dakotas, Iowa, Montana), where we think new power generation likely needs to be moved further to reach demand centers. Location matters for levelized cost of electricity. Again, we think this evidence also supports our power transmission thesis.

Overall the data suggest that there are growing bottlenecks to inter-connect renewables to power grids; especially in areas with a surge of activity, where power quality is increasingly important, and in more remote areas that require new transmission infrastructure. We think this trend will continue. It would be helpful to debottleneck the bottlenecks, to sustain the upwards trajectory of wind and solar. But we do think the terms of trade are shifting in favor of grid operators, power electronics, transmission infrastructure, developers that can use their own power and consumers that can demand shift.

Solar surface: silver thrifting?

silver use in solar

Ramping new energies is creating bottlenecks in materials. But how much can material use be thrifted away? This 13-page note is a case study of silver intensity in the solar industry, which halved in the past decade, and could halve again. Conclusions matter for solar companies, silver markets, other bottlenecks.

Copyright: Thunder Said Energy, 2019-2023.